TSTP Solution File: SCT068-1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SCT068-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:38:15 EDT 2024
% Result : Unsatisfiable 155.92s 20.08s
% Output : CNFRefutation 157.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SCT068-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.15 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.36 % Computer : n003.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8042.1875MB
% 0.11/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Apr 29 20:18:18 EDT 2024
% 0.11/0.36 % CPUTime :
% 0.18/0.41 % Drodi V3.6.0
% 155.92/20.08 % Refutation found
% 155.92/20.08 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 155.92/20.08 % SZS output start CNFRefutation for theBenchmark
% 155.92/20.08 fof(f2,axiom,(
% 155.92/20.08 (![V_R,T_a]: (( c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(V_R,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))| c_Wellfounded_Owf(V_R,T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f3,axiom,(
% 155.92/20.08 (![V_A,T_a]: (c_Lattices_Oupper__semilattice__class_Osup(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f4,axiom,(
% 155.92/20.08 (![T_a,V_x]: (( ~ class_Lattices_Oupper__semilattice(T_a)| c_Lattices_Oupper__semilattice__class_Osup(V_x,V_x,T_a) = V_x ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f7,axiom,(
% 155.92/20.08 (![V_P,V_Rb,V_R,T_a]: (( hBOOL(hAPP(V_P,V_Rb))| ~ hBOOL(hAPP(V_P,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(V_P,V_R,T_a)))| ~ c_Wellfounded_Owf(V_R,T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f9,axiom,(
% 155.92/20.08 (![V_P,T_a,T_b,V_Q]: (hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f14,axiom,(
% 155.92/20.08 (![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)) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f15,axiom,(
% 155.92/20.08 (![V_A,V_B,T_a]: (c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_HOL_Ouminus__class_Ouminus(V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f30,axiom,(
% 155.92/20.08 (![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)) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f31,axiom,(
% 155.92/20.08 (![V_A,V_B,T_a]: (c_lessequals(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f40,axiom,(
% 155.92/20.08 (![V_A,V_B,T_a]: (c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,V_A,tc_fun(T_a,tc_bool)) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f43,axiom,(
% 155.92/20.08 (![V_r,T_a]: (( c_Wellfounded_Oacyclic(V_r,T_a)| ~ c_Wellfounded_Owf(V_r,T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f65,axiom,(
% 155.92/20.08 (![V_c,T_b,T_a,V_A,V_x]: (( c_Set_Oimage(c_COMBK(V_c,T_b,T_a),V_A,T_a,T_b) = c_Set_Oinsert(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b)| ~ c_in(V_x,V_A,T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f69,axiom,(
% 155.92/20.08 (![V_x,V_A,T_a,V_B]: (( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))| ~ c_in(V_x,V_B,T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f77,axiom,(
% 155.92/20.08 (![V_A,T_a]: (c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f79,axiom,(
% 155.92/20.08 (![T_a,V_f,V_A,T_b]: (( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Set_Oimage(V_f,V_A,T_b,T_a)| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f92,axiom,(
% 155.92/20.08 (![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)) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f94,axiom,(
% 155.92/20.08 (![V_R,T_b,T_a]: (c_Relation_OImage(V_R,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)) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f102,axiom,(
% 155.92/20.08 (![T_a,V_x]: (( ~ class_Lattices_Obounded__lattice(T_a)| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(T_a),V_x,T_a) = c_Orderings_Obot__class_Obot(T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f112,axiom,(
% 155.92/20.08 (![V_A,T_a]: (c_HOL_Ominus__class_Ominus(V_A,V_A,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f123,axiom,(
% 155.92/20.08 (![V_A,V_B,T_a,V_C]: (c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f124,axiom,(
% 155.92/20.08 (![V_A,V_B,V_C,T_a]: (c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f127,axiom,(
% 155.92/20.08 (![T_a,V_B]: (c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = V_B ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f128,axiom,(
% 155.92/20.08 (![V_A,T_a]: (c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f131,axiom,(
% 155.92/20.08 (![T_a,V_x]: (~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f133,axiom,(
% 155.92/20.08 (![V_A,V_B,T_a,V_C]: (c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f134,axiom,(
% 155.92/20.08 (![V_c,T_a,T_b,V_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)| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f139,axiom,(
% 155.92/20.08 (![V_A,V_C,T_a,V_B]: (c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f145,axiom,(
% 155.92/20.08 (![V_r,T_a]: (( c_Wellfounded_Oacyclic(V_r,T_a)| ~ c_Wellfounded_Oacyclic(c_Relation_Oconverse(V_r,T_a,T_a),T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f148,axiom,(
% 155.92/20.08 (![V_A,V_B,T_a]: (c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f150,axiom,(
% 155.92/20.08 (![T_a,V_x,V_y]: (( ~ class_Lattices_Oupper__semilattice(T_a)| c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) != V_y| c_lessequals(V_x,V_y,T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f181,axiom,(
% 155.92/20.08 (![V_A,V_B,T_a]: (c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool)) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f189,axiom,(
% 155.92/20.08 (![V_A,V_B,T_a]: (c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f196,axiom,(
% 155.92/20.08 (![V_A,V_B,T_a]: (c_Lattices_Olower__semilattice__class_Oinf(V_A,c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f198,axiom,(
% 155.92/20.08 (![V_P,V_a,V_r,T_a]: (( hBOOL(hAPP(V_P,V_a))| ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(V_P,V_r,T_a)))| ~ c_Wellfounded_Owf(V_r,T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f227,axiom,(
% 155.92/20.08 (![V_a,V_b,V_A,T_a]: (( c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a)| ~ c_in(V_a,V_A,T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f237,axiom,(
% 155.92/20.08 (![V_c,V_B,T_a,V_A]: (( ~ c_in(V_c,V_B,T_a)| ~ c_in(V_c,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f241,axiom,(
% 155.92/20.08 (![V_x,V_A,T_a]: (c_in(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f245,axiom,(
% 155.92/20.08 (![V_c,V_A,T_a,V_B]: (( c_in(V_c,V_A,T_a)| ~ c_in(V_c,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f265,axiom,(
% 155.92/20.08 (![V_f,V_a,V_B,T_b,T_a]: (c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f277,axiom,(
% 155.92/20.08 (![V_A,V_B,T_a]: (c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f309,axiom,(
% 155.92/20.08 (![V_A,V_B,V_C,T_a]: (c_HOL_Ominus__class_Ominus(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f310,axiom,(
% 155.92/20.08 (![V_A,V_B,T_a,V_C]: (c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_HOL_Ominus__class_Ominus(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f342,axiom,(
% 155.92/20.08 (![V_P,V_a,V_r,T_a]: (( hBOOL(hAPP(V_P,V_a))| ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(V_P,V_r,T_a)))| ~ c_in(V_a,c_Wellfounded_Oacc(V_r,T_a),T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f345,axiom,(
% 155.92/20.08 (![V_r,T_a]: (c_Transitive__Closure_Otrancl(V_r,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_r,c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(V_r,T_a),V_r,T_a,T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f349,axiom,(
% 155.92/20.08 (![V_r,T_a]: (( c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(V_r,T_a),T_a)| ~ c_Wellfounded_Oacyclic(V_r,T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f353,axiom,(
% 155.92/20.08 (![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)) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f365,axiom,(
% 155.92/20.08 (![V_P,V_a,V_y,V_r,T_a]: (( hBOOL(hAPP(V_P,V_a))| hBOOL(hAPP(V_P,V_y))| ~ c_in(c_Pair(V_y,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(V_P,V_r,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a))| ~ c_Wellfounded_Owf(V_r,T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f368,axiom,(
% 155.92/20.08 (![V_P,V_a,V_y,V_r,T_a]: (( hBOOL(hAPP(V_P,V_a))| hBOOL(hAPP(V_P,V_y))| ~ c_in(c_Pair(V_y,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(V_P,V_r,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a))| ~ c_Wellfounded_Owf(V_r,T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f372,axiom,(
% 155.92/20.08 (![V_x,T_a,V_r]: (( ~ c_in(c_Pair(V_x,V_x,T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a))| ~ c_Wellfounded_Oacyclic(V_r,T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f375,axiom,(
% 155.92/20.08 (![V_x,V_r,V_z,T_a]: (( c_in(c_Pair(V_x,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(V_r,V_x,V_z,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a))| c_in(c_Pair(V_x,V_z,T_a,T_a),V_r,tc_prod(T_a,T_a))| ~ c_in(c_Pair(V_x,V_z,T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a)) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f381,axiom,(
% 155.92/20.08 (![V_R,T_a]: (( c_Wellfounded_Owf(V_R,T_a)| c_lessequals(c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(V_R,T_a),c_Relation_OImage(V_R,c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(V_R,T_a),T_a,T_a),tc_fun(T_a,tc_bool)) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f384,axiom,(
% 155.92/20.08 (![V_r,T_a]: (( c_Wellfounded_Owf(V_r,T_a)| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(V_r,T_a),c_Wellfounded_Oacc(V_r,T_a),T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f388,axiom,(
% 155.92/20.08 (![V_A,V_c,T_a]: (( c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(V_A,V_c,T_a),V_A,T_a)| ~ c_in(V_c,c_Relation_OId__on(V_A,T_a),tc_prod(T_a,T_a)) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f389,axiom,(
% 155.92/20.08 (![V_c,V_A,T_a]: (( V_c = c_Pair(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(V_A,V_c,T_a),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(V_A,V_c,T_a),T_a,T_a)| ~ c_in(V_c,c_Relation_OId__on(V_A,T_a),tc_prod(T_a,T_a)) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f396,axiom,(
% 155.92/20.08 (![V_r,T_a]: (c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(V_r,T_a),c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) = c_Transitive__Closure_Ortrancl(V_r,T_a) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f402,axiom,(
% 155.92/20.08 (![V_r,T_a]: (( c_Relation_Oirrefl(V_r,T_a)| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(V_r,T_a),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(V_r,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f406,axiom,(
% 155.92/20.08 (![V_r,T_a]: (( c_Nitpick_Orefl_H(V_r,T_a)| ~ c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(V_r,T_a),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(V_r,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f409,axiom,(
% 155.92/20.08 (![V_A,V_b,V_r,T_b,T_a]: (( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(V_A,V_b,V_r,T_b,T_a),V_b,T_b,T_a),V_r,tc_prod(T_b,T_a))| ~ c_in(V_b,c_Relation_OImage(V_r,V_A,T_b,T_a),T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f410,axiom,(
% 155.92/20.08 (![V_R,V_x,T_a]: (( c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(V_R,V_x,T_a),V_x,T_a,T_a),V_R,tc_prod(T_a,T_a))| c_in(V_x,c_Wellfounded_Oacc(V_R,T_a),T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f411,axiom,(
% 155.92/20.08 (![V_P,V_a,V_y,V_r,T_a]: (( hBOOL(hAPP(V_P,V_a))| hBOOL(hAPP(V_P,V_y))| ~ c_in(c_Pair(V_y,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(V_P,V_r,T_a),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) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f414,axiom,(
% 155.92/20.08 (![V_A,V_C,T_a,T_b,V_B,V_x]: (( c_lessequals(c_Product__Type_OSigma(V_A,c_COMBK(V_C,tc_fun(T_a,tc_bool),T_b),T_b,T_a),c_Product__Type_OSigma(V_B,c_COMBK(V_C,tc_fun(T_a,tc_bool),T_b),T_b,T_a),tc_fun(tc_prod(T_b,T_a),tc_bool))| ~ c_lessequals(V_A,V_B,tc_fun(T_b,tc_bool))| ~ c_in(V_x,V_C,T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f415,axiom,(
% 155.92/20.08 (![V_A,V_B,T_b,V_C,T_a,V_x]: (( c_lessequals(V_A,V_B,tc_fun(T_b,tc_bool))| ~ c_lessequals(c_Product__Type_OSigma(V_A,c_COMBK(V_C,tc_fun(T_a,tc_bool),T_b),T_b,T_a),c_Product__Type_OSigma(V_B,c_COMBK(V_C,tc_fun(T_a,tc_bool),T_b),T_b,T_a),tc_fun(tc_prod(T_b,T_a),tc_bool))| ~ c_in(V_x,V_C,T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f432,axiom,(
% 155.92/20.08 (![V_Q,V_x,V_P,T_a]: (( hBOOL(hAPP(V_Q,V_x))| ~ c_lessequals(V_P,V_Q,tc_fun(T_a,tc_bool))| ~ hBOOL(hAPP(V_P,V_x)) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f433,axiom,(
% 155.92/20.08 (![V_r,T_a,V_s]: (( c_Relation_Oantisym(V_r,T_a)| ~ c_Relation_Oantisym(V_s,T_a)| ~ c_lessequals(V_r,V_s,tc_fun(tc_prod(T_a,T_a),tc_bool)) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f439,axiom,(
% 155.92/20.08 (![V_A,T_a]: (c_lessequals(V_A,V_A,tc_fun(T_a,tc_bool)) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f447,axiom,(
% 155.92/20.08 (![V_A,V_B,T_a]: (( V_A = V_B| ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f458,axiom,(
% 155.92/20.08 (![V_b,V_r,T_a,T_b]: (( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(V_b,V_r,T_a,T_b),V_b,T_b,T_a),V_r,tc_prod(T_b,T_a))| ~ c_in(V_b,c_Relation_ORange(V_r,T_b,T_a),T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f463,axiom,(
% 155.92/20.08 (![V_p,V_r,T_a]: (( c_in(V_p,c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))| ~ c_in(V_p,V_r,tc_prod(T_a,T_a)) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f464,axiom,(
% 155.92/20.08 (![V_p,V_r,T_a]: (( c_in(V_p,c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a))| ~ c_in(V_p,V_r,tc_prod(T_a,T_a)) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f481,axiom,(
% 155.92/20.08 (![V_f,V_x,V_A,T_a,T_b]: (( c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b)| ~ c_in(V_x,V_A,T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f485,axiom,(
% 155.92/20.08 (![V_x,V_r,T_a]: (( c_in(V_x,c_Wellfounded_Oacc(V_r,T_a),T_a)| ~ c_Wellfounded_Owf(V_r,T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f493,axiom,(
% 155.92/20.08 (![V_r,T_a]: (c_Relation_ODomain(c_Transitive__Closure_Otrancl(V_r,T_a),T_a,T_a) = c_Relation_ODomain(V_r,T_a,T_a) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f494,axiom,(
% 155.92/20.08 (![V_A,V_b,V_r,T_b,T_a]: (( c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(V_A,V_b,V_r,T_b,T_a),V_A,T_b)| ~ c_in(V_b,c_Relation_OImage(V_r,V_A,T_b,T_a),T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f498,axiom,(
% 155.92/20.08 (![V_R,T_b,T_a]: (c_Relation_Orel__comp(V_R,c_Relation_OId(T_b),T_a,T_b,T_b) = V_R ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f500,axiom,(
% 155.92/20.08 (![V_r,T_a]: (( c_Wellfounded_Owf(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(V_r,T_a),T_a,T_a),T_a)| ~ c_Wellfounded_Owf(c_Relation_Oconverse(V_r,T_a,T_a),T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f501,axiom,(
% 155.92/20.08 (![V_A,V_r,T_a]: (( c_Relation_Orefl__on(V_A,V_r,T_a)| ~ c_Relation_Orefl__on(V_A,c_Relation_Oconverse(V_r,T_a,T_a),T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f511,axiom,(
% 155.92/20.08 (![V_r,T_a]: (c_Relation_ORange(c_Transitive__Closure_Otrancl(V_r,T_a),T_a,T_a) = c_Relation_ORange(V_r,T_a,T_a) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f523,axiom,(
% 155.92/20.08 (![T_a]: (c_Relation_Oconverse(c_Relation_OId(T_a),T_a,T_a) = c_Relation_OId(T_a) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f527,axiom,(
% 155.92/20.08 (![V_r,T_a]: (c_Transitive__Closure_Otrancl(c_Relation_Oconverse(V_r,T_a,T_a),T_a) = c_Relation_Oconverse(c_Transitive__Closure_Otrancl(V_r,T_a),T_a,T_a) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f530,axiom,(
% 155.92/20.08 (![V_r,T_a]: (( c_Relation_Orel__comp(c_Relation_Oconverse(V_r,T_a,T_a),V_r,T_a,T_a,T_a) != V_r| c_Equiv__Relations_Oequiv(c_Relation_ODomain(V_r,T_a,T_a),V_r,T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f532,axiom,(
% 155.92/20.08 (![V_r,T_a,T_b]: (c_Relation_ORange(c_Relation_Oconverse(V_r,T_a,T_b),T_b,T_a) = c_Relation_ODomain(V_r,T_a,T_b) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f533,axiom,(
% 155.92/20.08 (![V_Q,V_r,T_a,V_xa]: (( c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(V_Q,V_r,T_a),V_Q,T_a)| ~ c_in(V_xa,V_Q,T_a)| ~ c_Wellfounded_Owf(V_r,T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f534,axiom,(
% 155.92/20.08 (![V_A,T_a]: (c_Relation_ORange(c_Relation_OId__on(V_A,T_a),T_a,T_a) = V_A ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f536,axiom,(
% 155.92/20.08 (![V_r,T_a,T_b]: (c_Relation_Oconverse(c_Relation_Oconverse(V_r,T_a,T_b),T_b,T_a) = V_r ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f538,axiom,(
% 155.92/20.08 (![V_r,T_a,V_A]: (( c_Relation_Orel__comp(c_Relation_Oconverse(V_r,T_a,T_a),V_r,T_a,T_a,T_a) = V_r| ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a) ) ))),
% 155.92/20.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.08 fof(f543,axiom,(
% 155.92/20.08 (![V_A,V_r,T_a]: (( c_Relation_Orefl__on(V_A,V_r,T_a)| ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f544,axiom,(
% 155.92/20.09 (![V_r,T_a]: (c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(V_r,T_a,T_a),T_a) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(V_r,T_a),T_a,T_a) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f548,axiom,(
% 155.92/20.09 (![V_r,T_b,T_a]: (c_Relation_ODomain(c_Relation_Oconverse(V_r,T_b,T_a),T_a,T_b) = c_Relation_ORange(V_r,T_b,T_a) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f556,axiom,(
% 155.92/20.09 (![V_R,T_a]: (c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(V_R,T_a),T_a) = c_Transitive__Closure_Ortrancl(V_R,T_a) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f558,axiom,(
% 155.92/20.09 (![V_x,V_r,T_a]: (( c_in(V_x,c_Wellfounded_Oacc(V_r,T_a),T_a)| c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(V_r,V_x,T_a),V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f565,axiom,(
% 155.92/20.09 (![V_a,V_r,T_a,T_b]: (( c_in(c_Pair(V_a,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(V_a,V_r,T_a,T_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) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f566,axiom,(
% 155.92/20.09 (![V_P,V_x,V_ya,V_r]: (( hBOOL(hAPP(V_P,V_x))| c_in(V_ya,c_Wellfounded_Oacc(V_r,t_a),t_a)| ~ c_in(c_Pair(V_ya,v_sko__Wellfounded__Xacc__Xinduct__1(V_P,V_r),t_a,t_a),V_r,tc_prod(t_a,t_a))| ~ c_in(V_x,c_Wellfounded_Oacc(V_r,t_a),t_a) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f569,axiom,(
% 155.92/20.09 (![V_a,V_r,T_a,T_b]: (( c_in(c_Pair(V_a,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(V_a,V_r,T_a,T_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) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f572,axiom,(
% 155.92/20.09 (![V_a,V_r,T_a,T_b]: (( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(V_a,V_r,T_a,T_b),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) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f574,axiom,(
% 155.92/20.09 (![V_f,V_y1,V_y2,V_z1,V_z2,T_b,V_r2,T_a,V_r1,T_c]: (( hAPP(hAPP(V_f,V_y1),V_y2) = hAPP(hAPP(V_f,V_z1),V_z2)| ~ c_in(c_Pair(V_y2,V_z2,T_b,T_b),V_r2,tc_prod(T_b,T_b))| ~ c_in(c_Pair(V_y1,V_z1,T_a,T_a),V_r1,tc_prod(T_a,T_a))| ~ c_Equiv__Relations_Ocongruent2(V_r1,V_r2,V_f,T_a,T_b,T_c) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f575,axiom,(
% 155.92/20.09 (![V_y,V_z,V_x,T_a,T_b,V_r]: (( V_y = V_z| ~ c_in(c_Pair(V_x,V_z,T_a,T_b),V_r,tc_prod(T_a,T_b))| ~ c_in(c_Pair(V_x,V_y,T_a,T_b),V_r,tc_prod(T_a,T_b))| ~ c_Relation_Osingle__valued(V_r,T_a,T_b) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f578,axiom,(
% 155.92/20.09 (![V_R,V_x,V_y,T_a,T_b]: (( c_FunDef_Oin__rel(V_R,V_x,V_y,T_a,T_b)| ~ c_in(c_Pair(V_x,V_y,T_a,T_b),V_R,tc_prod(T_a,T_b)) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f579,axiom,(
% 155.92/20.09 (![V_x,V_y,T_a,T_b,V_R]: (( c_in(c_Pair(V_x,V_y,T_a,T_b),V_R,tc_prod(T_a,T_b))| ~ c_FunDef_Oin__rel(V_R,V_x,V_y,T_a,T_b) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f580,axiom,(
% 155.92/20.09 (![V_x,V_z,T_a,V_r,V_y]: (( c_in(c_Pair(V_x,V_z,T_a,T_a),V_r,tc_prod(T_a,T_a))| ~ c_in(c_Pair(V_y,V_z,T_a,T_a),V_r,tc_prod(T_a,T_a))| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))| ~ c_Relation_Otrans(V_r,T_a) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f585,axiom,(
% 155.92/20.09 (![V_x,T_a,V_r]: (( ~ c_in(c_Pair(V_x,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))| ~ c_Relation_Oirrefl(V_r,T_a) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f592,axiom,(
% 155.92/20.09 (![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)) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f594,axiom,(
% 155.92/20.09 (![V_x,V_a,T_a,V_r]: (( ~ c_in(c_Pair(V_x,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a))| ~ c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))| ~ c_Wellfounded_Owf(V_r,T_a) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f595,axiom,(
% 155.92/20.09 (![V_x,V_y,T_a,V_r]: (( V_x = V_y| ~ c_in(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))| ~ c_Relation_Oantisym(V_r,T_a) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f597,axiom,(
% 155.92/20.09 (![V_f,V_y,V_z,T_a,V_r,T_b]: (( hAPP(V_f,V_y) = hAPP(V_f,V_z)| ~ c_in(c_Pair(V_y,V_z,T_a,T_a),V_r,tc_prod(T_a,T_a))| ~ c_Equiv__Relations_Ocongruent(V_r,V_f,T_a,T_b) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f598,axiom,(
% 155.92/20.09 (![V_x,V_y,T_a,V_A]: (( V_x = V_y| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Relation_OId__on(V_A,T_a),tc_prod(T_a,T_a)) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f600,axiom,(
% 155.92/20.09 (![V_a,V_b,T_a]: (( V_a = V_b| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Relation_OId(T_a),tc_prod(T_a,T_a)) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f601,axiom,(
% 155.92/20.09 (![V_x,T_a,V_r]: (( c_in(c_Pair(V_x,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))| ~ c_Nitpick_Orefl_H(V_r,T_a) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f602,axiom,(
% 155.92/20.09 (![V_a,T_a,V_r]: (( ~ c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a))| ~ c_Wellfounded_Owf(V_r,T_a) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f605,axiom,(
% 155.92/20.09 (![V_y,V_x,T_a,V_r]: (( c_in(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))| ~ c_Relation_Osym(V_r,T_a) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f610,axiom,(
% 155.92/20.09 (![V_x,T_a]: (c_in(c_Pair(V_x,V_x,T_a,T_a),c_Relation_OId(T_a),tc_prod(T_a,T_a)) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f627,axiom,(
% 155.92/20.09 (![V_a,V_r,T_a,V_b]: (( c_in(V_a,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_b,c_Wellfounded_Oacc(V_r,T_a),T_a) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f629,axiom,(
% 155.92/20.09 (![V_b,V_r,V_A,T_a,T_b,V_a]: (( c_in(V_b,c_Relation_OImage(V_r,V_A,T_a,T_b),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_a,V_A,T_a) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f631,axiom,(
% 155.92/20.09 (![V_x,V_A,T_a,V_y]: (( c_in(V_x,V_A,T_a)| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Relation_OId__on(V_A,T_a),tc_prod(T_a,T_a)) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f632,axiom,(
% 155.92/20.09 (![V_x,T_a,V_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))| ~ c_in(V_x,V_A,T_a) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f633,axiom,(
% 155.92/20.09 (![V_y,V_A,T_a,V_x,V_r]: (( c_in(V_y,V_A,T_a)| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))| ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f634,axiom,(
% 155.92/20.09 (![V_x,V_A,T_a,V_y,V_r]: (( c_in(V_x,V_A,T_a)| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))| ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f635,axiom,(
% 155.92/20.09 (![V_a,V_r,T_b,T_a,V_x]: (( c_in(V_a,c_Relation_ORange(V_r,T_b,T_a),T_a)| ~ c_in(c_Pair(V_x,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a)) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f637,axiom,(
% 155.92/20.09 (![V_a,V_r,T_a,T_b,V_x]: (( c_in(V_a,c_Relation_ODomain(V_r,T_a,T_b),T_a)| ~ c_in(c_Pair(V_a,V_x,T_a,T_b),V_r,tc_prod(T_a,T_b)) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f641,axiom,(
% 155.92/20.09 (![V_xa,V_x,T_a,V_r,V_A]: (( c_in(c_Pair(V_xa,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))| c_in(c_Pair(V_x,V_xa,T_a,T_a),V_r,tc_prod(T_a,T_a))| V_x = V_xa| ~ c_in(V_xa,V_A,T_a)| ~ c_in(V_x,V_A,T_a)| ~ c_Relation_Ototal__on(V_A,V_r,T_a) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f642,axiom,(
% 155.92/20.09 (![V_x,T_a,V_r,V_A]: (( c_in(c_Pair(V_x,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))| ~ c_in(V_x,V_A,T_a)| ~ c_Relation_Orefl__on(V_A,V_r,T_a) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f643,axiom,(
% 155.92/20.09 (![V_y,V_A,T_a,V_x,V_r]: (( c_in(V_y,V_A,T_a)| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))| ~ c_Relation_Orefl__on(V_A,V_r,T_a) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f644,axiom,(
% 155.92/20.09 (![V_x,V_A,T_a,V_y,V_r]: (( c_in(V_x,V_A,T_a)| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))| ~ c_Relation_Orefl__on(V_A,V_r,T_a) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f646,axiom,(
% 155.92/20.09 v_a____ != v_b____ ),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f647,axiom,(
% 155.92/20.09 v_a_H____ != v_b_H____ ),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f648,axiom,(
% 155.92/20.09 (![V_a,V_b,T_a,T_b,V_a_H,V_b_H]: (( c_Pair(V_a,V_b,T_a,T_b) != c_Pair(V_a_H,V_b_H,T_a,T_b)| V_b = V_b_H ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f650,axiom,(
% 155.92/20.09 (![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)) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f651,axiom,(
% 155.92/20.09 (![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)) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f652,axiom,(
% 155.92/20.09 ( 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_b____ = v_a_H____| v_a____ = v_b_H____ ) ),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f654,axiom,(
% 155.92/20.09 (![V_x,V_S,T_a]: (( c_in(V_x,V_S,T_a)| ~ hBOOL(hAPP(V_S,V_x)) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f655,axiom,(
% 155.92/20.09 (![V_S,V_x,T_a]: (( hBOOL(hAPP(V_S,V_x))| ~ c_in(V_x,V_S,T_a) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f660,axiom,(
% 155.92/20.09 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))) ),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f661,axiom,(
% 155.92/20.09 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))) ),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f664,axiom,(
% 155.92/20.09 (![V_a,V_b,V_P,V_c,V_P_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_b,V_c,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_c,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,V_c)),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,V_c)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))| ~ c_in(V_P_H,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))| ~ c_in(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_c| V_b = V_c| V_a = V_b ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f665,axiom,(
% 155.92/20.09 (![V_b,V_c,V_P_H,V_a,V_P]: (( c_in(c_Pair(V_b,V_c,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))| ~ c_in(c_Pair(V_b,V_c,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,V_c)),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,V_c)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))| ~ c_in(V_P_H,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))| ~ c_in(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_c| V_b = V_c| V_a = V_b ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f666,axiom,(
% 155.92/20.09 (![V_a,V_b,V_P,V_c,V_P_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_b,V_c,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_c,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,V_c)),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,V_c)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))| ~ c_in(V_P_H,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))| ~ c_in(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_c| V_b = V_c| V_a = V_b ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f667,axiom,(
% 155.92/20.09 (![V_b,V_c,V_P_H,V_a,V_P]: (( c_in(c_Pair(V_b,V_c,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))| c_in(c_Pair(V_b,V_c,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,V_c)),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,V_c)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))| ~ c_in(V_P_H,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))| ~ c_in(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_c| V_b = V_c| V_a = V_b ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f668,axiom,(
% 155.92/20.09 v_b____ = v_a_H____ ),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f669,axiom,(
% 155.92/20.09 v_a____ != v_b_H____ ),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f670,negated_conjecture,(
% 155.92/20.09 ( ~ 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)) ) ),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f671,negated_conjecture,(
% 155.92/20.09 ( 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)) ) ),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f672,axiom,(
% 155.92/20.09 (![T_2,T_1]: (( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))| ~ class_Lattices_Olattice(T_1) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f673,axiom,(
% 155.92/20.09 (![T_2,T_1]: (( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))| ~ class_Lattices_Olattice(T_1) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f675,axiom,(
% 155.92/20.09 (![T_2,T_1]: (( class_Lattices_Obounded__lattice(tc_fun(T_2,T_1))| ~ class_Lattices_Obounded__lattice(T_1) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f676,axiom,(
% 155.92/20.09 (![T_2,T_1]: (( class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))| ~ class_Lattices_Oboolean__algebra(T_1) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f677,axiom,(
% 155.92/20.09 (![T_2,T_1]: (( class_Orderings_Opreorder(tc_fun(T_2,T_1))| ~ class_Orderings_Opreorder(T_1) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f678,axiom,(
% 155.92/20.09 (![T_2,T_1]: (( class_Lattices_Olattice(tc_fun(T_2,T_1))| ~ class_Lattices_Olattice(T_1) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f679,axiom,(
% 155.92/20.09 (![T_2,T_1]: (( class_Orderings_Oorder(tc_fun(T_2,T_1))| ~ class_Orderings_Oorder(T_1) ) ))),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f685,axiom,(
% 155.92/20.09 class_Lattices_Obounded__lattice(tc_bool) ),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f686,axiom,(
% 155.92/20.09 class_Lattices_Oboolean__algebra(tc_bool) ),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f687,axiom,(
% 155.92/20.09 class_Orderings_Opreorder(tc_bool) ),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f688,axiom,(
% 155.92/20.09 class_Lattices_Olattice(tc_bool) ),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f689,axiom,(
% 155.92/20.09 class_Orderings_Oorder(tc_bool) ),
% 155.92/20.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 155.92/20.09 fof(f696,plain,(
% 155.92/20.09 ![X0,X1]: (~c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(X0,X1)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))|c_Wellfounded_Owf(X0,X1))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f2])).
% 155.92/20.09 fof(f697,plain,(
% 155.92/20.09 ![X0,X1]: (c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_fun(X1,tc_bool))=X0)),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f3])).
% 155.92/20.09 fof(f698,plain,(
% 155.92/20.09 ![T_a]: (~class_Lattices_Oupper__semilattice(T_a)|(![V_x]: c_Lattices_Oupper__semilattice__class_Osup(V_x,V_x,T_a)=V_x))),
% 155.92/20.09 inference(miniscoping,[status(esa)],[f4])).
% 155.92/20.09 fof(f699,plain,(
% 155.92/20.09 ![X0,X1]: (~class_Lattices_Oupper__semilattice(X0)|c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X0)=X1)),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f698])).
% 155.92/20.09 fof(f702,plain,(
% 155.92/20.09 ![V_R,T_a]: ((![V_P]: ((![V_Rb]: hBOOL(hAPP(V_P,V_Rb)))|~hBOOL(hAPP(V_P,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(V_P,V_R,T_a)))))|~c_Wellfounded_Owf(V_R,T_a))),
% 155.92/20.09 inference(miniscoping,[status(esa)],[f7])).
% 155.92/20.09 fof(f703,plain,(
% 155.92/20.09 ![X0,X1,X2,X3]: (hBOOL(hAPP(X0,X1))|~hBOOL(hAPP(X0,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X0,X2,X3)))|~c_Wellfounded_Owf(X2,X3))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f702])).
% 155.92/20.09 fof(f705,plain,(
% 155.92/20.09 ![X0,X1,X2,X3]: (hAPP(c_COMBK(X0,X1,X2),X3)=X0)),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f9])).
% 155.92/20.09 fof(f712,plain,(
% 155.92/20.09 ![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)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f14])).
% 155.92/20.09 fof(f713,plain,(
% 155.92/20.09 ![X0,X1,X2]: (c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool))=c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f15])).
% 155.92/20.09 fof(f734,plain,(
% 155.92/20.09 ![X0,X1,X2]: (c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f30])).
% 155.92/20.09 fof(f735,plain,(
% 155.92/20.09 ![X0,X1,X2]: (c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f31])).
% 155.92/20.09 fof(f752,plain,(
% 155.92/20.09 ![X0,X1,X2]: (c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool))=c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f40])).
% 155.92/20.09 fof(f757,plain,(
% 155.92/20.09 ![X0,X1]: (c_Wellfounded_Oacyclic(X0,X1)|~c_Wellfounded_Owf(X0,X1))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f43])).
% 155.92/20.09 fof(f787,plain,(
% 155.92/20.09 ![T_a,V_A]: ((![V_c,T_b]: c_Set_Oimage(c_COMBK(V_c,T_b,T_a),V_A,T_a,T_b)=c_Set_Oinsert(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b))|(![V_x]: ~c_in(V_x,V_A,T_a)))),
% 155.92/20.09 inference(miniscoping,[status(esa)],[f65])).
% 155.92/20.09 fof(f788,plain,(
% 155.92/20.09 ![X0,X1,X2,X3,X4]: (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)|~c_in(X4,X3,X2))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f787])).
% 155.92/20.09 fof(f792,plain,(
% 155.92/20.09 ![V_x,T_a,V_B]: ((![V_A]: c_HOL_Ominus__class_Ominus(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))=c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)))|~c_in(V_x,V_B,T_a))),
% 155.92/20.09 inference(miniscoping,[status(esa)],[f69])).
% 155.92/20.09 fof(f793,plain,(
% 155.92/20.09 ![X0,X1,X2,X3]: (c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X0,X1,X2),X3,tc_fun(X2,tc_bool))=c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool))|~c_in(X0,X3,X2))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f792])).
% 155.92/20.09 fof(f806,plain,(
% 155.92/20.09 ![X0,X1]: (c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X1,tc_bool)),X0,tc_fun(X1,tc_bool))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f77])).
% 155.92/20.09 fof(f808,plain,(
% 155.92/20.09 ![V_A,T_b]: ((![T_a,V_f]: ~c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))=c_Set_Oimage(V_f,V_A,T_b,T_a))|V_A=c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)))),
% 155.92/20.09 inference(miniscoping,[status(esa)],[f79])).
% 155.92/20.09 fof(f809,plain,(
% 155.92/20.09 ![X0,X1,X2,X3]: (~c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))=c_Set_Oimage(X1,X2,X3,X0)|X2=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f808])).
% 155.92/20.09 fof(f823,plain,(
% 155.92/20.09 ![X0,X1,X2]: (~c_Set_Oinsert(X0,X1,X2)=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f92])).
% 155.92/20.09 fof(f825,plain,(
% 155.92/20.09 ![X0,X1,X2]: (c_Relation_OImage(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1,X2)=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f94])).
% 155.92/20.09 fof(f836,plain,(
% 155.92/20.09 ![T_a]: (~class_Lattices_Obounded__lattice(T_a)|(![V_x]: c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(T_a),V_x,T_a)=c_Orderings_Obot__class_Obot(T_a)))),
% 155.92/20.09 inference(miniscoping,[status(esa)],[f102])).
% 155.92/20.09 fof(f837,plain,(
% 155.92/20.09 ![X0,X1]: (~class_Lattices_Obounded__lattice(X0)|c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X0),X1,X0)=c_Orderings_Obot__class_Obot(X0))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f836])).
% 155.92/20.09 fof(f849,plain,(
% 155.92/20.09 ![X0,X1]: (c_HOL_Ominus__class_Ominus(X0,X0,tc_fun(X1,tc_bool))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f112])).
% 155.92/20.09 fof(f868,plain,(
% 155.92/20.09 ![X0,X1,X2,X3]: (c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool))=c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f123])).
% 155.92/20.09 fof(f869,plain,(
% 155.92/20.09 ![X0,X1,X2,X3]: (c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))=c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f124])).
% 155.92/20.09 fof(f874,plain,(
% 155.92/20.09 ![X0,X1]: (c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool))=X1)),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f127])).
% 155.92/20.09 fof(f875,plain,(
% 155.92/20.09 ![X0,X1]: (c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool))=X0)),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f128])).
% 155.92/20.09 fof(f878,plain,(
% 155.92/20.09 ![X0,X1]: (~hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f131])).
% 155.92/20.09 fof(f880,plain,(
% 155.92/20.09 ![X0,X1,X2,X3]: (c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool))=c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f133])).
% 155.92/20.09 fof(f881,plain,(
% 155.92/20.09 ![T_b,V_A]: ((![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))|V_A=c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)))),
% 155.92/20.09 inference(miniscoping,[status(esa)],[f134])).
% 155.92/20.09 fof(f882,plain,(
% 155.92/20.09 ![X0,X1,X2,X3]: (c_Set_Oimage(c_COMBK(X0,X1,X2),X3,X2,X1)=c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)|X3=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f881])).
% 155.92/20.09 fof(f891,plain,(
% 155.92/20.09 ![X0,X1,X2,X3]: (c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))=c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f139])).
% 155.92/20.09 fof(f902,plain,(
% 155.92/20.09 ![X0,X1]: (c_Wellfounded_Oacyclic(X0,X1)|~c_Wellfounded_Oacyclic(c_Relation_Oconverse(X0,X1,X1),X1))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f145])).
% 155.92/20.09 fof(f906,plain,(
% 155.92/20.09 ![X0,X1,X2]: (c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))=X0)),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f148])).
% 155.92/20.09 fof(f908,plain,(
% 155.92/20.09 ![X0,X1,X2]: (~class_Lattices_Oupper__semilattice(X0)|~c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0)=X2|c_lessequals(X1,X2,X0))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f150])).
% 155.92/20.09 fof(f958,plain,(
% 155.92/20.09 ![X0,X1,X2]: (c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool))=c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f181])).
% 155.92/20.09 fof(f970,plain,(
% 155.92/20.09 ![X0,X1,X2]: (c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))=c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f189])).
% 155.92/20.09 fof(f981,plain,(
% 155.92/20.09 ![X0,X1,X2]: (c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f196])).
% 155.92/20.09 fof(f983,plain,(
% 155.92/20.09 ![V_r,T_a]: ((![V_P]: ((![V_a]: hBOOL(hAPP(V_P,V_a)))|~hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(V_P,V_r,T_a)))))|~c_Wellfounded_Owf(V_r,T_a))),
% 155.92/20.09 inference(miniscoping,[status(esa)],[f198])).
% 155.92/20.09 fof(f984,plain,(
% 155.92/20.09 ![X0,X1,X2,X3]: (hBOOL(hAPP(X0,X1))|~hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X0,X2,X3)))|~c_Wellfounded_Owf(X2,X3))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f983])).
% 155.92/20.09 fof(f1026,plain,(
% 155.92/20.09 ![V_a,V_A,T_a]: ((![V_b]: c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a))|~c_in(V_a,V_A,T_a))),
% 155.92/20.09 inference(miniscoping,[status(esa)],[f227])).
% 155.92/20.09 fof(f1027,plain,(
% 155.92/20.09 ![X0,X1,X2,X3]: (c_in(X0,c_Set_Oinsert(X1,X2,X3),X3)|~c_in(X0,X2,X3))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f1026])).
% 155.92/20.09 fof(f1041,plain,(
% 155.92/20.09 ![V_c,V_B,T_a]: (~c_in(V_c,V_B,T_a)|(![V_A]: ~c_in(V_c,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)))),
% 155.92/20.09 inference(miniscoping,[status(esa)],[f237])).
% 155.92/20.09 fof(f1042,plain,(
% 155.92/20.09 ![X0,X1,X2,X3]: (~c_in(X0,X1,X2)|~c_in(X0,c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f1041])).
% 155.92/20.09 fof(f1047,plain,(
% 155.92/20.09 ![X0,X1,X2]: (c_in(X0,c_Set_Oinsert(X0,X1,X2),X2))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f241])).
% 155.92/20.09 fof(f1052,plain,(
% 155.92/20.09 ![V_c,V_A,T_a]: (c_in(V_c,V_A,T_a)|(![V_B]: ~c_in(V_c,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)))),
% 155.92/20.09 inference(miniscoping,[status(esa)],[f245])).
% 155.92/20.09 fof(f1053,plain,(
% 155.92/20.09 ![X0,X1,X2,X3]: (c_in(X0,X1,X2)|~c_in(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),X2))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f1052])).
% 155.92/20.09 fof(f1086,plain,(
% 155.92/20.09 ![X0,X1,X2,X3,X4]: (c_Set_Oimage(X0,c_Set_Oinsert(X1,X2,X3),X3,X4)=c_Set_Oinsert(hAPP(X0,X1),c_Set_Oimage(X0,X2,X3,X4),X4))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f265])).
% 155.92/20.09 fof(f1106,plain,(
% 155.92/20.09 ![X0,X1,X2]: (c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f277])).
% 155.92/20.09 fof(f1160,plain,(
% 155.92/20.09 ![X0,X1,X2,X3]: (c_HOL_Ominus__class_Ominus(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))=c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X0,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f309])).
% 155.92/20.09 fof(f1161,plain,(
% 155.92/20.09 ![X0,X1,X2,X3]: (c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool))=c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f310])).
% 155.92/20.09 fof(f1213,plain,(
% 155.92/20.09 ![V_a,V_r,T_a]: ((![V_P]: (hBOOL(hAPP(V_P,V_a))|~hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(V_P,V_r,T_a)))))|~c_in(V_a,c_Wellfounded_Oacc(V_r,T_a),T_a))),
% 155.92/20.09 inference(miniscoping,[status(esa)],[f342])).
% 155.92/20.09 fof(f1214,plain,(
% 155.92/20.09 ![X0,X1,X2,X3]: (hBOOL(hAPP(X0,X1))|~hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,X2,X3)))|~c_in(X1,c_Wellfounded_Oacc(X2,X3),X3))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f1213])).
% 155.92/20.09 fof(f1217,plain,(
% 155.92/20.09 ![X0,X1]: (c_Transitive__Closure_Otrancl(X0,X1)=c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X0,X1),X0,X1,X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f345])).
% 155.92/20.09 fof(f1221,plain,(
% 155.92/20.09 ![X0,X1]: (c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X0,X1),X1)|~c_Wellfounded_Oacyclic(X0,X1))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f349])).
% 155.92/20.09 fof(f1225,plain,(
% 155.92/20.09 ![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)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f353])).
% 155.92/20.09 fof(f1241,plain,(
% 155.92/20.09 ![V_r,T_a]: ((![V_P,V_y]: (((![V_a]: hBOOL(hAPP(V_P,V_a)))|hBOOL(hAPP(V_P,V_y)))|~c_in(c_Pair(V_y,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(V_P,V_r,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a))))|~c_Wellfounded_Owf(V_r,T_a))),
% 155.92/20.09 inference(miniscoping,[status(esa)],[f365])).
% 155.92/20.09 fof(f1242,plain,(
% 155.92/20.09 ![X0,X1,X2,X3,X4]: (hBOOL(hAPP(X0,X1))|hBOOL(hAPP(X0,X2))|~c_in(c_Pair(X2,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X0,X3,X4),X4,X4),X3,tc_prod(X4,X4))|~c_Wellfounded_Owf(X3,X4))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f1241])).
% 155.92/20.09 fof(f1247,plain,(
% 155.92/20.09 ![V_r,T_a]: ((![V_P,V_y]: (((![V_a]: hBOOL(hAPP(V_P,V_a)))|hBOOL(hAPP(V_P,V_y)))|~c_in(c_Pair(V_y,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(V_P,V_r,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a))))|~c_Wellfounded_Owf(V_r,T_a))),
% 155.92/20.09 inference(miniscoping,[status(esa)],[f368])).
% 155.92/20.09 fof(f1248,plain,(
% 155.92/20.09 ![X0,X1,X2,X3,X4]: (hBOOL(hAPP(X0,X1))|hBOOL(hAPP(X0,X2))|~c_in(c_Pair(X2,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X0,X3,X4),X4,X4),X3,tc_prod(X4,X4))|~c_Wellfounded_Owf(X3,X4))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f1247])).
% 155.92/20.09 fof(f1253,plain,(
% 155.92/20.09 ![T_a,V_r]: ((![V_x]: ~c_in(c_Pair(V_x,V_x,T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a)))|~c_Wellfounded_Oacyclic(V_r,T_a))),
% 155.92/20.09 inference(miniscoping,[status(esa)],[f372])).
% 155.92/20.09 fof(f1254,plain,(
% 155.92/20.09 ![X0,X1,X2]: (~c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Otrancl(X2,X1),tc_prod(X1,X1))|~c_Wellfounded_Oacyclic(X2,X1))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f1253])).
% 155.92/20.09 fof(f1257,plain,(
% 155.92/20.09 ![X0,X1,X2,X3]: (c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X1,X0,X2,X3),X3,X3),X1,tc_prod(X3,X3))|c_in(c_Pair(X0,X2,X3,X3),X1,tc_prod(X3,X3))|~c_in(c_Pair(X0,X2,X3,X3),c_Transitive__Closure_Otrancl(X1,X3),tc_prod(X3,X3)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f375])).
% 155.92/20.09 fof(f1264,plain,(
% 155.92/20.09 ![X0,X1]: (c_Wellfounded_Owf(X0,X1)|c_lessequals(c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(X0,X1),c_Relation_OImage(X0,c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(X0,X1),X1,X1),tc_fun(X1,tc_bool)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f381])).
% 155.92/20.09 fof(f1268,plain,(
% 155.92/20.09 ![X0,X1]: (c_Wellfounded_Owf(X0,X1)|~c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X0,X1),c_Wellfounded_Oacc(X0,X1),X1))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f384])).
% 155.92/20.09 fof(f1273,plain,(
% 155.92/20.09 ![X0,X1,X2]: (c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X0,X1,X2),X0,X2)|~c_in(X1,c_Relation_OId__on(X0,X2),tc_prod(X2,X2)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f388])).
% 155.92/20.09 fof(f1274,plain,(
% 155.92/20.09 ![X0,X1,X2]: (X0=c_Pair(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X1,X0,X2),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X1,X0,X2),X2,X2)|~c_in(X0,c_Relation_OId__on(X1,X2),tc_prod(X2,X2)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f389])).
% 155.92/20.09 fof(f1283,plain,(
% 155.92/20.09 ![X0,X1]: (c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool))=c_Transitive__Closure_Ortrancl(X0,X1))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f396])).
% 155.92/20.09 fof(f1289,plain,(
% 155.92/20.09 ![X0,X1]: (c_Relation_Oirrefl(X0,X1)|c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X0,X1),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X0,X1),X1,X1),X0,tc_prod(X1,X1)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f402])).
% 155.92/20.09 fof(f1294,plain,(
% 155.92/20.09 ![X0,X1]: (c_Nitpick_Orefl_H(X0,X1)|~c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X0,X1),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X0,X1),X1,X1),X0,tc_prod(X1,X1)))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f406])).
% 155.92/20.09 fof(f1299,plain,(
% 155.92/20.09 ![X0,X1,X2,X3,X4]: (c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X0,X1,X2,X3,X4),X1,X3,X4),X2,tc_prod(X3,X4))|~c_in(X1,c_Relation_OImage(X2,X0,X3,X4),X4))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f409])).
% 155.92/20.09 fof(f1300,plain,(
% 155.92/20.09 ![X0,X1,X2]: (c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X1,X2),X1,X2,X2),X0,tc_prod(X2,X2))|c_in(X1,c_Wellfounded_Oacc(X0,X2),X2))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f410])).
% 155.92/20.09 fof(f1301,plain,(
% 155.92/20.09 ![V_a,V_r,T_a]: ((![V_P,V_y]: ((hBOOL(hAPP(V_P,V_a))|hBOOL(hAPP(V_P,V_y)))|~c_in(c_Pair(V_y,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(V_P,V_r,T_a),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))),
% 155.92/20.09 inference(miniscoping,[status(esa)],[f411])).
% 155.92/20.09 fof(f1302,plain,(
% 155.92/20.09 ![X0,X1,X2,X3,X4]: (hBOOL(hAPP(X0,X1))|hBOOL(hAPP(X0,X2))|~c_in(c_Pair(X2,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,X3,X4),X4,X4),X3,tc_prod(X4,X4))|~c_in(X1,c_Wellfounded_Oacc(X3,X4),X4))),
% 155.92/20.09 inference(cnf_transformation,[status(esa)],[f1301])).
% 155.92/20.09 fof(f1306,plain,(
% 155.92/20.09 ![V_C,T_a]: ((![V_A,T_b,V_B]: (c_lessequals(c_Product__Type_OSigma(V_A,c_COMBK(V_C,tc_fun(T_a,tc_bool),T_b),T_b,T_a),c_Product__Type_OSigma(V_B,c_COMBK(V_C,tc_fun(T_a,tc_bool),T_b),T_b,T_a),tc_fun(tc_prod(T_b,T_a),tc_bool))|~c_lessequals(V_A,V_B,tc_fun(T_b,tc_bool))))|(![V_x]: ~c_in(V_x,V_C,T_a)))),
% 155.92/20.09 inference(miniscoping,[status(esa)],[f414])).
% 156.17/20.09 fof(f1307,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4,X5]: (c_lessequals(c_Product__Type_OSigma(X0,c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,X2),c_Product__Type_OSigma(X4,c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,X2),tc_fun(tc_prod(X3,X2),tc_bool))|~c_lessequals(X0,X4,tc_fun(X3,tc_bool))|~c_in(X5,X1,X2))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1306])).
% 156.17/20.09 fof(f1308,plain,(
% 156.17/20.09 ![V_C,T_a]: ((![V_A,V_B,T_b]: (c_lessequals(V_A,V_B,tc_fun(T_b,tc_bool))|~c_lessequals(c_Product__Type_OSigma(V_A,c_COMBK(V_C,tc_fun(T_a,tc_bool),T_b),T_b,T_a),c_Product__Type_OSigma(V_B,c_COMBK(V_C,tc_fun(T_a,tc_bool),T_b),T_b,T_a),tc_fun(tc_prod(T_b,T_a),tc_bool))))|(![V_x]: ~c_in(V_x,V_C,T_a)))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f415])).
% 156.17/20.09 fof(f1309,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4,X5]: (c_lessequals(X0,X1,tc_fun(X2,tc_bool))|~c_lessequals(c_Product__Type_OSigma(X0,c_COMBK(X3,tc_fun(X4,tc_bool),X2),X2,X4),c_Product__Type_OSigma(X1,c_COMBK(X3,tc_fun(X4,tc_bool),X2),X2,X4),tc_fun(tc_prod(X2,X4),tc_bool))|~c_in(X5,X3,X4))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1308])).
% 156.17/20.09 fof(f1336,plain,(
% 156.17/20.09 ![V_x,V_P]: ((![V_Q]: (hBOOL(hAPP(V_Q,V_x))|(![T_a]: ~c_lessequals(V_P,V_Q,tc_fun(T_a,tc_bool)))))|~hBOOL(hAPP(V_P,V_x)))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f432])).
% 156.17/20.09 fof(f1337,plain,(
% 156.17/20.09 ![X0,X1,X2,X3]: (hBOOL(hAPP(X0,X1))|~c_lessequals(X2,X0,tc_fun(X3,tc_bool))|~hBOOL(hAPP(X2,X1)))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1336])).
% 156.17/20.09 fof(f1338,plain,(
% 156.17/20.09 ![X0,X1,X2]: (c_Relation_Oantisym(X0,X1)|~c_Relation_Oantisym(X2,X1)|~c_lessequals(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool)))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f433])).
% 156.17/20.09 fof(f1349,plain,(
% 156.17/20.09 ![X0,X1]: (c_lessequals(X0,X0,tc_fun(X1,tc_bool)))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f439])).
% 156.17/20.09 fof(f1359,plain,(
% 156.17/20.09 ![X0,X1,X2]: (X0=X1|~c_lessequals(X1,X0,tc_fun(X2,tc_bool))|~c_lessequals(X0,X1,tc_fun(X2,tc_bool)))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f447])).
% 156.17/20.09 fof(f1376,plain,(
% 156.17/20.09 ![X0,X1,X2,X3]: (c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,X1,X2,X3),X0,X3,X2),X1,tc_prod(X3,X2))|~c_in(X0,c_Relation_ORange(X1,X3,X2),X2))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f458])).
% 156.17/20.09 fof(f1382,plain,(
% 156.17/20.09 ![X0,X1,X2]: (c_in(X0,c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))|~c_in(X0,X1,tc_prod(X2,X2)))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f463])).
% 156.17/20.09 fof(f1383,plain,(
% 156.17/20.09 ![X0,X1,X2]: (c_in(X0,c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2))|~c_in(X0,X1,tc_prod(X2,X2)))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f464])).
% 156.17/20.09 fof(f1407,plain,(
% 156.17/20.09 ![V_x,V_A,T_a]: ((![V_f,T_b]: c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b))|~c_in(V_x,V_A,T_a))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f481])).
% 156.17/20.09 fof(f1408,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4]: (c_in(hAPP(X0,X1),c_Set_Oimage(X0,X2,X3,X4),X4)|~c_in(X1,X2,X3))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1407])).
% 156.17/20.09 fof(f1415,plain,(
% 156.17/20.09 ![V_r,T_a]: ((![V_x]: c_in(V_x,c_Wellfounded_Oacc(V_r,T_a),T_a))|~c_Wellfounded_Owf(V_r,T_a))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f485])).
% 156.17/20.09 fof(f1416,plain,(
% 156.17/20.09 ![X0,X1,X2]: (c_in(X0,c_Wellfounded_Oacc(X1,X2),X2)|~c_Wellfounded_Owf(X1,X2))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1415])).
% 156.17/20.09 fof(f1426,plain,(
% 156.17/20.09 ![X0,X1]: (c_Relation_ODomain(c_Transitive__Closure_Otrancl(X0,X1),X1,X1)=c_Relation_ODomain(X0,X1,X1))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f493])).
% 156.17/20.09 fof(f1427,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4]: (c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X0,X1,X2,X3,X4),X0,X3)|~c_in(X1,c_Relation_OImage(X2,X0,X3,X4),X4))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f494])).
% 156.17/20.09 fof(f1431,plain,(
% 156.17/20.09 ![X0,X1,X2]: (c_Relation_Orel__comp(X0,c_Relation_OId(X1),X2,X1,X1)=X0)),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f498])).
% 156.17/20.09 fof(f1433,plain,(
% 156.17/20.09 ![X0,X1]: (c_Wellfounded_Owf(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X0,X1),X1,X1),X1)|~c_Wellfounded_Owf(c_Relation_Oconverse(X0,X1,X1),X1))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f500])).
% 156.17/20.09 fof(f1434,plain,(
% 156.17/20.09 ![X0,X1,X2]: (c_Relation_Orefl__on(X0,X1,X2)|~c_Relation_Orefl__on(X0,c_Relation_Oconverse(X1,X2,X2),X2))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f501])).
% 156.17/20.09 fof(f1444,plain,(
% 156.17/20.09 ![X0,X1]: (c_Relation_ORange(c_Transitive__Closure_Otrancl(X0,X1),X1,X1)=c_Relation_ORange(X0,X1,X1))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f511])).
% 156.17/20.09 fof(f1458,plain,(
% 156.17/20.09 ![X0]: (c_Relation_Oconverse(c_Relation_OId(X0),X0,X0)=c_Relation_OId(X0))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f523])).
% 156.17/20.09 fof(f1462,plain,(
% 156.17/20.09 ![X0,X1]: (c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X0,X1,X1),X1)=c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X0,X1),X1,X1))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f527])).
% 156.17/20.09 fof(f1466,plain,(
% 156.17/20.09 ![X0,X1]: (~c_Relation_Orel__comp(c_Relation_Oconverse(X0,X1,X1),X0,X1,X1,X1)=X0|c_Equiv__Relations_Oequiv(c_Relation_ODomain(X0,X1,X1),X0,X1))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f530])).
% 156.17/20.09 fof(f1468,plain,(
% 156.17/20.09 ![X0,X1,X2]: (c_Relation_ORange(c_Relation_Oconverse(X0,X1,X2),X2,X1)=c_Relation_ODomain(X0,X1,X2))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f532])).
% 156.17/20.09 fof(f1469,plain,(
% 156.17/20.09 ![V_r,T_a]: ((![V_Q]: (c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(V_Q,V_r,T_a),V_Q,T_a)|(![V_xa]: ~c_in(V_xa,V_Q,T_a))))|~c_Wellfounded_Owf(V_r,T_a))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f533])).
% 156.17/20.09 fof(f1470,plain,(
% 156.17/20.09 ![X0,X1,X2,X3]: (c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X0,X1,X2),X0,X2)|~c_in(X3,X0,X2)|~c_Wellfounded_Owf(X1,X2))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1469])).
% 156.17/20.09 fof(f1471,plain,(
% 156.17/20.09 ![X0,X1]: (c_Relation_ORange(c_Relation_OId__on(X0,X1),X1,X1)=X0)),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f534])).
% 156.17/20.09 fof(f1474,plain,(
% 156.17/20.09 ![X0,X1,X2]: (c_Relation_Oconverse(c_Relation_Oconverse(X0,X1,X2),X2,X1)=X0)),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f536])).
% 156.17/20.09 fof(f1476,plain,(
% 156.17/20.09 ![V_r,T_a]: (c_Relation_Orel__comp(c_Relation_Oconverse(V_r,T_a,T_a),V_r,T_a,T_a,T_a)=V_r|(![V_A]: ~c_Equiv__Relations_Oequiv(V_A,V_r,T_a)))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f538])).
% 156.17/20.09 fof(f1477,plain,(
% 156.17/20.09 ![X0,X1,X2]: (c_Relation_Orel__comp(c_Relation_Oconverse(X0,X1,X1),X0,X1,X1,X1)=X0|~c_Equiv__Relations_Oequiv(X2,X0,X1))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1476])).
% 156.17/20.09 fof(f1483,plain,(
% 156.17/20.09 ![X0,X1,X2]: (c_Relation_Orefl__on(X0,X1,X2)|~c_Equiv__Relations_Oequiv(X0,X1,X2))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f543])).
% 156.17/20.09 fof(f1484,plain,(
% 156.17/20.09 ![X0,X1]: (c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X0,X1,X1),X1)=c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f544])).
% 156.17/20.09 fof(f1490,plain,(
% 156.17/20.09 ![X0,X1,X2]: (c_Relation_ODomain(c_Relation_Oconverse(X0,X1,X2),X2,X1)=c_Relation_ORange(X0,X1,X2))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f548])).
% 156.17/20.09 fof(f1500,plain,(
% 156.17/20.09 ![X0,X1]: (c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X0,X1),X1)=c_Transitive__Closure_Ortrancl(X0,X1))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f556])).
% 156.17/20.09 fof(f1502,plain,(
% 156.17/20.09 ![X0,X1,X2]: (c_in(X0,c_Wellfounded_Oacc(X1,X2),X2)|c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X1,X0,X2),X0,X2,X2),X1,tc_prod(X2,X2)))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f558])).
% 156.17/20.09 fof(f1513,plain,(
% 156.17/20.09 ![X0,X1,X2,X3]: (c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X0,X1,X2,X3),X2,X3),X1,tc_prod(X2,X3))|~c_in(X0,c_Relation_ODomain(X1,X2,X3),X2))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f565])).
% 156.17/20.09 fof(f1514,plain,(
% 156.17/20.09 ![V_x,V_r]: ((![V_P,V_ya]: ((hBOOL(hAPP(V_P,V_x))|c_in(V_ya,c_Wellfounded_Oacc(V_r,t_a),t_a))|~c_in(c_Pair(V_ya,v_sko__Wellfounded__Xacc__Xinduct__1(V_P,V_r),t_a,t_a),V_r,tc_prod(t_a,t_a))))|~c_in(V_x,c_Wellfounded_Oacc(V_r,t_a),t_a))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f566])).
% 156.17/20.09 fof(f1515,plain,(
% 156.17/20.09 ![X0,X1,X2,X3]: (hBOOL(hAPP(X0,X1))|c_in(X2,c_Wellfounded_Oacc(X3,t_a),t_a)|~c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinduct__1(X0,X3),t_a,t_a),X3,tc_prod(t_a,t_a))|~c_in(X1,c_Wellfounded_Oacc(X3,t_a),t_a))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1514])).
% 156.17/20.09 fof(f1520,plain,(
% 156.17/20.09 ![X0,X1,X2,X3]: (c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X0,X1,X2,X3),X2,X3),X1,tc_prod(X2,X3))|~c_in(X0,c_Relation_ODomain(X1,X2,X3),X2))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f569])).
% 156.17/20.09 fof(f1524,plain,(
% 156.17/20.09 ![X0,X1,X2,X3]: (c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,X1,X2,X3),X0,X3,X2),X1,tc_prod(X3,X2))|~c_in(X0,c_Relation_ORange(X1,X3,X2),X2))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f572])).
% 156.17/20.09 fof(f1527,plain,(
% 156.17/20.09 ![V_f,T_b,V_r2,T_a,V_r1]: ((![V_y1,V_z1]: ((![V_y2,V_z2]: (hAPP(hAPP(V_f,V_y1),V_y2)=hAPP(hAPP(V_f,V_z1),V_z2)|~c_in(c_Pair(V_y2,V_z2,T_b,T_b),V_r2,tc_prod(T_b,T_b))))|~c_in(c_Pair(V_y1,V_z1,T_a,T_a),V_r1,tc_prod(T_a,T_a))))|(![T_c]: ~c_Equiv__Relations_Ocongruent2(V_r1,V_r2,V_f,T_a,T_b,T_c)))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f574])).
% 156.17/20.09 fof(f1528,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4,X5,X6,X7,X8,X9]: (hAPP(hAPP(X0,X1),X2)=hAPP(hAPP(X0,X3),X4)|~c_in(c_Pair(X2,X4,X5,X5),X6,tc_prod(X5,X5))|~c_in(c_Pair(X1,X3,X7,X7),X8,tc_prod(X7,X7))|~c_Equiv__Relations_Ocongruent2(X8,X6,X0,X7,X5,X9))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1527])).
% 156.17/20.09 fof(f1529,plain,(
% 156.17/20.09 ![T_a,T_b,V_r]: ((![V_y,V_x]: ((![V_z]: (V_y=V_z|~c_in(c_Pair(V_x,V_z,T_a,T_b),V_r,tc_prod(T_a,T_b))))|~c_in(c_Pair(V_x,V_y,T_a,T_b),V_r,tc_prod(T_a,T_b))))|~c_Relation_Osingle__valued(V_r,T_a,T_b))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f575])).
% 156.17/20.09 fof(f1530,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4,X5]: (X0=X1|~c_in(c_Pair(X2,X1,X3,X4),X5,tc_prod(X3,X4))|~c_in(c_Pair(X2,X0,X3,X4),X5,tc_prod(X3,X4))|~c_Relation_Osingle__valued(X5,X3,X4))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1529])).
% 156.17/20.09 fof(f1535,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4]: (c_FunDef_Oin__rel(X0,X1,X2,X3,X4)|~c_in(c_Pair(X1,X2,X3,X4),X0,tc_prod(X3,X4)))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f578])).
% 156.17/20.09 fof(f1536,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4]: (c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3))|~c_FunDef_Oin__rel(X4,X0,X1,X2,X3))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f579])).
% 156.17/20.09 fof(f1537,plain,(
% 156.17/20.09 ![T_a,V_r]: ((![V_x,V_y]: ((![V_z]: (c_in(c_Pair(V_x,V_z,T_a,T_a),V_r,tc_prod(T_a,T_a))|~c_in(c_Pair(V_y,V_z,T_a,T_a),V_r,tc_prod(T_a,T_a))))|~c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))))|~c_Relation_Otrans(V_r,T_a))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f580])).
% 156.17/20.09 fof(f1538,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4]: (c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2))|~c_in(c_Pair(X4,X1,X2,X2),X3,tc_prod(X2,X2))|~c_in(c_Pair(X0,X4,X2,X2),X3,tc_prod(X2,X2))|~c_Relation_Otrans(X3,X2))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1537])).
% 156.17/20.09 fof(f1544,plain,(
% 156.17/20.09 ![T_a,V_r]: ((![V_x]: ~c_in(c_Pair(V_x,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)))|~c_Relation_Oirrefl(V_r,T_a))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f585])).
% 156.17/20.09 fof(f1545,plain,(
% 156.17/20.09 ![X0,X1,X2]: (~c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1))|~c_Relation_Oirrefl(X2,X1))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1544])).
% 156.17/20.09 fof(f1557,plain,(
% 156.17/20.09 ![X0,X1,X2]: (c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(X2,X1),tc_prod(X1,X1)))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f592])).
% 156.17/20.09 fof(f1559,plain,(
% 156.17/20.09 ![T_a,V_r]: ((![V_x,V_a]: (~c_in(c_Pair(V_x,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a))|~c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))))|~c_Wellfounded_Owf(V_r,T_a))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f594])).
% 156.17/20.09 fof(f1560,plain,(
% 156.17/20.09 ![X0,X1,X2,X3]: (~c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2))|~c_in(c_Pair(X1,X0,X2,X2),X3,tc_prod(X2,X2))|~c_Wellfounded_Owf(X3,X2))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1559])).
% 156.17/20.09 fof(f1561,plain,(
% 156.17/20.09 ![T_a,V_r]: ((![V_x,V_y]: ((V_x=V_y|~c_in(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)))|~c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))))|~c_Relation_Oantisym(V_r,T_a))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f595])).
% 156.17/20.09 fof(f1562,plain,(
% 156.17/20.09 ![X0,X1,X2,X3]: (X0=X1|~c_in(c_Pair(X1,X0,X2,X2),X3,tc_prod(X2,X2))|~c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2))|~c_Relation_Oantisym(X3,X2))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1561])).
% 156.17/20.09 fof(f1565,plain,(
% 156.17/20.09 ![V_f,T_a,V_r]: ((![V_y,V_z]: (hAPP(V_f,V_y)=hAPP(V_f,V_z)|~c_in(c_Pair(V_y,V_z,T_a,T_a),V_r,tc_prod(T_a,T_a))))|(![T_b]: ~c_Equiv__Relations_Ocongruent(V_r,V_f,T_a,T_b)))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f597])).
% 156.17/20.09 fof(f1566,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4,X5]: (hAPP(X0,X1)=hAPP(X0,X2)|~c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))|~c_Equiv__Relations_Ocongruent(X4,X0,X3,X5))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1565])).
% 156.17/20.09 fof(f1567,plain,(
% 156.17/20.09 ![V_x,V_y]: (V_x=V_y|(![T_a,V_A]: ~c_in(c_Pair(V_x,V_y,T_a,T_a),c_Relation_OId__on(V_A,T_a),tc_prod(T_a,T_a))))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f598])).
% 156.17/20.09 fof(f1568,plain,(
% 156.17/20.09 ![X0,X1,X2,X3]: (X0=X1|~c_in(c_Pair(X0,X1,X2,X2),c_Relation_OId__on(X3,X2),tc_prod(X2,X2)))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1567])).
% 156.17/20.09 fof(f1571,plain,(
% 156.17/20.09 ![V_a,V_b]: (V_a=V_b|(![T_a]: ~c_in(c_Pair(V_a,V_b,T_a,T_a),c_Relation_OId(T_a),tc_prod(T_a,T_a))))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f600])).
% 156.17/20.09 fof(f1572,plain,(
% 156.17/20.09 ![X0,X1,X2]: (X0=X1|~c_in(c_Pair(X0,X1,X2,X2),c_Relation_OId(X2),tc_prod(X2,X2)))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1571])).
% 156.17/20.09 fof(f1573,plain,(
% 156.17/20.09 ![T_a,V_r]: ((![V_x]: c_in(c_Pair(V_x,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)))|~c_Nitpick_Orefl_H(V_r,T_a))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f601])).
% 156.17/20.09 fof(f1574,plain,(
% 156.17/20.09 ![X0,X1,X2]: (c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1))|~c_Nitpick_Orefl_H(X2,X1))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1573])).
% 156.17/20.09 fof(f1575,plain,(
% 156.17/20.09 ![T_a,V_r]: ((![V_a]: ~c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a)))|~c_Wellfounded_Owf(V_r,T_a))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f602])).
% 156.17/20.09 fof(f1576,plain,(
% 156.17/20.09 ![X0,X1,X2]: (~c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1))|~c_Wellfounded_Owf(X2,X1))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1575])).
% 156.17/20.09 fof(f1581,plain,(
% 156.17/20.09 ![T_a,V_r]: ((![V_y,V_x]: (c_in(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))|~c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))))|~c_Relation_Osym(V_r,T_a))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f605])).
% 156.17/20.09 fof(f1582,plain,(
% 156.17/20.09 ![X0,X1,X2,X3]: (c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2))|~c_in(c_Pair(X1,X0,X2,X2),X3,tc_prod(X2,X2))|~c_Relation_Osym(X3,X2))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1581])).
% 156.17/20.09 fof(f1591,plain,(
% 156.17/20.09 ![X0,X1]: (c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId(X1),tc_prod(X1,X1)))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f610])).
% 156.17/20.09 fof(f1616,plain,(
% 156.17/20.09 ![V_r,T_a,V_b]: ((![V_a]: (c_in(V_a,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_b,c_Wellfounded_Oacc(V_r,T_a),T_a))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f627])).
% 156.17/20.09 fof(f1617,plain,(
% 156.17/20.09 ![X0,X1,X2,X3]: (c_in(X0,c_Wellfounded_Oacc(X1,X2),X2)|~c_in(c_Pair(X0,X3,X2,X2),X1,tc_prod(X2,X2))|~c_in(X3,c_Wellfounded_Oacc(X1,X2),X2))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1616])).
% 156.17/20.09 fof(f1620,plain,(
% 156.17/20.09 ![V_A,T_a,V_a]: ((![V_b,V_r,T_b]: (c_in(V_b,c_Relation_OImage(V_r,V_A,T_a,T_b),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_a,V_A,T_a))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f629])).
% 156.17/20.09 fof(f1621,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4,X5]: (c_in(X0,c_Relation_OImage(X1,X2,X3,X4),X4)|~c_in(c_Pair(X5,X0,X3,X4),X1,tc_prod(X3,X4))|~c_in(X5,X2,X3))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1620])).
% 156.17/20.09 fof(f1624,plain,(
% 156.17/20.09 ![V_x,V_A,T_a]: (c_in(V_x,V_A,T_a)|(![V_y]: ~c_in(c_Pair(V_x,V_y,T_a,T_a),c_Relation_OId__on(V_A,T_a),tc_prod(T_a,T_a))))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f631])).
% 156.17/20.09 fof(f1625,plain,(
% 156.17/20.09 ![X0,X1,X2,X3]: (c_in(X0,X1,X2)|~c_in(c_Pair(X0,X3,X2,X2),c_Relation_OId__on(X1,X2),tc_prod(X2,X2)))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1624])).
% 156.17/20.09 fof(f1626,plain,(
% 156.17/20.09 ![X0,X1,X2]: (c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId__on(X2,X1),tc_prod(X1,X1))|~c_in(X0,X2,X1))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f632])).
% 156.17/20.09 fof(f1627,plain,(
% 156.17/20.09 ![V_A,T_a,V_r]: ((![V_y]: (c_in(V_y,V_A,T_a)|(![V_x]: ~c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a)))))|~c_Equiv__Relations_Oequiv(V_A,V_r,T_a))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f633])).
% 156.17/20.09 fof(f1628,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4]: (c_in(X0,X1,X2)|~c_in(c_Pair(X3,X0,X2,X2),X4,tc_prod(X2,X2))|~c_Equiv__Relations_Oequiv(X1,X4,X2))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1627])).
% 156.17/20.09 fof(f1629,plain,(
% 156.17/20.09 ![V_A,T_a,V_r]: ((![V_x]: (c_in(V_x,V_A,T_a)|(![V_y]: ~c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a)))))|~c_Equiv__Relations_Oequiv(V_A,V_r,T_a))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f634])).
% 156.17/20.09 fof(f1630,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4]: (c_in(X0,X1,X2)|~c_in(c_Pair(X0,X3,X2,X2),X4,tc_prod(X2,X2))|~c_Equiv__Relations_Oequiv(X1,X4,X2))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1629])).
% 156.17/20.09 fof(f1631,plain,(
% 156.17/20.09 ![V_a,V_r,T_b,T_a]: (c_in(V_a,c_Relation_ORange(V_r,T_b,T_a),T_a)|(![V_x]: ~c_in(c_Pair(V_x,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a))))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f635])).
% 156.17/20.09 fof(f1632,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4]: (c_in(X0,c_Relation_ORange(X1,X2,X3),X3)|~c_in(c_Pair(X4,X0,X2,X3),X1,tc_prod(X2,X3)))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1631])).
% 156.17/20.09 fof(f1635,plain,(
% 156.17/20.09 ![V_a,V_r,T_a,T_b]: (c_in(V_a,c_Relation_ODomain(V_r,T_a,T_b),T_a)|(![V_x]: ~c_in(c_Pair(V_a,V_x,T_a,T_b),V_r,tc_prod(T_a,T_b))))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f637])).
% 156.17/20.09 fof(f1636,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4]: (c_in(X0,c_Relation_ODomain(X1,X2,X3),X2)|~c_in(c_Pair(X0,X4,X2,X3),X1,tc_prod(X2,X3)))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1635])).
% 156.17/20.09 fof(f1643,plain,(
% 156.17/20.09 ![T_a,V_r,V_A]: ((![V_x]: ((![V_xa]: (((c_in(c_Pair(V_xa,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))|c_in(c_Pair(V_x,V_xa,T_a,T_a),V_r,tc_prod(T_a,T_a)))|V_x=V_xa)|~c_in(V_xa,V_A,T_a)))|~c_in(V_x,V_A,T_a)))|~c_Relation_Ototal__on(V_A,V_r,T_a))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f641])).
% 156.17/20.09 fof(f1644,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4]: (c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2))|c_in(c_Pair(X1,X0,X2,X2),X3,tc_prod(X2,X2))|X1=X0|~c_in(X0,X4,X2)|~c_in(X1,X4,X2)|~c_Relation_Ototal__on(X4,X3,X2))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1643])).
% 156.17/20.09 fof(f1645,plain,(
% 156.17/20.09 ![T_a,V_r,V_A]: ((![V_x]: (c_in(c_Pair(V_x,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))|~c_in(V_x,V_A,T_a)))|~c_Relation_Orefl__on(V_A,V_r,T_a))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f642])).
% 156.17/20.09 fof(f1646,plain,(
% 156.17/20.09 ![X0,X1,X2,X3]: (c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1))|~c_in(X0,X3,X1)|~c_Relation_Orefl__on(X3,X2,X1))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1645])).
% 156.17/20.09 fof(f1647,plain,(
% 156.17/20.09 ![V_A,T_a,V_r]: ((![V_y]: (c_in(V_y,V_A,T_a)|(![V_x]: ~c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a)))))|~c_Relation_Orefl__on(V_A,V_r,T_a))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f643])).
% 156.17/20.09 fof(f1648,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4]: (c_in(X0,X1,X2)|~c_in(c_Pair(X3,X0,X2,X2),X4,tc_prod(X2,X2))|~c_Relation_Orefl__on(X1,X4,X2))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1647])).
% 156.17/20.09 fof(f1649,plain,(
% 156.17/20.09 ![V_A,T_a,V_r]: ((![V_x]: (c_in(V_x,V_A,T_a)|(![V_y]: ~c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a)))))|~c_Relation_Orefl__on(V_A,V_r,T_a))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f644])).
% 156.17/20.09 fof(f1650,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4]: (c_in(X0,X1,X2)|~c_in(c_Pair(X0,X3,X2,X2),X4,tc_prod(X2,X2))|~c_Relation_Orefl__on(X1,X4,X2))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1649])).
% 156.17/20.09 fof(f1653,plain,(
% 156.17/20.09 ~v_a____=v_b____),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f646])).
% 156.17/20.09 fof(f1654,plain,(
% 156.17/20.09 ~v_a_H____=v_b_H____),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f647])).
% 156.17/20.09 fof(f1655,plain,(
% 156.17/20.09 ![V_b,V_b_H]: ((![V_a,T_a,T_b,V_a_H]: ~c_Pair(V_a,V_b,T_a,T_b)=c_Pair(V_a_H,V_b_H,T_a,T_b))|V_b=V_b_H)),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f648])).
% 156.17/20.09 fof(f1656,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4,X5]: (~c_Pair(X0,X1,X2,X3)=c_Pair(X4,X5,X2,X3)|X1=X5)),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1655])).
% 156.17/20.09 fof(f1659,plain,(
% 156.17/20.09 ![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)))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f650])).
% 156.17/20.09 fof(f1660,plain,(
% 156.17/20.09 ![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)))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f651])).
% 156.17/20.09 fof(f1661,plain,(
% 156.17/20.09 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_b____=v_a_H____|v_a____=v_b_H____),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f652])).
% 156.17/20.09 fof(f1663,plain,(
% 156.17/20.09 ![V_x,V_S]: ((![T_a]: c_in(V_x,V_S,T_a))|~hBOOL(hAPP(V_S,V_x)))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f654])).
% 156.17/20.09 fof(f1664,plain,(
% 156.17/20.09 ![X0,X1,X2]: (c_in(X0,X1,X2)|~hBOOL(hAPP(X1,X0)))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1663])).
% 156.17/20.09 fof(f1665,plain,(
% 156.17/20.09 ![V_S,V_x]: (hBOOL(hAPP(V_S,V_x))|(![T_a]: ~c_in(V_x,V_S,T_a)))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f655])).
% 156.17/20.09 fof(f1666,plain,(
% 156.17/20.09 ![X0,X1,X2]: (hBOOL(hAPP(X0,X1))|~c_in(X1,X0,X2))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1665])).
% 156.17/20.09 fof(f1671,plain,(
% 156.17/20.09 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)))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f660])).
% 156.17/20.09 fof(f1672,plain,(
% 156.17/20.09 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)))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f661])).
% 156.17/20.09 fof(f1675,plain,(
% 156.17/20.09 ![V_a,V_b]: ((![V_c]: (((![V_P]: ((![V_P_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_b,V_c,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_c,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,V_c)),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,V_c)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~c_in(V_P_H,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))))|~c_in(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_c)|V_b=V_c))|V_a=V_b)),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f664])).
% 156.17/20.09 fof(f1676,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4]: (c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__CHAINED__1(X2,X4,X0,X1,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,X4,X0,X1,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~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=X3|X1=X3|X0=X1)),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1675])).
% 156.17/20.09 fof(f1677,plain,(
% 156.17/20.09 ![V_b,V_a]: ((![V_c]: (((![V_P]: ((![V_P_H]: ((((c_in(c_Pair(V_b,V_c,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)))|~c_in(c_Pair(V_b,V_c,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,V_c)),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,V_c)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~c_in(V_P_H,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))))|~c_in(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_c)|V_b=V_c))|V_a=V_b)),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f665])).
% 156.17/20.09 fof(f1678,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4]: (c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X3,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X4,X2,X3,X0,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X3,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__CHAINED__1(X4,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(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X3=X1|X0=X1|X3=X0)),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1677])).
% 156.17/20.09 fof(f1679,plain,(
% 156.17/20.09 ![V_a,V_b]: ((![V_c]: (((![V_P]: ((![V_P_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_b,V_c,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_c,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,V_c)),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,V_c)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~c_in(V_P_H,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))))|~c_in(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_c)|V_b=V_c))|V_a=V_b)),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f666])).
% 156.17/20.09 fof(f1680,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4]: (c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__CHAINED__1(X2,X4,X0,X1,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,X4,X0,X1,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~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=X3|X1=X3|X0=X1)),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1679])).
% 156.17/20.09 fof(f1681,plain,(
% 156.17/20.09 ![V_b,V_a]: ((![V_c]: (((![V_P]: ((![V_P_H]: ((((c_in(c_Pair(V_b,V_c,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)))|c_in(c_Pair(V_b,V_c,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,V_c)),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,V_c)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~c_in(V_P_H,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))))|~c_in(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_c)|V_b=V_c))|V_a=V_b)),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f667])).
% 156.17/20.09 fof(f1682,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4]: (c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X3,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X4,X2,X3,X0,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X3,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__CHAINED__1(X4,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(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X3=X1|X0=X1|X3=X0)),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1681])).
% 156.17/20.09 fof(f1683,plain,(
% 156.17/20.09 v_b____=v_a_H____),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f668])).
% 156.17/20.09 fof(f1684,plain,(
% 156.17/20.09 ~v_a____=v_b_H____),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f669])).
% 156.17/20.09 fof(f1685,plain,(
% 156.17/20.09 ~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))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f670])).
% 156.17/20.09 fof(f1686,plain,(
% 156.17/20.09 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))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f671])).
% 156.17/20.09 fof(f1687,plain,(
% 156.17/20.09 ![T_1]: ((![T_2]: class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1)))|~class_Lattices_Olattice(T_1))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f672])).
% 156.17/20.09 fof(f1688,plain,(
% 156.17/20.09 ![X0,X1]: (class_Lattices_Oupper__semilattice(tc_fun(X0,X1))|~class_Lattices_Olattice(X1))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1687])).
% 156.17/20.09 fof(f1689,plain,(
% 156.17/20.09 ![T_1]: ((![T_2]: class_Lattices_Olower__semilattice(tc_fun(T_2,T_1)))|~class_Lattices_Olattice(T_1))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f673])).
% 156.17/20.09 fof(f1690,plain,(
% 156.17/20.09 ![X0,X1]: (class_Lattices_Olower__semilattice(tc_fun(X0,X1))|~class_Lattices_Olattice(X1))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1689])).
% 156.17/20.09 fof(f1693,plain,(
% 156.17/20.09 ![T_1]: ((![T_2]: class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)))|~class_Lattices_Obounded__lattice(T_1))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f675])).
% 156.17/20.09 fof(f1694,plain,(
% 156.17/20.09 ![X0,X1]: (class_Lattices_Obounded__lattice(tc_fun(X0,X1))|~class_Lattices_Obounded__lattice(X1))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1693])).
% 156.17/20.09 fof(f1695,plain,(
% 156.17/20.09 ![T_1]: ((![T_2]: class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)))|~class_Lattices_Oboolean__algebra(T_1))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f676])).
% 156.17/20.09 fof(f1696,plain,(
% 156.17/20.09 ![X0,X1]: (class_Lattices_Oboolean__algebra(tc_fun(X0,X1))|~class_Lattices_Oboolean__algebra(X1))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1695])).
% 156.17/20.09 fof(f1697,plain,(
% 156.17/20.09 ![T_1]: ((![T_2]: class_Orderings_Opreorder(tc_fun(T_2,T_1)))|~class_Orderings_Opreorder(T_1))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f677])).
% 156.17/20.09 fof(f1698,plain,(
% 156.17/20.09 ![X0,X1]: (class_Orderings_Opreorder(tc_fun(X0,X1))|~class_Orderings_Opreorder(X1))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1697])).
% 156.17/20.09 fof(f1699,plain,(
% 156.17/20.09 ![T_1]: ((![T_2]: class_Lattices_Olattice(tc_fun(T_2,T_1)))|~class_Lattices_Olattice(T_1))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f678])).
% 156.17/20.09 fof(f1700,plain,(
% 156.17/20.09 ![X0,X1]: (class_Lattices_Olattice(tc_fun(X0,X1))|~class_Lattices_Olattice(X1))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1699])).
% 156.17/20.09 fof(f1701,plain,(
% 156.17/20.09 ![T_1]: ((![T_2]: class_Orderings_Oorder(tc_fun(T_2,T_1)))|~class_Orderings_Oorder(T_1))),
% 156.17/20.09 inference(miniscoping,[status(esa)],[f679])).
% 156.17/20.09 fof(f1702,plain,(
% 156.17/20.09 ![X0,X1]: (class_Orderings_Oorder(tc_fun(X0,X1))|~class_Orderings_Oorder(X1))),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f1701])).
% 156.17/20.09 fof(f1710,plain,(
% 156.17/20.09 class_Lattices_Obounded__lattice(tc_bool)),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f685])).
% 156.17/20.09 fof(f1711,plain,(
% 156.17/20.09 class_Lattices_Oboolean__algebra(tc_bool)),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f686])).
% 156.17/20.09 fof(f1712,plain,(
% 156.17/20.09 class_Orderings_Opreorder(tc_bool)),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f687])).
% 156.17/20.09 fof(f1713,plain,(
% 156.17/20.09 class_Lattices_Olattice(tc_bool)),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f688])).
% 156.17/20.09 fof(f1714,plain,(
% 156.17/20.09 class_Orderings_Oorder(tc_bool)),
% 156.17/20.09 inference(cnf_transformation,[status(esa)],[f689])).
% 156.17/20.09 fof(f1720,plain,(
% 156.17/20.09 spl0_0 <=> 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))),
% 156.17/20.09 introduced(split_symbol_definition)).
% 156.17/20.09 fof(f1721,plain,(
% 156.17/20.09 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))|~spl0_0),
% 156.17/20.09 inference(component_clause,[status(thm)],[f1720])).
% 156.17/20.09 fof(f1722,plain,(
% 156.17/20.09 ~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))|spl0_0),
% 156.17/20.09 inference(component_clause,[status(thm)],[f1720])).
% 156.17/20.09 fof(f1723,plain,(
% 156.17/20.09 spl0_1 <=> 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))),
% 156.17/20.09 introduced(split_symbol_definition)).
% 156.17/20.09 fof(f1724,plain,(
% 156.17/20.09 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))|~spl0_1),
% 156.17/20.09 inference(component_clause,[status(thm)],[f1723])).
% 156.17/20.09 fof(f1726,plain,(
% 156.17/20.09 spl0_2 <=> v_b____=v_a_H____),
% 156.17/20.09 introduced(split_symbol_definition)).
% 156.17/20.09 fof(f1729,plain,(
% 156.17/20.09 spl0_3 <=> v_a____=v_b_H____),
% 156.17/20.09 introduced(split_symbol_definition)).
% 156.17/20.09 fof(f1730,plain,(
% 156.17/20.09 v_a____=v_b_H____|~spl0_3),
% 156.17/20.09 inference(component_clause,[status(thm)],[f1729])).
% 156.17/20.09 fof(f1732,plain,(
% 156.17/20.09 spl0_0|~spl0_1|spl0_2|spl0_3),
% 156.17/20.09 inference(split_clause,[status(thm)],[f1661,f1720,f1723,f1726,f1729])).
% 156.17/20.09 fof(f1736,plain,(
% 156.17/20.09 ~spl0_0|~spl0_1),
% 156.17/20.09 inference(split_clause,[status(thm)],[f1685,f1720,f1723])).
% 156.17/20.09 fof(f1737,plain,(
% 156.17/20.09 spl0_1|spl0_0),
% 156.17/20.09 inference(split_clause,[status(thm)],[f1686,f1723,f1720])).
% 156.17/20.09 fof(f1740,plain,(
% 156.17/20.09 ~v_b____=v_b_H____),
% 156.17/20.09 inference(backward_demodulation,[status(thm)],[f1683,f1654])).
% 156.17/20.09 fof(f1741,plain,(
% 156.17/20.09 ![X0]: (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)))),
% 156.17/20.09 inference(forward_demodulation,[status(thm)],[f1683,f1659])).
% 156.17/20.09 fof(f1742,plain,(
% 156.17/20.09 ![X0]: (c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,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)))),
% 156.17/20.09 inference(forward_demodulation,[status(thm)],[f1683,f1660])).
% 156.17/20.09 fof(f1746,plain,(
% 156.17/20.09 spl0_4 <=> ~class_Lattices_Oupper__semilattice(tc_fun(X0,tc_bool))),
% 156.17/20.09 introduced(split_symbol_definition)).
% 156.17/20.09 fof(f1747,plain,(
% 156.17/20.09 ![X0]: (~class_Lattices_Oupper__semilattice(tc_fun(X0,tc_bool))|~spl0_4)),
% 156.17/20.09 inference(component_clause,[status(thm)],[f1746])).
% 156.17/20.09 fof(f1749,plain,(
% 156.17/20.09 spl0_5 <=> X1=X1),
% 156.17/20.09 introduced(split_symbol_definition)).
% 156.17/20.09 fof(f1752,plain,(
% 156.17/20.09 ![X0,X1]: (~class_Lattices_Oupper__semilattice(tc_fun(X0,tc_bool))|X1=X1)),
% 156.17/20.09 inference(paramodulation,[status(thm)],[f697,f699])).
% 156.17/20.09 fof(f1753,plain,(
% 156.17/20.09 spl0_4|spl0_5),
% 156.17/20.09 inference(split_clause,[status(thm)],[f1752,f1746,f1749])).
% 156.17/20.09 fof(f1757,plain,(
% 156.17/20.09 ~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))|spl0_0),
% 156.17/20.09 inference(forward_demodulation,[status(thm)],[f1683,f1722])).
% 156.17/20.09 fof(f1765,plain,(
% 156.17/20.09 spl0_6 <=> hBOOL(hAPP(c_COMBK(X0,X1,X2),X3))|~hBOOL(X0)),
% 156.17/20.09 introduced(split_symbol_definition)).
% 156.17/20.09 fof(f1768,plain,(
% 156.17/20.09 spl0_7 <=> ~c_Wellfounded_Owf(X4,X5)),
% 156.17/20.09 introduced(split_symbol_definition)).
% 156.17/20.09 fof(f1769,plain,(
% 156.17/20.09 ![X0,X1]: (~c_Wellfounded_Owf(X0,X1)|~spl0_7)),
% 156.17/20.09 inference(component_clause,[status(thm)],[f1768])).
% 156.17/20.09 fof(f1771,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4,X5]: (hBOOL(hAPP(c_COMBK(X0,X1,X2),X3))|~hBOOL(X0)|~c_Wellfounded_Owf(X4,X5))),
% 156.17/20.09 inference(paramodulation,[status(thm)],[f705,f703])).
% 156.17/20.09 fof(f1772,plain,(
% 156.17/20.09 spl0_6|spl0_7),
% 156.17/20.09 inference(split_clause,[status(thm)],[f1771,f1765,f1768])).
% 156.17/20.09 fof(f1785,plain,(
% 156.17/20.09 ~class_Lattices_Olattice(tc_bool)|~spl0_4),
% 156.17/20.09 inference(resolution,[status(thm)],[f1688,f1747])).
% 156.17/20.09 fof(f1786,plain,(
% 156.17/20.09 $false|~spl0_4),
% 156.17/20.09 inference(forward_subsumption_resolution,[status(thm)],[f1785,f1713])).
% 156.17/20.09 fof(f1787,plain,(
% 156.17/20.09 ~spl0_4),
% 156.17/20.09 inference(contradiction_clause,[status(thm)],[f1786])).
% 156.17/20.09 fof(f1797,plain,(
% 156.17/20.09 spl0_9 <=> ~class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool))),
% 156.17/20.09 introduced(split_symbol_definition)).
% 156.17/20.09 fof(f1798,plain,(
% 156.17/20.09 ![X0]: (~class_Lattices_Olower__semilattice(tc_fun(X0,tc_bool))|~spl0_9)),
% 156.17/20.09 inference(component_clause,[status(thm)],[f1797])).
% 156.17/20.09 fof(f1865,plain,(
% 156.17/20.09 ![X0,X1]: (c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X0,X1),X1)|~c_Wellfounded_Oacyclic(c_Transitive__Closure_Otrancl(X0,X1),X1))),
% 156.17/20.09 inference(paramodulation,[status(thm)],[f1500,f1221])).
% 156.17/20.09 fof(f1874,plain,(
% 156.17/20.09 ![X0]: (~hBOOL(hAPP(hAPP(v_P_H____,X0),c_Pair(v_b____,v_b_H____,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)))),
% 156.17/20.09 inference(resolution,[status(thm)],[f1664,f1742])).
% 156.17/20.09 fof(f1878,plain,(
% 156.17/20.09 ![X0]: (hBOOL(hAPP(hAPP(v_P_H____,X0),c_Pair(v_b____,v_b_H____,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)))),
% 156.17/20.09 inference(resolution,[status(thm)],[f1666,f1741])).
% 156.17/20.09 fof(f1939,plain,(
% 156.17/20.09 ![X0,X1]: (c_Wellfounded_Oacyclic(X0,X1)|~c_Wellfounded_Owf(c_Relation_Oconverse(X0,X1,X1),X1))),
% 156.17/20.09 inference(resolution,[status(thm)],[f902,f757])).
% 156.17/20.09 fof(f1950,plain,(
% 156.17/20.09 ![X0,X1,X2]: (~c_Wellfounded_Owf(X0,X1)|hBOOL(hAPP(c_Wellfounded_Oacc(X0,X1),X2)))),
% 156.17/20.09 inference(resolution,[status(thm)],[f1416,f1666])).
% 156.17/20.09 fof(f2026,plain,(
% 156.17/20.09 spl0_10 <=> ~class_Lattices_Oboolean__algebra(X0)),
% 156.17/20.09 introduced(split_symbol_definition)).
% 156.17/20.09 fof(f2027,plain,(
% 156.17/20.09 ![X0]: (~class_Lattices_Oboolean__algebra(X0)|~spl0_10)),
% 156.17/20.09 inference(component_clause,[status(thm)],[f2026])).
% 156.17/20.09 fof(f2094,plain,(
% 156.17/20.09 spl0_12 <=> ~c_Wellfounded_Owf(X0,X1)|hBOOL(hAPP(c_Wellfounded_Oacc(X0,X1),X2))),
% 156.17/20.09 introduced(split_symbol_definition)).
% 156.17/20.09 fof(f2097,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4]: (~c_Wellfounded_Owf(X0,X1)|hBOOL(hAPP(c_Wellfounded_Oacc(X0,X1),X2))|~c_Wellfounded_Owf(X3,X4))),
% 156.17/20.09 inference(resolution,[status(thm)],[f1950,f703])).
% 156.17/20.09 fof(f2098,plain,(
% 156.17/20.09 spl0_12|spl0_7),
% 156.17/20.09 inference(split_clause,[status(thm)],[f2097,f2094,f1768])).
% 156.17/20.09 fof(f2099,plain,(
% 156.17/20.09 ![X0,X1]: (~c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(X0,X1)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))|~spl0_7)),
% 156.17/20.09 inference(backward_subsumption_resolution,[status(thm)],[f696,f1769])).
% 156.17/20.09 fof(f2121,plain,(
% 156.17/20.09 ![X0,X1]: (~class_Lattices_Oupper__semilattice(X0)|c_lessequals(X1,X1,X0)|~class_Lattices_Oupper__semilattice(X0))),
% 156.17/20.09 inference(resolution,[status(thm)],[f908,f699])).
% 156.17/20.09 fof(f2122,plain,(
% 156.17/20.09 ![X0,X1]: (~class_Lattices_Oupper__semilattice(X0)|c_lessequals(X1,X1,X0))),
% 156.17/20.09 inference(duplicate_literals_removal,[status(esa)],[f2121])).
% 156.17/20.09 fof(f2135,plain,(
% 156.17/20.09 ![X0,X1,X2,X3]: (~c_in(X0,X1,X2)|hBOOL(hAPP(c_Set_Oinsert(X3,X1,X2),X0)))),
% 156.17/20.09 inference(resolution,[status(thm)],[f1027,f1666])).
% 156.17/20.09 fof(f2428,plain,(
% 156.17/20.09 spl0_14 <=> ~class_Lattices_Obounded__lattice(tc_fun(X0,tc_bool))),
% 156.17/20.09 introduced(split_symbol_definition)).
% 156.17/20.09 fof(f2429,plain,(
% 156.17/20.09 ![X0]: (~class_Lattices_Obounded__lattice(tc_fun(X0,tc_bool))|~spl0_14)),
% 156.17/20.09 inference(component_clause,[status(thm)],[f2428])).
% 156.17/20.09 fof(f2515,plain,(
% 156.17/20.09 spl0_15 <=> ~class_Lattices_Oboolean__algebra(tc_fun(X0,tc_bool))),
% 156.17/20.09 introduced(split_symbol_definition)).
% 156.17/20.09 fof(f2516,plain,(
% 156.17/20.09 ![X0]: (~class_Lattices_Oboolean__algebra(tc_fun(X0,tc_bool))|~spl0_15)),
% 156.17/20.09 inference(component_clause,[status(thm)],[f2515])).
% 156.17/20.09 fof(f2594,plain,(
% 156.17/20.09 ![X0,X1]: (c_Relation_ORange(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X0,X1,X1),X1),X1,X1)=c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1))),
% 156.17/20.09 inference(paramodulation,[status(thm)],[f1484,f1468])).
% 156.17/20.09 fof(f3118,plain,(
% 156.17/20.09 ![X0,X1,X2]: (~c_Relation_Oirrefl(X0,X1)|~hBOOL(hAPP(X0,c_Pair(X2,X2,X1,X1))))),
% 156.17/20.09 inference(resolution,[status(thm)],[f1545,f1664])).
% 156.17/20.09 fof(f3316,plain,(
% 156.17/20.09 spl0_17 <=> ~c_Nitpick_Orefl_H(c_Relation_OId(X0),X0)),
% 156.17/20.09 introduced(split_symbol_definition)).
% 156.17/20.09 fof(f3317,plain,(
% 156.17/20.09 ![X0]: (~c_Nitpick_Orefl_H(c_Relation_OId(X0),X0)|~spl0_17)),
% 156.17/20.09 inference(component_clause,[status(thm)],[f3316])).
% 156.17/20.09 fof(f3326,plain,(
% 156.17/20.09 ![X0,X1,X2]: (~c_Nitpick_Orefl_H(X0,X1)|hBOOL(hAPP(X0,c_Pair(X2,X2,X1,X1))))),
% 156.17/20.09 inference(resolution,[status(thm)],[f1574,f1666])).
% 156.17/20.09 fof(f3436,plain,(
% 156.17/20.09 spl0_18 <=> 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)),
% 156.17/20.09 introduced(split_symbol_definition)).
% 156.17/20.09 fof(f3437,plain,(
% 156.17/20.09 ![X0,X1]: (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)|~spl0_18)),
% 156.17/20.09 inference(component_clause,[status(thm)],[f3436])).
% 156.17/20.09 fof(f3439,plain,(
% 156.17/20.09 spl0_19 <=> ~c_in(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)),
% 156.17/20.09 introduced(split_symbol_definition)).
% 156.17/20.09 fof(f3442,plain,(
% 156.17/20.09 ![X0,X1,X2,X3]: (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)|~c_in(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3))),
% 156.17/20.09 inference(paramodulation,[status(thm)],[f712,f788])).
% 156.17/20.09 fof(f3443,plain,(
% 156.17/20.09 spl0_18|spl0_19),
% 156.17/20.09 inference(split_clause,[status(thm)],[f3442,f3436,f3439])).
% 156.17/20.09 fof(f3444,plain,(
% 156.17/20.09 $false|~spl0_18),
% 156.17/20.09 inference(forward_subsumption_resolution,[status(thm)],[f3437,f823])).
% 156.17/20.09 fof(f3445,plain,(
% 156.17/20.09 ~spl0_18),
% 156.17/20.09 inference(contradiction_clause,[status(thm)],[f3444])).
% 156.17/20.09 fof(f3568,plain,(
% 156.17/20.09 ![X0,X1,X2]: (c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))=c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X1,X0),tc_fun(X0,tc_bool))|~c_in(X2,c_Set_Oinsert(X2,X1,X0),X0))),
% 156.17/20.09 inference(paramodulation,[status(thm)],[f849,f793])).
% 156.17/20.09 fof(f3569,plain,(
% 156.17/20.09 ![X0,X1,X2]: (c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))=c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X1,X0),tc_fun(X0,tc_bool)))),
% 156.17/20.09 inference(forward_subsumption_resolution,[status(thm)],[f3568,f1047])).
% 156.17/20.09 fof(f3786,plain,(
% 156.17/20.09 ![X0,X1,X2,X3]: (~c_in(X0,X1,X2)|~hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X0)))),
% 156.17/20.09 inference(resolution,[status(thm)],[f1042,f1664])).
% 156.17/20.09 fof(f3801,plain,(
% 156.17/20.09 ![X0,X1,X2,X3]: (c_in(X0,X1,X2)|~hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),X0)))),
% 156.17/20.09 inference(resolution,[status(thm)],[f1053,f1664])).
% 156.17/20.09 fof(f4063,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4,X5,X6]: (c_in(X0,c_Set_Oimage(c_COMBK(X0,X1,X2),X3,X4,X5),X5)|~c_in(X6,X3,X4))),
% 156.17/20.09 inference(paramodulation,[status(thm)],[f705,f1408])).
% 156.17/20.09 fof(f4065,plain,(
% 156.17/20.09 spl0_20 <=> ~c_Nitpick_Orefl_H(c_Relation_OId__on(X1,X2),X2)),
% 156.17/20.09 introduced(split_symbol_definition)).
% 156.17/20.09 fof(f4066,plain,(
% 156.17/20.09 ![X0,X1]: (~c_Nitpick_Orefl_H(c_Relation_OId__on(X0,X1),X1)|~spl0_20)),
% 156.17/20.09 inference(component_clause,[status(thm)],[f4065])).
% 156.17/20.09 fof(f4321,plain,(
% 156.17/20.09 spl0_21 <=> ~c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))=c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),
% 156.17/20.09 introduced(split_symbol_definition)).
% 156.17/20.09 fof(f4322,plain,(
% 156.17/20.09 ![X0]: (~c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))=c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))|~spl0_21)),
% 156.17/20.09 inference(component_clause,[status(thm)],[f4321])).
% 156.17/20.09 fof(f4324,plain,(
% 156.17/20.09 spl0_22 <=> c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),
% 156.17/20.09 introduced(split_symbol_definition)).
% 156.17/20.09 fof(f4329,plain,(
% 156.17/20.09 $false|~spl0_21),
% 156.17/20.09 inference(trivial_equality_resolution,[status(esa)],[f4322])).
% 156.17/20.09 fof(f4330,plain,(
% 156.17/20.09 ~spl0_21),
% 156.17/20.09 inference(contradiction_clause,[status(thm)],[f4329])).
% 156.17/20.09 fof(f5562,plain,(
% 156.17/20.09 ![X0,X1,X2]: (~c_in(X0,X1,tc_prod(X2,X2))|hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X1,X2),X0)))),
% 156.17/20.09 inference(resolution,[status(thm)],[f1382,f1666])).
% 156.17/20.09 fof(f5567,plain,(
% 156.17/20.09 ![X0]: (hBOOL(hAPP(c_Transitive__Closure_Ortrancl(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b____,v_b_H____,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)))),
% 156.17/20.09 inference(resolution,[status(thm)],[f5562,f1741])).
% 156.17/20.09 fof(f5647,plain,(
% 156.17/20.09 ![X0,X1,X2]: (~c_in(X0,X1,tc_prod(X2,X2))|hBOOL(hAPP(c_Transitive__Closure_Otrancl(X1,X2),X0)))),
% 156.17/20.09 inference(resolution,[status(thm)],[f1383,f1666])).
% 156.17/20.09 fof(f5652,plain,(
% 156.17/20.09 ![X0]: (hBOOL(hAPP(c_Transitive__Closure_Otrancl(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b____,v_b_H____,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)))),
% 156.17/20.09 inference(resolution,[status(thm)],[f5647,f1741])).
% 156.17/20.09 fof(f6527,plain,(
% 156.17/20.09 spl0_24 <=> c_in(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)),
% 156.17/20.09 introduced(split_symbol_definition)).
% 156.17/20.09 fof(f6528,plain,(
% 156.17/20.09 ![X0,X1]: (c_in(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)|~spl0_24)),
% 156.17/20.09 inference(component_clause,[status(thm)],[f6527])).
% 156.17/20.09 fof(f7580,plain,(
% 156.17/20.09 ![X0,X1,X2]: (~c_Wellfounded_Oacyclic(X0,X1)|~c_in(c_Pair(X2,X2,X1,X1),X0,tc_prod(X1,X1)))),
% 156.17/20.09 inference(resolution,[status(thm)],[f1254,f1383])).
% 156.17/20.09 fof(f7948,plain,(
% 156.17/20.09 spl0_25 <=> c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)=c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)),
% 156.17/20.09 introduced(split_symbol_definition)).
% 156.17/20.09 fof(f7951,plain,(
% 156.17/20.09 spl0_26 <=> X2=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))|X2=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),
% 156.17/20.09 introduced(split_symbol_definition)).
% 156.17/20.09 fof(f7952,plain,(
% 156.17/20.09 ![X0,X1]: (X0=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))|X0=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))|~spl0_26)),
% 156.17/20.09 inference(component_clause,[status(thm)],[f7951])).
% 156.17/20.09 fof(f7954,plain,(
% 156.17/20.09 ![X0,X1,X2,X3]: (c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)=c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)|X2=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))|X2=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))),
% 156.17/20.09 inference(paramodulation,[status(thm)],[f882,f882])).
% 156.17/20.09 fof(f7955,plain,(
% 156.17/20.09 spl0_25|spl0_26),
% 156.17/20.09 inference(split_clause,[status(thm)],[f7954,f7948,f7951])).
% 156.17/20.09 fof(f7956,plain,(
% 156.17/20.09 ![X0,X1,X2]: (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)|c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))),
% 156.17/20.09 inference(paramodulation,[status(thm)],[f712,f882])).
% 156.17/20.09 fof(f7957,plain,(
% 156.17/20.09 spl0_18|spl0_22),
% 156.17/20.09 inference(split_clause,[status(thm)],[f7956,f3436,f4324])).
% 156.17/20.09 fof(f7958,plain,(
% 156.17/20.09 spl0_27 <=> c_in(X0,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1)),
% 156.17/20.09 introduced(split_symbol_definition)).
% 156.17/20.09 fof(f7961,plain,(
% 156.17/20.09 spl0_28 <=> ~c_in(X2,X3,X4)|X3=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))),
% 156.17/20.09 introduced(split_symbol_definition)).
% 156.17/20.09 fof(f7962,plain,(
% 156.17/20.09 ![X0,X1,X2]: (~c_in(X0,X1,X2)|X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))|~spl0_28)),
% 156.17/20.09 inference(component_clause,[status(thm)],[f7961])).
% 156.17/20.09 fof(f7964,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4]: (c_in(X0,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1)|~c_in(X2,X3,X4)|X3=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))),
% 156.17/20.09 inference(paramodulation,[status(thm)],[f882,f4063])).
% 156.17/20.09 fof(f7965,plain,(
% 156.17/20.09 spl0_27|spl0_28),
% 156.17/20.09 inference(split_clause,[status(thm)],[f7964,f7958,f7961])).
% 156.17/20.09 fof(f7977,plain,(
% 156.17/20.09 spl0_29 <=> ~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)),
% 156.17/20.09 introduced(split_symbol_definition)).
% 156.17/20.09 fof(f7978,plain,(
% 156.17/20.09 ![X0,X1]: (~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)|~spl0_29)),
% 156.17/20.09 inference(component_clause,[status(thm)],[f7977])).
% 156.17/20.09 fof(f7980,plain,(
% 156.17/20.09 ![X0,X1,X2,X3]: (~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)|X2=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))|X2=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))),
% 156.17/20.09 inference(paramodulation,[status(thm)],[f882,f809])).
% 156.17/20.09 fof(f7981,plain,(
% 156.17/20.09 spl0_29|spl0_26),
% 156.17/20.09 inference(split_clause,[status(thm)],[f7980,f7977,f7951])).
% 156.17/20.09 fof(f7986,plain,(
% 156.17/20.09 ![X0,X1]: (X0=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))|~spl0_26)),
% 156.17/20.09 inference(duplicate_literals_removal,[status(esa)],[f7952])).
% 156.17/20.09 fof(f8060,plain,(
% 156.17/20.09 ![X0,X1,X2]: (~c_in(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2)|~spl0_29|~spl0_28)),
% 156.17/20.09 inference(resolution,[status(thm)],[f7978,f7962])).
% 156.17/20.09 fof(f8063,plain,(
% 156.17/20.09 $false|~spl0_29|~spl0_28),
% 156.17/20.09 inference(resolution,[status(thm)],[f8060,f1047])).
% 156.17/20.09 fof(f8064,plain,(
% 156.17/20.09 ~spl0_29|~spl0_28),
% 156.17/20.09 inference(contradiction_clause,[status(thm)],[f8063])).
% 156.17/20.09 fof(f8066,plain,(
% 156.17/20.09 $false|~spl0_26),
% 156.17/20.09 inference(backward_subsumption_resolution,[status(thm)],[f823,f7986])).
% 156.17/20.09 fof(f8067,plain,(
% 156.17/20.09 ~spl0_26),
% 156.17/20.09 inference(contradiction_clause,[status(thm)],[f8066])).
% 156.17/20.09 fof(f8275,plain,(
% 156.17/20.09 ![X0,X1,X2,X3]: (c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool))=c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)))),
% 156.17/20.09 inference(forward_demodulation,[status(thm)],[f880,f891])).
% 156.17/20.09 fof(f8333,plain,(
% 156.17/20.09 ![X0,X1,X2]: (c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))=X0)),
% 156.17/20.09 inference(forward_demodulation,[status(thm)],[f958,f906])).
% 156.17/20.09 fof(f8814,plain,(
% 156.17/20.09 ![X0,X1,X2]: (~c_Wellfounded_Owf(X0,X1)|~hBOOL(hAPP(X0,c_Pair(X2,X2,X1,X1))))),
% 156.17/20.09 inference(resolution,[status(thm)],[f1576,f1664])).
% 156.17/20.09 fof(f8835,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4]: (~c_Wellfounded_Owf(c_Set_Oinsert(X0,X1,X2),X3)|~c_in(c_Pair(X4,X4,X3,X3),X1,X2))),
% 156.17/20.09 inference(resolution,[status(thm)],[f8814,f2135])).
% 156.17/20.09 fof(f9621,plain,(
% 156.17/20.09 ![X0,X1,X2,X3]: (~c_in(X0,X1,X2)|~c_Wellfounded_Owf(X3,X2)|hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X1,X3,X2))))),
% 156.17/20.09 inference(resolution,[status(thm)],[f1470,f1666])).
% 156.17/20.09 fof(f10280,plain,(
% 156.17/20.09 ![X0,X1]: (~c_Wellfounded_Owf(c_Relation_Oconverse(X0,X1,X1),X1)|c_Wellfounded_Oacyclic(c_Transitive__Closure_Otrancl(X0,X1),X1))),
% 156.17/20.09 inference(resolution,[status(thm)],[f1433,f1939])).
% 156.17/20.09 fof(f10302,plain,(
% 156.17/20.09 ![X0,X1]: (~c_Wellfounded_Owf(X0,X1)|c_Wellfounded_Oacyclic(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X0,X1,X1),X1),X1))),
% 156.17/20.09 inference(paramodulation,[status(thm)],[f1474,f10280])).
% 156.17/20.09 fof(f10303,plain,(
% 156.17/20.09 ![X0,X1]: (~c_Wellfounded_Owf(X0,X1)|c_Wellfounded_Oacyclic(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X0,X1),X1,X1),X1))),
% 156.17/20.09 inference(forward_demodulation,[status(thm)],[f1462,f10302])).
% 156.17/20.09 fof(f10445,plain,(
% 156.17/20.09 ![X0,X1]: (~c_Wellfounded_Owf(X0,X1)|c_Wellfounded_Oacyclic(c_Transitive__Closure_Otrancl(X0,X1),X1))),
% 156.17/20.09 inference(resolution,[status(thm)],[f10303,f902])).
% 156.17/20.09 fof(f10942,plain,(
% 156.17/20.09 spl0_30 <=> ~class_Lattices_Olattice(tc_fun(X0,tc_bool))),
% 156.17/20.09 introduced(split_symbol_definition)).
% 156.17/20.09 fof(f10943,plain,(
% 156.17/20.09 ![X0]: (~class_Lattices_Olattice(tc_fun(X0,tc_bool))|~spl0_30)),
% 156.17/20.09 inference(component_clause,[status(thm)],[f10942])).
% 156.17/20.09 fof(f11515,plain,(
% 156.17/20.09 ![X0,X1,X2]: (c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))=X1)),
% 156.17/20.09 inference(paramodulation,[status(thm)],[f981,f8333])).
% 156.17/20.09 fof(f11516,plain,(
% 156.17/20.09 ![X0,X1,X2]: (c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))=X0)),
% 156.17/20.09 inference(forward_demodulation,[status(thm)],[f874,f11515])).
% 156.17/20.09 fof(f11618,plain,(
% 156.17/20.09 ![X0,X1,X2,X3]: (~c_in(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3)|~hBOOL(hAPP(X2,X0)))),
% 156.17/20.09 inference(paramodulation,[status(thm)],[f11516,f3786])).
% 156.17/20.09 fof(f12082,plain,(
% 156.17/20.09 ![X0,X1,X2,X3]: (~c_in(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)|~c_Wellfounded_Owf(X3,X2))),
% 156.17/20.09 inference(resolution,[status(thm)],[f9621,f878])).
% 156.17/20.09 fof(f12087,plain,(
% 156.17/20.09 spl0_31 <=> ~hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3))),
% 156.17/20.09 introduced(split_symbol_definition)).
% 156.17/20.09 fof(f12090,plain,(
% 156.17/20.09 ![X0,X1,X2,X3]: (~c_Wellfounded_Owf(X0,X1)|~hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3)))),
% 156.17/20.09 inference(resolution,[status(thm)],[f12082,f1664])).
% 156.17/20.09 fof(f12091,plain,(
% 156.17/20.09 spl0_7|spl0_31),
% 156.17/20.09 inference(split_clause,[status(thm)],[f12090,f1768,f12087])).
% 156.17/20.09 fof(f12224,plain,(
% 156.17/20.09 ![X0,X1,X2,X3]: (~hBOOL(hAPP(X0,X1))|~hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X2,X0,tc_fun(X3,tc_bool)),X1)))),
% 156.17/20.09 inference(resolution,[status(thm)],[f11618,f1664])).
% 156.17/20.09 fof(f12304,plain,(
% 156.17/20.09 ![X0,X1,X2]: (c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X0,X1,X2),X0,X2)|~hBOOL(hAPP(c_Relation_OId__on(X0,X2),X1)))),
% 156.17/20.09 inference(resolution,[status(thm)],[f1273,f1664])).
% 156.17/20.09 fof(f12439,plain,(
% 156.17/20.09 ![X0,X1,X2]: (~hBOOL(hAPP(c_Relation_OId__on(X0,X1),X2))|hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X0,X2,X1))))),
% 156.17/20.09 inference(resolution,[status(thm)],[f12304,f1666])).
% 156.17/20.09 fof(f12455,plain,(
% 156.17/20.09 ![X0,X1,X2]: (~hBOOL(hAPP(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1),X2)))),
% 156.17/20.09 inference(resolution,[status(thm)],[f12439,f878])).
% 156.17/20.09 fof(f12456,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4]: (~hBOOL(hAPP(c_Relation_OId__on(c_COMBK(X0,X1,X2),X3),X4))|hBOOL(X0))),
% 156.17/20.09 inference(paramodulation,[status(thm)],[f705,f12439])).
% 156.17/20.09 fof(f12457,plain,(
% 156.17/20.09 ![X0,X1,X2,X3]: (~hBOOL(hAPP(c_Relation_OId__on(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1),X2),X3)))),
% 156.17/20.09 inference(resolution,[status(thm)],[f12455,f12439])).
% 156.17/20.09 fof(f12481,plain,(
% 156.17/20.09 ![X0,X1,X2,X3,X4,X5]: (hBOOL(X0)|~hBOOL(hAPP(c_Relation_OId__on(c_Relation_OId__on(c_COMBK(X0,X1,X2),X3),X4),X5)))),
% 156.17/20.09 inference(resolution,[status(thm)],[f12456,f12439])).
% 156.17/20.09 fof(f12550,plain,(
% 156.17/20.09 ![X0,X1,X2]: (c_Relation_Oantisym(X0,X1)|~c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1))),
% 156.17/20.09 inference(resolution,[status(thm)],[f1338,f735])).
% 156.17/20.09 fof(f12551,plain,(
% 156.17/20.09 ![X0,X1,X2]: (c_Relation_Oantisym(X0,X1)|~c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X2,X0,tc_fun(tc_prod(X1,X1),tc_bool)),X1))),
% 156.17/20.09 inference(resolution,[status(thm)],[f1338,f734])).
% 156.17/20.09 fof(f12832,plain,(
% 156.17/20.09 ![X0]: (c_FunDef_Oin__rel(hAPP(v_P_H____,X0),v_b____,v_b_H____,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)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1535,f1741])).
% 156.17/20.10 fof(f12852,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (c_FunDef_Oin__rel(X0,X1,X2,X3,X4)|~hBOOL(hAPP(X0,c_Pair(X1,X2,X3,X4))))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1535,f1664])).
% 156.17/20.10 fof(f12914,plain,(
% 156.17/20.10 ![X0]: (~c_FunDef_Oin__rel(hAPP(v_P_H____,X0),v_b____,v_b_H____,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)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1536,f1742])).
% 156.17/20.10 fof(f12916,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (~c_FunDef_Oin__rel(c_Relation_OId__on(X0,X1),X2,X3,X1,X1)|X2=X3)),
% 156.17/20.10 inference(resolution,[status(thm)],[f1536,f1568])).
% 156.17/20.10 fof(f12917,plain,(
% 156.17/20.10 ![X0,X1,X2]: (~c_FunDef_Oin__rel(c_Relation_OId(X0),X1,X2,X0,X0)|X1=X2)),
% 156.17/20.10 inference(resolution,[status(thm)],[f1536,f1572])).
% 156.17/20.10 fof(f12939,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (~c_FunDef_Oin__rel(X0,X1,X2,X3,X4)|hBOOL(hAPP(X0,c_Pair(X1,X2,X3,X4))))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1536,f1666])).
% 156.17/20.10 fof(f12983,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6,X7,X8]: (~c_FunDef_Oin__rel(c_Relation_OId__on(c_Relation_OId__on(c_COMBK(X0,X1,X2),X3),X4),X5,X6,X7,X8)|hBOOL(X0))),
% 156.17/20.10 inference(resolution,[status(thm)],[f12939,f12481])).
% 156.17/20.10 fof(f12984,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6]: (~c_FunDef_Oin__rel(c_Relation_OId__on(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1),X2),X3,X4,X5,X6))),
% 156.17/20.10 inference(resolution,[status(thm)],[f12939,f12457])).
% 156.17/20.10 fof(f12985,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6,X7]: (~c_FunDef_Oin__rel(c_Relation_OId__on(c_COMBK(X0,X1,X2),X3),X4,X5,X6,X7)|hBOOL(X0))),
% 156.17/20.10 inference(resolution,[status(thm)],[f12939,f12456])).
% 156.17/20.10 fof(f12986,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (~c_FunDef_Oin__rel(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1),X2,X3,X4,X5))),
% 156.17/20.10 inference(resolution,[status(thm)],[f12939,f12455])).
% 156.17/20.10 fof(f13198,plain,(
% 156.17/20.10 hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P_H____))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1671,f1666])).
% 156.17/20.10 fof(f13199,plain,(
% 156.17/20.10 hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1672,f1666])).
% 156.17/20.10 fof(f13383,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (~c_Set_Oimage(X0,c_Set_Oinsert(X1,X2,X3),X3,X4)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f1086,f823])).
% 156.17/20.10 fof(f15189,plain,(
% 156.17/20.10 ![X0,X1,X2]: (c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Set_Oinsert(X1,X0,X2),tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))=X0)),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f3569,f8333])).
% 156.17/20.10 fof(f15190,plain,(
% 156.17/20.10 ![X0,X1,X2]: (c_Lattices_Olower__semilattice__class_Oinf(X0,c_Set_Oinsert(X1,X0,X2),tc_fun(X2,tc_bool))=X0)),
% 156.17/20.10 inference(forward_demodulation,[status(thm)],[f875,f15189])).
% 156.17/20.10 fof(f20941,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool))=c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)))),
% 156.17/20.10 inference(forward_demodulation,[status(thm)],[f8275,f1161])).
% 156.17/20.10 fof(f21637,plain,(
% 156.17/20.10 spl0_32 <=> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f21638,plain,(
% 156.17/20.10 ![X0,X1]: (hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1))|~spl0_32)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f21637])).
% 156.17/20.10 fof(f22509,plain,(
% 156.17/20.10 spl0_33 <=> ~c_in(X0,X1,X2)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f22510,plain,(
% 156.17/20.10 ![X0,X1,X2]: (~c_in(X0,X1,X2)|~spl0_33)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f22509])).
% 156.17/20.10 fof(f23540,plain,(
% 156.17/20.10 ![X0,X1]: (c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X0),c_Transitive__Closure_Otrancl(X1,X0),tc_fun(tc_prod(X0,X0),tc_bool))=c_Transitive__Closure_Ortrancl(X1,X0))),
% 156.17/20.10 inference(forward_demodulation,[status(thm)],[f958,f1283])).
% 156.17/20.10 fof(f23553,plain,(
% 156.17/20.10 ![X0,X1]: (c_Relation_Oantisym(c_Transitive__Closure_Otrancl(X0,X1),X1)|~c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X0,X1),X1))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f23540,f12551])).
% 156.17/20.10 fof(f24070,plain,(
% 156.17/20.10 spl0_34 <=> hBOOL(hAPP(X0,X1))|~hBOOL(hAPP(X0,X1))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f24073,plain,(
% 156.17/20.10 ![X0,X1,X2]: (hBOOL(hAPP(X0,X1))|~hBOOL(hAPP(X0,X1))|~class_Lattices_Oupper__semilattice(tc_fun(X2,tc_bool)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1337,f2122])).
% 156.17/20.10 fof(f24074,plain,(
% 156.17/20.10 spl0_34|spl0_4),
% 156.17/20.10 inference(split_clause,[status(thm)],[f24073,f24070,f1746])).
% 156.17/20.10 fof(f24078,plain,(
% 156.17/20.10 spl0_35 <=> ~class_Orderings_Oorder(tc_fun(X2,tc_bool))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f24079,plain,(
% 156.17/20.10 ![X0]: (~class_Orderings_Oorder(tc_fun(X0,tc_bool))|~spl0_35)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f24078])).
% 156.17/20.10 fof(f24083,plain,(
% 156.17/20.10 spl0_36 <=> ~class_Orderings_Opreorder(tc_fun(X2,tc_bool))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f24084,plain,(
% 156.17/20.10 ![X0]: (~class_Orderings_Opreorder(tc_fun(X0,tc_bool))|~spl0_36)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f24083])).
% 156.17/20.10 fof(f24151,plain,(
% 156.17/20.10 ![X0,X1,X2]: (c_Equiv__Relations_Oequiv(c_Relation_ODomain(X0,X1,X1),X0,X1)|~c_Equiv__Relations_Oequiv(X2,X0,X1))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1466,f1477])).
% 156.17/20.10 fof(f24152,plain,(
% 156.17/20.10 ![X0]: (~c_Relation_Oconverse(c_Relation_OId(X0),X0,X0)=c_Relation_OId(X0)|c_Equiv__Relations_Oequiv(c_Relation_ODomain(c_Relation_OId(X0),X0,X0),c_Relation_OId(X0),X0))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f1431,f1466])).
% 156.17/20.10 fof(f24153,plain,(
% 156.17/20.10 ![X0]: (~c_Relation_OId(X0)=c_Relation_OId(X0)|c_Equiv__Relations_Oequiv(c_Relation_ODomain(c_Relation_OId(X0),X0,X0),c_Relation_OId(X0),X0))),
% 156.17/20.10 inference(forward_demodulation,[status(thm)],[f1458,f24152])).
% 156.17/20.10 fof(f24154,plain,(
% 156.17/20.10 ![X0]: (c_Equiv__Relations_Oequiv(c_Relation_ODomain(c_Relation_OId(X0),X0,X0),c_Relation_OId(X0),X0))),
% 156.17/20.10 inference(trivial_equality_resolution,[status(esa)],[f24153])).
% 156.17/20.10 fof(f24220,plain,(
% 156.17/20.10 ![X0,X1]: (c_Relation_Oantisym(X0,X1)|~c_Relation_Oantisym(c_Transitive__Closure_Otrancl(X0,X1),X1))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f1217,f12550])).
% 156.17/20.10 fof(f24250,plain,(
% 156.17/20.10 ![X0,X1]: (c_Lattices_Oupper__semilattice__class_Osup(X0,c_Transitive__Closure_Otrancl(X0,X1),tc_fun(tc_prod(X1,X1),tc_bool))=c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X0,X1),X0,X1,X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f1217,f970])).
% 156.17/20.10 fof(f24251,plain,(
% 156.17/20.10 ![X0,X1]: (c_Lattices_Oupper__semilattice__class_Osup(X0,c_Transitive__Closure_Otrancl(X0,X1),tc_fun(tc_prod(X1,X1),tc_bool))=c_Transitive__Closure_Otrancl(X0,X1))),
% 156.17/20.10 inference(forward_demodulation,[status(thm)],[f1217,f24250])).
% 156.17/20.10 fof(f24357,plain,(
% 156.17/20.10 ![X0,X1]: (c_Relation_Oantisym(X0,X1)|~c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X0,X1),X1))),
% 156.17/20.10 inference(resolution,[status(thm)],[f24220,f23553])).
% 156.17/20.10 fof(f24365,plain,(
% 156.17/20.10 ![X0,X1]: (c_Relation_Oantisym(X0,X1)|~c_Wellfounded_Oacyclic(c_Transitive__Closure_Otrancl(X0,X1),X1))),
% 156.17/20.10 inference(resolution,[status(thm)],[f24357,f1865])).
% 156.17/20.10 fof(f24366,plain,(
% 156.17/20.10 ![X0,X1]: (c_Relation_Oantisym(X0,X1)|~c_Wellfounded_Oacyclic(X0,X1))),
% 156.17/20.10 inference(resolution,[status(thm)],[f24357,f1221])).
% 156.17/20.10 fof(f24438,plain,(
% 156.17/20.10 ![X0,X1,X2]: (~c_Equiv__Relations_Oequiv(X0,X1,X2)|c_Relation_Orefl__on(c_Relation_ODomain(X1,X2,X2),X1,X2))),
% 156.17/20.10 inference(resolution,[status(thm)],[f24151,f1483])).
% 156.17/20.10 fof(f24448,plain,(
% 156.17/20.10 ![X0,X1,X2]: (~c_Equiv__Relations_Oequiv(X0,c_Relation_Oconverse(X1,X2,X2),X2)|c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),X1,X2))),
% 156.17/20.10 inference(resolution,[status(thm)],[f24438,f1434])).
% 156.17/20.10 fof(f24449,plain,(
% 156.17/20.10 ![X0,X1,X2]: (~c_Equiv__Relations_Oequiv(X0,c_Relation_Oconverse(X1,X2,X2),X2)|c_Relation_Orefl__on(c_Relation_ORange(X1,X2,X2),X1,X2))),
% 156.17/20.10 inference(forward_demodulation,[status(thm)],[f1490,f24448])).
% 156.17/20.10 fof(f24453,plain,(
% 156.17/20.10 ![X0,X1,X2]: (~c_Equiv__Relations_Oequiv(X0,c_Transitive__Closure_Otrancl(X1,X2),X2)|c_Relation_Orefl__on(c_Relation_ODomain(X1,X2,X2),c_Transitive__Closure_Otrancl(X1,X2),X2))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f1426,f24438])).
% 156.17/20.10 fof(f25063,plain,(
% 156.17/20.10 ![X0,X1,X2]: (~c_Equiv__Relations_Oequiv(X0,X1,X2)|c_Relation_Orefl__on(c_Relation_ORange(c_Relation_Oconverse(X1,X2,X2),X2,X2),c_Relation_Oconverse(X1,X2,X2),X2))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f1474,f24449])).
% 156.17/20.10 fof(f25064,plain,(
% 156.17/20.10 ![X0,X1,X2]: (~c_Equiv__Relations_Oequiv(X0,X1,X2)|c_Relation_Orefl__on(c_Relation_ODomain(X1,X2,X2),c_Relation_Oconverse(X1,X2,X2),X2))),
% 156.17/20.10 inference(forward_demodulation,[status(thm)],[f1468,f25063])).
% 156.17/20.10 fof(f26501,plain,(
% 156.17/20.10 ![X0,X1]: (c_lessequals(c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(X0,X1),c_Relation_OImage(X0,c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(X0,X1),X1,X1),tc_fun(X1,tc_bool))|~spl0_7)),
% 156.17/20.10 inference(forward_subsumption_resolution,[status(thm)],[f1264,f1769])).
% 156.17/20.10 fof(f26505,plain,(
% 156.17/20.10 ![X0,X1]: (c_Relation_OImage(X0,c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(X0,X1),X1,X1)=c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(X0,X1)|~c_lessequals(c_Relation_OImage(X0,c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(X0,X1),X1,X1),c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(X0,X1),tc_fun(X1,tc_bool))|~spl0_7)),
% 156.17/20.10 inference(resolution,[status(thm)],[f26501,f1359])).
% 156.17/20.10 fof(f26539,plain,(
% 156.17/20.10 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))|~spl0_0),
% 156.17/20.10 inference(forward_demodulation,[status(thm)],[f1683,f1721])).
% 156.17/20.10 fof(f26539,plain,(
% 156.17/20.10 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))|~spl0_0),
% 156.17/20.10 inference(forward_demodulation,[status(thm)],[f1683,f1721])).
% 156.17/20.10 fof(f26561,plain,(
% 156.17/20.10 ![X0,X1,X2]: (~c_in(X0,X1,X2)|c_FunDef_Oin__rel(c_Relation_OId__on(X1,X2),X0,X0,X2,X2))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1626,f1535])).
% 156.17/20.10 fof(f26563,plain,(
% 156.17/20.10 ![X0,X1,X2]: (~c_in(X0,X1,X2)|~c_Relation_Oirrefl(c_Relation_OId__on(X1,X2),X2))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1626,f1545])).
% 156.17/20.10 fof(f26829,plain,(
% 156.17/20.10 ![X0,X1]: (c_Relation_OImage(c_Relation_OId__on(X0,X1),c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(c_Relation_OId__on(X0,X1),X1),X1,X1)=c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(c_Relation_OId__on(X0,X1),X1)|~c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(c_Relation_OId__on(X0,X1),X1),tc_fun(X1,tc_bool)),c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(c_Relation_OId__on(X0,X1),X1),tc_fun(X1,tc_bool))|~spl0_7)),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f1225,f26505])).
% 156.17/20.10 fof(f26830,plain,(
% 156.17/20.10 ![X0,X1]: (c_Lattices_Olower__semilattice__class_Oinf(X0,c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(c_Relation_OId__on(X0,X1),X1),tc_fun(X1,tc_bool))=c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(c_Relation_OId__on(X0,X1),X1)|~c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(c_Relation_OId__on(X0,X1),X1),tc_fun(X1,tc_bool)),c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(c_Relation_OId__on(X0,X1),X1),tc_fun(X1,tc_bool))|~spl0_7)),
% 156.17/20.10 inference(forward_demodulation,[status(thm)],[f1225,f26829])).
% 156.17/20.10 fof(f26831,plain,(
% 156.17/20.10 ![X0,X1]: (c_Lattices_Olower__semilattice__class_Oinf(X0,c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(c_Relation_OId__on(X0,X1),X1),tc_fun(X1,tc_bool))=c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(c_Relation_OId__on(X0,X1),X1)|~spl0_7)),
% 156.17/20.10 inference(forward_subsumption_resolution,[status(thm)],[f26830,f1106])).
% 156.17/20.10 fof(f26833,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (~c_in(X0,c_Relation_OId__on(c_COMBK(X1,X2,X3),X4),X5)|hBOOL(X1))),
% 156.17/20.10 inference(resolution,[status(thm)],[f26561,f12983])).
% 156.17/20.10 fof(f26834,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (~c_in(X0,c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2),X3))),
% 156.17/20.10 inference(resolution,[status(thm)],[f26561,f12984])).
% 156.17/20.10 fof(f26835,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (~c_in(X0,c_COMBK(X1,X2,X3),X4)|hBOOL(X1))),
% 156.17/20.10 inference(resolution,[status(thm)],[f26561,f12985])).
% 156.17/20.10 fof(f26836,plain,(
% 156.17/20.10 ![X0,X1,X2]: (~c_in(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2))),
% 156.17/20.10 inference(resolution,[status(thm)],[f26561,f12986])).
% 156.17/20.10 fof(f26845,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (~c_in(X0,c_Relation_OImage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X4),X4))),
% 156.17/20.10 inference(resolution,[status(thm)],[f26836,f1427])).
% 156.17/20.10 fof(f26862,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6]: (hBOOL(X0)|~c_in(X1,c_Relation_OImage(X2,c_COMBK(X0,X3,X4),X5,X6),X6))),
% 156.17/20.10 inference(resolution,[status(thm)],[f26835,f1427])).
% 156.17/20.10 fof(f26916,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (~c_in(c_Pair(X0,X1,X2,X2),c_Relation_OId__on(X3,X2),tc_prod(X2,X2))|X1=c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X3,c_Pair(X0,X1,X2,X2),X2))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1274,f1656])).
% 156.17/20.10 fof(f26964,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (~hBOOL(hAPP(c_Relation_OImage(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X3),X4)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f26845,f1664])).
% 156.17/20.10 fof(f26984,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6]: (hBOOL(X0)|~hBOOL(hAPP(c_Relation_OImage(X1,c_COMBK(X0,X2,X3),X4,X5),X6)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f26862,f1664])).
% 156.17/20.10 fof(f27090,plain,(
% 156.17/20.10 ![X0]: (~class_Lattices_Obounded__lattice(tc_fun(X0,tc_bool))|c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0)=c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))|~spl0_7)),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f26831,f837])).
% 156.17/20.10 fof(f27091,plain,(
% 156.17/20.10 ![X0]: (~class_Lattices_Obounded__lattice(tc_fun(X0,tc_bool))|~spl0_7)),
% 156.17/20.10 inference(forward_subsumption_resolution,[status(thm)],[f27090,f2099])).
% 156.17/20.10 fof(f27195,plain,(
% 156.17/20.10 ~class_Lattices_Obounded__lattice(tc_bool)|~spl0_7),
% 156.17/20.10 inference(resolution,[status(thm)],[f27091,f1694])).
% 156.17/20.10 fof(f27196,plain,(
% 156.17/20.10 $false|~spl0_7),
% 156.17/20.10 inference(forward_subsumption_resolution,[status(thm)],[f27195,f1710])).
% 156.17/20.10 fof(f27197,plain,(
% 156.17/20.10 ~spl0_7),
% 156.17/20.10 inference(contradiction_clause,[status(thm)],[f27196])).
% 156.17/20.10 fof(f28696,plain,(
% 156.17/20.10 ![X0,X1]: (~c_Wellfounded_Owf(X0,X1)|c_Relation_Oantisym(X0,X1))),
% 156.17/20.10 inference(resolution,[status(thm)],[f10445,f24365])).
% 156.17/20.10 fof(f29432,plain,(
% 156.17/20.10 ![X0,X1]: (c_Relation_Oirrefl(c_Relation_OId__on(X0,X1),X1)|c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(c_Relation_OId__on(X0,X1),X1)=c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X0,c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(c_Relation_OId__on(X0,X1),X1),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(c_Relation_OId__on(X0,X1),X1),X1,X1),X1))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1289,f26916])).
% 156.17/20.10 fof(f29434,plain,(
% 156.17/20.10 ![X0,X1]: (c_Relation_Oirrefl(c_Relation_OId__on(X0,X1),X1)|c_in(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(c_Relation_OId__on(X0,X1),X1),X0,X1))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1289,f1625])).
% 156.17/20.10 fof(f29439,plain,(
% 156.17/20.10 ![X0,X1]: (c_Relation_Oirrefl(X0,X1)|c_FunDef_Oin__rel(X0,c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X0,X1),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X0,X1),X1,X1))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1289,f1535])).
% 156.17/20.10 fof(f29816,plain,(
% 156.17/20.10 ![X0,X1]: (~hBOOL(hAPP(c_Relation_OId__on(X0,X1),c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(c_Relation_OId__on(X0,X1),X1),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(c_Relation_OId__on(X0,X1),X1),X1,X1)))|hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(c_Relation_OId__on(X0,X1),X1)))|c_Relation_Oirrefl(c_Relation_OId__on(X0,X1),X1))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f29432,f12439])).
% 156.17/20.10 fof(f29817,plain,(
% 156.17/20.10 ![X0,X1]: (~hBOOL(hAPP(c_Relation_OId__on(X0,X1),c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(c_Relation_OId__on(X0,X1),X1),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(c_Relation_OId__on(X0,X1),X1),X1,X1)))|hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(c_Relation_OId__on(X0,X1),X1))))),
% 156.17/20.10 inference(forward_subsumption_resolution,[status(thm)],[f29816,f3118])).
% 156.17/20.10 fof(f29819,plain,(
% 156.17/20.10 ![X0,X1]: (hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(c_Relation_OId__on(X0,X1),X1)))|~c_FunDef_Oin__rel(c_Relation_OId__on(X0,X1),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(c_Relation_OId__on(X0,X1),X1),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(c_Relation_OId__on(X0,X1),X1),X1,X1))),
% 156.17/20.10 inference(resolution,[status(thm)],[f29817,f12939])).
% 156.17/20.10 fof(f29820,plain,(
% 156.17/20.10 ![X0,X1]: (hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(c_Relation_OId__on(X0,X1),X1)))|~c_Nitpick_Orefl_H(c_Relation_OId__on(X0,X1),X1))),
% 156.17/20.10 inference(resolution,[status(thm)],[f29817,f3326])).
% 156.17/20.10 fof(f29821,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6]: (~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Relation_OImage(X0,c_COMBK(X1,X2,X3),X4,X5),X6),X6)|hBOOL(X1))),
% 156.17/20.10 inference(resolution,[status(thm)],[f29820,f26984])).
% 156.17/20.10 fof(f29825,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X3),X3)|c_in(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(c_Relation_OId__on(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X3),X3),X0,X2))),
% 156.17/20.10 inference(resolution,[status(thm)],[f29820,f3801])).
% 156.17/20.10 fof(f29830,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (~c_Nitpick_Orefl_H(c_Relation_OId__on(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X3),X3)|~c_in(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(c_Relation_OId__on(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X3),X3),X1,X2))),
% 156.17/20.10 inference(resolution,[status(thm)],[f29820,f3786])).
% 156.17/20.10 fof(f29848,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Lattices_Olower__semilattice__class_Oinf(X0,c_COMBK(X1,X2,X3),tc_fun(X4,tc_bool)),X5),X5)|hBOOL(X1))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f1225,f29821])).
% 156.17/20.10 fof(f29879,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6]: (~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ominus__class_Ominus(c_COMBK(X1,X2,X3),X4,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),X6),X6)|hBOOL(X1))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f20941,f29848])).
% 156.17/20.10 fof(f29885,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Lattices_Olower__semilattice__class_Oinf(c_COMBK(X0,X1,X2),X3,tc_fun(X4,tc_bool)),X5),X5)|hBOOL(X0))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f752,f29848])).
% 156.17/20.10 fof(f29889,plain,(
% 156.17/20.10 spl0_61 <=> ~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1),X1)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f29892,plain,(
% 156.17/20.10 spl0_62 <=> hBOOL(X2)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f29893,plain,(
% 156.17/20.10 ![X0]: (hBOOL(X0)|~spl0_62)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f29892])).
% 156.17/20.10 fof(f29895,plain,(
% 156.17/20.10 ![X0,X1,X2]: (~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1),X1)|hBOOL(X2))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f981,f29885])).
% 156.17/20.10 fof(f29896,plain,(
% 156.17/20.10 spl0_61|spl0_62),
% 156.17/20.10 inference(split_clause,[status(thm)],[f29895,f29889,f29892])).
% 156.17/20.10 fof(f29900,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6]: (~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(c_COMBK(X1,X2,X3),X4,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),X6),X6)|hBOOL(X1))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f869,f29885])).
% 156.17/20.10 fof(f30027,plain,(
% 156.17/20.10 ![X0,X1]: (c_Nitpick_Orefl_H(c_Relation_OId__on(X0,X1),X1)|~c_in(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(c_Relation_OId__on(X0,X1),X1),X0,X1))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1294,f1626])).
% 156.17/20.10 fof(f30031,plain,(
% 156.17/20.10 ![X0]: (c_Nitpick_Orefl_H(c_Relation_OId(X0),X0))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1294,f1591])).
% 156.17/20.10 fof(f30380,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (~c_in(X0,c_Relation_OImage(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X3,X4),X4))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1299,f26836])).
% 156.17/20.10 fof(f30400,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (c_in(X0,c_Wellfounded_Oacc(c_COMBK(X1,X2,X3),X4),X4)|hBOOL(X1))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1300,f26835])).
% 156.17/20.10 fof(f30407,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (c_in(X0,c_Wellfounded_Oacc(c_Relation_OId__on(c_COMBK(X1,X2,X3),X4),X5),X5)|hBOOL(X1))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1300,f26833])).
% 156.17/20.10 fof(f30408,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (c_in(X0,c_Wellfounded_Oacc(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2),X3),X3))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1300,f26834])).
% 156.17/20.10 fof(f30424,plain,(
% 156.17/20.10 ![X0,X1,X2]: (c_in(X0,c_Wellfounded_Oacc(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2),X2))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1300,f26836])).
% 156.17/20.10 fof(f30440,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (hBOOL(hAPP(X0,X1))|hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,c_Transitive__Closure_Ortrancl(X2,X3),X3)))|~c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X2,X3),X3),X3))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1302,f1557])).
% 156.17/20.10 fof(f30441,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (hBOOL(hAPP(X0,X1))|~c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X2,X3),X3),X3))),
% 156.17/20.10 inference(forward_subsumption_resolution,[status(thm)],[f30440,f1214])).
% 156.17/20.10 fof(f30442,plain,(
% 156.17/20.10 ![X0,X1,X2]: (hBOOL(hAPP(X0,X1))|hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,c_Relation_OId(X2),X2)))|~c_in(X1,c_Wellfounded_Oacc(c_Relation_OId(X2),X2),X2))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1302,f1591])).
% 156.17/20.10 fof(f30443,plain,(
% 156.17/20.10 ![X0,X1,X2]: (hBOOL(hAPP(X0,X1))|~c_in(X1,c_Wellfounded_Oacc(c_Relation_OId(X2),X2),X2))),
% 156.17/20.10 inference(forward_subsumption_resolution,[status(thm)],[f30442,f1214])).
% 156.17/20.10 fof(f30445,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (hBOOL(hAPP(X0,X1))|hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,X2,X3)))|~c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)|~c_Nitpick_Orefl_H(X2,X3))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1302,f1574])).
% 156.17/20.10 fof(f30446,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (hBOOL(hAPP(X0,X1))|~c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)|~c_Nitpick_Orefl_H(X2,X3))),
% 156.17/20.10 inference(forward_subsumption_resolution,[status(thm)],[f30445,f1214])).
% 156.17/20.10 fof(f30542,plain,(
% 156.17/20.10 spl0_63 <=> ~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),X2),X2)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f30545,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),X2),X2)|hBOOL(X3))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f3569,f29879])).
% 156.17/20.10 fof(f30546,plain,(
% 156.17/20.10 spl0_63|spl0_62),
% 156.17/20.10 inference(split_clause,[status(thm)],[f30545,f30542,f29892])).
% 156.17/20.10 fof(f30587,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6]: (~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Lattices_Olower__semilattice__class_Oinf(c_COMBK(X0,X1,X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),X6),X6)|hBOOL(X0))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f869,f29900])).
% 156.17/20.10 fof(f30588,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6]: (~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_COMBK(X0,X1,X2),X3,tc_fun(X4,tc_bool)),X5,tc_fun(X4,tc_bool)),X6),X6)|hBOOL(X0))),
% 156.17/20.10 inference(forward_demodulation,[status(thm)],[f868,f30587])).
% 156.17/20.10 fof(f30856,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (~hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X3))|~spl0_62)),
% 156.17/20.10 inference(backward_subsumption_resolution,[status(thm)],[f12224,f29893])).
% 156.17/20.10 fof(f30857,plain,(
% 156.17/20.10 $false|~spl0_62),
% 156.17/20.10 inference(forward_subsumption_resolution,[status(thm)],[f30856,f29893])).
% 156.17/20.10 fof(f30858,plain,(
% 156.17/20.10 ~spl0_62),
% 156.17/20.10 inference(contradiction_clause,[status(thm)],[f30857])).
% 156.17/20.10 fof(f31085,plain,(
% 156.17/20.10 spl0_64 <=> c_lessequals(X0,X1,tc_fun(X2,tc_bool))|~c_lessequals(X0,X1,tc_fun(X2,tc_bool))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f31088,plain,(
% 156.17/20.10 spl0_65 <=> ~c_in(X3,X4,X5)|~c_in(X6,X4,X5)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f31089,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (~c_in(X0,X1,X2)|~c_in(X3,X1,X2)|~spl0_65)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f31088])).
% 156.17/20.10 fof(f31091,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6]: (c_lessequals(X0,X1,tc_fun(X2,tc_bool))|~c_in(X3,X4,X5)|~c_lessequals(X0,X1,tc_fun(X2,tc_bool))|~c_in(X6,X4,X5))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1309,f1307])).
% 156.17/20.10 fof(f31092,plain,(
% 156.17/20.10 spl0_64|spl0_65),
% 156.17/20.10 inference(split_clause,[status(thm)],[f31091,f31085,f31088])).
% 156.17/20.10 fof(f31095,plain,(
% 156.17/20.10 spl0_66 <=> c_lessequals(X0,X0,tc_fun(X1,tc_bool))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f31098,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (c_lessequals(X0,X0,tc_fun(X1,tc_bool))|~c_in(X2,X3,X4))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1309,f1349])).
% 156.17/20.10 fof(f31099,plain,(
% 156.17/20.10 spl0_66|spl0_33),
% 156.17/20.10 inference(split_clause,[status(thm)],[f31098,f31095,f22509])).
% 156.17/20.10 fof(f31203,plain,(
% 156.17/20.10 ![X0,X1,X2]: (c_in(X0,c_Wellfounded_Oacc(X1,X2),X2)|~spl0_33)),
% 156.17/20.10 inference(backward_subsumption_resolution,[status(thm)],[f1300,f22510])).
% 156.17/20.10 fof(f31204,plain,(
% 156.17/20.10 $false|~spl0_33),
% 156.17/20.10 inference(forward_subsumption_resolution,[status(thm)],[f31203,f22510])).
% 156.17/20.10 fof(f31205,plain,(
% 156.17/20.10 ~spl0_33),
% 156.17/20.10 inference(contradiction_clause,[status(thm)],[f31204])).
% 156.17/20.10 fof(f31325,plain,(
% 156.17/20.10 spl0_67 <=> ~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)),X2),X2)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f31328,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)),X2),X2)|hBOOL(X3))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f981,f30588])).
% 156.17/20.10 fof(f31329,plain,(
% 156.17/20.10 spl0_67|spl0_62),
% 156.17/20.10 inference(split_clause,[status(thm)],[f31328,f31325,f29892])).
% 156.17/20.10 fof(f31820,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Set_Oinsert(X1,X0,X2),tc_fun(X2,tc_bool)),X3),X3)|c_in(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(c_Relation_OId__on(X0,X3),X3),X0,X2))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f15190,f29825])).
% 156.17/20.10 fof(f31821,plain,(
% 156.17/20.10 ![X0,X1,X2]: (~c_Nitpick_Orefl_H(c_Relation_OId__on(X0,X1),X1)|c_in(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(c_Relation_OId__on(X0,X1),X1),X0,X2))),
% 156.17/20.10 inference(forward_demodulation,[status(thm)],[f15190,f31820])).
% 156.17/20.10 fof(f31948,plain,(
% 156.17/20.10 ![X0,X1,X2]: (hBOOL(hAPP(c_Wellfounded_Oacc(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1),X2)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f30424,f1666])).
% 156.17/20.10 fof(f35603,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (~c_in(X0,c_Relation_ORange(c_COMBK(X1,X2,X3),X4,X5),X5)|hBOOL(X1))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1376,f26835])).
% 156.17/20.10 fof(f35604,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (~c_in(X0,c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X3),X3))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1376,f26836])).
% 156.17/20.10 fof(f35736,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (hBOOL(X0)|~c_Nitpick_Orefl_H(c_Relation_OId__on(c_HOL_Ominus__class_Ominus(X1,c_Wellfounded_Oacc(c_COMBK(X0,X2,X3),X4),tc_fun(X4,tc_bool)),X5),X5))),
% 156.17/20.10 inference(resolution,[status(thm)],[f30400,f29830])).
% 156.17/20.10 fof(f35738,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (hBOOL(X0)|hBOOL(hAPP(c_Wellfounded_Oacc(c_COMBK(X0,X1,X2),X3),X4)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f30400,f1666])).
% 156.17/20.10 fof(f35828,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6]: (hBOOL(X0)|~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X1,c_Wellfounded_Oacc(c_COMBK(X0,X2,X3),X4),tc_fun(X4,tc_bool)),X5,tc_fun(X4,tc_bool)),X6),X6))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f8275,f35736])).
% 156.17/20.10 fof(f35840,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6]: (hBOOL(X0)|~c_Nitpick_Orefl_H(c_Relation_OId__on(c_HOL_Ominus__class_Ominus(X1,c_Lattices_Oupper__semilattice__class_Osup(c_Wellfounded_Oacc(c_COMBK(X0,X2,X3),X4),X5,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),X6),X6))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f1160,f35828])).
% 156.17/20.10 fof(f35851,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6]: (hBOOL(X0)|~c_Nitpick_Orefl_H(c_Relation_OId__on(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_Wellfounded_Oacc(c_COMBK(X0,X2,X3),X4),tc_fun(X4,tc_bool)),X5,tc_fun(X4,tc_bool)),X6),X6))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f713,f35828])).
% 156.17/20.10 fof(f35876,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (hBOOL(X0)|~c_Nitpick_Orefl_H(c_Relation_OId__on(c_HOL_Ominus__class_Ominus(X1,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_COMBK(X0,X2,X3),tc_prod(X4,X4)),X4),tc_fun(tc_prod(X4,X4),tc_bool)),X5),X5))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f24251,f35840])).
% 156.17/20.10 fof(f35920,plain,(
% 156.17/20.10 spl0_74 <=> ~c_Nitpick_Orefl_H(c_Relation_OId__on(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),X3),X3)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f35923,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (hBOOL(X0)|~c_Nitpick_Orefl_H(c_Relation_OId__on(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),X3),X3))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f849,f35851])).
% 156.17/20.10 fof(f35924,plain,(
% 156.17/20.10 spl0_62|spl0_74),
% 156.17/20.10 inference(split_clause,[status(thm)],[f35923,f29892,f35920])).
% 156.17/20.10 fof(f36010,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (hBOOL(X0)|~hBOOL(hAPP(c_Relation_OId__on(c_COMBK(X0,X1,X2),X3),X4)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f26833,f1664])).
% 156.17/20.10 fof(f36991,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (~hBOOL(hAPP(c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X2),X3)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f35604,f1664])).
% 156.17/20.10 fof(f37240,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (~hBOOL(hAPP(c_Relation_OImage(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X2,X3),X4)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f30380,f1664])).
% 156.17/20.10 fof(f37247,plain,(
% 156.17/20.10 ![X0,X1,X2]: (hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(c_Relation_OId__on(c_Wellfounded_Oacc(c_Relation_OId(X1),X1),X2),X2)))|~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Wellfounded_Oacc(c_Relation_OId(X1),X1),X2),X2))),
% 156.17/20.10 inference(resolution,[status(thm)],[f30443,f31821])).
% 156.17/20.10 fof(f37252,plain,(
% 156.17/20.10 spl0_75 <=> hBOOL(hAPP(X0,X1))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f37253,plain,(
% 156.17/20.10 ![X0,X1]: (hBOOL(hAPP(X0,X1))|~spl0_75)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f37252])).
% 156.17/20.10 fof(f37255,plain,(
% 156.17/20.10 spl0_76 <=> ~c_Wellfounded_Owf(c_Relation_OId(X2),X2)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f37258,plain,(
% 156.17/20.10 ![X0,X1,X2]: (hBOOL(hAPP(X0,X1))|~c_Wellfounded_Owf(c_Relation_OId(X2),X2))),
% 156.17/20.10 inference(resolution,[status(thm)],[f30443,f1416])).
% 156.17/20.10 fof(f37259,plain,(
% 156.17/20.10 spl0_75|spl0_76),
% 156.17/20.10 inference(split_clause,[status(thm)],[f37258,f37252,f37255])).
% 156.17/20.10 fof(f37321,plain,(
% 156.17/20.10 $false|~spl0_75),
% 156.17/20.10 inference(backward_subsumption_resolution,[status(thm)],[f878,f37253])).
% 156.17/20.10 fof(f37322,plain,(
% 156.17/20.10 ~spl0_75),
% 156.17/20.10 inference(contradiction_clause,[status(thm)],[f37321])).
% 156.17/20.10 fof(f37919,plain,(
% 156.17/20.10 spl0_77 <=> ~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Wellfounded_Oacc(c_Relation_OId(X1),X1),X2),X2)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f37922,plain,(
% 156.17/20.10 ![X0,X1,X2]: (hBOOL(X0)|~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Wellfounded_Oacc(c_Relation_OId(X1),X1),X2),X2))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f705,f37247])).
% 156.17/20.10 fof(f37923,plain,(
% 156.17/20.10 spl0_62|spl0_77),
% 156.17/20.10 inference(split_clause,[status(thm)],[f37922,f29892,f37919])).
% 156.17/20.10 fof(f38288,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (hBOOL(X0)|~hBOOL(hAPP(c_Relation_ORange(c_COMBK(X0,X1,X2),X3,X4),X5)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f35603,f1664])).
% 156.17/20.10 fof(f38468,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (~c_in(X0,c_Relation_ODomain(c_COMBK(X1,X2,X3),X4,X5),X4)|hBOOL(X1))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1513,f26835])).
% 156.17/20.10 fof(f38469,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (~c_in(X0,c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X3),X2))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1513,f26836])).
% 156.17/20.10 fof(f38573,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (~hBOOL(hAPP(c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X2),X3)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f38469,f1664])).
% 156.17/20.10 fof(f38585,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (hBOOL(X0)|~hBOOL(hAPP(c_Relation_ODomain(c_COMBK(X0,X1,X2),X3,X4),X5)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f38468,f1664])).
% 156.17/20.10 fof(f39168,plain,(
% 156.17/20.10 ![X0,X1,X2]: (hAPP(hAPP(X0,v_b____),v_b____)=hAPP(hAPP(X0,v_b_H____),v_b_H____)|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,X1),hAPP(v_P_H____,X1),X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1528,f1741])).
% 156.17/20.10 fof(f39169,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6]: (hAPP(hAPP(X0,X1),v_b____)=hAPP(hAPP(X0,X2),v_b_H____)|~c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))|~c_Equiv__Relations_Ocongruent2(X4,hAPP(v_P_H____,X5),X0,X3,tc_Arrow__Order__Mirabelle_Oalt,X6)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1528,f1741])).
% 156.17/20.10 fof(f39175,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (hAPP(hAPP(X0,X1),v_a____)=hAPP(hAPP(X0,X2),v_b____)|~c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))|~c_Equiv__Relations_Ocongruent2(X4,v_F(v_P____),X0,X3,tc_Arrow__Order__Mirabelle_Oalt,X5)|~spl0_1)),
% 156.17/20.10 inference(resolution,[status(thm)],[f1528,f1724])).
% 156.17/20.10 fof(f39226,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6]: (hAPP(hAPP(X0,v_b____),X1)=hAPP(hAPP(X0,v_b_H____),X2)|~c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,X5),X4,X0,tc_Arrow__Order__Mirabelle_Oalt,X3,X6)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1528,f1741])).
% 156.17/20.10 fof(f39282,plain,(
% 156.17/20.10 ![X0,X1,X2]: (hAPP(hAPP(X0,v_b____),v_a____)=hAPP(hAPP(X0,v_b_H____),v_b____)|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,X1),v_F(v_P____),X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_1)),
% 156.17/20.10 inference(resolution,[status(thm)],[f39175,f1741])).
% 156.17/20.10 fof(f39703,plain,(
% 156.17/20.10 ![X0,X1]: (X0=v_b_H____|~c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Osingle__valued(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1530,f1741])).
% 156.17/20.10 fof(f39704,plain,(
% 156.17/20.10 ![X0,X1]: (X0=v_b____|~c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Osingle__valued(hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,X1),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1530,f1874])).
% 156.17/20.10 fof(f39705,plain,(
% 156.17/20.10 ![X0,X1]: (X0=v_b____|~c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Osingle__valued(hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,X1),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1530,f12914])).
% 156.17/20.10 fof(f39706,plain,(
% 156.17/20.10 spl0_78 <=> X0=v_b____|~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))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f39707,plain,(
% 156.17/20.10 ![X0]: (X0=v_b____|~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))|~spl0_78)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f39706])).
% 156.17/20.10 fof(f39709,plain,(
% 156.17/20.10 spl0_79 <=> c_Relation_Osingle__valued(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f39712,plain,(
% 156.17/20.10 ![X0]: (X0=v_b____|~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_Osingle__valued(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~spl0_1)),
% 156.17/20.10 inference(resolution,[status(thm)],[f1530,f1724])).
% 156.17/20.10 fof(f39713,plain,(
% 156.17/20.10 spl0_78|~spl0_79|~spl0_1),
% 156.17/20.10 inference(split_clause,[status(thm)],[f39712,f39706,f39709,f1723])).
% 156.17/20.10 fof(f39922,plain,(
% 156.17/20.10 spl0_84 <=> X0=v_b_H____|~c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f39923,plain,(
% 156.17/20.10 ![X0]: (X0=v_b_H____|~c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_84)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f39922])).
% 156.17/20.10 fof(f39925,plain,(
% 156.17/20.10 spl0_85 <=> c_Relation_Osingle__valued(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f39928,plain,(
% 156.17/20.10 ![X0]: (X0=v_b_H____|~c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Osingle__valued(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~spl0_0)),
% 156.17/20.10 inference(resolution,[status(thm)],[f26539,f1530])).
% 156.17/20.10 fof(f39929,plain,(
% 156.17/20.10 spl0_84|~spl0_85|~spl0_0),
% 156.17/20.10 inference(split_clause,[status(thm)],[f39928,f39922,f39925,f1720])).
% 156.17/20.10 fof(f39990,plain,(
% 156.17/20.10 ![X0,X1]: (X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~hBOOL(hAPP(hAPP(v_P_H____,X1),c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))),
% 156.17/20.10 inference(resolution,[status(thm)],[f39703,f1664])).
% 156.17/20.10 fof(f40123,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(c_Relation_OId__on(c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X1,X2),X2),X3),X3)))|~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X1,X2),X2),X3),X3))),
% 156.17/20.10 inference(resolution,[status(thm)],[f30441,f31821])).
% 156.17/20.10 fof(f40132,plain,(
% 156.17/20.10 spl0_88 <=> ~c_Wellfounded_Owf(c_Transitive__Closure_Ortrancl(X2,X3),X3)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f40135,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (hBOOL(hAPP(X0,X1))|~c_Wellfounded_Owf(c_Transitive__Closure_Ortrancl(X2,X3),X3))),
% 156.17/20.10 inference(resolution,[status(thm)],[f30441,f1416])).
% 156.17/20.10 fof(f40136,plain,(
% 156.17/20.10 spl0_75|spl0_88),
% 156.17/20.10 inference(split_clause,[status(thm)],[f40135,f37252,f40132])).
% 156.17/20.10 fof(f40292,plain,(
% 156.17/20.10 spl0_89 <=> c_in(c_Pair(X0,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(X0,v_b____,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))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f40293,plain,(
% 156.17/20.10 ![X0]: (c_in(c_Pair(X0,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(X0,v_b____,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))|~spl0_89)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f40292])).
% 156.17/20.10 fof(f40295,plain,(
% 156.17/20.10 spl0_90 <=> c_Relation_Otrans(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f40300,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1538,f1741])).
% 156.17/20.10 fof(f40301,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,X1),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1538,f1874])).
% 156.17/20.10 fof(f40302,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,X1),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1538,f12914])).
% 156.17/20.10 fof(f40362,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1538,f1741])).
% 156.17/20.10 fof(f40363,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,X1),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1538,f1874])).
% 156.17/20.10 fof(f40364,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,X1),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1538,f12914])).
% 156.17/20.10 fof(f40689,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,X1),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))),
% 156.17/20.10 inference(resolution,[status(thm)],[f40300,f1874])).
% 156.17/20.10 fof(f40690,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,X1),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 inference(resolution,[status(thm)],[f40300,f12914])).
% 156.17/20.10 fof(f40691,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P____,X1),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))),
% 156.17/20.10 inference(resolution,[status(thm)],[f40300,f1664])).
% 156.17/20.10 fof(f40740,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~hBOOL(hAPP(hAPP(v_P_H____,X1),c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))),
% 156.17/20.10 inference(resolution,[status(thm)],[f40362,f1664])).
% 156.17/20.10 fof(f41108,plain,(
% 156.17/20.10 spl0_95 <=> ~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X0,X1),X1),X2),X2)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f41111,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X0,X1),X1),X2),X2)|hBOOL(X3))),
% 156.17/20.10 inference(resolution,[status(thm)],[f40123,f36010])).
% 156.17/20.10 fof(f41112,plain,(
% 156.17/20.10 spl0_95|spl0_62),
% 156.17/20.10 inference(split_clause,[status(thm)],[f41111,f41108,f29892])).
% 156.17/20.10 fof(f41287,plain,(
% 156.17/20.10 spl0_96 <=> ~c_Nitpick_Orefl_H(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Osingle__valued(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f41288,plain,(
% 156.17/20.10 ![X0]: (~c_Nitpick_Orefl_H(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Osingle__valued(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_96)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f41287])).
% 156.17/20.10 fof(f41290,plain,(
% 156.17/20.10 spl0_97 <=> v_b____=v_b_H____),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f41291,plain,(
% 156.17/20.10 v_b____=v_b_H____|~spl0_97),
% 156.17/20.10 inference(component_clause,[status(thm)],[f41290])).
% 156.17/20.10 fof(f41293,plain,(
% 156.17/20.10 ![X0]: (~c_Nitpick_Orefl_H(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|v_b____=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1574,f39703])).
% 156.17/20.10 fof(f41294,plain,(
% 156.17/20.10 spl0_96|spl0_97),
% 156.17/20.10 inference(split_clause,[status(thm)],[f41293,f41287,f41290])).
% 156.17/20.10 fof(f41561,plain,(
% 156.17/20.10 $false|~spl0_97),
% 156.17/20.10 inference(forward_subsumption_resolution,[status(thm)],[f41291,f1740])).
% 156.17/20.10 fof(f41562,plain,(
% 156.17/20.10 ~spl0_97),
% 156.17/20.10 inference(contradiction_clause,[status(thm)],[f41561])).
% 156.17/20.10 fof(f42380,plain,(
% 156.17/20.10 spl0_106 <=> c_in(c_Pair(v_b_H____,v_b____,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))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f42381,plain,(
% 156.17/20.10 c_in(c_Pair(v_b_H____,v_b____,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))|~spl0_106),
% 156.17/20.10 inference(component_clause,[status(thm)],[f42380])).
% 156.17/20.10 fof(f42383,plain,(
% 156.17/20.10 spl0_107 <=> c_Wellfounded_Owf(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f42386,plain,(
% 156.17/20.10 ~c_in(c_Pair(v_b_H____,v_b____,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_Wellfounded_Owf(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_0),
% 156.17/20.10 inference(resolution,[status(thm)],[f1560,f26539])).
% 156.17/20.10 fof(f42387,plain,(
% 156.17/20.10 ~spl0_106|~spl0_107|~spl0_0),
% 156.17/20.10 inference(split_clause,[status(thm)],[f42386,f42380,f42383,f1720])).
% 156.17/20.10 fof(f42388,plain,(
% 156.17/20.10 ![X0]: (~c_in(c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Wellfounded_Owf(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1560,f1741])).
% 156.17/20.10 fof(f42389,plain,(
% 156.17/20.10 ![X0]: (~c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Wellfounded_Owf(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,X0),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1560,f1874])).
% 156.17/20.10 fof(f42390,plain,(
% 156.17/20.10 ![X0]: (~c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Wellfounded_Owf(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,X0),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1560,f12914])).
% 156.17/20.10 fof(f42925,plain,(
% 156.17/20.10 ![X0]: (~c_Wellfounded_Owf(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~hBOOL(hAPP(hAPP(v_P_H____,X0),c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))),
% 156.17/20.10 inference(resolution,[status(thm)],[f42388,f1664])).
% 156.17/20.10 fof(f42988,plain,(
% 156.17/20.10 spl0_108 <=> c_Relation_Oantisym(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f42991,plain,(
% 156.17/20.10 v_b_H____=v_b____|~c_in(c_Pair(v_b_H____,v_b____,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_Relation_Oantisym(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_0),
% 156.17/20.10 inference(resolution,[status(thm)],[f1562,f26539])).
% 156.17/20.10 fof(f42992,plain,(
% 156.17/20.10 spl0_97|~spl0_106|~spl0_108|~spl0_0),
% 156.17/20.10 inference(split_clause,[status(thm)],[f42991,f41290,f42380,f42988,f1720])).
% 156.17/20.10 fof(f42993,plain,(
% 156.17/20.10 spl0_109 <=> ~c_in(c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~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))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f42994,plain,(
% 156.17/20.10 ![X0]: (~c_in(c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~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))|~spl0_109)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f42993])).
% 156.17/20.10 fof(f42996,plain,(
% 156.17/20.10 ![X0]: (v_b_H____=v_b____|~c_in(c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~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)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1562,f1741])).
% 156.17/20.10 fof(f42997,plain,(
% 156.17/20.10 spl0_97|spl0_109),
% 156.17/20.10 inference(split_clause,[status(thm)],[f42996,f41290,f42993])).
% 156.17/20.10 fof(f42998,plain,(
% 156.17/20.10 spl0_110 <=> v_b____=v_a____),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f42999,plain,(
% 156.17/20.10 v_b____=v_a____|~spl0_110),
% 156.17/20.10 inference(component_clause,[status(thm)],[f42998])).
% 156.17/20.10 fof(f43001,plain,(
% 156.17/20.10 spl0_111 <=> ~c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Oantisym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,X0),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f43002,plain,(
% 156.17/20.10 ![X0]: (~c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Oantisym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,X0),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_111)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f43001])).
% 156.17/20.10 fof(f43004,plain,(
% 156.17/20.10 ![X0]: (v_b____=v_a____|~c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Oantisym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,X0),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1562,f1874])).
% 156.17/20.10 fof(f43005,plain,(
% 156.17/20.10 spl0_110|spl0_111),
% 156.17/20.10 inference(split_clause,[status(thm)],[f43004,f42998,f43001])).
% 156.17/20.10 fof(f43006,plain,(
% 156.17/20.10 spl0_112 <=> ~c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Oantisym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,X0),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f43007,plain,(
% 156.17/20.10 ![X0]: (~c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Oantisym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,X0),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~spl0_112)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f43006])).
% 156.17/20.10 fof(f43009,plain,(
% 156.17/20.10 ![X0]: (v_b____=v_a____|~c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Oantisym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,X0),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1562,f12914])).
% 156.17/20.10 fof(f43010,plain,(
% 156.17/20.10 spl0_110|spl0_112),
% 156.17/20.10 inference(split_clause,[status(thm)],[f43009,f42998,f43006])).
% 156.17/20.10 fof(f43053,plain,(
% 156.17/20.10 $false|~spl0_110),
% 156.17/20.10 inference(forward_subsumption_resolution,[status(thm)],[f42999,f1653])).
% 156.17/20.10 fof(f43054,plain,(
% 156.17/20.10 ~spl0_110),
% 156.17/20.10 inference(contradiction_clause,[status(thm)],[f43053])).
% 156.17/20.10 fof(f43062,plain,(
% 156.17/20.10 ![X0,X1,X2]: (hAPP(X0,v_b____)=hAPP(X0,v_b_H____)|~c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,X1),X0,tc_Arrow__Order__Mirabelle_Oalt,X2)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1566,f1741])).
% 156.17/20.10 fof(f43137,plain,(
% 156.17/20.10 ![X0]: (~c_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~hBOOL(hAPP(hAPP(v_P_H____,X0),c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_109)),
% 156.17/20.10 inference(resolution,[status(thm)],[f42994,f1664])).
% 156.17/20.10 fof(f44482,plain,(
% 156.17/20.10 spl0_118 <=> ~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X2),X2)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f44485,plain,(
% 156.17/20.10 ![X0,X1,X2]: (hBOOL(X0)|~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X2),X2))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f849,f35876])).
% 156.17/20.10 fof(f44486,plain,(
% 156.17/20.10 spl0_62|spl0_118),
% 156.17/20.10 inference(split_clause,[status(thm)],[f44485,f29892,f44482])).
% 156.17/20.10 fof(f44888,plain,(
% 156.17/20.10 spl0_122 <=> c_Relation_Osym(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f44891,plain,(
% 156.17/20.10 c_in(c_Pair(v_b_H____,v_b____,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_Relation_Osym(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_0),
% 156.17/20.10 inference(resolution,[status(thm)],[f1582,f26539])).
% 156.17/20.10 fof(f44892,plain,(
% 156.17/20.10 spl0_106|~spl0_122|~spl0_0),
% 156.17/20.10 inference(split_clause,[status(thm)],[f44891,f42380,f44888,f1720])).
% 156.17/20.10 fof(f44893,plain,(
% 156.17/20.10 ![X0]: (c_in(c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1582,f1741])).
% 156.17/20.10 fof(f44894,plain,(
% 156.17/20.10 ![X0]: (c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Osym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,X0),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1582,f1874])).
% 156.17/20.10 fof(f44895,plain,(
% 156.17/20.10 ![X0]: (c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Osym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,X0),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1582,f12914])).
% 156.17/20.10 fof(f45369,plain,(
% 156.17/20.10 ![X0]: (~c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_109)),
% 156.17/20.10 inference(resolution,[status(thm)],[f44893,f42994])).
% 156.17/20.10 fof(f45370,plain,(
% 156.17/20.10 ![X0]: (~c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_109)),
% 156.17/20.10 inference(duplicate_literals_removal,[status(esa)],[f45369])).
% 156.17/20.10 fof(f45373,plain,(
% 156.17/20.10 ![X0]: (~c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f44893,f40362])).
% 156.17/20.10 fof(f45374,plain,(
% 156.17/20.10 ![X0]: (~c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 inference(duplicate_literals_removal,[status(esa)],[f45373])).
% 156.17/20.10 fof(f45379,plain,(
% 156.17/20.10 spl0_123 <=> ~c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~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_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f45380,plain,(
% 156.17/20.10 ![X0]: (~c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~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_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_123)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f45379])).
% 156.17/20.10 fof(f45382,plain,(
% 156.17/20.10 ![X0]: (~c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_b____=v_b_H____|~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_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 inference(resolution,[status(thm)],[f44893,f1562])).
% 156.17/20.10 fof(f45383,plain,(
% 156.17/20.10 spl0_123|spl0_97),
% 156.17/20.10 inference(split_clause,[status(thm)],[f45382,f45379,f41290])).
% 156.17/20.10 fof(f45389,plain,(
% 156.17/20.10 ![X0,X1]: (~c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X1,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_b____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 inference(resolution,[status(thm)],[f44893,f1538])).
% 156.17/20.10 fof(f45391,plain,(
% 156.17/20.10 ![X0,X1]: (~c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|X1=v_b____|~c_in(c_Pair(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Osingle__valued(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 inference(resolution,[status(thm)],[f44893,f1530])).
% 156.17/20.10 fof(f45399,plain,(
% 156.17/20.10 ![X0]: (~c_Relation_Osym(hAPP(v_P_H____,X0),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))|~c_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_123)),
% 156.17/20.10 inference(forward_subsumption_resolution,[status(thm)],[f45380,f1742])).
% 156.17/20.10 fof(f46181,plain,(
% 156.17/20.10 ![X0,X1]: (hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(c_Relation_OId__on(X0,X1),X1)))|c_Relation_Oirrefl(c_Relation_OId__on(X0,X1),X1))),
% 156.17/20.10 inference(resolution,[status(thm)],[f29819,f29439])).
% 156.17/20.10 fof(f46186,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (c_Relation_Oirrefl(c_Relation_OId__on(c_Relation_ODomain(c_COMBK(X0,X1,X2),X3,X4),X5),X5)|hBOOL(X0))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46181,f38585])).
% 156.17/20.10 fof(f46187,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (c_Relation_Oirrefl(c_Relation_OId__on(c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X2),X3),X3))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46181,f38573])).
% 156.17/20.10 fof(f46189,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (c_Relation_Oirrefl(c_Relation_OId__on(c_Relation_OImage(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X2,X3),X4),X4))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46181,f37240])).
% 156.17/20.10 fof(f46190,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (c_Relation_Oirrefl(c_Relation_OId__on(c_Relation_OImage(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X3),X4),X4))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46181,f26964])).
% 156.17/20.10 fof(f46191,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (c_Relation_Oirrefl(c_Relation_OId__on(c_Relation_ORange(c_COMBK(X0,X1,X2),X3,X4),X5),X5)|hBOOL(X0))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46181,f38288])).
% 156.17/20.10 fof(f46192,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (c_Relation_Oirrefl(c_Relation_OId__on(c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X2),X3),X3))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46181,f36991])).
% 156.17/20.10 fof(f46199,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (~c_in(X0,c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X3),X4))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46187,f26563])).
% 156.17/20.10 fof(f46212,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X3),X4),X4))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46199,f1502])).
% 156.17/20.10 fof(f46220,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (~c_in(X0,c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X3),X4))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46192,f26563])).
% 156.17/20.10 fof(f46307,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (c_in(X0,c_Wellfounded_Oacc(c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X3),X4),X4))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46220,f1502])).
% 156.17/20.10 fof(f46310,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (~c_in(X0,c_Relation_ODomain(c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X3),X4,X5),X4))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46220,f1520])).
% 156.17/20.10 fof(f46316,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6]: (hBOOL(X0)|~c_in(X1,c_Relation_ODomain(c_COMBK(X0,X2,X3),X4,X5),X6))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46186,f26563])).
% 156.17/20.10 fof(f46329,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6]: (hBOOL(X0)|c_in(X1,c_Wellfounded_Oacc(c_Relation_ODomain(c_COMBK(X0,X2,X3),X4,X5),X6),X6))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46316,f1502])).
% 156.17/20.10 fof(f46337,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (~c_in(X0,c_Relation_OImage(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X3,X4),X5))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46189,f26563])).
% 156.17/20.10 fof(f46351,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (c_in(X0,c_Wellfounded_Oacc(c_Relation_OImage(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X3,X4),X5),X5))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46337,f1502])).
% 156.17/20.10 fof(f46360,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (~c_in(X0,c_Relation_OImage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X4),X5))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46190,f26563])).
% 156.17/20.10 fof(f46376,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (c_in(X0,c_Wellfounded_Oacc(c_Relation_OImage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X4),X5),X5))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46360,f1502])).
% 156.17/20.10 fof(f46384,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (~c_in(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X3,tc_bool)),X4))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f1225,f46360])).
% 156.17/20.10 fof(f46387,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6]: (hBOOL(X0)|~c_in(X1,c_Relation_ORange(c_COMBK(X0,X2,X3),X4,X5),X6))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46191,f26563])).
% 156.17/20.10 fof(f46400,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6]: (hBOOL(X0)|c_in(X1,c_Wellfounded_Oacc(c_Relation_ORange(c_COMBK(X0,X2,X3),X4,X5),X6),X6))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46387,f1502])).
% 156.17/20.10 fof(f47085,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (X0=X1|~c_in(c_Pair(X0,X1,X2,X2),c_Wellfounded_Oacc(c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X5),tc_prod(X2,X2)),tc_prod(X2,X2))|~c_Relation_Oantisym(c_Wellfounded_Oacc(c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X5),tc_prod(X2,X2)),X2))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46212,f1562])).
% 156.17/20.10 fof(f47086,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (X0=X1|~c_Relation_Oantisym(c_Wellfounded_Oacc(c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X4),tc_prod(X5,X5)),X5))),
% 156.17/20.10 inference(forward_subsumption_resolution,[status(thm)],[f47085,f46212])).
% 156.17/20.10 fof(f47110,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X2),X3),X4)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46212,f1666])).
% 156.17/20.10 fof(f47132,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (X0=X1|~c_in(c_Pair(X0,X1,X2,X2),c_Wellfounded_Oacc(c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X5),tc_prod(X2,X2)),tc_prod(X2,X2))|~c_Relation_Oantisym(c_Wellfounded_Oacc(c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X5),tc_prod(X2,X2)),X2))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46307,f1562])).
% 156.17/20.10 fof(f47133,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (X0=X1|~c_Relation_Oantisym(c_Wellfounded_Oacc(c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X4),tc_prod(X5,X5)),X5))),
% 156.17/20.10 inference(forward_subsumption_resolution,[status(thm)],[f47132,f46307])).
% 156.17/20.10 fof(f47157,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X2),X3),X4)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46307,f1666])).
% 156.17/20.10 fof(f47237,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (~hBOOL(hAPP(c_Relation_ODomain(c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X2),X3,X4),X5)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46310,f1664])).
% 156.17/20.10 fof(f47284,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6]: (hBOOL(X0)|hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_ODomain(c_COMBK(X0,X1,X2),X3,X4),X5),X6)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46329,f1666])).
% 156.17/20.10 fof(f47436,plain,(
% 156.17/20.10 spl0_144 <=> ~c_Nitpick_Orefl_H(c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X4),X5)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f47439,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (hBOOL(hAPP(X0,X1))|~c_Nitpick_Orefl_H(c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X4),X5))),
% 156.17/20.10 inference(resolution,[status(thm)],[f30446,f46307])).
% 156.17/20.10 fof(f47440,plain,(
% 156.17/20.10 spl0_75|spl0_144),
% 156.17/20.10 inference(split_clause,[status(thm)],[f47439,f37252,f47436])).
% 156.17/20.10 fof(f47441,plain,(
% 156.17/20.10 spl0_145 <=> ~c_Nitpick_Orefl_H(c_Relation_ODomain(c_COMBK(X2,X3,X4),X5,X6),X7)|hBOOL(X2)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f47444,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6,X7]: (hBOOL(hAPP(X0,X1))|~c_Nitpick_Orefl_H(c_Relation_ODomain(c_COMBK(X2,X3,X4),X5,X6),X7)|hBOOL(X2))),
% 156.17/20.10 inference(resolution,[status(thm)],[f30446,f46329])).
% 156.17/20.10 fof(f47445,plain,(
% 156.17/20.10 spl0_75|spl0_145),
% 156.17/20.10 inference(split_clause,[status(thm)],[f47444,f37252,f47441])).
% 156.17/20.10 fof(f47446,plain,(
% 156.17/20.10 spl0_146 <=> ~c_Nitpick_Orefl_H(c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X4),X5)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f47449,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (hBOOL(hAPP(X0,X1))|~c_Nitpick_Orefl_H(c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X4),X5))),
% 156.17/20.10 inference(resolution,[status(thm)],[f30446,f46212])).
% 156.17/20.10 fof(f47450,plain,(
% 156.17/20.10 spl0_75|spl0_146),
% 156.17/20.10 inference(split_clause,[status(thm)],[f47449,f37252,f47446])).
% 156.17/20.10 fof(f47456,plain,(
% 156.17/20.10 spl0_148 <=> ~c_Nitpick_Orefl_H(c_COMBK(X2,X3,X4),X5)|hBOOL(X2)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f47459,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (hBOOL(hAPP(X0,X1))|~c_Nitpick_Orefl_H(c_COMBK(X2,X3,X4),X5)|hBOOL(X2))),
% 156.17/20.10 inference(resolution,[status(thm)],[f30446,f30400])).
% 156.17/20.10 fof(f47460,plain,(
% 156.17/20.10 spl0_75|spl0_148),
% 156.17/20.10 inference(split_clause,[status(thm)],[f47459,f37252,f47456])).
% 156.17/20.10 fof(f47461,plain,(
% 156.17/20.10 spl0_149 <=> ~c_Nitpick_Orefl_H(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f47469,plain,(
% 156.17/20.10 spl0_150 <=> ~c_Nitpick_Orefl_H(c_Relation_OId__on(c_COMBK(X2,X3,X4),X5),X6)|hBOOL(X2)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f47472,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6]: (hBOOL(hAPP(X0,X1))|~c_Nitpick_Orefl_H(c_Relation_OId__on(c_COMBK(X2,X3,X4),X5),X6)|hBOOL(X2))),
% 156.17/20.10 inference(resolution,[status(thm)],[f30446,f30407])).
% 156.17/20.10 fof(f47473,plain,(
% 156.17/20.10 spl0_75|spl0_150),
% 156.17/20.10 inference(split_clause,[status(thm)],[f47472,f37252,f47469])).
% 156.17/20.10 fof(f47474,plain,(
% 156.17/20.10 spl0_151 <=> ~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3),X4)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f47477,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (hBOOL(hAPP(X0,X1))|~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3),X4))),
% 156.17/20.10 inference(resolution,[status(thm)],[f30446,f30408])).
% 156.17/20.10 fof(f47478,plain,(
% 156.17/20.10 spl0_75|spl0_151),
% 156.17/20.10 inference(split_clause,[status(thm)],[f47477,f37252,f47474])).
% 156.17/20.10 fof(f47481,plain,(
% 156.17/20.10 spl0_152 <=> ~c_Nitpick_Orefl_H(X2,X3)|~c_Wellfounded_Owf(X2,X3)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f47484,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (hBOOL(hAPP(X0,X1))|~c_Nitpick_Orefl_H(X2,X3)|~c_Wellfounded_Owf(X2,X3))),
% 156.17/20.10 inference(resolution,[status(thm)],[f30446,f1416])).
% 156.17/20.10 fof(f47485,plain,(
% 156.17/20.10 spl0_75|spl0_152),
% 156.17/20.10 inference(split_clause,[status(thm)],[f47484,f37252,f47481])).
% 156.17/20.10 fof(f47635,plain,(
% 156.17/20.10 spl0_153 <=> 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))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f47636,plain,(
% 156.17/20.10 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))|~spl0_153),
% 156.17/20.10 inference(component_clause,[status(thm)],[f47635])).
% 156.17/20.10 fof(f47638,plain,(
% 156.17/20.10 spl0_154 <=> c_Relation_Osym(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f47641,plain,(
% 156.17/20.10 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_Osym(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_1),
% 156.17/20.10 inference(resolution,[status(thm)],[f1724,f1582])).
% 156.17/20.10 fof(f47642,plain,(
% 156.17/20.10 spl0_153|~spl0_154|~spl0_1),
% 156.17/20.10 inference(split_clause,[status(thm)],[f47641,f47635,f47638,f1723])).
% 156.17/20.10 fof(f47645,plain,(
% 156.17/20.10 spl0_155 <=> c_Relation_Oantisym(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f47648,plain,(
% 156.17/20.10 v_b____=v_a____|~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)|~spl0_1),
% 156.17/20.10 inference(resolution,[status(thm)],[f1724,f1562])).
% 156.17/20.10 fof(f47649,plain,(
% 156.17/20.10 spl0_110|~spl0_153|~spl0_155|~spl0_1),
% 156.17/20.10 inference(split_clause,[status(thm)],[f47648,f42998,f47635,f47645,f1723])).
% 156.17/20.10 fof(f47650,plain,(
% 156.17/20.10 spl0_156 <=> c_Wellfounded_Owf(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f47655,plain,(
% 156.17/20.10 spl0_157 <=> 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))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f47656,plain,(
% 156.17/20.10 ![X0]: (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))|~spl0_157)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f47655])).
% 156.17/20.10 fof(f47658,plain,(
% 156.17/20.10 spl0_158 <=> c_Relation_Otrans(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f47661,plain,(
% 156.17/20.10 ![X0]: (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))|~c_Relation_Otrans(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_1)),
% 156.17/20.10 inference(resolution,[status(thm)],[f1724,f1538])).
% 156.17/20.10 fof(f47662,plain,(
% 156.17/20.10 spl0_157|~spl0_158|~spl0_1),
% 156.17/20.10 inference(split_clause,[status(thm)],[f47661,f47655,f47658,f1723])).
% 156.17/20.10 fof(f47663,plain,(
% 156.17/20.10 spl0_159 <=> 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))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f47664,plain,(
% 156.17/20.10 ![X0]: (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))|~spl0_159)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f47663])).
% 156.17/20.10 fof(f47666,plain,(
% 156.17/20.10 ![X0]: (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))|~c_Relation_Otrans(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_1)),
% 156.17/20.10 inference(resolution,[status(thm)],[f1724,f1538])).
% 156.17/20.10 fof(f47667,plain,(
% 156.17/20.10 spl0_159|~spl0_158|~spl0_1),
% 156.17/20.10 inference(split_clause,[status(thm)],[f47666,f47663,f47658,f1723])).
% 156.17/20.10 fof(f47690,plain,(
% 156.17/20.10 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_Osym(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_153),
% 156.17/20.10 inference(resolution,[status(thm)],[f47636,f1582])).
% 156.17/20.10 fof(f47691,plain,(
% 156.17/20.10 spl0_1|~spl0_154|~spl0_153),
% 156.17/20.10 inference(split_clause,[status(thm)],[f47690,f1723,f47638,f47635])).
% 156.17/20.10 fof(f47697,plain,(
% 156.17/20.10 spl0_160 <=> 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))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f47698,plain,(
% 156.17/20.10 ![X0]: (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))|~spl0_160)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f47697])).
% 156.17/20.10 fof(f47700,plain,(
% 156.17/20.10 ![X0]: (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))|~c_Relation_Otrans(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_153)),
% 156.17/20.10 inference(resolution,[status(thm)],[f47636,f1538])).
% 156.17/20.10 fof(f47701,plain,(
% 156.17/20.10 spl0_160|~spl0_158|~spl0_153),
% 156.17/20.10 inference(split_clause,[status(thm)],[f47700,f47697,f47658,f47635])).
% 156.17/20.10 fof(f47702,plain,(
% 156.17/20.10 spl0_161 <=> 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))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f47703,plain,(
% 156.17/20.10 ![X0]: (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))|~spl0_161)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f47702])).
% 156.17/20.10 fof(f47705,plain,(
% 156.17/20.10 ![X0]: (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))|~c_Relation_Otrans(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_153)),
% 156.17/20.10 inference(resolution,[status(thm)],[f47636,f1538])).
% 156.17/20.10 fof(f47706,plain,(
% 156.17/20.10 spl0_161|~spl0_158|~spl0_153),
% 156.17/20.10 inference(split_clause,[status(thm)],[f47705,f47702,f47658,f47635])).
% 156.17/20.10 fof(f47707,plain,(
% 156.17/20.10 spl0_162 <=> X0=v_a____|~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))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f47708,plain,(
% 156.17/20.10 ![X0]: (X0=v_a____|~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))|~spl0_162)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f47707])).
% 156.17/20.10 fof(f47757,plain,(
% 156.17/20.10 ![X0,X1,X2]: (hAPP(hAPP(X0,v_b_H____),v_a____)=hAPP(hAPP(X0,v_b____),v_b____)|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,X1),v_F(v_P____),X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2)|~c_Relation_Osym(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_1)),
% 156.17/20.10 inference(resolution,[status(thm)],[f39175,f44893])).
% 156.17/20.10 fof(f47765,plain,(
% 156.17/20.10 ![X0,X1,X2]: (hAPP(hAPP(X0,v_b____),v_a____)=hAPP(hAPP(X0,v_b_H____),v_b____)|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,X1),v_F(v_P____),X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_1)),
% 156.17/20.10 inference(resolution,[status(thm)],[f39175,f1741])).
% 156.17/20.10 fof(f47929,plain,(
% 156.17/20.10 spl0_163 <=> ~c_Nitpick_Orefl_H(c_Relation_OImage(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X4,X5),X6)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f47932,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6]: (hBOOL(hAPP(X0,X1))|~c_Nitpick_Orefl_H(c_Relation_OImage(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X4,X5),X6))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46351,f30446])).
% 156.17/20.10 fof(f47933,plain,(
% 156.17/20.10 spl0_75|spl0_163),
% 156.17/20.10 inference(split_clause,[status(thm)],[f47932,f37252,f47929])).
% 156.17/20.10 fof(f47936,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OImage(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X2,X3),X4),X5)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46351,f1666])).
% 156.17/20.10 fof(f47979,plain,(
% 156.17/20.10 spl0_164 <=> ~c_Nitpick_Orefl_H(c_Relation_OImage(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X5),X6)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f47982,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6]: (hBOOL(hAPP(X0,X1))|~c_Nitpick_Orefl_H(c_Relation_OImage(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X5),X6))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46376,f30446])).
% 156.17/20.10 fof(f47983,plain,(
% 156.17/20.10 spl0_75|spl0_164),
% 156.17/20.10 inference(split_clause,[status(thm)],[f47982,f37252,f47979])).
% 156.17/20.10 fof(f47986,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OImage(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X3),X4),X5)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46376,f1666])).
% 156.17/20.10 fof(f47987,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (c_in(X0,c_Wellfounded_Oacc(c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X3,tc_bool)),X4),X4))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f1225,f46376])).
% 156.17/20.10 fof(f48113,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (~c_in(X0,c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X3,tc_bool)),X4))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f752,f46384])).
% 156.17/20.10 fof(f48157,plain,(
% 156.17/20.10 spl0_165 <=> hBOOL(X0)|~c_Nitpick_Orefl_H(c_Relation_ORange(c_COMBK(X0,X3,X4),X5,X6),X7)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f48160,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6,X7]: (hBOOL(X0)|hBOOL(hAPP(X1,X2))|~c_Nitpick_Orefl_H(c_Relation_ORange(c_COMBK(X0,X3,X4),X5,X6),X7))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46400,f30446])).
% 156.17/20.10 fof(f48161,plain,(
% 156.17/20.10 spl0_165|spl0_75),
% 156.17/20.10 inference(split_clause,[status(thm)],[f48160,f48157,f37252])).
% 156.17/20.10 fof(f48164,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6]: (hBOOL(X0)|hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_ORange(c_COMBK(X0,X1,X2),X3,X4),X5),X6)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f46400,f1666])).
% 156.17/20.10 fof(f48418,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6]: (hBOOL(X0)|c_Relation_Oirrefl(c_Relation_OId__on(c_Relation_OImage(X1,c_COMBK(X0,X2,X3),X4,X5),X6),X6))),
% 156.17/20.10 inference(resolution,[status(thm)],[f26984,f46181])).
% 156.17/20.10 fof(f49073,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (c_in(X0,c_Wellfounded_Oacc(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X3,tc_bool)),X4),X4))),
% 156.17/20.10 inference(resolution,[status(thm)],[f48113,f1502])).
% 156.17/20.10 fof(f49080,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (~hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,tc_fun(X2,tc_bool)),X3)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f48113,f1664])).
% 156.17/20.10 fof(f49089,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (~c_in(X0,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X3,tc_bool)),X4))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f713,f48113])).
% 156.17/20.10 fof(f49182,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6,X7]: (hBOOL(X0)|~c_in(X1,c_Relation_OImage(X2,c_COMBK(X0,X3,X4),X5,X6),X7))),
% 156.17/20.10 inference(resolution,[status(thm)],[f48418,f26563])).
% 156.17/20.10 fof(f49183,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5]: (hBOOL(X0)|c_Relation_Oirrefl(c_Relation_OId__on(c_Lattices_Olower__semilattice__class_Oinf(X1,c_COMBK(X0,X2,X3),tc_fun(X4,tc_bool)),X5),X5))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f1225,f48418])).
% 156.17/20.10 fof(f49197,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6,X7]: (hBOOL(X0)|c_in(X1,c_Wellfounded_Oacc(c_Relation_OImage(X2,c_COMBK(X0,X3,X4),X5,X6),X7),X7))),
% 156.17/20.10 inference(resolution,[status(thm)],[f49182,f1502])).
% 156.17/20.10 fof(f49205,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6]: (hBOOL(X0)|~c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,c_COMBK(X0,X3,X4),tc_fun(X5,tc_bool)),X6))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f1225,f49182])).
% 156.17/20.10 fof(f49219,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (c_in(X0,c_Wellfounded_Oacc(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X3,tc_bool)),X4),X4))),
% 156.17/20.10 inference(resolution,[status(thm)],[f49089,f1502])).
% 156.17/20.10 fof(f49384,plain,(
% 156.17/20.10 spl0_175 <=> v_b____=v_b____),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f49387,plain,(
% 156.17/20.10 spl0_176 <=> ~c_Relation_Osingle__valued(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,X0),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~hBOOL(hAPP(hAPP(v_P_H____,X0),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f49390,plain,(
% 156.17/20.10 ![X0]: (v_b____=v_b____|~c_Relation_Osingle__valued(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,X0),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~hBOOL(hAPP(hAPP(v_P_H____,X0),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))),
% 156.17/20.10 inference(resolution,[status(thm)],[f39704,f1874])).
% 156.17/20.10 fof(f49391,plain,(
% 156.17/20.10 spl0_175|spl0_176),
% 156.17/20.10 inference(split_clause,[status(thm)],[f49390,f49384,f49387])).
% 156.17/20.10 fof(f49392,plain,(
% 156.17/20.10 spl0_177 <=> ~c_Relation_Osingle__valued(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,X0),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~c_FunDef_Oin__rel(hAPP(v_P_H____,X0),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f49395,plain,(
% 156.17/20.10 ![X0]: (v_b____=v_b____|~c_Relation_Osingle__valued(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,X0),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~c_FunDef_Oin__rel(hAPP(v_P_H____,X0),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 inference(resolution,[status(thm)],[f39704,f12914])).
% 156.17/20.10 fof(f49396,plain,(
% 156.17/20.10 spl0_175|spl0_177),
% 156.17/20.10 inference(split_clause,[status(thm)],[f49395,f49384,f49392])).
% 156.17/20.10 fof(f49400,plain,(
% 156.17/20.10 spl0_178 <=> ~c_Relation_Osingle__valued(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,X0),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~c_Nitpick_Orefl_H(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f49403,plain,(
% 156.17/20.10 ![X0]: (v_a____=v_b____|~c_Relation_Osingle__valued(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,X0),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~c_Nitpick_Orefl_H(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 inference(resolution,[status(thm)],[f39704,f1574])).
% 156.17/20.10 fof(f49404,plain,(
% 156.17/20.10 spl0_110|spl0_178),
% 156.17/20.10 inference(split_clause,[status(thm)],[f49403,f42998,f49400])).
% 156.17/20.10 fof(f49439,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (~hBOOL(hAPP(c_Relation_OId__on(c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X2),X3),X4)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f12304,f46199])).
% 156.17/20.10 fof(f49457,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (~hBOOL(hAPP(c_Relation_OId__on(c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X2),X3),X4)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f12304,f46220])).
% 156.17/20.10 fof(f49529,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (c_Relation_Oirrefl(c_Relation_OId__on(c_Relation_OId__on(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1),X2),X3),X3))),
% 156.17/20.10 inference(resolution,[status(thm)],[f12457,f46181])).
% 156.17/20.10 fof(f49598,plain,(
% 156.17/20.10 ![X0]: (c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(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)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1617,f1741])).
% 156.17/20.10 fof(f49599,plain,(
% 156.17/20.10 spl0_179 <=> c_in(v_a____,c_Wellfounded_Oacc(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f49600,plain,(
% 156.17/20.10 c_in(v_a____,c_Wellfounded_Oacc(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_179),
% 156.17/20.10 inference(component_clause,[status(thm)],[f49599])).
% 156.17/20.10 fof(f49602,plain,(
% 156.17/20.10 spl0_180 <=> c_in(v_b____,c_Wellfounded_Oacc(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f49604,plain,(
% 156.17/20.10 ~c_in(v_b____,c_Wellfounded_Oacc(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|spl0_180),
% 156.17/20.10 inference(component_clause,[status(thm)],[f49602])).
% 156.17/20.10 fof(f49605,plain,(
% 156.17/20.10 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)|~spl0_1),
% 156.17/20.10 inference(resolution,[status(thm)],[f1617,f1724])).
% 156.17/20.10 fof(f49606,plain,(
% 156.17/20.10 spl0_179|~spl0_180|~spl0_1),
% 156.17/20.10 inference(split_clause,[status(thm)],[f49605,f49599,f49602,f1723])).
% 156.17/20.10 fof(f49666,plain,(
% 156.17/20.10 ~hBOOL(hAPP(c_Wellfounded_Oacc(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt),v_b____))|spl0_180),
% 156.17/20.10 inference(resolution,[status(thm)],[f49604,f1664])).
% 156.17/20.10 fof(f49923,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (c_Relation_Oirrefl(c_Relation_OId__on(c_Relation_OId__on(c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X2),X3),X4),X4))),
% 156.17/20.10 inference(resolution,[status(thm)],[f49439,f46181])).
% 156.17/20.10 fof(f49928,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (c_Relation_Oirrefl(c_Relation_OId__on(c_Relation_OId__on(c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X2),X3),X4),X4))),
% 156.17/20.10 inference(resolution,[status(thm)],[f49457,f46181])).
% 156.17/20.10 fof(f49930,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (~c_in(X0,c_Relation_OId__on(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2),X3),X4))),
% 156.17/20.10 inference(resolution,[status(thm)],[f49529,f26563])).
% 156.17/20.10 fof(f49947,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4]: (c_in(X0,c_Wellfounded_Oacc(c_Relation_OId__on(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2),X3),X4),X4))),
% 156.17/20.10 inference(resolution,[status(thm)],[f49930,f1502])).
% 156.17/20.10 fof(f50070,plain,(
% 156.17/20.10 spl0_184 <=> ~c_Relation_Osingle__valued(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,X0),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,X0),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f50073,plain,(
% 156.17/20.10 ![X0]: (v_b____=v_b____|~c_Relation_Osingle__valued(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,X0),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,X0),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 inference(resolution,[status(thm)],[f39705,f12914])).
% 156.17/20.10 fof(f50074,plain,(
% 156.17/20.10 spl0_175|spl0_184),
% 156.17/20.10 inference(split_clause,[status(thm)],[f50073,f49384,f50070])).
% 156.17/20.10 fof(f50078,plain,(
% 156.17/20.10 spl0_185 <=> ~c_Relation_Osingle__valued(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,X0),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_Nitpick_Orefl_H(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f50081,plain,(
% 156.17/20.10 ![X0]: (v_a____=v_b____|~c_Relation_Osingle__valued(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,X0),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_Nitpick_Orefl_H(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 inference(resolution,[status(thm)],[f39705,f1574])).
% 156.17/20.10 fof(f50082,plain,(
% 156.17/20.10 spl0_110|spl0_185),
% 156.17/20.10 inference(split_clause,[status(thm)],[f50081,f42998,f50078])).
% 156.17/20.10 fof(f50152,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(v_b_H____,c_Relation_OImage(hAPP(v_P_H____,X0),X1,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)|~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)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1621,f1741])).
% 156.17/20.10 fof(f50153,plain,(
% 156.17/20.10 ![X0]: (c_in(v_b____,c_Relation_OImage(v_F(v_P____),X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~spl0_1)),
% 156.17/20.10 inference(resolution,[status(thm)],[f1621,f1724])).
% 156.17/20.10 fof(f50225,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1628,f1741])).
% 156.17/20.10 fof(f50246,plain,(
% 156.17/20.10 ![X0,X1,X2]: (c_in(X0,X1,X2)|~c_Equiv__Relations_Oequiv(X1,c_Relation_OId(X2),X2))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1628,f1591])).
% 156.17/20.10 fof(f50289,plain,(
% 156.17/20.10 spl0_186 <=> c_in(v_b____,c_Relation_ODomain(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f50292,plain,(
% 156.17/20.10 spl0_187 <=> ~c_Equiv__Relations_Oequiv(X0,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f50301,plain,(
% 156.17/20.10 spl0_188 <=> c_in(v_b____,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f50302,plain,(
% 156.17/20.10 c_in(v_b____,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_188),
% 156.17/20.10 inference(component_clause,[status(thm)],[f50301])).
% 156.17/20.10 fof(f50304,plain,(
% 156.17/20.10 spl0_189 <=> c_in(v_a____,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f50307,plain,(
% 156.17/20.10 c_in(v_b____,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_1),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f825,f50153])).
% 156.17/20.10 fof(f50308,plain,(
% 156.17/20.10 spl0_188|~spl0_189|~spl0_1),
% 156.17/20.10 inference(split_clause,[status(thm)],[f50307,f50301,f50304,f1723])).
% 156.17/20.10 fof(f50311,plain,(
% 156.17/20.10 spl0_190 <=> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_b____))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f50312,plain,(
% 156.17/20.10 hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_b____))|~spl0_190),
% 156.17/20.10 inference(component_clause,[status(thm)],[f50311])).
% 156.17/20.10 fof(f50488,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(X0,c_Relation_ODomain(c_Relation_OId(X1),X1,X1),X1))),
% 156.17/20.10 inference(resolution,[status(thm)],[f50246,f24154])).
% 156.17/20.10 fof(f50504,plain,(
% 156.17/20.10 spl0_194 <=> hBOOL(hAPP(X0,X1))|~c_in(X1,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_OId(tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f50505,plain,(
% 156.17/20.10 ![X0,X1]: (hBOOL(hAPP(X0,X1))|~c_in(X1,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_OId(tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a)|~spl0_194)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f50504])).
% 156.17/20.10 fof(f50507,plain,(
% 156.17/20.10 spl0_195 <=> c_in(X2,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_OId(tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f50508,plain,(
% 156.17/20.10 ![X0]: (c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_OId(tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a)|~spl0_195)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f50507])).
% 156.17/20.10 fof(f50510,plain,(
% 156.17/20.10 ![X0,X1,X2]: (hBOOL(hAPP(X0,X1))|c_in(X2,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_OId(tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a)|~c_in(X1,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_OId(tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a))),
% 156.17/20.10 inference(resolution,[status(thm)],[f50488,f1515])).
% 156.17/20.10 fof(f50511,plain,(
% 156.17/20.10 spl0_194|spl0_195),
% 156.17/20.10 inference(split_clause,[status(thm)],[f50510,f50504,f50507])).
% 156.17/20.10 fof(f50552,plain,(
% 156.17/20.10 ![X0,X1]: (hBOOL(hAPP(c_Relation_ODomain(c_Relation_OId(X0),X0,X0),X1)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f50488,f1666])).
% 156.17/20.10 fof(f50561,plain,(
% 156.17/20.10 ![X0,X1]: (~c_Wellfounded_Owf(c_Relation_ODomain(c_Relation_OId(X0),X0,X0),X1))),
% 156.17/20.10 inference(resolution,[status(thm)],[f50552,f8814])).
% 156.17/20.10 fof(f50612,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1630,f1741])).
% 156.17/20.10 fof(f50680,plain,(
% 156.17/20.10 ![X0,X1,X2]: (c_in(X0,c_Relation_ORange(X1,X2,X2),X2)|c_in(X0,c_Wellfounded_Oacc(X1,X2),X2))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1632,f1502])).
% 156.17/20.10 fof(f50683,plain,(
% 156.17/20.10 ![X0]: (c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_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)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1632,f1741])).
% 156.17/20.10 fof(f50704,plain,(
% 156.17/20.10 ![X0,X1,X2]: (c_in(X0,c_Relation_ORange(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1632,f1557])).
% 156.17/20.10 fof(f50718,plain,(
% 156.17/20.10 ![X0,X1,X2]: (c_in(X0,c_Relation_ORange(X1,X2,X2),X2)|~c_Nitpick_Orefl_H(X1,X2))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1632,f1574])).
% 156.17/20.10 fof(f50758,plain,(
% 156.17/20.10 spl0_196 <=> 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)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f50760,plain,(
% 156.17/20.10 ~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)|spl0_196),
% 156.17/20.10 inference(component_clause,[status(thm)],[f50758])).
% 156.17/20.10 fof(f51053,plain,(
% 156.17/20.10 spl0_200 <=> hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(c_Relation_OId__on(c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_OId(tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a),t_a)))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f51054,plain,(
% 156.17/20.10 ![X0]: (hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(c_Relation_OId__on(c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_OId(tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a),t_a)))|~spl0_200)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f51053])).
% 156.17/20.10 fof(f51056,plain,(
% 156.17/20.10 spl0_201 <=> c_Relation_Oirrefl(c_Relation_OId__on(c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_OId(tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a),t_a)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f51059,plain,(
% 156.17/20.10 ![X0]: (hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(c_Relation_OId__on(c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_OId(tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a),t_a)))|c_Relation_Oirrefl(c_Relation_OId__on(c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_OId(tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a),t_a)|~spl0_194)),
% 156.17/20.10 inference(resolution,[status(thm)],[f50505,f29434])).
% 156.17/20.10 fof(f51060,plain,(
% 156.17/20.10 spl0_200|spl0_201|~spl0_194),
% 156.17/20.10 inference(split_clause,[status(thm)],[f51059,f51053,f51056,f50504])).
% 156.17/20.10 fof(f51062,plain,(
% 156.17/20.10 spl0_202 <=> c_Wellfounded_Owf(c_Relation_ODomain(c_Relation_OId(tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f51065,plain,(
% 156.17/20.10 ![X0,X1]: (hBOOL(hAPP(X0,X1))|~c_Wellfounded_Owf(c_Relation_ODomain(c_Relation_OId(tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a)|~spl0_194)),
% 156.17/20.10 inference(resolution,[status(thm)],[f50505,f1416])).
% 156.17/20.10 fof(f51066,plain,(
% 156.17/20.10 spl0_75|~spl0_202|~spl0_194),
% 156.17/20.10 inference(split_clause,[status(thm)],[f51065,f37252,f51062,f50504])).
% 156.17/20.10 fof(f51191,plain,(
% 156.17/20.10 ~class_Lattices_Olattice(tc_bool)|~spl0_9),
% 156.17/20.10 inference(resolution,[status(thm)],[f1798,f1690])).
% 156.17/20.10 fof(f51192,plain,(
% 156.17/20.10 $false|~spl0_9),
% 156.17/20.10 inference(forward_subsumption_resolution,[status(thm)],[f51191,f1713])).
% 156.17/20.10 fof(f51193,plain,(
% 156.17/20.10 ~spl0_9),
% 156.17/20.10 inference(contradiction_clause,[status(thm)],[f51192])).
% 156.17/20.10 fof(f51255,plain,(
% 156.17/20.10 ![X0,X1]: (c_Nitpick_Orefl_H(c_Relation_OId__on(c_Relation_ORange(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X1),X1))),
% 156.17/20.10 inference(resolution,[status(thm)],[f50704,f30027])).
% 156.17/20.10 fof(f51303,plain,(
% 156.17/20.10 ![X0,X1,X2]: (hBOOL(hAPP(c_Relation_ORange(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f50704,f1666])).
% 156.17/20.10 fof(f51304,plain,(
% 156.17/20.10 ![X0,X1,X2]: (c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f2594,f50704])).
% 156.17/20.10 fof(f51372,plain,(
% 156.17/20.10 ![X0,X1,X2]: (hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f51304,f1666])).
% 156.17/20.10 fof(f51456,plain,(
% 156.17/20.10 ![X0,X1,X2]: (~c_Nitpick_Orefl_H(X0,X1)|hBOOL(hAPP(c_Relation_ORange(X0,X1,X1),X2)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f50718,f1666])).
% 156.17/20.10 fof(f51460,plain,(
% 156.17/20.10 ![X0,X1,X2]: (c_in(X0,c_Relation_ODomain(X1,X2,X2),X2)|~c_Nitpick_Orefl_H(c_Relation_Oconverse(X1,X2,X2),X2))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f1468,f50718])).
% 156.17/20.10 fof(f51461,plain,(
% 156.17/20.10 ![X0,X1,X2]: (c_in(X0,c_Relation_ORange(X1,X2,X2),X2)|~c_Nitpick_Orefl_H(c_Transitive__Closure_Otrancl(X1,X2),X2))),
% 156.17/20.10 inference(paramodulation,[status(thm)],[f1444,f50718])).
% 156.17/20.10 fof(f51580,plain,(
% 156.17/20.10 ![X0]: (c_in(v_b____,c_Relation_ODomain(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1636,f1741])).
% 156.17/20.10 fof(f51612,plain,(
% 156.17/20.10 ![X0,X1,X2]: (c_in(X0,c_Relation_ODomain(X1,X2,X2),X2)|~c_Nitpick_Orefl_H(X1,X2))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1636,f1574])).
% 156.17/20.10 fof(f51886,plain,(
% 156.17/20.10 $false|~spl0_200),
% 156.17/20.10 inference(resolution,[status(thm)],[f51054,f47237])).
% 156.17/20.10 fof(f51887,plain,(
% 156.17/20.10 ~spl0_200),
% 156.17/20.10 inference(contradiction_clause,[status(thm)],[f51886])).
% 156.17/20.10 fof(f51889,plain,(
% 156.17/20.10 c_Wellfounded_Owf(c_Relation_ODomain(c_Relation_OId(tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a)|~spl0_195),
% 156.17/20.10 inference(resolution,[status(thm)],[f50508,f1268])).
% 156.17/20.10 fof(f51890,plain,(
% 156.17/20.10 $false|~spl0_195),
% 156.17/20.10 inference(forward_subsumption_resolution,[status(thm)],[f51889,f50561])).
% 156.17/20.10 fof(f51891,plain,(
% 156.17/20.10 ~spl0_195),
% 156.17/20.10 inference(contradiction_clause,[status(thm)],[f51890])).
% 156.17/20.10 fof(f51909,plain,(
% 156.17/20.10 spl0_211 <=> X0=X1),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f51910,plain,(
% 156.17/20.10 ![X0,X1]: (X0=X1|~spl0_211)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f51909])).
% 156.17/20.10 fof(f51939,plain,(
% 156.17/20.10 $false|~spl0_211),
% 156.17/20.10 inference(backward_subsumption_resolution,[status(thm)],[f13383,f51910])).
% 156.17/20.10 fof(f51940,plain,(
% 156.17/20.10 ~spl0_211),
% 156.17/20.10 inference(contradiction_clause,[status(thm)],[f51939])).
% 156.17/20.10 fof(f52650,plain,(
% 156.17/20.10 spl0_214 <=> 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(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f52653,plain,(
% 156.17/20.10 ![X0,X1]: (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))|v_b_H____=v_b____|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_109)),
% 156.17/20.10 inference(resolution,[status(thm)],[f1644,f42994])).
% 156.17/20.10 fof(f52654,plain,(
% 156.17/20.10 spl0_214|spl0_97|~spl0_109),
% 156.17/20.10 inference(split_clause,[status(thm)],[f52653,f52650,f41290,f42993])).
% 156.17/20.10 fof(f52655,plain,(
% 156.17/20.10 spl0_215 <=> 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(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f52658,plain,(
% 156.17/20.10 ![X0,X1]: (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))|v_b_H____=v_b____|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1644,f42388])).
% 156.17/20.10 fof(f52659,plain,(
% 156.17/20.10 spl0_215|spl0_97),
% 156.17/20.10 inference(split_clause,[status(thm)],[f52658,f52655,f41290])).
% 156.17/20.10 fof(f52661,plain,(
% 156.17/20.10 spl0_216 <=> c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|hAPP(hAPP(X2,v_b____),v_b____)=hAPP(hAPP(X2,v_b_H____),v_b_H____)|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,X0),hAPP(v_P_H____,X0),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f52662,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|hAPP(hAPP(X2,v_b____),v_b____)=hAPP(hAPP(X2,v_b_H____),v_b_H____)|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,X0),hAPP(v_P_H____,X0),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3)|~spl0_216)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f52661])).
% 156.17/20.10 fof(f52664,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=v_b____|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|hAPP(hAPP(X2,v_b____),v_b____)=hAPP(hAPP(X2,v_b_H____),v_b_H____)|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,X0),hAPP(v_P_H____,X0),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1644,f39168])).
% 156.17/20.10 fof(f52665,plain,(
% 156.17/20.10 spl0_216|spl0_110),
% 156.17/20.10 inference(split_clause,[status(thm)],[f52664,f52661,f42998])).
% 156.17/20.10 fof(f52666,plain,(
% 156.17/20.10 spl0_217 <=> c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b____,c_Relation_ODomain(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f52667,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b____,c_Relation_ODomain(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_217)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f52666])).
% 156.17/20.10 fof(f52669,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=v_b____|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b____,c_Relation_ODomain(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1644,f51580])).
% 156.17/20.10 fof(f52670,plain,(
% 156.17/20.10 spl0_217|spl0_110),
% 156.17/20.10 inference(split_clause,[status(thm)],[f52669,f52666,f42998])).
% 156.17/20.10 fof(f52671,plain,(
% 156.17/20.10 spl0_218 <=> c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f52672,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_218)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f52671])).
% 156.17/20.10 fof(f52674,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=v_b____|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1644,f50683])).
% 156.17/20.10 fof(f52675,plain,(
% 156.17/20.10 spl0_218|spl0_110),
% 156.17/20.10 inference(split_clause,[status(thm)],[f52674,f52671,f42998])).
% 156.17/20.10 fof(f52676,plain,(
% 156.17/20.10 spl0_219 <=> c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X2,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f52677,plain,(
% 156.17/20.10 ![X0,X1,X2]: (c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X2,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_219)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f52676])).
% 156.17/20.10 fof(f52679,plain,(
% 156.17/20.10 ![X0,X1,X2]: (c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=v_b____|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X2,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1644,f50612])).
% 156.17/20.10 fof(f52680,plain,(
% 156.17/20.10 spl0_219|spl0_110),
% 156.17/20.10 inference(split_clause,[status(thm)],[f52679,f52676,f42998])).
% 156.17/20.10 fof(f52681,plain,(
% 156.17/20.10 spl0_220 <=> c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X2,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f52682,plain,(
% 156.17/20.10 ![X0,X1,X2]: (c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X2,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_220)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f52681])).
% 156.17/20.10 fof(f52684,plain,(
% 156.17/20.10 ![X0,X1,X2]: (c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=v_b____|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X2,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1644,f50225])).
% 156.17/20.10 fof(f52685,plain,(
% 156.17/20.10 spl0_220|spl0_110),
% 156.17/20.10 inference(split_clause,[status(thm)],[f52684,f52681,f42998])).
% 156.17/20.10 fof(f52686,plain,(
% 156.17/20.10 spl0_221 <=> c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b_H____,c_Relation_OImage(hAPP(v_P_H____,X0),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f52687,plain,(
% 156.17/20.10 ![X0,X1,X2]: (c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b_H____,c_Relation_OImage(hAPP(v_P_H____,X0),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~spl0_221)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f52686])).
% 156.17/20.10 fof(f52689,plain,(
% 156.17/20.10 ![X0,X1,X2]: (c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=v_b____|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b_H____,c_Relation_OImage(hAPP(v_P_H____,X0),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1644,f50152])).
% 156.17/20.10 fof(f52690,plain,(
% 156.17/20.10 spl0_221|spl0_110),
% 156.17/20.10 inference(split_clause,[status(thm)],[f52689,f52686,f42998])).
% 156.17/20.10 fof(f52691,plain,(
% 156.17/20.10 spl0_222 <=> c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f52692,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_222)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f52691])).
% 156.17/20.10 fof(f52694,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=v_b____|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1644,f49598])).
% 156.17/20.10 fof(f52695,plain,(
% 156.17/20.10 spl0_222|spl0_110),
% 156.17/20.10 inference(split_clause,[status(thm)],[f52694,f52691,f42998])).
% 156.17/20.10 fof(f52696,plain,(
% 156.17/20.10 spl0_223 <=> c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,X0),c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f52699,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=v_b____|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,X0),c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_109)),
% 156.17/20.10 inference(resolution,[status(thm)],[f1644,f43137])).
% 156.17/20.10 fof(f52700,plain,(
% 156.17/20.10 spl0_223|spl0_110|~spl0_109),
% 156.17/20.10 inference(split_clause,[status(thm)],[f52699,f52696,f42998,f42993])).
% 156.17/20.10 fof(f52701,plain,(
% 156.17/20.10 spl0_224 <=> c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f52704,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=v_b____|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_109)),
% 156.17/20.10 inference(resolution,[status(thm)],[f1644,f45370])).
% 156.17/20.10 fof(f52705,plain,(
% 156.17/20.10 spl0_224|spl0_110|~spl0_109),
% 156.17/20.10 inference(split_clause,[status(thm)],[f52704,f52701,f42998,f42993])).
% 156.17/20.10 fof(f52706,plain,(
% 156.17/20.10 spl0_225 <=> c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_Nitpick_Orefl_H(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Osingle__valued(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f52709,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=v_b____|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_Nitpick_Orefl_H(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Osingle__valued(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~spl0_96)),
% 156.17/20.10 inference(resolution,[status(thm)],[f1644,f41288])).
% 156.17/20.10 fof(f52710,plain,(
% 156.17/20.10 spl0_225|spl0_110|~spl0_96),
% 156.17/20.10 inference(split_clause,[status(thm)],[f52709,f52706,f42998,f41287])).
% 156.17/20.10 fof(f52711,plain,(
% 156.17/20.10 spl0_226 <=> c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,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(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f52712,plain,(
% 156.17/20.10 ![X0,X1,X2]: (c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,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(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_226)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f52711])).
% 156.17/20.10 fof(f52714,plain,(
% 156.17/20.10 ![X0,X1,X2]: (c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=v_b____|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,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(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1644,f40300])).
% 156.17/20.10 fof(f52715,plain,(
% 156.17/20.10 spl0_226|spl0_110),
% 156.17/20.10 inference(split_clause,[status(thm)],[f52714,f52711,f42998])).
% 156.17/20.10 fof(f52716,plain,(
% 156.17/20.10 spl0_227 <=> c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(c_Transitive__Closure_Otrancl(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f52719,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=v_b____|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(c_Transitive__Closure_Otrancl(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1644,f5652])).
% 156.17/20.10 fof(f52720,plain,(
% 156.17/20.10 spl0_227|spl0_110),
% 156.17/20.10 inference(split_clause,[status(thm)],[f52719,f52716,f42998])).
% 156.17/20.10 fof(f52721,plain,(
% 156.17/20.10 spl0_228 <=> c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(c_Transitive__Closure_Ortrancl(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f52724,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=v_b____|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(c_Transitive__Closure_Ortrancl(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1644,f5567])).
% 156.17/20.10 fof(f52725,plain,(
% 156.17/20.10 spl0_228|spl0_110),
% 156.17/20.10 inference(split_clause,[status(thm)],[f52724,f52721,f42998])).
% 156.17/20.10 fof(f52726,plain,(
% 156.17/20.10 spl0_229 <=> c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(hAPP(v_P_H____,X0),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f52727,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(hAPP(v_P_H____,X0),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_229)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f52726])).
% 156.17/20.10 fof(f52729,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=v_b____|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(hAPP(v_P_H____,X0),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1644,f1878])).
% 156.17/20.10 fof(f52730,plain,(
% 156.17/20.10 spl0_229|spl0_110),
% 156.17/20.10 inference(split_clause,[status(thm)],[f52729,f52726,f42998])).
% 156.17/20.10 fof(f52731,plain,(
% 156.17/20.10 spl0_230 <=> c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|c_FunDef_Oin__rel(hAPP(v_P_H____,X0),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f52732,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|c_FunDef_Oin__rel(hAPP(v_P_H____,X0),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~spl0_230)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f52731])).
% 156.17/20.10 fof(f52734,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=v_b____|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|c_FunDef_Oin__rel(hAPP(v_P_H____,X0),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1644,f12832])).
% 156.17/20.10 fof(f52735,plain,(
% 156.17/20.10 spl0_230|spl0_110),
% 156.17/20.10 inference(split_clause,[status(thm)],[f52734,f52731,f42998])).
% 156.17/20.10 fof(f52736,plain,(
% 156.17/20.10 spl0_231 <=> c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oantisym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,X0),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f52739,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_b____=v_a____|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oantisym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,X0),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~spl0_112)),
% 156.17/20.10 inference(resolution,[status(thm)],[f1644,f43007])).
% 156.17/20.10 fof(f52740,plain,(
% 156.17/20.10 spl0_231|spl0_110|~spl0_112),
% 156.17/20.10 inference(split_clause,[status(thm)],[f52739,f52736,f42998,f43006])).
% 156.17/20.10 fof(f52741,plain,(
% 156.17/20.10 spl0_232 <=> c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oantisym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,X0),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f52744,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_b____=v_a____|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oantisym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,X0),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_111)),
% 156.17/20.10 inference(resolution,[status(thm)],[f1644,f43002])).
% 156.17/20.10 fof(f52745,plain,(
% 156.17/20.10 spl0_232|spl0_110|~spl0_111),
% 156.17/20.10 inference(split_clause,[status(thm)],[f52744,f52741,f42998,f43001])).
% 156.17/20.10 fof(f52746,plain,(
% 156.17/20.10 spl0_233 <=> ~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f52749,plain,(
% 156.17/20.10 ![X0]: (c_in(c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_b____=v_b_H____|~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt)|spl0_0)),
% 156.17/20.10 inference(resolution,[status(thm)],[f1644,f1757])).
% 156.17/20.10 fof(f52750,plain,(
% 156.17/20.10 spl0_106|spl0_97|spl0_233|spl0_0),
% 156.17/20.10 inference(split_clause,[status(thm)],[f52749,f42380,f41290,f52746,f1720])).
% 156.17/20.10 fof(f52751,plain,(
% 156.17/20.10 spl0_234 <=> c_in(c_Pair(v_b_H____,v_b____,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(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f52754,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_b_H____,v_b____,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))|v_b____=v_b_H____|~c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_123)),
% 156.17/20.10 inference(resolution,[status(thm)],[f1644,f45399])).
% 156.17/20.10 fof(f52755,plain,(
% 156.17/20.10 spl0_234|spl0_97|~spl0_123),
% 156.17/20.10 inference(split_clause,[status(thm)],[f52754,f52751,f41290,f45379])).
% 156.17/20.10 fof(f52756,plain,(
% 156.17/20.10 spl0_235 <=> c_in(c_Pair(v_b_H____,v_b____,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(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f52757,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_b_H____,v_b____,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(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_235)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f52756])).
% 156.17/20.10 fof(f52759,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_b_H____,v_b____,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))|v_b____=v_b_H____|~c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1644,f1742])).
% 156.17/20.10 fof(f52760,plain,(
% 156.17/20.10 spl0_235|spl0_97),
% 156.17/20.10 inference(split_clause,[status(thm)],[f52759,f52756,f41290])).
% 156.17/20.10 fof(f52965,plain,(
% 156.17/20.10 ![X0]: (c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X0,v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_106)),
% 156.17/20.10 inference(resolution,[status(thm)],[f42381,f1630])).
% 156.17/20.10 fof(f52966,plain,(
% 156.17/20.10 ![X0]: (c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X0,v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_106)),
% 156.17/20.10 inference(resolution,[status(thm)],[f42381,f1628])).
% 156.17/20.10 fof(f52968,plain,(
% 156.17/20.10 spl0_237 <=> c_in(v_b_H____,c_Wellfounded_Oacc(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f52971,plain,(
% 156.17/20.10 spl0_238 <=> c_in(v_b____,c_Wellfounded_Oacc(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f52974,plain,(
% 156.17/20.10 c_in(v_b_H____,c_Wellfounded_Oacc(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,c_Wellfounded_Oacc(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_106),
% 156.17/20.10 inference(resolution,[status(thm)],[f42381,f1617])).
% 156.17/20.10 fof(f52975,plain,(
% 156.17/20.10 spl0_237|~spl0_238|~spl0_106),
% 156.17/20.10 inference(split_clause,[status(thm)],[f52974,f52968,f52971,f42380])).
% 156.17/20.10 fof(f52976,plain,(
% 156.17/20.10 spl0_239 <=> 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))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f52977,plain,(
% 156.17/20.10 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))|~spl0_239),
% 156.17/20.10 inference(component_clause,[status(thm)],[f52976])).
% 156.17/20.10 fof(f52979,plain,(
% 156.17/20.10 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))|~c_Relation_Osym(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_106),
% 156.17/20.10 inference(resolution,[status(thm)],[f42381,f1582])).
% 156.17/20.10 fof(f52980,plain,(
% 156.17/20.10 spl0_239|~spl0_122|~spl0_106),
% 156.17/20.10 inference(split_clause,[status(thm)],[f52979,f52976,f44888,f42380])).
% 156.17/20.10 fof(f52983,plain,(
% 156.17/20.10 spl0_240 <=> c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f52986,plain,(
% 156.17/20.10 ![X0]: (c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_106)),
% 156.17/20.10 inference(resolution,[status(thm)],[f42381,f1538])).
% 156.17/20.10 fof(f52987,plain,(
% 156.17/20.10 spl0_240|~spl0_90|~spl0_106),
% 156.17/20.10 inference(split_clause,[status(thm)],[f52986,f52983,f40295,f42380])).
% 156.17/20.10 fof(f52988,plain,(
% 156.17/20.10 spl0_241 <=> c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X0,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))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f52989,plain,(
% 156.17/20.10 ![X0]: (c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X0,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))|~spl0_241)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f52988])).
% 156.17/20.10 fof(f52991,plain,(
% 156.17/20.10 ![X0]: (c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X0,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_Relation_Otrans(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_106)),
% 156.17/20.10 inference(resolution,[status(thm)],[f42381,f1538])).
% 156.17/20.10 fof(f52992,plain,(
% 156.17/20.10 spl0_241|~spl0_90|~spl0_106),
% 156.17/20.10 inference(split_clause,[status(thm)],[f52991,f52988,f40295,f42380])).
% 156.17/20.10 fof(f52998,plain,(
% 156.17/20.10 ![X0,X1]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(v_b_H____,c_Relation_ODomain(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_235)),
% 156.17/20.10 inference(resolution,[status(thm)],[f52757,f1636])).
% 156.17/20.10 fof(f52999,plain,(
% 156.17/20.10 ![X0,X1]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(v_b____,c_Relation_ORange(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_235)),
% 156.17/20.10 inference(resolution,[status(thm)],[f52757,f1632])).
% 156.17/20.10 fof(f53004,plain,(
% 156.17/20.10 ![X0,X1,X2]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(v_b____,c_Relation_OImage(hAPP(v_P_H____,X1),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~spl0_235)),
% 156.17/20.10 inference(resolution,[status(thm)],[f52757,f1621])).
% 156.17/20.10 fof(f53005,plain,(
% 156.17/20.10 ![X0,X1]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_235)),
% 156.17/20.10 inference(resolution,[status(thm)],[f52757,f1617])).
% 156.17/20.10 fof(f53009,plain,(
% 156.17/20.10 ![X0,X1,X2]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_235)),
% 156.17/20.10 inference(resolution,[status(thm)],[f52757,f1538])).
% 156.17/20.10 fof(f53010,plain,(
% 156.17/20.10 ![X0,X1,X2]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_235)),
% 156.17/20.10 inference(resolution,[status(thm)],[f52757,f1538])).
% 156.17/20.10 fof(f53011,plain,(
% 156.17/20.10 ![X0,X1]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|hBOOL(hAPP(c_Transitive__Closure_Ortrancl(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_235)),
% 156.17/20.10 inference(resolution,[status(thm)],[f52757,f5562])).
% 156.17/20.10 fof(f53012,plain,(
% 156.17/20.10 ![X0,X1]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|hBOOL(hAPP(c_Transitive__Closure_Otrancl(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_235)),
% 156.17/20.10 inference(resolution,[status(thm)],[f52757,f5647])).
% 156.17/20.10 fof(f53013,plain,(
% 156.17/20.10 ![X0,X1]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|hBOOL(hAPP(hAPP(v_P_H____,X1),c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_235)),
% 156.17/20.10 inference(resolution,[status(thm)],[f52757,f1666])).
% 156.17/20.10 fof(f53017,plain,(
% 156.17/20.10 spl0_242 <=> c_in(v_b_H____,c_Relation_ODomain(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f53020,plain,(
% 156.17/20.10 spl0_243 <=> ~c_Equiv__Relations_Oequiv(X0,v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f53023,plain,(
% 156.17/20.10 ![X0]: (c_in(v_b_H____,c_Relation_ODomain(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X0,v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_106)),
% 156.17/20.10 inference(resolution,[status(thm)],[f52965,f24151])).
% 156.17/20.10 fof(f53024,plain,(
% 156.17/20.10 spl0_242|spl0_243|~spl0_106),
% 156.17/20.10 inference(split_clause,[status(thm)],[f53023,f53017,f53020,f42380])).
% 156.17/20.10 fof(f53025,plain,(
% 156.17/20.10 spl0_244 <=> c_in(v_b____,c_Relation_ODomain(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f53028,plain,(
% 156.17/20.10 ![X0]: (c_in(v_b____,c_Relation_ODomain(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X0,v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_106)),
% 156.17/20.10 inference(resolution,[status(thm)],[f52966,f24151])).
% 156.17/20.10 fof(f53029,plain,(
% 156.17/20.10 spl0_244|spl0_243|~spl0_106),
% 156.17/20.10 inference(split_clause,[status(thm)],[f53028,f53025,f53020,f42380])).
% 156.17/20.10 fof(f53074,plain,(
% 156.17/20.10 spl0_245 <=> hAPP(hAPP(X0,v_b____),v_a____)=hAPP(hAPP(X0,v_b_H____),v_b____)|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,X1),v_F(v_P____),X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2)|c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X3,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X3,hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f53077,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (hAPP(hAPP(X0,v_b____),v_a____)=hAPP(hAPP(X0,v_b_H____),v_b____)|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,X1),v_F(v_P____),X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2)|c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=v_b____|~c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X3,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X3,hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_1)),
% 156.17/20.10 inference(resolution,[status(thm)],[f39282,f1644])).
% 156.17/20.10 fof(f53078,plain,(
% 156.17/20.10 spl0_245|spl0_110|~spl0_1),
% 156.17/20.10 inference(split_clause,[status(thm)],[f53077,f53074,f42998,f1723])).
% 156.17/20.10 fof(f53123,plain,(
% 156.17/20.10 spl0_246 <=> hAPP(hAPP(X0,v_b____),X1)=hAPP(hAPP(X0,v_b_H____),X2)|~c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,X5),X4,X0,tc_Arrow__Order__Mirabelle_Oalt,X3,X6)|c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X7,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X7,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X7,hAPP(v_P____,X5),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f53124,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6,X7]: (hAPP(hAPP(X0,v_b____),X1)=hAPP(hAPP(X0,v_b_H____),X2)|~c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,X5),X4,X0,tc_Arrow__Order__Mirabelle_Oalt,X3,X6)|c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X7,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X7,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X7,hAPP(v_P____,X5),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_246)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f53123])).
% 156.17/20.10 fof(f53126,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6,X7]: (hAPP(hAPP(X0,v_b____),X1)=hAPP(hAPP(X0,v_b_H____),X2)|~c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,X5),X4,X0,tc_Arrow__Order__Mirabelle_Oalt,X3,X6)|c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=v_b____|~c_in(v_b____,X7,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X7,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X7,hAPP(v_P____,X5),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 inference(resolution,[status(thm)],[f39226,f1644])).
% 156.17/20.10 fof(f53127,plain,(
% 156.17/20.10 spl0_246|spl0_110),
% 156.17/20.10 inference(split_clause,[status(thm)],[f53126,f53123,f42998])).
% 156.17/20.10 fof(f53146,plain,(
% 156.17/20.10 spl0_247 <=> hAPP(hAPP(X0,X1),v_b____)=hAPP(hAPP(X0,X2),v_b_H____)|~c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))|~c_Equiv__Relations_Ocongruent2(X4,hAPP(v_P_H____,X5),X0,X3,tc_Arrow__Order__Mirabelle_Oalt,X6)|c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X7,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X7,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X7,hAPP(v_P____,X5),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f53147,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6,X7]: (hAPP(hAPP(X0,X1),v_b____)=hAPP(hAPP(X0,X2),v_b_H____)|~c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))|~c_Equiv__Relations_Ocongruent2(X4,hAPP(v_P_H____,X5),X0,X3,tc_Arrow__Order__Mirabelle_Oalt,X6)|c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X7,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X7,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X7,hAPP(v_P____,X5),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_247)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f53146])).
% 156.17/20.10 fof(f53149,plain,(
% 156.17/20.10 ![X0,X1,X2,X3,X4,X5,X6,X7]: (hAPP(hAPP(X0,X1),v_b____)=hAPP(hAPP(X0,X2),v_b_H____)|~c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))|~c_Equiv__Relations_Ocongruent2(X4,hAPP(v_P_H____,X5),X0,X3,tc_Arrow__Order__Mirabelle_Oalt,X6)|c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=v_b____|~c_in(v_b____,X7,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X7,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X7,hAPP(v_P____,X5),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 inference(resolution,[status(thm)],[f39169,f1644])).
% 156.17/20.10 fof(f53150,plain,(
% 156.17/20.10 spl0_247|spl0_110),
% 156.17/20.10 inference(split_clause,[status(thm)],[f53149,f53146,f42998])).
% 156.17/20.10 fof(f53154,plain,(
% 156.17/20.10 spl0_248 <=> hAPP(X0,v_b____)=hAPP(X0,v_b_H____)|~c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,X1),X0,tc_Arrow__Order__Mirabelle_Oalt,X2)|c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X3,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X3,hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f53155,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (hAPP(X0,v_b____)=hAPP(X0,v_b_H____)|~c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,X1),X0,tc_Arrow__Order__Mirabelle_Oalt,X2)|c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X3,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X3,hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_248)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f53154])).
% 156.17/20.10 fof(f53157,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (hAPP(X0,v_b____)=hAPP(X0,v_b_H____)|~c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,X1),X0,tc_Arrow__Order__Mirabelle_Oalt,X2)|c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=v_b____|~c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X3,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X3,hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 inference(resolution,[status(thm)],[f43062,f1644])).
% 156.17/20.10 fof(f53158,plain,(
% 156.17/20.10 spl0_248|spl0_110),
% 156.17/20.10 inference(split_clause,[status(thm)],[f53157,f53154,f42998])).
% 156.17/20.10 fof(f53501,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1648,f1741])).
% 156.17/20.10 fof(f53561,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1650,f1741])).
% 156.17/20.10 fof(f53636,plain,(
% 156.17/20.10 spl0_249 <=> hAPP(hAPP(X0,v_b_H____),v_a____)=hAPP(hAPP(X0,v_b____),v_b____)|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,X1),v_F(v_P____),X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2)|~c_Relation_Osym(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X3,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X3,hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f53639,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (hAPP(hAPP(X0,v_b_H____),v_a____)=hAPP(hAPP(X0,v_b____),v_b____)|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,X1),v_F(v_P____),X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2)|~c_Relation_Osym(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=v_b____|~c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X3,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X3,hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_1)),
% 156.17/20.10 inference(resolution,[status(thm)],[f47757,f1644])).
% 156.17/20.10 fof(f53640,plain,(
% 156.17/20.10 spl0_249|spl0_110|~spl0_1),
% 156.17/20.10 inference(split_clause,[status(thm)],[f53639,f53636,f42998,f1723])).
% 156.17/20.10 fof(f53730,plain,(
% 156.17/20.10 spl0_250 <=> ~c_Relation_Osingle__valued(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f53731,plain,(
% 156.17/20.10 ![X0,X1]: (~c_Relation_Osingle__valued(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_250)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f53730])).
% 156.17/20.10 fof(f53733,plain,(
% 156.17/20.10 ![X0,X1]: (v_b____=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 inference(resolution,[status(thm)],[f39703,f1646])).
% 156.17/20.10 fof(f53734,plain,(
% 156.17/20.10 spl0_97|spl0_250),
% 156.17/20.10 inference(split_clause,[status(thm)],[f53733,f41290,f53730])).
% 156.17/20.10 fof(f54256,plain,(
% 156.17/20.10 spl0_253 <=> c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_b_H____|~c_in(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X2,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),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(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f54259,plain,(
% 156.17/20.10 spl0_254 <=> 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)))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f54261,plain,(
% 156.17/20.10 ~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)))|spl0_254),
% 156.17/20.10 inference(component_clause,[status(thm)],[f54259])).
% 156.17/20.10 fof(f54262,plain,(
% 156.17/20.10 ![X0,X1,X2]: (c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_b_H____=v_b____|X0=v_b_H____|~c_in(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X2,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),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(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_235)),
% 156.17/20.10 inference(resolution,[status(thm)],[f1676,f52757])).
% 156.17/20.10 fof(f54263,plain,(
% 156.17/20.10 spl0_253|~spl0_106|~spl0_254|spl0_97|~spl0_235),
% 156.17/20.10 inference(split_clause,[status(thm)],[f54262,f54256,f42380,f54259,f41290,f52756])).
% 156.17/20.10 fof(f54264,plain,(
% 156.17/20.10 spl0_255 <=> c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_b_H____|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),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(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f54267,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_b_H____=v_b____|X0=v_b_H____|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),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(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1676,f44893])).
% 156.17/20.10 fof(f54268,plain,(
% 156.17/20.10 spl0_255|~spl0_106|~spl0_254|spl0_97),
% 156.17/20.10 inference(split_clause,[status(thm)],[f54267,f54264,f42380,f54259,f41290])).
% 156.17/20.10 fof(f54275,plain,(
% 156.17/20.10 spl0_257 <=> c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_a____|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f54278,plain,(
% 156.17/20.10 spl0_258 <=> 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)))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f54280,plain,(
% 156.17/20.10 ~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)))|spl0_258),
% 156.17/20.10 inference(component_clause,[status(thm)],[f54278])).
% 156.17/20.10 fof(f54281,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_a____=v_b____|X0=v_a____|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1676,f1874])).
% 156.17/20.10 fof(f54282,plain,(
% 156.17/20.10 spl0_257|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.10 inference(split_clause,[status(thm)],[f54281,f54275,f1723,f54278,f42998])).
% 156.17/20.10 fof(f54283,plain,(
% 156.17/20.10 spl0_259 <=> c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_a____|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f54286,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_a____=v_b____|X0=v_a____|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1676,f12914])).
% 156.17/20.10 fof(f54287,plain,(
% 156.17/20.10 spl0_259|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.10 inference(split_clause,[status(thm)],[f54286,f54283,f1723,f54278,f42998])).
% 156.17/20.10 fof(f54292,plain,(
% 156.17/20.10 $false|spl0_0|~spl0_239),
% 156.17/20.10 inference(forward_subsumption_resolution,[status(thm)],[f52977,f1757])).
% 156.17/20.10 fof(f54293,plain,(
% 156.17/20.10 spl0_0|~spl0_239),
% 156.17/20.10 inference(contradiction_clause,[status(thm)],[f54292])).
% 156.17/20.10 fof(f54296,plain,(
% 156.17/20.10 spl0_260 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b_H____=X0|v_b____=X0|~c_in(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X2,hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f54297,plain,(
% 156.17/20.10 ![X0,X1,X2]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b_H____=X0|v_b____=X0|~c_in(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X2,hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_260)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f54296])).
% 156.17/20.10 fof(f54299,plain,(
% 156.17/20.10 ![X0,X1,X2]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b_H____,v_b____,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____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b_H____=X0|v_b____=X0|v_b_H____=v_b____|~c_in(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X2,hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_235)),
% 156.17/20.10 inference(resolution,[status(thm)],[f1678,f52757])).
% 156.17/20.10 fof(f54300,plain,(
% 156.17/20.10 spl0_260|~spl0_106|~spl0_254|spl0_97|~spl0_235),
% 156.17/20.10 inference(split_clause,[status(thm)],[f54299,f54296,f42380,f54259,f41290,f52756])).
% 156.17/20.10 fof(f54301,plain,(
% 156.17/20.10 spl0_261 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b_H____=X0|v_b____=X0|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f54302,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b_H____=X0|v_b____=X0|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_261)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f54301])).
% 156.17/20.10 fof(f54304,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b_H____,v_b____,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____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b_H____=X0|v_b____=X0|v_b_H____=v_b____|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1678,f44893])).
% 156.17/20.10 fof(f54305,plain,(
% 156.17/20.10 spl0_261|~spl0_106|~spl0_254|spl0_97),
% 156.17/20.10 inference(split_clause,[status(thm)],[f54304,f54301,f42380,f54259,f41290])).
% 156.17/20.10 fof(f54312,plain,(
% 156.17/20.10 spl0_263 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f54313,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_263)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f54312])).
% 156.17/20.10 fof(f54315,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X0|v_b____=X0|v_a____=v_b____|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1678,f1874])).
% 156.17/20.10 fof(f54316,plain,(
% 156.17/20.10 spl0_263|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.10 inference(split_clause,[status(thm)],[f54315,f54312,f1723,f54278,f42998])).
% 156.17/20.10 fof(f54317,plain,(
% 156.17/20.10 spl0_264 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f54318,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~spl0_264)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f54317])).
% 156.17/20.10 fof(f54320,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X0|v_b____=X0|v_a____=v_b____|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1678,f12914])).
% 156.17/20.10 fof(f54321,plain,(
% 156.17/20.10 spl0_264|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.10 inference(split_clause,[status(thm)],[f54320,f54317,f1723,f54278,f42998])).
% 156.17/20.10 fof(f54327,plain,(
% 156.17/20.10 spl0_265 <=> c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_b_H____|~c_Relation_Oantisym(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),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(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f54330,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_b_H____=v_b____|X0=v_b_H____|~c_Relation_Oantisym(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),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(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_109)),
% 156.17/20.10 inference(resolution,[status(thm)],[f1680,f42994])).
% 156.17/20.10 fof(f54331,plain,(
% 156.17/20.10 spl0_265|~spl0_106|~spl0_254|spl0_97|~spl0_109),
% 156.17/20.10 inference(split_clause,[status(thm)],[f54330,f54327,f42380,f54259,f41290,f42993])).
% 156.17/20.10 fof(f54332,plain,(
% 156.17/20.10 spl0_266 <=> c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_b_H____|~c_Wellfounded_Owf(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),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(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f54335,plain,(
% 156.17/20.10 ![X0,X1]: (c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_b_H____=v_b____|X0=v_b_H____|~c_Wellfounded_Owf(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),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(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1680,f42388])).
% 156.17/20.10 fof(f54336,plain,(
% 156.17/20.10 spl0_266|~spl0_106|~spl0_254|spl0_97),
% 156.17/20.10 inference(split_clause,[status(thm)],[f54335,f54332,f42380,f54259,f41290])).
% 156.17/20.10 fof(f54337,plain,(
% 156.17/20.10 spl0_267 <=> c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=X2|v_b_H____=X2|X0=v_b_H____|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f54338,plain,(
% 156.17/20.10 ![X0,X1,X2]: (c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=X2|v_b_H____=X2|X0=v_b_H____|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_267)),
% 156.17/20.10 inference(component_clause,[status(thm)],[f54337])).
% 156.17/20.10 fof(f54340,plain,(
% 156.17/20.10 ![X0,X1,X2]: (c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=X2|v_b_H____=X2|X0=v_b_H____|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.10 inference(resolution,[status(thm)],[f1680,f40362])).
% 156.17/20.10 fof(f54341,plain,(
% 156.17/20.10 spl0_267|~spl0_254),
% 156.17/20.10 inference(split_clause,[status(thm)],[f54340,f54337,f54259])).
% 156.17/20.10 fof(f54342,plain,(
% 156.17/20.10 spl0_268 <=> c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_a____|hAPP(hAPP(X2,v_b_H____),v_a____)=hAPP(hAPP(X2,v_b____),v_b____)|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),v_F(v_P____),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3)|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f54345,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_a____=v_b____|X0=v_a____|hAPP(hAPP(X2,v_b_H____),v_a____)=hAPP(hAPP(X2,v_b____),v_b____)|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),v_F(v_P____),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3)|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_1)),
% 156.17/20.10 inference(resolution,[status(thm)],[f1680,f47757])).
% 156.17/20.10 fof(f54346,plain,(
% 156.17/20.10 spl0_268|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.10 inference(split_clause,[status(thm)],[f54345,f54342,f1723,f54278,f42998])).
% 156.17/20.10 fof(f54347,plain,(
% 156.17/20.10 spl0_269 <=> c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_a____|hAPP(X2,v_b____)=hAPP(X2,v_b_H____)|~c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),X2,tc_Arrow__Order__Mirabelle_Oalt,X3)),
% 156.17/20.10 introduced(split_symbol_definition)).
% 156.17/20.10 fof(f54350,plain,(
% 156.17/20.10 ![X0,X1,X2,X3]: (c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_a____=v_b____|X0=v_a____|hAPP(X2,v_b____)=hAPP(X2,v_b_H____)|~c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),X2,tc_Arrow__Order__Mirabelle_Oalt,X3))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1680,f43062])).
% 156.17/20.11 fof(f54351,plain,(
% 156.17/20.11 spl0_269|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54350,f54347,f1723,f54278,f42998])).
% 156.17/20.11 fof(f54352,plain,(
% 156.17/20.11 spl0_270 <=> c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_a____|hAPP(hAPP(X2,X3),v_b____)=hAPP(hAPP(X2,X4),v_b_H____)|~c_in(c_Pair(X3,X4,X5,X5),X6,tc_prod(X5,X5))|~c_Equiv__Relations_Ocongruent2(X6,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),X2,X5,tc_Arrow__Order__Mirabelle_Oalt,X7)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54355,plain,(
% 156.17/20.11 ![X0,X1,X2,X3,X4,X5,X6,X7]: (c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_a____=v_b____|X0=v_a____|hAPP(hAPP(X2,X3),v_b____)=hAPP(hAPP(X2,X4),v_b_H____)|~c_in(c_Pair(X3,X4,X5,X5),X6,tc_prod(X5,X5))|~c_Equiv__Relations_Ocongruent2(X6,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),X2,X5,tc_Arrow__Order__Mirabelle_Oalt,X7))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1680,f39169])).
% 156.17/20.11 fof(f54356,plain,(
% 156.17/20.11 spl0_270|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54355,f54352,f1723,f54278,f42998])).
% 156.17/20.11 fof(f54357,plain,(
% 156.17/20.11 spl0_271 <=> c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_a____|hAPP(hAPP(X2,v_b____),X3)=hAPP(hAPP(X2,v_b_H____),X4)|~c_in(c_Pair(X3,X4,X5,X5),X6,tc_prod(X5,X5))|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),X6,X2,tc_Arrow__Order__Mirabelle_Oalt,X5,X7)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54360,plain,(
% 156.17/20.11 ![X0,X1,X2,X3,X4,X5,X6,X7]: (c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_a____=v_b____|X0=v_a____|hAPP(hAPP(X2,v_b____),X3)=hAPP(hAPP(X2,v_b_H____),X4)|~c_in(c_Pair(X3,X4,X5,X5),X6,tc_prod(X5,X5))|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),X6,X2,tc_Arrow__Order__Mirabelle_Oalt,X5,X7))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1680,f39226])).
% 156.17/20.11 fof(f54361,plain,(
% 156.17/20.11 spl0_271|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54360,f54357,f1723,f54278,f42998])).
% 156.17/20.11 fof(f54362,plain,(
% 156.17/20.11 spl0_272 <=> c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_a____|hAPP(hAPP(X2,v_b____),v_a____)=hAPP(hAPP(X2,v_b_H____),v_b____)|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),v_F(v_P____),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54365,plain,(
% 156.17/20.11 ![X0,X1,X2,X3]: (c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_a____=v_b____|X0=v_a____|hAPP(hAPP(X2,v_b____),v_a____)=hAPP(hAPP(X2,v_b_H____),v_b____)|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),v_F(v_P____),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3)|~spl0_1)),
% 156.17/20.11 inference(resolution,[status(thm)],[f1680,f39282])).
% 156.17/20.11 fof(f54366,plain,(
% 156.17/20.11 spl0_272|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54365,f54362,f1723,f54278,f42998])).
% 156.17/20.11 fof(f54367,plain,(
% 156.17/20.11 spl0_273 <=> c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_a____|hAPP(hAPP(X2,v_b____),v_b____)=hAPP(hAPP(X2,v_b_H____),v_b_H____)|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54370,plain,(
% 156.17/20.11 ![X0,X1,X2,X3]: (c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_a____=v_b____|X0=v_a____|hAPP(hAPP(X2,v_b____),v_b____)=hAPP(hAPP(X2,v_b_H____),v_b_H____)|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1680,f39168])).
% 156.17/20.11 fof(f54371,plain,(
% 156.17/20.11 spl0_273|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54370,f54367,f1723,f54278,f42998])).
% 156.17/20.11 fof(f54372,plain,(
% 156.17/20.11 spl0_274 <=> c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_a____|c_in(v_b____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54375,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_a____=v_b____|X0=v_a____|c_in(v_b____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1680,f51580])).
% 156.17/20.11 fof(f54376,plain,(
% 156.17/20.11 spl0_274|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54375,f54372,f1723,f54278,f42998])).
% 156.17/20.11 fof(f54377,plain,(
% 156.17/20.11 spl0_275 <=> c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_a____|c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54380,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_a____=v_b____|X0=v_a____|c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1680,f50683])).
% 156.17/20.11 fof(f54381,plain,(
% 156.17/20.11 spl0_275|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54380,f54377,f1723,f54278,f42998])).
% 156.17/20.11 fof(f54382,plain,(
% 156.17/20.11 spl0_276 <=> c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_a____|c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X2,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54385,plain,(
% 156.17/20.11 ![X0,X1,X2]: (c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_a____=v_b____|X0=v_a____|c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X2,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1680,f50612])).
% 156.17/20.11 fof(f54386,plain,(
% 156.17/20.11 spl0_276|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54385,f54382,f1723,f54278,f42998])).
% 156.17/20.11 fof(f54387,plain,(
% 156.17/20.11 spl0_277 <=> c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_a____|c_in(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X2,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54390,plain,(
% 156.17/20.11 ![X0,X1,X2]: (c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_a____=v_b____|X0=v_a____|c_in(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X2,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1680,f50225])).
% 156.17/20.11 fof(f54391,plain,(
% 156.17/20.11 spl0_277|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54390,f54387,f1723,f54278,f42998])).
% 156.17/20.11 fof(f54392,plain,(
% 156.17/20.11 spl0_278 <=> c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_a____|c_in(v_b_H____,c_Relation_OImage(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54395,plain,(
% 156.17/20.11 ![X0,X1,X2]: (c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_a____=v_b____|X0=v_a____|c_in(v_b_H____,c_Relation_OImage(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1680,f50152])).
% 156.17/20.11 fof(f54396,plain,(
% 156.17/20.11 spl0_278|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54395,f54392,f1723,f54278,f42998])).
% 156.17/20.11 fof(f54397,plain,(
% 156.17/20.11 spl0_279 <=> c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_a____|c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54400,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_a____=v_b____|X0=v_a____|c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1680,f49598])).
% 156.17/20.11 fof(f54401,plain,(
% 156.17/20.11 spl0_279|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54400,f54397,f1723,f54278,f42998])).
% 156.17/20.11 fof(f54402,plain,(
% 156.17/20.11 spl0_280 <=> c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_a____|~c_Relation_Oantisym(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54405,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_a____=v_b____|X0=v_a____|~c_Relation_Oantisym(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_109)),
% 156.17/20.11 inference(resolution,[status(thm)],[f1680,f43137])).
% 156.17/20.11 fof(f54406,plain,(
% 156.17/20.11 spl0_280|~spl0_1|~spl0_258|spl0_110|~spl0_109),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54405,f54402,f1723,f54278,f42998,f42993])).
% 156.17/20.11 fof(f54407,plain,(
% 156.17/20.11 spl0_281 <=> c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_a____|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oantisym(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54410,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_a____=v_b____|X0=v_a____|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oantisym(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_109)),
% 156.17/20.11 inference(resolution,[status(thm)],[f1680,f45370])).
% 156.17/20.11 fof(f54411,plain,(
% 156.17/20.11 spl0_281|~spl0_1|~spl0_258|spl0_110|~spl0_109),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54410,f54407,f1723,f54278,f42998,f42993])).
% 156.17/20.11 fof(f54412,plain,(
% 156.17/20.11 spl0_282 <=> c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_a____|~c_Nitpick_Orefl_H(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54415,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_a____=v_b____|X0=v_a____|~c_Nitpick_Orefl_H(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~spl0_96)),
% 156.17/20.11 inference(resolution,[status(thm)],[f1680,f41288])).
% 156.17/20.11 fof(f54416,plain,(
% 156.17/20.11 spl0_282|~spl0_1|~spl0_258|spl0_110|~spl0_96),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54415,f54412,f1723,f54278,f42998,f41287])).
% 156.17/20.11 fof(f54417,plain,(
% 156.17/20.11 spl0_283 <=> c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_a____|c_in(c_Pair(X2,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54420,plain,(
% 156.17/20.11 ![X0,X1,X2]: (c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_a____=v_b____|X0=v_a____|c_in(c_Pair(X2,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1680,f40300])).
% 156.17/20.11 fof(f54421,plain,(
% 156.17/20.11 spl0_283|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54420,f54417,f1723,f54278,f42998])).
% 156.17/20.11 fof(f54422,plain,(
% 156.17/20.11 spl0_284 <=> c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_a____|hBOOL(hAPP(c_Transitive__Closure_Otrancl(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54425,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_a____=v_b____|X0=v_a____|hBOOL(hAPP(c_Transitive__Closure_Otrancl(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1680,f5652])).
% 156.17/20.11 fof(f54426,plain,(
% 156.17/20.11 spl0_284|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54425,f54422,f1723,f54278,f42998])).
% 156.17/20.11 fof(f54427,plain,(
% 156.17/20.11 spl0_285 <=> c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_a____|hBOOL(hAPP(c_Transitive__Closure_Ortrancl(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54430,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_a____=v_b____|X0=v_a____|hBOOL(hAPP(c_Transitive__Closure_Ortrancl(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1680,f5567])).
% 156.17/20.11 fof(f54431,plain,(
% 156.17/20.11 spl0_285|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54430,f54427,f1723,f54278,f42998])).
% 156.17/20.11 fof(f54432,plain,(
% 156.17/20.11 spl0_286 <=> c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_a____|hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54435,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_a____=v_b____|X0=v_a____|hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1680,f1878])).
% 156.17/20.11 fof(f54436,plain,(
% 156.17/20.11 spl0_286|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54435,f54432,f1723,f54278,f42998])).
% 156.17/20.11 fof(f54437,plain,(
% 156.17/20.11 spl0_287 <=> c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_a____|c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54440,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_a____=v_b____|X0=v_a____|c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_a____,v_b____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1680,f12832])).
% 156.17/20.11 fof(f54441,plain,(
% 156.17/20.11 spl0_287|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54440,f54437,f1723,f54278,f42998])).
% 156.17/20.11 fof(f54442,plain,(
% 156.17/20.11 spl0_288 <=> c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_a____|X0=v_b____|~c_Relation_Oantisym(hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X0,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_b____,v_a____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54445,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_a____|v_b____=v_a____|X0=v_b____|~c_Relation_Oantisym(hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X0,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_b____,v_a____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~spl0_112)),
% 156.17/20.11 inference(resolution,[status(thm)],[f1680,f43007])).
% 156.17/20.11 fof(f54446,plain,(
% 156.17/20.11 spl0_288|~spl0_153|~spl0_258|spl0_110|~spl0_112),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54445,f54442,f47635,f54278,f42998,f43006])).
% 156.17/20.11 fof(f54447,plain,(
% 156.17/20.11 spl0_289 <=> c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_a____|X0=v_b____|~c_Relation_Oantisym(hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X0,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_b____,v_a____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54450,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X0,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_a____|v_b____=v_a____|X0=v_b____|~c_Relation_Oantisym(hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X0,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X0,v_b____,v_a____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_111)),
% 156.17/20.11 inference(resolution,[status(thm)],[f1680,f43002])).
% 156.17/20.11 fof(f54451,plain,(
% 156.17/20.11 spl0_289|~spl0_153|~spl0_258|spl0_110|~spl0_111),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54450,f54447,f47635,f54278,f42998,f43001])).
% 156.17/20.11 fof(f54457,plain,(
% 156.17/20.11 spl0_291 <=> c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b_H____|X0=v_b____|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54458,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b_H____|X0=v_b____|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_291)),
% 156.17/20.11 inference(component_clause,[status(thm)],[f54457])).
% 156.17/20.11 fof(f54460,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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))|c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b_H____|v_b____=v_b_H____|X0=v_b____|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1680,f1742])).
% 156.17/20.11 fof(f54461,plain,(
% 156.17/20.11 spl0_291|~spl0_239|~spl0_254|spl0_97),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54460,f54457,f52976,f54259,f41290])).
% 156.17/20.11 fof(f54462,plain,(
% 156.17/20.11 spl0_292 <=> c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=X2|v_b____=X2|X0=v_b____|X2=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b____,X2)),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(X1,v_P_H____,X0,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54465,plain,(
% 156.17/20.11 ![X0,X1,X2]: (c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=X2|v_b____=X2|X0=v_b____|X2=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b____,X2)),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(X1,v_P_H____,X0,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1680,f39703])).
% 156.17/20.11 fof(f54466,plain,(
% 156.17/20.11 spl0_292|~spl0_254),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54465,f54462,f54259])).
% 156.17/20.11 fof(f54485,plain,(
% 156.17/20.11 ~hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____))|spl0_258),
% 156.17/20.11 inference(resolution,[status(thm)],[f54280,f1664])).
% 156.17/20.11 fof(f54486,plain,(
% 156.17/20.11 $false|spl0_258),
% 156.17/20.11 inference(forward_subsumption_resolution,[status(thm)],[f54485,f13199])).
% 156.17/20.11 fof(f54487,plain,(
% 156.17/20.11 spl0_258),
% 156.17/20.11 inference(contradiction_clause,[status(thm)],[f54486])).
% 156.17/20.11 fof(f54597,plain,(
% 156.17/20.11 c_in(v_b_H____,c_Relation_ORange(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_0),
% 156.17/20.11 inference(resolution,[status(thm)],[f26539,f1632])).
% 156.17/20.11 fof(f54749,plain,(
% 156.17/20.11 spl0_298 <=> hBOOL(X0)|~c_Nitpick_Orefl_H(c_Relation_OImage(X3,c_COMBK(X0,X4,X5),X6,X7),X8)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54752,plain,(
% 156.17/20.11 ![X0,X1,X2,X3,X4,X5,X6,X7,X8]: (hBOOL(X0)|hBOOL(hAPP(X1,X2))|~c_Nitpick_Orefl_H(c_Relation_OImage(X3,c_COMBK(X0,X4,X5),X6,X7),X8))),
% 156.17/20.11 inference(resolution,[status(thm)],[f49197,f30446])).
% 156.17/20.11 fof(f54753,plain,(
% 156.17/20.11 spl0_298|spl0_75),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54752,f54749,f37252])).
% 156.17/20.11 fof(f54756,plain,(
% 156.17/20.11 ![X0,X1,X2,X3,X4,X5,X6,X7]: (hBOOL(X0)|hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OImage(X1,c_COMBK(X0,X2,X3),X4,X5),X6),X7)))),
% 156.17/20.11 inference(resolution,[status(thm)],[f49197,f1666])).
% 156.17/20.11 fof(f54781,plain,(
% 156.17/20.11 ![X0,X1,X2,X3,X4,X5]: (hBOOL(X0)|~c_Nitpick_Orefl_H(c_Lattices_Olower__semilattice__class_Oinf(X1,c_COMBK(X0,X2,X3),tc_fun(X4,tc_bool)),X5))),
% 156.17/20.11 inference(resolution,[status(thm)],[f49205,f1574])).
% 156.17/20.11 fof(f54857,plain,(
% 156.17/20.11 spl0_299 <=> c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b____|X2=v_a____),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54860,plain,(
% 156.17/20.11 ![X0,X1,X2]: (c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b____|v_a____=v_b____|X2=v_a____)),
% 156.17/20.11 inference(resolution,[status(thm)],[f53501,f1680])).
% 156.17/20.11 fof(f54861,plain,(
% 156.17/20.11 spl0_299|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54860,f54857,f1723,f54278,f42998])).
% 156.17/20.11 fof(f54862,plain,(
% 156.17/20.11 spl0_300 <=> c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X2,hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54865,plain,(
% 156.17/20.11 ![X0,X1,X2]: (c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=v_b____|~c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X2,hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.11 inference(resolution,[status(thm)],[f53501,f1644])).
% 156.17/20.11 fof(f54866,plain,(
% 156.17/20.11 spl0_300|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54865,f54862,f42998])).
% 156.17/20.11 fof(f54964,plain,(
% 156.17/20.11 spl0_301 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b_H____=X0|v_b____=X0|~c_Relation_Oantisym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54965,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b_H____=X0|v_b____=X0|~c_Relation_Oantisym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_301)),
% 156.17/20.11 inference(component_clause,[status(thm)],[f54964])).
% 156.17/20.11 fof(f54967,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b_H____,v_b____,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____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b_H____=X0|v_b____=X0|v_b_H____=v_b____|~c_Relation_Oantisym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_109)),
% 156.17/20.11 inference(resolution,[status(thm)],[f1682,f42994])).
% 156.17/20.11 fof(f54968,plain,(
% 156.17/20.11 spl0_301|~spl0_106|~spl0_254|spl0_97|~spl0_109),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54967,f54964,f42380,f54259,f41290,f42993])).
% 156.17/20.11 fof(f54969,plain,(
% 156.17/20.11 spl0_302 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b_H____=X0|v_b____=X0|~c_Wellfounded_Owf(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54970,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b_H____=X0|v_b____=X0|~c_Wellfounded_Owf(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_302)),
% 156.17/20.11 inference(component_clause,[status(thm)],[f54969])).
% 156.17/20.11 fof(f54972,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b_H____,v_b____,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____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b_H____=X0|v_b____=X0|v_b_H____=v_b____|~c_Wellfounded_Owf(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1682,f42388])).
% 156.17/20.11 fof(f54973,plain,(
% 156.17/20.11 spl0_302|~spl0_106|~spl0_254|spl0_97),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54972,f54969,f42380,f54259,f41290])).
% 156.17/20.11 fof(f54974,plain,(
% 156.17/20.11 spl0_303 <=> c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P_H____,X2,v_b_H____,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)))|v_b_H____=X1|X0=X1|v_b_H____=X0|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X2,v_b_H____,X0,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X2,v_b_H____,X0,X1)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X2,v_b_H____,X0,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54975,plain,(
% 156.17/20.11 ![X0,X1,X2]: (c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P_H____,X2,v_b_H____,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)))|v_b_H____=X1|X0=X1|v_b_H____=X0|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X2,v_b_H____,X0,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X2,v_b_H____,X0,X1)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X2,v_b_H____,X0,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_303)),
% 156.17/20.11 inference(component_clause,[status(thm)],[f54974])).
% 156.17/20.11 fof(f54977,plain,(
% 156.17/20.11 ![X0,X1,X2]: (c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P_H____,X2,v_b_H____,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(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b_H____=X1|X0=X1|v_b_H____=X0|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X2,v_b_H____,X0,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X2,v_b_H____,X0,X1)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X2,v_b_H____,X0,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1682,f40362])).
% 156.17/20.11 fof(f54978,plain,(
% 156.17/20.11 spl0_303|~spl0_254),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54977,f54974,f54259])).
% 156.17/20.11 fof(f54979,plain,(
% 156.17/20.11 spl0_304 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|c_in(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X2,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54982,plain,(
% 156.17/20.11 ![X0,X1,X2]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X0|v_b____=X0|v_a____=v_b____|c_in(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X2,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1682,f53501])).
% 156.17/20.11 fof(f54983,plain,(
% 156.17/20.11 spl0_304|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54982,f54979,f1723,f54278,f42998])).
% 156.17/20.11 fof(f54984,plain,(
% 156.17/20.11 spl0_305 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|hAPP(X2,v_b____)=hAPP(X2,v_b_H____)|~c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),X2,tc_Arrow__Order__Mirabelle_Oalt,X3)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54985,plain,(
% 156.17/20.11 ![X0,X1,X2,X3]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|hAPP(X2,v_b____)=hAPP(X2,v_b_H____)|~c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),X2,tc_Arrow__Order__Mirabelle_Oalt,X3)|~spl0_305)),
% 156.17/20.11 inference(component_clause,[status(thm)],[f54984])).
% 156.17/20.11 fof(f54987,plain,(
% 156.17/20.11 ![X0,X1,X2,X3]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X0|v_b____=X0|v_a____=v_b____|hAPP(X2,v_b____)=hAPP(X2,v_b_H____)|~c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),X2,tc_Arrow__Order__Mirabelle_Oalt,X3))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1682,f43062])).
% 156.17/20.11 fof(f54988,plain,(
% 156.17/20.11 spl0_305|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54987,f54984,f1723,f54278,f42998])).
% 156.17/20.11 fof(f54989,plain,(
% 156.17/20.11 spl0_306 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|hAPP(hAPP(X2,X3),v_b____)=hAPP(hAPP(X2,X4),v_b_H____)|~c_in(c_Pair(X3,X4,X5,X5),X6,tc_prod(X5,X5))|~c_Equiv__Relations_Ocongruent2(X6,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),X2,X5,tc_Arrow__Order__Mirabelle_Oalt,X7)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54990,plain,(
% 156.17/20.11 ![X0,X1,X2,X3,X4,X5,X6,X7]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|hAPP(hAPP(X2,X3),v_b____)=hAPP(hAPP(X2,X4),v_b_H____)|~c_in(c_Pair(X3,X4,X5,X5),X6,tc_prod(X5,X5))|~c_Equiv__Relations_Ocongruent2(X6,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),X2,X5,tc_Arrow__Order__Mirabelle_Oalt,X7)|~spl0_306)),
% 156.17/20.11 inference(component_clause,[status(thm)],[f54989])).
% 156.17/20.11 fof(f54992,plain,(
% 156.17/20.11 ![X0,X1,X2,X3,X4,X5,X6,X7]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X0|v_b____=X0|v_a____=v_b____|hAPP(hAPP(X2,X3),v_b____)=hAPP(hAPP(X2,X4),v_b_H____)|~c_in(c_Pair(X3,X4,X5,X5),X6,tc_prod(X5,X5))|~c_Equiv__Relations_Ocongruent2(X6,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),X2,X5,tc_Arrow__Order__Mirabelle_Oalt,X7))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1682,f39169])).
% 156.17/20.11 fof(f54993,plain,(
% 156.17/20.11 spl0_306|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54992,f54989,f1723,f54278,f42998])).
% 156.17/20.11 fof(f54994,plain,(
% 156.17/20.11 spl0_307 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|hAPP(hAPP(X2,v_b____),X3)=hAPP(hAPP(X2,v_b_H____),X4)|~c_in(c_Pair(X3,X4,X5,X5),X6,tc_prod(X5,X5))|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),X6,X2,tc_Arrow__Order__Mirabelle_Oalt,X5,X7)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f54995,plain,(
% 156.17/20.11 ![X0,X1,X2,X3,X4,X5,X6,X7]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|hAPP(hAPP(X2,v_b____),X3)=hAPP(hAPP(X2,v_b_H____),X4)|~c_in(c_Pair(X3,X4,X5,X5),X6,tc_prod(X5,X5))|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),X6,X2,tc_Arrow__Order__Mirabelle_Oalt,X5,X7)|~spl0_307)),
% 156.17/20.11 inference(component_clause,[status(thm)],[f54994])).
% 156.17/20.11 fof(f54997,plain,(
% 156.17/20.11 ![X0,X1,X2,X3,X4,X5,X6,X7]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X0|v_b____=X0|v_a____=v_b____|hAPP(hAPP(X2,v_b____),X3)=hAPP(hAPP(X2,v_b_H____),X4)|~c_in(c_Pair(X3,X4,X5,X5),X6,tc_prod(X5,X5))|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),X6,X2,tc_Arrow__Order__Mirabelle_Oalt,X5,X7))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1682,f39226])).
% 156.17/20.11 fof(f54998,plain,(
% 156.17/20.11 spl0_307|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f54997,f54994,f1723,f54278,f42998])).
% 156.17/20.11 fof(f54999,plain,(
% 156.17/20.11 spl0_308 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|hAPP(hAPP(X2,v_b____),v_b____)=hAPP(hAPP(X2,v_b_H____),v_b_H____)|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f55002,plain,(
% 156.17/20.11 ![X0,X1,X2,X3]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X0|v_b____=X0|v_a____=v_b____|hAPP(hAPP(X2,v_b____),v_b____)=hAPP(hAPP(X2,v_b_H____),v_b_H____)|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1682,f39168])).
% 156.17/20.11 fof(f55003,plain,(
% 156.17/20.11 spl0_308|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f55002,f54999,f1723,f54278,f42998])).
% 156.17/20.11 fof(f55004,plain,(
% 156.17/20.11 spl0_309 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|c_in(v_b____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f55005,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|c_in(v_b____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_309)),
% 156.17/20.11 inference(component_clause,[status(thm)],[f55004])).
% 156.17/20.11 fof(f55007,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X0|v_b____=X0|v_a____=v_b____|c_in(v_b____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1682,f51580])).
% 156.17/20.11 fof(f55008,plain,(
% 156.17/20.11 spl0_309|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f55007,f55004,f1723,f54278,f42998])).
% 156.17/20.11 fof(f55009,plain,(
% 156.17/20.11 spl0_310 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f55010,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_310)),
% 156.17/20.11 inference(component_clause,[status(thm)],[f55009])).
% 156.17/20.11 fof(f55012,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X0|v_b____=X0|v_a____=v_b____|c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1682,f50683])).
% 156.17/20.11 fof(f55013,plain,(
% 156.17/20.11 spl0_310|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f55012,f55009,f1723,f54278,f42998])).
% 156.17/20.11 fof(f55014,plain,(
% 156.17/20.11 spl0_311 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X2,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f55015,plain,(
% 156.17/20.11 ![X0,X1,X2]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X2,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_311)),
% 156.17/20.11 inference(component_clause,[status(thm)],[f55014])).
% 156.17/20.11 fof(f55017,plain,(
% 156.17/20.11 ![X0,X1,X2]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X0|v_b____=X0|v_a____=v_b____|c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X2,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1682,f50612])).
% 156.17/20.11 fof(f55018,plain,(
% 156.17/20.11 spl0_311|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f55017,f55014,f1723,f54278,f42998])).
% 156.17/20.11 fof(f55019,plain,(
% 156.17/20.11 spl0_312 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|c_in(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X2,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f55020,plain,(
% 156.17/20.11 ![X0,X1,X2]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|c_in(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X2,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_312)),
% 156.17/20.11 inference(component_clause,[status(thm)],[f55019])).
% 156.17/20.11 fof(f55022,plain,(
% 156.17/20.11 ![X0,X1,X2]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X0|v_b____=X0|v_a____=v_b____|c_in(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X2,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1682,f50225])).
% 156.17/20.11 fof(f55023,plain,(
% 156.17/20.11 spl0_312|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f55022,f55019,f1723,f54278,f42998])).
% 156.17/20.11 fof(f55024,plain,(
% 156.17/20.11 spl0_313 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|c_in(v_b_H____,c_Relation_OImage(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f55025,plain,(
% 156.17/20.11 ![X0,X1,X2]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|c_in(v_b_H____,c_Relation_OImage(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~spl0_313)),
% 156.17/20.11 inference(component_clause,[status(thm)],[f55024])).
% 156.17/20.11 fof(f55027,plain,(
% 156.17/20.11 ![X0,X1,X2]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X0|v_b____=X0|v_a____=v_b____|c_in(v_b_H____,c_Relation_OImage(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1682,f50152])).
% 156.17/20.11 fof(f55028,plain,(
% 156.17/20.11 spl0_313|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f55027,f55024,f1723,f54278,f42998])).
% 156.17/20.11 fof(f55029,plain,(
% 156.17/20.11 spl0_314 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f55030,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_314)),
% 156.17/20.11 inference(component_clause,[status(thm)],[f55029])).
% 156.17/20.11 fof(f55032,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X0|v_b____=X0|v_a____=v_b____|c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1682,f49598])).
% 156.17/20.11 fof(f55033,plain,(
% 156.17/20.11 spl0_314|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f55032,f55029,f1723,f54278,f42998])).
% 156.17/20.11 fof(f55034,plain,(
% 156.17/20.11 spl0_315 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|~c_Relation_Oantisym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f55037,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X0|v_b____=X0|v_a____=v_b____|~c_Relation_Oantisym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_109)),
% 156.17/20.11 inference(resolution,[status(thm)],[f1682,f43137])).
% 156.17/20.11 fof(f55038,plain,(
% 156.17/20.11 spl0_315|~spl0_1|~spl0_258|spl0_110|~spl0_109),
% 156.17/20.11 inference(split_clause,[status(thm)],[f55037,f55034,f1723,f54278,f42998,f42993])).
% 156.17/20.11 fof(f55039,plain,(
% 156.17/20.11 spl0_316 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oantisym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f55042,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X0|v_b____=X0|v_a____=v_b____|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oantisym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_109)),
% 156.17/20.11 inference(resolution,[status(thm)],[f1682,f45370])).
% 156.17/20.11 fof(f55043,plain,(
% 156.17/20.11 spl0_316|~spl0_1|~spl0_258|spl0_110|~spl0_109),
% 156.17/20.11 inference(split_clause,[status(thm)],[f55042,f55039,f1723,f54278,f42998,f42993])).
% 156.17/20.11 fof(f55044,plain,(
% 156.17/20.11 spl0_317 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|~c_Nitpick_Orefl_H(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f55047,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X0|v_b____=X0|v_a____=v_b____|~c_Nitpick_Orefl_H(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~spl0_96)),
% 156.17/20.11 inference(resolution,[status(thm)],[f1682,f41288])).
% 156.17/20.11 fof(f55048,plain,(
% 156.17/20.11 spl0_317|~spl0_1|~spl0_258|spl0_110|~spl0_96),
% 156.17/20.11 inference(split_clause,[status(thm)],[f55047,f55044,f1723,f54278,f42998,f41287])).
% 156.17/20.11 fof(f55049,plain,(
% 156.17/20.11 spl0_318 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|c_in(c_Pair(X2,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f55050,plain,(
% 156.17/20.11 ![X0,X1,X2]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|c_in(c_Pair(X2,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_318)),
% 156.17/20.11 inference(component_clause,[status(thm)],[f55049])).
% 156.17/20.11 fof(f55052,plain,(
% 156.17/20.11 ![X0,X1,X2]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X0|v_b____=X0|v_a____=v_b____|c_in(c_Pair(X2,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1682,f40300])).
% 156.17/20.11 fof(f55053,plain,(
% 156.17/20.11 spl0_318|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f55052,f55049,f1723,f54278,f42998])).
% 156.17/20.11 fof(f55054,plain,(
% 156.17/20.11 spl0_319 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|hBOOL(hAPP(c_Transitive__Closure_Otrancl(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f55057,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X0|v_b____=X0|v_a____=v_b____|hBOOL(hAPP(c_Transitive__Closure_Otrancl(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1682,f5652])).
% 156.17/20.11 fof(f55058,plain,(
% 156.17/20.11 spl0_319|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f55057,f55054,f1723,f54278,f42998])).
% 156.17/20.11 fof(f55059,plain,(
% 156.17/20.11 spl0_320 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|hBOOL(hAPP(c_Transitive__Closure_Ortrancl(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f55062,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X0|v_b____=X0|v_a____=v_b____|hBOOL(hAPP(c_Transitive__Closure_Ortrancl(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1682,f5567])).
% 156.17/20.11 fof(f55063,plain,(
% 156.17/20.11 spl0_320|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f55062,f55059,f1723,f54278,f42998])).
% 156.17/20.11 fof(f55064,plain,(
% 156.17/20.11 spl0_321 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f55065,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_321)),
% 156.17/20.11 inference(component_clause,[status(thm)],[f55064])).
% 156.17/20.11 fof(f55067,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X0|v_b____=X0|v_a____=v_b____|hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1682,f1878])).
% 156.17/20.11 fof(f55068,plain,(
% 156.17/20.11 spl0_321|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f55067,f55064,f1723,f54278,f42998])).
% 156.17/20.11 fof(f55069,plain,(
% 156.17/20.11 spl0_322 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f55070,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X0|v_b____=X0|c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~spl0_322)),
% 156.17/20.11 inference(component_clause,[status(thm)],[f55069])).
% 156.17/20.11 fof(f55072,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X0|v_b____=X0|v_a____=v_b____|c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X0)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1682,f12832])).
% 156.17/20.11 fof(f55073,plain,(
% 156.17/20.11 spl0_322|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f55072,f55069,f1723,f54278,f42998])).
% 156.17/20.11 fof(f55074,plain,(
% 156.17/20.11 spl0_323 <=> c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b____=X0|v_a____=X0|~c_Relation_Oantisym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X0)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f55077,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X0|v_a____=X0|v_b____=v_a____|~c_Relation_Oantisym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X0)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~spl0_112)),
% 156.17/20.11 inference(resolution,[status(thm)],[f1682,f43007])).
% 156.17/20.11 fof(f55078,plain,(
% 156.17/20.11 spl0_323|~spl0_153|~spl0_258|spl0_110|~spl0_112),
% 156.17/20.11 inference(split_clause,[status(thm)],[f55077,f55074,f47635,f54278,f42998,f43006])).
% 156.17/20.11 fof(f55079,plain,(
% 156.17/20.11 spl0_324 <=> c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b____=X0|v_a____=X0|~c_Relation_Oantisym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X0)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f55082,plain,(
% 156.17/20.11 ![X0,X1]: (c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X0|v_a____=X0|v_b____=v_a____|~c_Relation_Oantisym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X0)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_111)),
% 156.17/20.11 inference(resolution,[status(thm)],[f1682,f43002])).
% 156.17/20.11 fof(f55083,plain,(
% 156.17/20.11 spl0_324|~spl0_153|~spl0_258|spl0_110|~spl0_111),
% 156.17/20.11 inference(split_clause,[status(thm)],[f55082,f55079,f47635,f54278,f42998,f43001])).
% 156.17/20.11 fof(f55094,plain,(
% 156.17/20.11 spl0_327 <=> c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P_H____,X2,v_b____,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)))|v_b____=X1|X0=X1|v_b____=X0|X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X2,v_b____,X0,X1)),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____,X2,v_b____,X0,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f55097,plain,(
% 156.17/20.11 ![X0,X1,X2]: (c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P_H____,X2,v_b____,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(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b____=X1|X0=X1|v_b____=X0|X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X2,v_b____,X0,X1)),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____,X2,v_b____,X0,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.11 inference(resolution,[status(thm)],[f1682,f39703])).
% 156.17/20.11 fof(f55098,plain,(
% 156.17/20.11 spl0_327|~spl0_254),
% 156.17/20.11 inference(split_clause,[status(thm)],[f55097,f55094,f54259])).
% 156.17/20.11 fof(f55310,plain,(
% 156.17/20.11 spl0_328 <=> c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X2|v_b____=X2),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f55313,plain,(
% 156.17/20.11 ![X0,X1,X2]: (c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X2|v_b____=X2|v_a____=v_b____)),
% 156.17/20.11 inference(resolution,[status(thm)],[f53561,f1682])).
% 156.17/20.11 fof(f55314,plain,(
% 156.17/20.11 spl0_328|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f55313,f55310,f1723,f54278,f42998])).
% 156.17/20.11 fof(f55315,plain,(
% 156.17/20.11 spl0_329 <=> c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b____|X2=v_a____),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f55318,plain,(
% 156.17/20.11 ![X0,X1,X2]: (c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b____|v_a____=v_b____|X2=v_a____)),
% 156.17/20.11 inference(resolution,[status(thm)],[f53561,f1680])).
% 156.17/20.11 fof(f55319,plain,(
% 156.17/20.11 spl0_329|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f55318,f55315,f1723,f54278,f42998])).
% 156.17/20.11 fof(f55320,plain,(
% 156.17/20.11 spl0_330 <=> c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X2,hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f55323,plain,(
% 156.17/20.11 ![X0,X1,X2]: (c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=v_b____|~c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X2,hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.11 inference(resolution,[status(thm)],[f53561,f1644])).
% 156.17/20.11 fof(f55324,plain,(
% 156.17/20.11 spl0_330|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f55323,f55320,f42998])).
% 156.17/20.11 fof(f55330,plain,(
% 156.17/20.11 ![X0,X1,X2,X3,X4,X5]: (~c_in(X0,c_Relation_OId__on(c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X3),X4),X5))),
% 156.17/20.11 inference(resolution,[status(thm)],[f49923,f26563])).
% 156.17/20.11 fof(f55344,plain,(
% 156.17/20.11 ![X0,X1,X2,X3,X4,X5]: (c_in(X0,c_Wellfounded_Oacc(c_Relation_OId__on(c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X3),X4),X5),X5))),
% 156.17/20.11 inference(resolution,[status(thm)],[f55330,f1502])).
% 156.17/20.11 fof(f55359,plain,(
% 156.17/20.11 ![X0,X1,X2,X3,X4,X5]: (~c_in(X0,c_Relation_OId__on(c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X3),X4),X5))),
% 156.17/20.11 inference(resolution,[status(thm)],[f49928,f26563])).
% 156.17/20.11 fof(f55373,plain,(
% 156.17/20.11 ![X0,X1,X2,X3,X4,X5]: (c_in(X0,c_Wellfounded_Oacc(c_Relation_OId__on(c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X3),X4),X5),X5))),
% 156.17/20.11 inference(resolution,[status(thm)],[f55359,f1502])).
% 156.17/20.11 fof(f55386,plain,(
% 156.17/20.11 spl0_331 <=> X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X2|v_b____=X2),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f55389,plain,(
% 156.17/20.11 ![X0,X1,X2]: (X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X2|v_b____=X2|v_a____=v_b____)),
% 156.17/20.11 inference(resolution,[status(thm)],[f39990,f1682])).
% 156.17/20.11 fof(f55390,plain,(
% 156.17/20.11 spl0_331|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f55389,f55386,f1723,f54278,f42998])).
% 156.17/20.11 fof(f55391,plain,(
% 156.17/20.11 spl0_332 <=> X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b____|X2=v_a____),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f55394,plain,(
% 156.17/20.11 ![X0,X1,X2]: (X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b____|v_a____=v_b____|X2=v_a____)),
% 156.17/20.11 inference(resolution,[status(thm)],[f39990,f1680])).
% 156.17/20.11 fof(f55395,plain,(
% 156.17/20.11 spl0_332|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f55394,f55391,f1723,f54278,f42998])).
% 156.17/20.11 fof(f55396,plain,(
% 156.17/20.11 spl0_333 <=> X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,X1),c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X2,hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f55399,plain,(
% 156.17/20.11 ![X0,X1,X2]: (X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,X1),c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=v_b____|~c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X2,hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.11 inference(resolution,[status(thm)],[f39990,f1644])).
% 156.17/20.11 fof(f55400,plain,(
% 156.17/20.11 spl0_333|spl0_110),
% 156.17/20.11 inference(split_clause,[status(thm)],[f55399,f55396,f42998])).
% 156.17/20.11 fof(f55422,plain,(
% 156.17/20.11 spl0_334 <=> ~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____,X1,X0,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,X0,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,X0,v_b____,X2)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(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(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,X0,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=X2|v_b____=X2|X0=v_b____),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f55425,plain,(
% 156.17/20.11 ![X0,X1,X2]: (~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____,X1,X0,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,X0,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,X0,v_b____,X2)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(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(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,X0,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=X2|v_b____=X2|X0=v_b____)),
% 156.17/20.11 inference(resolution,[status(thm)],[f40301,f1678])).
% 156.17/20.11 fof(f55426,plain,(
% 156.17/20.11 spl0_334|~spl0_258),
% 156.17/20.11 inference(split_clause,[status(thm)],[f55425,f55422,f54278])).
% 156.17/20.11 fof(f55427,plain,(
% 156.17/20.11 spl0_335 <=> ~c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,X0,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,X0,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,X0,v_b____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),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))|~c_in(c_Pair(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,X0,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b____|X0=v_b____|X2=X0),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f55430,plain,(
% 156.17/20.11 ![X0,X1,X2]: (~c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,X0,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,X0,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,X0,v_b____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),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))|~c_in(c_Pair(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,X0,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b____|X0=v_b____|X2=X0)),
% 156.17/20.11 inference(resolution,[status(thm)],[f40301,f1676])).
% 156.17/20.11 fof(f55431,plain,(
% 156.17/20.11 spl0_335|~spl0_258),
% 156.17/20.11 inference(split_clause,[status(thm)],[f55430,f55427,f54278])).
% 156.17/20.11 fof(f55500,plain,(
% 156.17/20.11 ![X0,X1,X2]: (~c_Nitpick_Orefl_H(X0,X1)|hBOOL(hAPP(c_Relation_ODomain(X0,X1,X1),X2)))),
% 156.17/20.11 inference(resolution,[status(thm)],[f51612,f1666])).
% 156.17/20.11 fof(f55523,plain,(
% 156.17/20.11 ![X0,X1,X2]: (c_in(X0,c_Relation_ODomain(X1,X2,X2),X2)|~c_Nitpick_Orefl_H(c_Transitive__Closure_Otrancl(X1,X2),X2))),
% 156.17/20.11 inference(paramodulation,[status(thm)],[f1426,f51612])).
% 156.17/20.11 fof(f55641,plain,(
% 156.17/20.11 ![X0,X1,X2]: (hBOOL(X0)|~c_Nitpick_Orefl_H(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2))),
% 156.17/20.11 inference(paramodulation,[status(thm)],[f806,f54781])).
% 156.17/20.11 fof(f55642,plain,(
% 156.17/20.11 spl0_62|spl0_149),
% 156.17/20.11 inference(split_clause,[status(thm)],[f55641,f29892,f47461])).
% 156.17/20.11 fof(f55643,plain,(
% 156.17/20.11 spl0_336 <=> ~c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f55646,plain,(
% 156.17/20.11 ![X0,X1,X2,X3]: (hBOOL(X0)|~c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3))),
% 156.17/20.11 inference(paramodulation,[status(thm)],[f806,f49205])).
% 156.17/20.11 fof(f55647,plain,(
% 156.17/20.11 spl0_62|spl0_336),
% 156.17/20.11 inference(split_clause,[status(thm)],[f55646,f29892,f55643])).
% 156.17/20.11 fof(f55972,plain,(
% 156.17/20.11 ~hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P_H____))|spl0_254),
% 156.17/20.11 inference(resolution,[status(thm)],[f54261,f1664])).
% 156.17/20.11 fof(f55973,plain,(
% 156.17/20.11 $false|spl0_254),
% 156.17/20.11 inference(forward_subsumption_resolution,[status(thm)],[f55972,f13198])).
% 156.17/20.11 fof(f55974,plain,(
% 156.17/20.11 spl0_254),
% 156.17/20.11 inference(contradiction_clause,[status(thm)],[f55973])).
% 156.17/20.11 fof(f55994,plain,(
% 156.17/20.11 spl0_337 <=> ~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|hAPP(hAPP(X3,v_b____),v_b____)=hAPP(hAPP(X3,v_b_H____),v_b_H____)|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4)|c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b____=X2|v_a____=X2),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f55997,plain,(
% 156.17/20.11 ![X0,X1,X2,X3,X4]: (~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|hAPP(hAPP(X3,v_b____),v_b____)=hAPP(hAPP(X3,v_b_H____),v_b_H____)|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4)|c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X2|v_a____=X2|v_b____=v_a____|~spl0_216)),
% 156.17/20.11 inference(resolution,[status(thm)],[f52662,f1678])).
% 156.17/20.11 fof(f55998,plain,(
% 156.17/20.11 spl0_337|~spl0_153|~spl0_258|spl0_110|~spl0_216),
% 156.17/20.11 inference(split_clause,[status(thm)],[f55997,f55994,f47635,f54278,f42998,f52661])).
% 156.17/20.11 fof(f55999,plain,(
% 156.17/20.11 spl0_338 <=> ~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|hAPP(hAPP(X3,v_b____),v_b____)=hAPP(hAPP(X3,v_b_H____),v_b_H____)|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4)|c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_a____|X2=v_b____),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56002,plain,(
% 156.17/20.11 ![X0,X1,X2,X3,X4]: (~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|hAPP(hAPP(X3,v_b____),v_b____)=hAPP(hAPP(X3,v_b_H____),v_b_H____)|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4)|c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_a____|v_b____=v_a____|X2=v_b____|~spl0_216)),
% 156.17/20.11 inference(resolution,[status(thm)],[f52662,f1676])).
% 156.17/20.11 fof(f56003,plain,(
% 156.17/20.11 spl0_338|~spl0_153|~spl0_258|spl0_110|~spl0_216),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56002,f55999,f47635,f54278,f42998,f52661])).
% 156.17/20.11 fof(f56033,plain,(
% 156.17/20.11 spl0_339 <=> ~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b____=X2|v_a____=X2),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56036,plain,(
% 156.17/20.11 ![X0,X1,X2]: (~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X2|v_a____=X2|v_b____=v_a____|~spl0_217)),
% 156.17/20.11 inference(resolution,[status(thm)],[f52667,f1678])).
% 156.17/20.11 fof(f56037,plain,(
% 156.17/20.11 spl0_339|~spl0_153|~spl0_258|spl0_110|~spl0_217),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56036,f56033,f47635,f54278,f42998,f52666])).
% 156.17/20.11 fof(f56038,plain,(
% 156.17/20.11 spl0_340 <=> ~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_a____|X2=v_b____),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56041,plain,(
% 156.17/20.11 ![X0,X1,X2]: (~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_a____|v_b____=v_a____|X2=v_b____|~spl0_217)),
% 156.17/20.11 inference(resolution,[status(thm)],[f52667,f1676])).
% 156.17/20.11 fof(f56042,plain,(
% 156.17/20.11 spl0_340|~spl0_153|~spl0_258|spl0_110|~spl0_217),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56041,f56038,f47635,f54278,f42998,f52666])).
% 156.17/20.11 fof(f56063,plain,(
% 156.17/20.11 spl0_341 <=> ~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b____=X2|v_a____=X2),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56066,plain,(
% 156.17/20.11 ![X0,X1,X2]: (~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X2|v_a____=X2|v_b____=v_a____|~spl0_218)),
% 156.17/20.11 inference(resolution,[status(thm)],[f52672,f1678])).
% 156.17/20.11 fof(f56067,plain,(
% 156.17/20.11 spl0_341|~spl0_153|~spl0_258|spl0_110|~spl0_218),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56066,f56063,f47635,f54278,f42998,f52671])).
% 156.17/20.11 fof(f56068,plain,(
% 156.17/20.11 spl0_342 <=> ~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_a____|X2=v_b____),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56071,plain,(
% 156.17/20.11 ![X0,X1,X2]: (~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_a____|v_b____=v_a____|X2=v_b____|~spl0_218)),
% 156.17/20.11 inference(resolution,[status(thm)],[f52672,f1676])).
% 156.17/20.11 fof(f56072,plain,(
% 156.17/20.11 spl0_342|~spl0_153|~spl0_258|spl0_110|~spl0_218),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56071,f56068,f47635,f54278,f42998,f52671])).
% 156.17/20.11 fof(f56093,plain,(
% 156.17/20.11 spl0_343 <=> ~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X3,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b____=X2|v_a____=X2),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56096,plain,(
% 156.17/20.11 ![X0,X1,X2,X3]: (~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X3,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X2|v_a____=X2|v_b____=v_a____|~spl0_219)),
% 156.17/20.11 inference(resolution,[status(thm)],[f52677,f1678])).
% 156.17/20.11 fof(f56097,plain,(
% 156.17/20.11 spl0_343|~spl0_153|~spl0_258|spl0_110|~spl0_219),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56096,f56093,f47635,f54278,f42998,f52676])).
% 156.17/20.11 fof(f56098,plain,(
% 156.17/20.11 spl0_344 <=> ~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X3,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_a____|X2=v_b____),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56101,plain,(
% 156.17/20.11 ![X0,X1,X2,X3]: (~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X3,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_a____|v_b____=v_a____|X2=v_b____|~spl0_219)),
% 156.17/20.11 inference(resolution,[status(thm)],[f52677,f1676])).
% 156.17/20.11 fof(f56102,plain,(
% 156.17/20.11 spl0_344|~spl0_153|~spl0_258|spl0_110|~spl0_219),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56101,f56098,f47635,f54278,f42998,f52676])).
% 156.17/20.11 fof(f56155,plain,(
% 156.17/20.11 spl0_345 <=> ~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3),X4),X5)),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56158,plain,(
% 156.17/20.11 ![X0,X1,X2,X3,X4,X5]: (hBOOL(hAPP(X0,X1))|~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3),X4),X5))),
% 156.17/20.11 inference(resolution,[status(thm)],[f49947,f30446])).
% 156.17/20.11 fof(f56159,plain,(
% 156.17/20.11 spl0_75|spl0_345),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56158,f37252,f56155])).
% 156.17/20.11 fof(f56162,plain,(
% 156.17/20.11 ![X0,X1,X2,X3,X4]: (hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1),X2),X3),X4)))),
% 156.17/20.11 inference(resolution,[status(thm)],[f49947,f1666])).
% 156.17/20.11 fof(f56185,plain,(
% 156.17/20.11 spl0_346 <=> ~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____,X1,X0,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,X0,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,X0,v_b____,X2)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(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(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,X0,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=X2|v_b____=X2|X0=v_b____),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56188,plain,(
% 156.17/20.11 ![X0,X1,X2]: (~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____,X1,X0,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,X0,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,X0,v_b____,X2)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(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(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,X0,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=X2|v_b____=X2|X0=v_b____)),
% 156.17/20.11 inference(resolution,[status(thm)],[f40302,f1678])).
% 156.17/20.11 fof(f56189,plain,(
% 156.17/20.11 spl0_346|~spl0_258),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56188,f56185,f54278])).
% 156.17/20.11 fof(f56190,plain,(
% 156.17/20.11 spl0_347 <=> ~c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,X0,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,X0,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,X0,v_b____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),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))|~c_in(c_Pair(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,X0,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b____|X0=v_b____|X2=X0),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56193,plain,(
% 156.17/20.11 ![X0,X1,X2]: (~c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,X0,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,X0,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,X0,v_b____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),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))|~c_in(c_Pair(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,X0,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b____|X0=v_b____|X2=X0)),
% 156.17/20.11 inference(resolution,[status(thm)],[f40302,f1676])).
% 156.17/20.11 fof(f56194,plain,(
% 156.17/20.11 spl0_347|~spl0_258),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56193,f56190,f54278])).
% 156.17/20.11 fof(f56315,plain,(
% 156.17/20.11 spl0_348 <=> 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____,X1,v_b____,X0,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,X0,X2)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,X0,X2)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X0,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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(X0,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,X0,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b____=X2|X0=X2|v_b____=X0),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56318,plain,(
% 156.17/20.11 ![X0,X1,X2]: (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____,X1,v_b____,X0,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,X0,X2)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,X0,X2)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X0,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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(X0,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,X0,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X2|X0=X2|v_b____=X0)),
% 156.17/20.11 inference(resolution,[status(thm)],[f40363,f1682])).
% 156.17/20.11 fof(f56319,plain,(
% 156.17/20.11 spl0_348|~spl0_258),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56318,f56315,f54278])).
% 156.17/20.11 fof(f56320,plain,(
% 156.17/20.11 spl0_349 <=> c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,X0)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=X0|v_b____=X0|X2=v_b____),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56323,plain,(
% 156.17/20.11 ![X0,X1,X2]: (c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,X0)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=X0|v_b____=X0|X2=v_b____)),
% 156.17/20.11 inference(resolution,[status(thm)],[f40363,f1680])).
% 156.17/20.11 fof(f56324,plain,(
% 156.17/20.11 spl0_349|~spl0_258),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56323,f56320,f54278])).
% 156.17/20.11 fof(f56340,plain,(
% 156.17/20.11 spl0_350 <=> 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____,X1,v_b____,X0,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,X0,X2)),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,X0,X2)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X0,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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(X0,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,X0,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b____=X2|X0=X2|v_b____=X0),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56343,plain,(
% 156.17/20.11 ![X0,X1,X2]: (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____,X1,v_b____,X0,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,X0,X2)),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,X0,X2)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X0,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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(X0,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,X0,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X2|X0=X2|v_b____=X0)),
% 156.17/20.11 inference(resolution,[status(thm)],[f40364,f1682])).
% 156.17/20.11 fof(f56344,plain,(
% 156.17/20.11 spl0_350|~spl0_258),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56343,f56340,f54278])).
% 156.17/20.11 fof(f56345,plain,(
% 156.17/20.11 spl0_351 <=> c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,X0)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=X0|v_b____=X0|X2=v_b____),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56348,plain,(
% 156.17/20.11 ![X0,X1,X2]: (c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,X0)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=X0|v_b____=X0|X2=v_b____)),
% 156.17/20.11 inference(resolution,[status(thm)],[f40364,f1680])).
% 156.17/20.11 fof(f56349,plain,(
% 156.17/20.11 spl0_351|~spl0_258),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56348,f56345,f54278])).
% 156.17/20.11 fof(f56627,plain,(
% 156.17/20.11 spl0_352 <=> ~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X3,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b____=X2|v_a____=X2),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56630,plain,(
% 156.17/20.11 ![X0,X1,X2,X3]: (~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X3,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X2|v_a____=X2|v_b____=v_a____|~spl0_220)),
% 156.17/20.11 inference(resolution,[status(thm)],[f52682,f1678])).
% 156.17/20.11 fof(f56631,plain,(
% 156.17/20.11 spl0_352|~spl0_153|~spl0_258|spl0_110|~spl0_220),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56630,f56627,f47635,f54278,f42998,f52681])).
% 156.17/20.11 fof(f56632,plain,(
% 156.17/20.11 spl0_353 <=> ~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X3,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_a____|X2=v_b____),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56635,plain,(
% 156.17/20.11 ![X0,X1,X2,X3]: (~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X3,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_a____|v_b____=v_a____|X2=v_b____|~spl0_220)),
% 156.17/20.11 inference(resolution,[status(thm)],[f52682,f1676])).
% 156.17/20.11 fof(f56636,plain,(
% 156.17/20.11 spl0_353|~spl0_153|~spl0_258|spl0_110|~spl0_220),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56635,f56632,f47635,f54278,f42998,f52681])).
% 156.17/20.11 fof(f56720,plain,(
% 156.17/20.11 spl0_354 <=> ~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b_H____,c_Relation_OImage(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b____=X2|v_a____=X2),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56723,plain,(
% 156.17/20.11 ![X0,X1,X2,X3]: (~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b_H____,c_Relation_OImage(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X2|v_a____=X2|v_b____=v_a____|~spl0_221)),
% 156.17/20.11 inference(resolution,[status(thm)],[f52687,f1678])).
% 156.17/20.11 fof(f56724,plain,(
% 156.17/20.11 spl0_354|~spl0_153|~spl0_258|spl0_110|~spl0_221),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56723,f56720,f47635,f54278,f42998,f52686])).
% 156.17/20.11 fof(f56725,plain,(
% 156.17/20.11 spl0_355 <=> ~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b_H____,c_Relation_OImage(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_a____|X2=v_b____),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56728,plain,(
% 156.17/20.11 ![X0,X1,X2,X3]: (~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b_H____,c_Relation_OImage(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_a____|v_b____=v_a____|X2=v_b____|~spl0_221)),
% 156.17/20.11 inference(resolution,[status(thm)],[f52687,f1676])).
% 156.17/20.11 fof(f56729,plain,(
% 156.17/20.11 spl0_355|~spl0_153|~spl0_258|spl0_110|~spl0_221),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56728,f56725,f47635,f54278,f42998,f52686])).
% 156.17/20.11 fof(f56752,plain,(
% 156.17/20.11 spl0_356 <=> ~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b____=X2|v_a____=X2),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56755,plain,(
% 156.17/20.11 ![X0,X1,X2]: (~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X2|v_a____=X2|v_b____=v_a____|~spl0_222)),
% 156.17/20.11 inference(resolution,[status(thm)],[f52692,f1678])).
% 156.17/20.11 fof(f56756,plain,(
% 156.17/20.11 spl0_356|~spl0_153|~spl0_258|spl0_110|~spl0_222),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56755,f56752,f47635,f54278,f42998,f52691])).
% 156.17/20.11 fof(f56757,plain,(
% 156.17/20.11 spl0_357 <=> ~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_a____|X2=v_b____),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56760,plain,(
% 156.17/20.11 ![X0,X1,X2]: (~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_a____|v_b____=v_a____|X2=v_b____|~spl0_222)),
% 156.17/20.11 inference(resolution,[status(thm)],[f52692,f1676])).
% 156.17/20.11 fof(f56761,plain,(
% 156.17/20.11 spl0_357|~spl0_153|~spl0_258|spl0_110|~spl0_222),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56760,f56757,f47635,f54278,f42998,f52691])).
% 156.17/20.11 fof(f56788,plain,(
% 156.17/20.11 spl0_358 <=> ~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X3,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X3,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b____=X2|v_a____=X2),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56791,plain,(
% 156.17/20.11 ![X0,X1,X2,X3]: (~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X3,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X3,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X2|v_a____=X2|v_b____=v_a____|~spl0_226)),
% 156.17/20.11 inference(resolution,[status(thm)],[f52712,f1678])).
% 156.17/20.11 fof(f56792,plain,(
% 156.17/20.11 spl0_358|~spl0_153|~spl0_258|spl0_110|~spl0_226),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56791,f56788,f47635,f54278,f42998,f52711])).
% 156.17/20.11 fof(f56793,plain,(
% 156.17/20.11 spl0_359 <=> ~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X3,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X3,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_a____|X2=v_b____),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56796,plain,(
% 156.17/20.11 ![X0,X1,X2,X3]: (~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X3,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X3,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_a____|v_b____=v_a____|X2=v_b____|~spl0_226)),
% 156.17/20.11 inference(resolution,[status(thm)],[f52712,f1676])).
% 156.17/20.11 fof(f56797,plain,(
% 156.17/20.11 spl0_359|~spl0_153|~spl0_258|spl0_110|~spl0_226),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56796,f56793,f47635,f54278,f42998,f52711])).
% 156.17/20.11 fof(f56818,plain,(
% 156.17/20.11 spl0_360 <=> ~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b____=X2|v_a____=X2),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56821,plain,(
% 156.17/20.11 ![X0,X1,X2]: (~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X2|v_a____=X2|v_b____=v_a____|~spl0_229)),
% 156.17/20.11 inference(resolution,[status(thm)],[f52727,f1678])).
% 156.17/20.11 fof(f56822,plain,(
% 156.17/20.11 spl0_360|~spl0_153|~spl0_258|spl0_110|~spl0_229),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56821,f56818,f47635,f54278,f42998,f52726])).
% 156.17/20.11 fof(f56823,plain,(
% 156.17/20.11 spl0_361 <=> ~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_a____|X2=v_b____),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56826,plain,(
% 156.17/20.11 ![X0,X1,X2]: (~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_a____|v_b____=v_a____|X2=v_b____|~spl0_229)),
% 156.17/20.11 inference(resolution,[status(thm)],[f52727,f1676])).
% 156.17/20.11 fof(f56827,plain,(
% 156.17/20.11 spl0_361|~spl0_153|~spl0_258|spl0_110|~spl0_229),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56826,f56823,f47635,f54278,f42998,f52726])).
% 156.17/20.11 fof(f56848,plain,(
% 156.17/20.11 spl0_362 <=> ~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b____=X2|v_a____=X2),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56851,plain,(
% 156.17/20.11 ![X0,X1,X2]: (~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X2|v_a____=X2|v_b____=v_a____|~spl0_230)),
% 156.17/20.11 inference(resolution,[status(thm)],[f52732,f1678])).
% 156.17/20.11 fof(f56852,plain,(
% 156.17/20.11 spl0_362|~spl0_153|~spl0_258|spl0_110|~spl0_230),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56851,f56848,f47635,f54278,f42998,f52731])).
% 156.17/20.11 fof(f56853,plain,(
% 156.17/20.11 spl0_363 <=> ~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_a____|X2=v_b____),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56856,plain,(
% 156.17/20.11 ![X0,X1,X2]: (~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_a____|v_b____=v_a____|X2=v_b____|~spl0_230)),
% 156.17/20.11 inference(resolution,[status(thm)],[f52732,f1676])).
% 156.17/20.11 fof(f56857,plain,(
% 156.17/20.11 spl0_363|~spl0_153|~spl0_258|spl0_110|~spl0_230),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56856,f56853,f47635,f54278,f42998,f52731])).
% 156.17/20.11 fof(f56895,plain,(
% 156.17/20.11 spl0_365 <=> ~c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,X0,v_b_H____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,X0,v_b_H____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,X0,v_b_H____,X2)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X0,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_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,X0,v_b_H____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=X2|v_b_H____=X2|X0=v_b_H____),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56898,plain,(
% 156.17/20.11 ![X0,X1,X2]: (~c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,X0,v_b_H____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,X0,v_b_H____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,X0,v_b_H____,X2)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X0,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_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,X0,v_b_H____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=X2|v_b_H____=X2|X0=v_b_H____)),
% 156.17/20.11 inference(resolution,[status(thm)],[f40689,f1678])).
% 156.17/20.11 fof(f56899,plain,(
% 156.17/20.11 spl0_365|~spl0_254),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56898,f56895,f54259])).
% 156.17/20.11 fof(f56900,plain,(
% 156.17/20.11 spl0_366 <=> ~c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X2,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X2,X0,v_b_H____)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X2,X0,v_b_H____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X0,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(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X2,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b_H____|X0=v_b_H____|X2=X0),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56903,plain,(
% 156.17/20.11 ![X0,X1,X2]: (~c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X2,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X2,X0,v_b_H____)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X2,X0,v_b_H____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X0,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(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X2,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b_H____|X0=v_b_H____|X2=X0)),
% 156.17/20.11 inference(resolution,[status(thm)],[f40689,f1676])).
% 156.17/20.11 fof(f56904,plain,(
% 156.17/20.11 spl0_366|~spl0_254),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56903,f56900,f54259])).
% 156.17/20.11 fof(f56954,plain,(
% 156.17/20.11 spl0_368 <=> ~c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,X0,v_b_H____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,X0,v_b_H____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,X0,v_b_H____,X2)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X0,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_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,X0,v_b_H____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=X2|v_b_H____=X2|X0=v_b_H____),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56957,plain,(
% 156.17/20.11 ![X0,X1,X2]: (~c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,X0,v_b_H____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,X0,v_b_H____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,X0,v_b_H____,X2)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X0,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_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,X0,v_b_H____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=X2|v_b_H____=X2|X0=v_b_H____)),
% 156.17/20.11 inference(resolution,[status(thm)],[f40690,f1678])).
% 156.17/20.11 fof(f56958,plain,(
% 156.17/20.11 spl0_368|~spl0_254),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56957,f56954,f54259])).
% 156.17/20.11 fof(f56959,plain,(
% 156.17/20.11 spl0_369 <=> ~c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X2,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X2,X0,v_b_H____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X2,X0,v_b_H____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X0,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(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X2,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b_H____|X0=v_b_H____|X2=X0),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f56962,plain,(
% 156.17/20.11 ![X0,X1,X2]: (~c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X2,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X2,X0,v_b_H____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X2,X0,v_b_H____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X0,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(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X2,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b_H____|X0=v_b_H____|X2=X0)),
% 156.17/20.11 inference(resolution,[status(thm)],[f40690,f1676])).
% 156.17/20.11 fof(f56963,plain,(
% 156.17/20.11 spl0_369|~spl0_254),
% 156.17/20.11 inference(split_clause,[status(thm)],[f56962,f56959,f54259])).
% 156.17/20.11 fof(f57000,plain,(
% 156.17/20.11 spl0_371 <=> ~c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,X0,v_b_H____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,X0,v_b_H____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X1,X0,v_b_H____,X2)),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X0,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_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,X0,v_b_H____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=X2|v_b_H____=X2|X0=v_b_H____),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f57003,plain,(
% 156.17/20.11 ![X0,X1,X2]: (~c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,X0,v_b_H____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,X0,v_b_H____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X1,X0,v_b_H____,X2)),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X0,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_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,X0,v_b_H____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=X2|v_b_H____=X2|X0=v_b_H____)),
% 156.17/20.11 inference(resolution,[status(thm)],[f40691,f1678])).
% 156.17/20.11 fof(f57004,plain,(
% 156.17/20.11 spl0_371|~spl0_254),
% 156.17/20.11 inference(split_clause,[status(thm)],[f57003,f57000,f54259])).
% 156.17/20.11 fof(f57005,plain,(
% 156.17/20.11 spl0_372 <=> ~c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X2,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X2,X0,v_b_H____)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P____,v_sko__CHAINED__1(X1,v_P_H____,X2,X0,v_b_H____)),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X0,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(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X2,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b_H____|X0=v_b_H____|X2=X0),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f57008,plain,(
% 156.17/20.11 ![X0,X1,X2]: (~c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X2,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X2,X0,v_b_H____)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P____,v_sko__CHAINED__1(X1,v_P_H____,X2,X0,v_b_H____)),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X0,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(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X2,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b_H____|X0=v_b_H____|X2=X0)),
% 156.17/20.11 inference(resolution,[status(thm)],[f40691,f1676])).
% 156.17/20.11 fof(f57009,plain,(
% 156.17/20.11 spl0_372|~spl0_254),
% 156.17/20.11 inference(split_clause,[status(thm)],[f57008,f57005,f54259])).
% 156.17/20.11 fof(f57471,plain,(
% 156.17/20.11 spl0_373 <=> ~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b_H____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X2|v_b____=X2),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f57474,plain,(
% 156.17/20.11 ![X0,X1,X2]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b_H____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X2|v_b____=X2|v_a____=v_b____|~spl0_235)),
% 156.17/20.11 inference(resolution,[status(thm)],[f52998,f1678])).
% 156.17/20.11 fof(f57475,plain,(
% 156.17/20.11 spl0_373|~spl0_1|~spl0_258|spl0_110|~spl0_235),
% 156.17/20.11 inference(split_clause,[status(thm)],[f57474,f57471,f1723,f54278,f42998,f52756])).
% 156.17/20.11 fof(f57476,plain,(
% 156.17/20.11 spl0_374 <=> ~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b_H____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b____|X2=v_a____),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f57479,plain,(
% 156.17/20.11 ![X0,X1,X2]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b_H____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b____|v_a____=v_b____|X2=v_a____|~spl0_235)),
% 156.17/20.11 inference(resolution,[status(thm)],[f52998,f1676])).
% 156.17/20.11 fof(f57480,plain,(
% 156.17/20.11 spl0_374|~spl0_1|~spl0_258|spl0_110|~spl0_235),
% 156.17/20.11 inference(split_clause,[status(thm)],[f57479,f57476,f1723,f54278,f42998,f52756])).
% 156.17/20.11 fof(f57547,plain,(
% 156.17/20.11 spl0_375 <=> ~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X2|v_b____=X2),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f57550,plain,(
% 156.17/20.11 ![X0,X1,X2]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X2|v_b____=X2|v_a____=v_b____|~spl0_235)),
% 156.17/20.11 inference(resolution,[status(thm)],[f52999,f1678])).
% 156.17/20.11 fof(f57551,plain,(
% 156.17/20.11 spl0_375|~spl0_1|~spl0_258|spl0_110|~spl0_235),
% 156.17/20.11 inference(split_clause,[status(thm)],[f57550,f57547,f1723,f54278,f42998,f52756])).
% 156.17/20.11 fof(f57552,plain,(
% 156.17/20.11 spl0_376 <=> ~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b____|X2=v_a____),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f57555,plain,(
% 156.17/20.11 ![X0,X1,X2]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b____|v_a____=v_b____|X2=v_a____|~spl0_235)),
% 156.17/20.11 inference(resolution,[status(thm)],[f52999,f1676])).
% 156.17/20.11 fof(f57556,plain,(
% 156.17/20.11 spl0_376|~spl0_1|~spl0_258|spl0_110|~spl0_235),
% 156.17/20.11 inference(split_clause,[status(thm)],[f57555,f57552,f1723,f54278,f42998,f52756])).
% 156.17/20.11 fof(f57628,plain,(
% 156.17/20.11 spl0_377 <=> ~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b____,c_Relation_OImage(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X2|v_b____=X2),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f57631,plain,(
% 156.17/20.11 ![X0,X1,X2,X3]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b____,c_Relation_OImage(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X2|v_b____=X2|v_a____=v_b____|~spl0_235)),
% 156.17/20.11 inference(resolution,[status(thm)],[f53004,f1678])).
% 156.17/20.11 fof(f57632,plain,(
% 156.17/20.11 spl0_377|~spl0_1|~spl0_258|spl0_110|~spl0_235),
% 156.17/20.11 inference(split_clause,[status(thm)],[f57631,f57628,f1723,f54278,f42998,f52756])).
% 156.17/20.11 fof(f57633,plain,(
% 156.17/20.11 spl0_378 <=> ~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b____,c_Relation_OImage(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b____|X2=v_a____),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f57636,plain,(
% 156.17/20.11 ![X0,X1,X2,X3]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b____,c_Relation_OImage(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b____|v_a____=v_b____|X2=v_a____|~spl0_235)),
% 156.17/20.11 inference(resolution,[status(thm)],[f53004,f1676])).
% 156.17/20.11 fof(f57637,plain,(
% 156.17/20.11 spl0_378|~spl0_1|~spl0_258|spl0_110|~spl0_235),
% 156.17/20.11 inference(split_clause,[status(thm)],[f57636,f57633,f1723,f54278,f42998,f52756])).
% 156.17/20.11 fof(f57675,plain,(
% 156.17/20.11 spl0_379 <=> ~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X2|v_b____=X2),
% 156.17/20.11 introduced(split_symbol_definition)).
% 156.17/20.11 fof(f57678,plain,(
% 156.17/20.11 ![X0,X1,X2]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X2|v_b____=X2|v_a____=v_b____|~spl0_235)),
% 156.17/20.12 inference(resolution,[status(thm)],[f53005,f1678])).
% 156.17/20.12 fof(f57679,plain,(
% 156.17/20.12 spl0_379|~spl0_1|~spl0_258|spl0_110|~spl0_235),
% 156.17/20.12 inference(split_clause,[status(thm)],[f57678,f57675,f1723,f54278,f42998,f52756])).
% 156.17/20.12 fof(f57680,plain,(
% 156.17/20.12 spl0_380 <=> ~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b____|X2=v_a____),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f57683,plain,(
% 156.17/20.12 ![X0,X1,X2]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b____|v_a____=v_b____|X2=v_a____|~spl0_235)),
% 156.17/20.12 inference(resolution,[status(thm)],[f53005,f1676])).
% 156.17/20.12 fof(f57684,plain,(
% 156.17/20.12 spl0_380|~spl0_1|~spl0_258|spl0_110|~spl0_235),
% 156.17/20.12 inference(split_clause,[status(thm)],[f57683,f57680,f1723,f54278,f42998,f52756])).
% 156.17/20.12 fof(f57879,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5]: (~c_Nitpick_Orefl_H(X0,X1)|c_FunDef_Oin__rel(c_Relation_ORange(X0,X1,X1),X2,X3,X4,X5))),
% 156.17/20.12 inference(resolution,[status(thm)],[f51456,f12852])).
% 156.17/20.12 fof(f57886,plain,(
% 156.17/20.12 ![X0,X1,X2]: (~c_Nitpick_Orefl_H(c_Transitive__Closure_Otrancl(X0,X1),X1)|hBOOL(hAPP(c_Relation_ORange(X0,X1,X1),X2)))),
% 156.17/20.12 inference(paramodulation,[status(thm)],[f1444,f51456])).
% 156.17/20.12 fof(f58069,plain,(
% 156.17/20.12 spl0_381 <=> hBOOL(hAPP(X0,X1))|hBOOL(hAPP(X0,X2))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58070,plain,(
% 156.17/20.12 ![X0,X1,X2]: (hBOOL(hAPP(X0,X1))|hBOOL(hAPP(X0,X2))|~spl0_381)),
% 156.17/20.12 inference(component_clause,[status(thm)],[f58069])).
% 156.17/20.12 fof(f58072,plain,(
% 156.17/20.12 spl0_382 <=> ~c_Wellfounded_Owf(c_Relation_ORange(c_Transitive__Closure_Ortrancl(X3,tc_prod(X4,X4)),tc_prod(X4,X4),tc_prod(X4,X4)),X4)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58075,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4]: (hBOOL(hAPP(X0,X1))|hBOOL(hAPP(X0,X2))|~c_Wellfounded_Owf(c_Relation_ORange(c_Transitive__Closure_Ortrancl(X3,tc_prod(X4,X4)),tc_prod(X4,X4),tc_prod(X4,X4)),X4))),
% 156.17/20.12 inference(resolution,[status(thm)],[f1248,f50704])).
% 156.17/20.12 fof(f58076,plain,(
% 156.17/20.12 spl0_381|spl0_382),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58075,f58069,f58072])).
% 156.17/20.12 fof(f58077,plain,(
% 156.17/20.12 spl0_383 <=> ~c_Wellfounded_Owf(c_Relation_ORange(X3,tc_prod(X4,X4),tc_prod(X4,X4)),X4)|~c_Nitpick_Orefl_H(X3,tc_prod(X4,X4))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58080,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4]: (hBOOL(hAPP(X0,X1))|hBOOL(hAPP(X0,X2))|~c_Wellfounded_Owf(c_Relation_ORange(X3,tc_prod(X4,X4),tc_prod(X4,X4)),X4)|~c_Nitpick_Orefl_H(X3,tc_prod(X4,X4)))),
% 156.17/20.12 inference(resolution,[status(thm)],[f1248,f50718])).
% 156.17/20.12 fof(f58081,plain,(
% 156.17/20.12 spl0_381|spl0_383),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58080,f58069,f58077])).
% 156.17/20.12 fof(f58082,plain,(
% 156.17/20.12 spl0_384 <=> ~c_Wellfounded_Owf(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,tc_prod(X4,X4)),tc_prod(X4,X4),tc_prod(X4,X4)),X4)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58085,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4]: (hBOOL(hAPP(X0,X1))|hBOOL(hAPP(X0,X2))|~c_Wellfounded_Owf(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,tc_prod(X4,X4)),tc_prod(X4,X4),tc_prod(X4,X4)),X4))),
% 156.17/20.12 inference(resolution,[status(thm)],[f1248,f51304])).
% 156.17/20.12 fof(f58086,plain,(
% 156.17/20.12 spl0_381|spl0_384),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58085,f58069,f58082])).
% 156.17/20.12 fof(f58087,plain,(
% 156.17/20.12 spl0_385 <=> ~c_Wellfounded_Owf(c_Relation_ODomain(c_Relation_OId(tc_prod(X3,X3)),tc_prod(X3,X3),tc_prod(X3,X3)),X3)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58090,plain,(
% 156.17/20.12 ![X0,X1,X2,X3]: (hBOOL(hAPP(X0,X1))|hBOOL(hAPP(X0,X2))|~c_Wellfounded_Owf(c_Relation_ODomain(c_Relation_OId(tc_prod(X3,X3)),tc_prod(X3,X3),tc_prod(X3,X3)),X3))),
% 156.17/20.12 inference(resolution,[status(thm)],[f1248,f50488])).
% 156.17/20.12 fof(f58091,plain,(
% 156.17/20.12 spl0_381|spl0_385),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58090,f58069,f58087])).
% 156.17/20.12 fof(f58092,plain,(
% 156.17/20.12 spl0_386 <=> ~c_Wellfounded_Owf(c_Relation_ODomain(X3,tc_prod(X4,X4),tc_prod(X4,X4)),X4)|~c_Nitpick_Orefl_H(X3,tc_prod(X4,X4))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58095,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4]: (hBOOL(hAPP(X0,X1))|hBOOL(hAPP(X0,X2))|~c_Wellfounded_Owf(c_Relation_ODomain(X3,tc_prod(X4,X4),tc_prod(X4,X4)),X4)|~c_Nitpick_Orefl_H(X3,tc_prod(X4,X4)))),
% 156.17/20.12 inference(resolution,[status(thm)],[f1248,f51612])).
% 156.17/20.12 fof(f58096,plain,(
% 156.17/20.12 spl0_381|spl0_386),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58095,f58069,f58092])).
% 156.17/20.12 fof(f58109,plain,(
% 156.17/20.12 spl0_388 <=> ~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Relation_OImage(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X5,X6),tc_prod(X7,X7)),X7)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58112,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6,X7]: (hBOOL(hAPP(X0,X1))|hBOOL(hAPP(X0,X2))|~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Relation_OImage(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X5,X6),tc_prod(X7,X7)),X7))),
% 156.17/20.12 inference(resolution,[status(thm)],[f1248,f46351])).
% 156.17/20.12 fof(f58113,plain,(
% 156.17/20.12 spl0_381|spl0_388),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58112,f58069,f58109])).
% 156.17/20.12 fof(f58114,plain,(
% 156.17/20.12 spl0_389 <=> ~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Relation_OImage(X3,c_COMBK(X4,X5,X6),X7,X8),tc_prod(X9,X9)),X9)|hBOOL(X4)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58117,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6,X7,X8,X9]: (hBOOL(hAPP(X0,X1))|hBOOL(hAPP(X0,X2))|~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Relation_OImage(X3,c_COMBK(X4,X5,X6),X7,X8),tc_prod(X9,X9)),X9)|hBOOL(X4))),
% 156.17/20.12 inference(resolution,[status(thm)],[f1248,f49197])).
% 156.17/20.12 fof(f58118,plain,(
% 156.17/20.12 spl0_381|spl0_389),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58117,f58069,f58114])).
% 156.17/20.12 fof(f58119,plain,(
% 156.17/20.12 spl0_390 <=> ~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Relation_OImage(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X5,X6),tc_prod(X7,X7)),X7)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58122,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6,X7]: (hBOOL(hAPP(X0,X1))|hBOOL(hAPP(X0,X2))|~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Relation_OImage(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X5,X6),tc_prod(X7,X7)),X7))),
% 156.17/20.12 inference(resolution,[status(thm)],[f1248,f46376])).
% 156.17/20.12 fof(f58123,plain,(
% 156.17/20.12 spl0_381|spl0_390),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58122,f58069,f58119])).
% 156.17/20.12 fof(f58124,plain,(
% 156.17/20.12 spl0_391 <=> ~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Relation_ORange(c_COMBK(X3,X4,X5),X6,X7),tc_prod(X8,X8)),X8)|hBOOL(X3)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58127,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6,X7,X8]: (hBOOL(hAPP(X0,X1))|hBOOL(hAPP(X0,X2))|~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Relation_ORange(c_COMBK(X3,X4,X5),X6,X7),tc_prod(X8,X8)),X8)|hBOOL(X3))),
% 156.17/20.12 inference(resolution,[status(thm)],[f1248,f46400])).
% 156.17/20.12 fof(f58128,plain,(
% 156.17/20.12 spl0_381|spl0_391),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58127,f58069,f58124])).
% 156.17/20.12 fof(f58129,plain,(
% 156.17/20.12 spl0_392 <=> ~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X5),tc_prod(X6,X6)),X6)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58134,plain,(
% 156.17/20.12 spl0_393 <=> ~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Relation_ODomain(c_COMBK(X3,X4,X5),X6,X7),tc_prod(X8,X8)),X8)|hBOOL(X3)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58137,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6,X7,X8]: (hBOOL(hAPP(X0,X1))|hBOOL(hAPP(X0,X2))|~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Relation_ODomain(c_COMBK(X3,X4,X5),X6,X7),tc_prod(X8,X8)),X8)|hBOOL(X3))),
% 156.17/20.12 inference(resolution,[status(thm)],[f1248,f46329])).
% 156.17/20.12 fof(f58138,plain,(
% 156.17/20.12 spl0_381|spl0_393),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58137,f58069,f58134])).
% 156.17/20.12 fof(f58139,plain,(
% 156.17/20.12 spl0_394 <=> ~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X5),tc_prod(X6,X6)),X6)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58144,plain,(
% 156.17/20.12 spl0_395 <=> ~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_COMBK(X3,X4,X5),tc_prod(X6,X6)),X6)|hBOOL(X3)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58147,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6]: (hBOOL(hAPP(X0,X1))|hBOOL(hAPP(X0,X2))|~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_COMBK(X3,X4,X5),tc_prod(X6,X6)),X6)|hBOOL(X3))),
% 156.17/20.12 inference(resolution,[status(thm)],[f1248,f30400])).
% 156.17/20.12 fof(f58148,plain,(
% 156.17/20.12 spl0_381|spl0_395),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58147,f58069,f58144])).
% 156.17/20.12 fof(f58149,plain,(
% 156.17/20.12 spl0_396 <=> ~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_prod(X4,X4)),X4)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58152,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4]: (hBOOL(hAPP(X0,X1))|hBOOL(hAPP(X0,X2))|~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_prod(X4,X4)),X4))),
% 156.17/20.12 inference(resolution,[status(thm)],[f1248,f30424])).
% 156.17/20.12 fof(f58153,plain,(
% 156.17/20.12 spl0_381|spl0_396),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58152,f58069,f58149])).
% 156.17/20.12 fof(f58154,plain,(
% 156.17/20.12 spl0_397 <=> ~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Relation_OId__on(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4),X5),tc_prod(X6,X6)),X6)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58157,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6]: (hBOOL(hAPP(X0,X1))|hBOOL(hAPP(X0,X2))|~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Relation_OId__on(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4),X5),tc_prod(X6,X6)),X6))),
% 156.17/20.12 inference(resolution,[status(thm)],[f1248,f49947])).
% 156.17/20.12 fof(f58158,plain,(
% 156.17/20.12 spl0_381|spl0_397),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58157,f58069,f58154])).
% 156.17/20.12 fof(f58159,plain,(
% 156.17/20.12 spl0_398 <=> ~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Relation_OId__on(c_COMBK(X3,X4,X5),X6),tc_prod(X7,X7)),X7)|hBOOL(X3)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58162,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6,X7]: (hBOOL(hAPP(X0,X1))|hBOOL(hAPP(X0,X2))|~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Relation_OId__on(c_COMBK(X3,X4,X5),X6),tc_prod(X7,X7)),X7)|hBOOL(X3))),
% 156.17/20.12 inference(resolution,[status(thm)],[f1248,f30407])).
% 156.17/20.12 fof(f58163,plain,(
% 156.17/20.12 spl0_381|spl0_398),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58162,f58069,f58159])).
% 156.17/20.12 fof(f58164,plain,(
% 156.17/20.12 spl0_399 <=> ~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4),tc_prod(X5,X5)),X5)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58167,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5]: (hBOOL(hAPP(X0,X1))|hBOOL(hAPP(X0,X2))|~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4),tc_prod(X5,X5)),X5))),
% 156.17/20.12 inference(resolution,[status(thm)],[f1248,f30408])).
% 156.17/20.12 fof(f58168,plain,(
% 156.17/20.12 spl0_381|spl0_399),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58167,f58069,f58164])).
% 156.17/20.12 fof(f58171,plain,(
% 156.17/20.12 spl0_400 <=> ~c_Wellfounded_Owf(c_Wellfounded_Oacc(X3,tc_prod(X4,X4)),X4)|~c_Wellfounded_Owf(X3,tc_prod(X4,X4))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58174,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4]: (hBOOL(hAPP(X0,X1))|hBOOL(hAPP(X0,X2))|~c_Wellfounded_Owf(c_Wellfounded_Oacc(X3,tc_prod(X4,X4)),X4)|~c_Wellfounded_Owf(X3,tc_prod(X4,X4)))),
% 156.17/20.12 inference(resolution,[status(thm)],[f1248,f1416])).
% 156.17/20.12 fof(f58175,plain,(
% 156.17/20.12 spl0_381|spl0_400),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58174,f58069,f58171])).
% 156.17/20.12 fof(f58241,plain,(
% 156.17/20.12 spl0_404 <=> ~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,X2,X3)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,X2,X3)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b_H____=X3|X2=X3|v_b_H____=X2),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58244,plain,(
% 156.17/20.12 ![X0,X1,X2,X3]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,X2,X3)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,X2,X3)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b_H____=X3|X2=X3|v_b_H____=X2|~spl0_235)),
% 156.17/20.12 inference(resolution,[status(thm)],[f53009,f1678])).
% 156.17/20.12 fof(f58245,plain,(
% 156.17/20.12 spl0_404|~spl0_254|~spl0_235),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58244,f58241,f54259,f52756])).
% 156.17/20.12 fof(f58246,plain,(
% 156.17/20.12 spl0_405 <=> ~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X2,v_b_H____,X3)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X1,v_P_H____,X2,v_b_H____,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X2,v_b_H____,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X2,v_b_H____,X3)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b_H____,X3,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(X2,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X2,v_b_H____,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=X3|v_b_H____=X3|X2=v_b_H____),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58249,plain,(
% 156.17/20.12 ![X0,X1,X2,X3]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X2,v_b_H____,X3)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X1,v_P_H____,X2,v_b_H____,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X2,v_b_H____,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X2,v_b_H____,X3)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b_H____,X3,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(X2,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X2,v_b_H____,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=X3|v_b_H____=X3|X2=v_b_H____|~spl0_235)),
% 156.17/20.12 inference(resolution,[status(thm)],[f53009,f1676])).
% 156.17/20.12 fof(f58250,plain,(
% 156.17/20.12 spl0_405|~spl0_254|~spl0_235),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58249,f58246,f54259,f52756])).
% 156.17/20.12 fof(f58289,plain,(
% 156.17/20.12 spl0_406 <=> ~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b____,X2,X3)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X1,v_b____,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b____,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b____,X2,X3)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,v_b____,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b____=X3|X2=X3|v_b____=X2),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58292,plain,(
% 156.17/20.12 ![X0,X1,X2,X3]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b____,X2,X3)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X1,v_b____,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b____,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b____,X2,X3)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,v_b____,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b____=X3|X2=X3|v_b____=X2|~spl0_235)),
% 156.17/20.12 inference(resolution,[status(thm)],[f53009,f1682])).
% 156.17/20.12 fof(f58293,plain,(
% 156.17/20.12 spl0_406|~spl0_254|~spl0_235),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58292,f58289,f54259,f52756])).
% 156.17/20.12 fof(f58294,plain,(
% 156.17/20.12 spl0_407 <=> ~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X2,v_b____,X3)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X1,v_P_H____,X2,v_b____,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X2,v_b____,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X2,v_b____,X3)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X3,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(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X2,v_b____,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=X3|v_b____=X3|X2=v_b____),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58297,plain,(
% 156.17/20.12 ![X0,X1,X2,X3]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X2,v_b____,X3)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X1,v_P_H____,X2,v_b____,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X2,v_b____,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X2,v_b____,X3)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X3,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(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X2,v_b____,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=X3|v_b____=X3|X2=v_b____|~spl0_235)),
% 156.17/20.12 inference(resolution,[status(thm)],[f53009,f1680])).
% 156.17/20.12 fof(f58298,plain,(
% 156.17/20.12 spl0_407|~spl0_254|~spl0_235),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58297,f58294,f54259,f52756])).
% 156.17/20.12 fof(f58326,plain,(
% 156.17/20.12 spl0_408 <=> ~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X3,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X3,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X2|v_b____=X2),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58329,plain,(
% 156.17/20.12 ![X0,X1,X2,X3]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X3,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X3,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X2|v_b____=X2|v_a____=v_b____|~spl0_235)),
% 156.17/20.12 inference(resolution,[status(thm)],[f53010,f1678])).
% 156.17/20.12 fof(f58330,plain,(
% 156.17/20.12 spl0_408|~spl0_1|~spl0_258|spl0_110|~spl0_235),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58329,f58326,f1723,f54278,f42998,f52756])).
% 156.17/20.12 fof(f58331,plain,(
% 156.17/20.12 spl0_409 <=> ~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X3,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X3,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b____|X2=v_a____),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58334,plain,(
% 156.17/20.12 ![X0,X1,X2,X3]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X3,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X3,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b____|v_a____=v_b____|X2=v_a____|~spl0_235)),
% 156.17/20.12 inference(resolution,[status(thm)],[f53010,f1676])).
% 156.17/20.12 fof(f58335,plain,(
% 156.17/20.12 spl0_409|~spl0_1|~spl0_258|spl0_110|~spl0_235),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58334,f58331,f1723,f54278,f42998,f52756])).
% 156.17/20.12 fof(f58360,plain,(
% 156.17/20.12 ![X0,X1,X2,X3]: (hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,tc_fun(X2,tc_bool)),X3))|~spl0_381)),
% 156.17/20.12 inference(resolution,[status(thm)],[f58070,f49080])).
% 156.17/20.12 fof(f58361,plain,(
% 156.17/20.12 $false|~spl0_381),
% 156.17/20.12 inference(forward_subsumption_resolution,[status(thm)],[f58360,f49080])).
% 156.17/20.12 fof(f58362,plain,(
% 156.17/20.12 ~spl0_381),
% 156.17/20.12 inference(contradiction_clause,[status(thm)],[f58361])).
% 156.17/20.12 fof(f58413,plain,(
% 156.17/20.12 spl0_410 <=> ~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(c_Transitive__Closure_Ortrancl(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X2|v_b____=X2),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58416,plain,(
% 156.17/20.12 ![X0,X1,X2]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(c_Transitive__Closure_Ortrancl(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X2|v_b____=X2|v_a____=v_b____|~spl0_235)),
% 156.17/20.12 inference(resolution,[status(thm)],[f53011,f1678])).
% 156.17/20.12 fof(f58417,plain,(
% 156.17/20.12 spl0_410|~spl0_1|~spl0_258|spl0_110|~spl0_235),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58416,f58413,f1723,f54278,f42998,f52756])).
% 156.17/20.12 fof(f58418,plain,(
% 156.17/20.12 spl0_411 <=> ~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(c_Transitive__Closure_Ortrancl(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b____|X2=v_a____),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58421,plain,(
% 156.17/20.12 ![X0,X1,X2]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(c_Transitive__Closure_Ortrancl(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b____|v_a____=v_b____|X2=v_a____|~spl0_235)),
% 156.17/20.12 inference(resolution,[status(thm)],[f53011,f1676])).
% 156.17/20.12 fof(f58422,plain,(
% 156.17/20.12 spl0_411|~spl0_1|~spl0_258|spl0_110|~spl0_235),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58421,f58418,f1723,f54278,f42998,f52756])).
% 156.17/20.12 fof(f58461,plain,(
% 156.17/20.12 spl0_412 <=> ~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(c_Transitive__Closure_Otrancl(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X2|v_b____=X2),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58464,plain,(
% 156.17/20.12 ![X0,X1,X2]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(c_Transitive__Closure_Otrancl(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X2|v_b____=X2|v_a____=v_b____|~spl0_235)),
% 156.17/20.12 inference(resolution,[status(thm)],[f53012,f1678])).
% 156.17/20.12 fof(f58465,plain,(
% 156.17/20.12 spl0_412|~spl0_1|~spl0_258|spl0_110|~spl0_235),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58464,f58461,f1723,f54278,f42998,f52756])).
% 156.17/20.12 fof(f58466,plain,(
% 156.17/20.12 spl0_413 <=> ~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(c_Transitive__Closure_Otrancl(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b____|X2=v_a____),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58469,plain,(
% 156.17/20.12 ![X0,X1,X2]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(c_Transitive__Closure_Otrancl(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b____|v_a____=v_b____|X2=v_a____|~spl0_235)),
% 156.17/20.12 inference(resolution,[status(thm)],[f53012,f1676])).
% 156.17/20.12 fof(f58470,plain,(
% 156.17/20.12 spl0_413|~spl0_1|~spl0_258|spl0_110|~spl0_235),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58469,f58466,f1723,f54278,f42998,f52756])).
% 156.17/20.12 fof(f58508,plain,(
% 156.17/20.12 spl0_414 <=> ~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X2|v_b____=X2),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58511,plain,(
% 156.17/20.12 ![X0,X1,X2]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X2|v_b____=X2|v_a____=v_b____|~spl0_235)),
% 156.17/20.12 inference(resolution,[status(thm)],[f53013,f1678])).
% 156.17/20.12 fof(f58512,plain,(
% 156.17/20.12 spl0_414|~spl0_1|~spl0_258|spl0_110|~spl0_235),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58511,f58508,f1723,f54278,f42998,f52756])).
% 156.17/20.12 fof(f58513,plain,(
% 156.17/20.12 spl0_415 <=> ~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b____|X2=v_a____),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58516,plain,(
% 156.17/20.12 ![X0,X1,X2]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_b____|v_a____=v_b____|X2=v_a____|~spl0_235)),
% 156.17/20.12 inference(resolution,[status(thm)],[f53013,f1676])).
% 156.17/20.12 fof(f58517,plain,(
% 156.17/20.12 spl0_415|~spl0_1|~spl0_258|spl0_110|~spl0_235),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58516,f58513,f1723,f54278,f42998,f52756])).
% 156.17/20.12 fof(f58540,plain,(
% 156.17/20.12 spl0_416 <=> ~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X0,v_b____,X1,X2)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X0,v_b____,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X0,v_b____,X1,X2)),c_Pair(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(v_P_H____,X0,v_b____,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X0,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b____=X2|X1=X2|v_b____=X1),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58543,plain,(
% 156.17/20.12 ![X0,X1,X2]: (~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X0,v_b____,X1,X2)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X0,v_b____,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X0,v_b____,X1,X2)),c_Pair(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(v_P_H____,X0,v_b____,X1,X2)),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_b____=X2|X1=X2|v_b____=X1)),
% 156.17/20.12 inference(resolution,[status(thm)],[f40740,f1678])).
% 156.17/20.12 fof(f58544,plain,(
% 156.17/20.12 spl0_416|~spl0_254),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58543,f58540,f54259])).
% 156.17/20.12 fof(f58545,plain,(
% 156.17/20.12 spl0_417 <=> ~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(X0,v_P_H____,X1,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X0,v_P_H____,X1,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(X0,v_P_H____,X1,v_b____,X2)),c_Pair(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X1,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____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X1,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P_H____,X1,v_b____,X2)),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)))|X1=X2|v_b____=X2|X1=v_b____),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58548,plain,(
% 156.17/20.12 ![X0,X1,X2]: (~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(X0,v_P_H____,X1,v_b____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X0,v_P_H____,X1,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(X0,v_P_H____,X1,v_b____,X2)),c_Pair(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X1,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____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X1,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P_H____,X1,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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)))|X1=X2|v_b____=X2|X1=v_b____)),
% 156.17/20.12 inference(resolution,[status(thm)],[f40740,f1676])).
% 156.17/20.12 fof(f58549,plain,(
% 156.17/20.12 spl0_417|~spl0_254),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58548,f58545,f54259])).
% 156.17/20.12 fof(f58603,plain,(
% 156.17/20.12 spl0_418 <=> ~c_Wellfounded_Owf(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X0,v_b____,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_b____,v_a____,X1)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_b____,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X0,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b____=X1|v_a____=X1),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58606,plain,(
% 156.17/20.12 ![X0,X1]: (~c_Wellfounded_Owf(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X0,v_b____,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_b____,v_a____,X1)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(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_a____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_b____,v_a____,X1)),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____=X1|v_a____=X1|v_b____=v_a____)),
% 156.17/20.12 inference(resolution,[status(thm)],[f42389,f1682])).
% 156.17/20.12 fof(f58607,plain,(
% 156.17/20.12 spl0_418|~spl0_153|~spl0_258|spl0_110),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58606,f58603,f47635,f54278,f42998])).
% 156.17/20.12 fof(f58608,plain,(
% 156.17/20.12 spl0_419 <=> ~c_Wellfounded_Owf(hAPP(v_P____,v_sko__CHAINED__1(X0,v_P____,X1,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(X0,v_P____,X1,v_b____,v_a____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X1,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(X1,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,X1,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)))|X1=v_a____|X1=v_b____),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58611,plain,(
% 156.17/20.12 ![X0,X1]: (~c_Wellfounded_Owf(hAPP(v_P____,v_sko__CHAINED__1(X0,v_P____,X1,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(X0,v_P____,X1,v_b____,v_a____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X1,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_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(X1,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,X1,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~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)))|X1=v_a____|v_b____=v_a____|X1=v_b____)),
% 156.17/20.12 inference(resolution,[status(thm)],[f42389,f1680])).
% 156.17/20.12 fof(f58612,plain,(
% 156.17/20.12 spl0_419|~spl0_153|~spl0_258|spl0_110),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58611,f58608,f47635,f54278,f42998])).
% 156.17/20.12 fof(f58613,plain,(
% 156.17/20.12 spl0_420 <=> ~c_Wellfounded_Owf(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,X0),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58616,plain,(
% 156.17/20.12 ![X0,X1]: (~c_Wellfounded_Owf(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,X0),c_Pair(v_b____,v_b_H____,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))|v_b____=v_a____|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.12 inference(resolution,[status(thm)],[f42389,f1644])).
% 156.17/20.12 fof(f58617,plain,(
% 156.17/20.12 spl0_420|spl0_110),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58616,f58613,f42998])).
% 156.17/20.12 fof(f58628,plain,(
% 156.17/20.12 spl0_421 <=> ~c_Wellfounded_Owf(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X0,v_b____,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_b____,v_a____,X1)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_b____,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X0,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b____=X1|v_a____=X1),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58631,plain,(
% 156.17/20.12 ![X0,X1]: (~c_Wellfounded_Owf(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X0,v_b____,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_b____,v_a____,X1)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(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_a____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_b____,v_a____,X1)),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____=X1|v_a____=X1|v_b____=v_a____)),
% 156.17/20.12 inference(resolution,[status(thm)],[f42390,f1682])).
% 156.17/20.12 fof(f58632,plain,(
% 156.17/20.12 spl0_421|~spl0_153|~spl0_258|spl0_110),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58631,f58628,f47635,f54278,f42998])).
% 156.17/20.12 fof(f58633,plain,(
% 156.17/20.12 spl0_422 <=> ~c_Wellfounded_Owf(hAPP(v_P____,v_sko__CHAINED__1(X0,v_P____,X1,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(X0,v_P____,X1,v_b____,v_a____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X1,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(X1,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,X1,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)))|X1=v_a____|X1=v_b____),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58636,plain,(
% 156.17/20.12 ![X0,X1]: (~c_Wellfounded_Owf(hAPP(v_P____,v_sko__CHAINED__1(X0,v_P____,X1,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(X0,v_P____,X1,v_b____,v_a____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X1,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_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(X1,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,X1,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~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)))|X1=v_a____|v_b____=v_a____|X1=v_b____)),
% 156.17/20.12 inference(resolution,[status(thm)],[f42390,f1680])).
% 156.17/20.12 fof(f58637,plain,(
% 156.17/20.12 spl0_422|~spl0_153|~spl0_258|spl0_110),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58636,f58633,f47635,f54278,f42998])).
% 156.17/20.12 fof(f58638,plain,(
% 156.17/20.12 spl0_423 <=> ~c_Wellfounded_Owf(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,X0),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f58641,plain,(
% 156.17/20.12 ![X0,X1]: (~c_Wellfounded_Owf(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,X0),v_b____,v_b_H____,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))|v_b____=v_a____|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.12 inference(resolution,[status(thm)],[f42390,f1644])).
% 156.17/20.12 fof(f58642,plain,(
% 156.17/20.12 spl0_423|spl0_110),
% 156.17/20.12 inference(split_clause,[status(thm)],[f58641,f58638,f42998])).
% 156.17/20.12 fof(f58651,plain,(
% 156.17/20.12 ![X0,X1,X2]: (c_in(X0,c_Relation_ORange(X1,X2,X2),X2)|~c_Nitpick_Orefl_H(c_Relation_Oconverse(X1,X2,X2),X2))),
% 156.17/20.12 inference(paramodulation,[status(thm)],[f1490,f51612])).
% 156.17/20.12 fof(f59335,plain,(
% 156.17/20.12 spl0_424 <=> hAPP(hAPP(X0,v_b____),X1)=hAPP(hAPP(X0,v_b_H____),X2)|~c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X5,v_b____,v_a____,X6)),X4,X0,tc_Arrow__Order__Mirabelle_Oalt,X3,X7)|~c_in(v_b____,X8,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X8,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X8,hAPP(v_P____,v_sko__CHAINED__1(v_P____,X5,v_b____,v_a____,X6)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__CHAINED__1(v_P____,X5,v_b____,v_a____,X6)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b____=X6|v_a____=X6),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f59338,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6,X7,X8]: (hAPP(hAPP(X0,v_b____),X1)=hAPP(hAPP(X0,v_b_H____),X2)|~c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X5,v_b____,v_a____,X6)),X4,X0,tc_Arrow__Order__Mirabelle_Oalt,X3,X7)|~c_in(v_b____,X8,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X8,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X8,hAPP(v_P____,v_sko__CHAINED__1(v_P____,X5,v_b____,v_a____,X6)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(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_a____,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__CHAINED__1(v_P____,X5,v_b____,v_a____,X6)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X6|v_a____=X6|v_b____=v_a____|~spl0_246)),
% 156.17/20.12 inference(resolution,[status(thm)],[f53124,f1678])).
% 156.17/20.12 fof(f59339,plain,(
% 156.17/20.12 spl0_424|~spl0_153|~spl0_258|spl0_110|~spl0_246),
% 156.17/20.12 inference(split_clause,[status(thm)],[f59338,f59335,f47635,f54278,f42998,f53123])).
% 156.17/20.12 fof(f59340,plain,(
% 156.17/20.12 spl0_425 <=> hAPP(hAPP(X0,v_b____),X1)=hAPP(hAPP(X0,v_b_H____),X2)|~c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(X5,v_P____,X6,v_b____,v_a____)),X4,X0,tc_Arrow__Order__Mirabelle_Oalt,X3,X7)|~c_in(v_b____,X8,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X8,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X8,hAPP(v_P____,v_sko__CHAINED__1(X5,v_P____,X6,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X6,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X6,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__CHAINED__1(X5,v_P____,X6,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X6=v_a____|X6=v_b____),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f59343,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6,X7,X8]: (hAPP(hAPP(X0,v_b____),X1)=hAPP(hAPP(X0,v_b_H____),X2)|~c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(X5,v_P____,X6,v_b____,v_a____)),X4,X0,tc_Arrow__Order__Mirabelle_Oalt,X3,X7)|~c_in(v_b____,X8,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X8,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X8,hAPP(v_P____,v_sko__CHAINED__1(X5,v_P____,X6,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X6,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(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(X6,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__CHAINED__1(X5,v_P____,X6,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X6=v_a____|v_b____=v_a____|X6=v_b____|~spl0_246)),
% 156.17/20.12 inference(resolution,[status(thm)],[f53124,f1676])).
% 156.17/20.12 fof(f59344,plain,(
% 156.17/20.12 spl0_425|~spl0_153|~spl0_258|spl0_110|~spl0_246),
% 156.17/20.12 inference(split_clause,[status(thm)],[f59343,f59340,f47635,f54278,f42998,f53123])).
% 156.17/20.12 fof(f59369,plain,(
% 156.17/20.12 spl0_426 <=> hAPP(hAPP(X0,X1),v_b____)=hAPP(hAPP(X0,X2),v_b_H____)|~c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))|~c_Equiv__Relations_Ocongruent2(X4,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X5,v_b____,v_a____,X6)),X0,X3,tc_Arrow__Order__Mirabelle_Oalt,X7)|~c_in(v_b____,X8,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X8,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X8,hAPP(v_P____,v_sko__CHAINED__1(v_P____,X5,v_b____,v_a____,X6)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__CHAINED__1(v_P____,X5,v_b____,v_a____,X6)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b____=X6|v_a____=X6),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f59372,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6,X7,X8]: (hAPP(hAPP(X0,X1),v_b____)=hAPP(hAPP(X0,X2),v_b_H____)|~c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))|~c_Equiv__Relations_Ocongruent2(X4,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X5,v_b____,v_a____,X6)),X0,X3,tc_Arrow__Order__Mirabelle_Oalt,X7)|~c_in(v_b____,X8,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X8,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X8,hAPP(v_P____,v_sko__CHAINED__1(v_P____,X5,v_b____,v_a____,X6)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(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_a____,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__CHAINED__1(v_P____,X5,v_b____,v_a____,X6)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X6|v_a____=X6|v_b____=v_a____|~spl0_247)),
% 156.17/20.12 inference(resolution,[status(thm)],[f53147,f1678])).
% 156.17/20.12 fof(f59373,plain,(
% 156.17/20.12 spl0_426|~spl0_153|~spl0_258|spl0_110|~spl0_247),
% 156.17/20.12 inference(split_clause,[status(thm)],[f59372,f59369,f47635,f54278,f42998,f53146])).
% 156.17/20.12 fof(f59374,plain,(
% 156.17/20.12 spl0_427 <=> hAPP(hAPP(X0,X1),v_b____)=hAPP(hAPP(X0,X2),v_b_H____)|~c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))|~c_Equiv__Relations_Ocongruent2(X4,hAPP(v_P_H____,v_sko__CHAINED__1(X5,v_P____,X6,v_b____,v_a____)),X0,X3,tc_Arrow__Order__Mirabelle_Oalt,X7)|~c_in(v_b____,X8,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X8,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X8,hAPP(v_P____,v_sko__CHAINED__1(X5,v_P____,X6,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X6,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X6,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__CHAINED__1(X5,v_P____,X6,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X6=v_a____|X6=v_b____),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f59377,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6,X7,X8]: (hAPP(hAPP(X0,X1),v_b____)=hAPP(hAPP(X0,X2),v_b_H____)|~c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))|~c_Equiv__Relations_Ocongruent2(X4,hAPP(v_P_H____,v_sko__CHAINED__1(X5,v_P____,X6,v_b____,v_a____)),X0,X3,tc_Arrow__Order__Mirabelle_Oalt,X7)|~c_in(v_b____,X8,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X8,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X8,hAPP(v_P____,v_sko__CHAINED__1(X5,v_P____,X6,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X6,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(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(X6,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__CHAINED__1(X5,v_P____,X6,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X6=v_a____|v_b____=v_a____|X6=v_b____|~spl0_247)),
% 156.17/20.12 inference(resolution,[status(thm)],[f53147,f1676])).
% 156.17/20.12 fof(f59378,plain,(
% 156.17/20.12 spl0_427|~spl0_153|~spl0_258|spl0_110|~spl0_247),
% 156.17/20.12 inference(split_clause,[status(thm)],[f59377,f59374,f47635,f54278,f42998,f53146])).
% 156.17/20.12 fof(f59403,plain,(
% 156.17/20.12 spl0_428 <=> hAPP(X0,v_b____)=hAPP(X0,v_b_H____)|~c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),X0,tc_Arrow__Order__Mirabelle_Oalt,X3)|~c_in(v_b____,X4,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X4,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X4,hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b____=X2|v_a____=X2),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f59406,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4]: (hAPP(X0,v_b____)=hAPP(X0,v_b_H____)|~c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),X0,tc_Arrow__Order__Mirabelle_Oalt,X3)|~c_in(v_b____,X4,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X4,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X4,hAPP(v_P____,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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_a____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_b____,v_a____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X2|v_a____=X2|v_b____=v_a____|~spl0_248)),
% 156.17/20.12 inference(resolution,[status(thm)],[f53155,f1678])).
% 156.17/20.12 fof(f59407,plain,(
% 156.17/20.12 spl0_428|~spl0_153|~spl0_258|spl0_110|~spl0_248),
% 156.17/20.12 inference(split_clause,[status(thm)],[f59406,f59403,f47635,f54278,f42998,f53154])).
% 156.17/20.12 fof(f59408,plain,(
% 156.17/20.12 spl0_429 <=> hAPP(X0,v_b____)=hAPP(X0,v_b_H____)|~c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),X0,tc_Arrow__Order__Mirabelle_Oalt,X3)|~c_in(v_b____,X4,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X4,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X4,hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_a____|X2=v_b____),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f59411,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4]: (hAPP(X0,v_b____)=hAPP(X0,v_b_H____)|~c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),X0,tc_Arrow__Order__Mirabelle_Oalt,X3)|~c_in(v_b____,X4,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X4,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X4,hAPP(v_P____,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_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(X2,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P____,X2,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X2=v_a____|v_b____=v_a____|X2=v_b____|~spl0_248)),
% 156.17/20.12 inference(resolution,[status(thm)],[f53155,f1676])).
% 156.17/20.12 fof(f59412,plain,(
% 156.17/20.12 spl0_429|~spl0_153|~spl0_258|spl0_110|~spl0_248),
% 156.17/20.12 inference(split_clause,[status(thm)],[f59411,f59408,f47635,f54278,f42998,f53154])).
% 156.17/20.12 fof(f59500,plain,(
% 156.17/20.12 $false|~spl0_188),
% 156.17/20.12 inference(forward_subsumption_resolution,[status(thm)],[f50302,f26836])).
% 156.17/20.12 fof(f59501,plain,(
% 156.17/20.12 ~spl0_188),
% 156.17/20.12 inference(contradiction_clause,[status(thm)],[f59500])).
% 156.17/20.12 fof(f59508,plain,(
% 156.17/20.12 ![X0,X1]: (~c_Relation_Osingle__valued(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Orefl__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_250)),
% 156.17/20.12 inference(forward_subsumption_resolution,[status(thm)],[f53731,f53561])).
% 156.17/20.12 fof(f59521,plain,(
% 156.17/20.12 spl0_434 <=> ~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,X1)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X2,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,X1)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X0,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X1|v_b____=X1),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f59524,plain,(
% 156.17/20.12 ![X0,X1,X2]: (~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,X1)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X2,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,X1)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(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____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,X1)),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____=X1|v_b____=X1|v_a____=v_b____|~spl0_250)),
% 156.17/20.12 inference(resolution,[status(thm)],[f59508,f1682])).
% 156.17/20.12 fof(f59525,plain,(
% 156.17/20.12 spl0_434|~spl0_1|~spl0_258|spl0_110|~spl0_250),
% 156.17/20.12 inference(split_clause,[status(thm)],[f59524,f59521,f1723,f54278,f42998,f53730])).
% 156.17/20.12 fof(f59526,plain,(
% 156.17/20.12 spl0_435 <=> ~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(X0,v_P____,X1,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X2,hAPP(v_P_H____,v_sko__CHAINED__1(X0,v_P____,X1,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X1,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(X1,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,X1,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)))|X1=v_b____|X1=v_a____),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f59529,plain,(
% 156.17/20.12 ![X0,X1,X2]: (~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(X0,v_P____,X1,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X2,hAPP(v_P_H____,v_sko__CHAINED__1(X0,v_P____,X1,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X1,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),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X1,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,X1,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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)))|X1=v_b____|v_a____=v_b____|X1=v_a____|~spl0_250)),
% 156.17/20.12 inference(resolution,[status(thm)],[f59508,f1680])).
% 156.17/20.12 fof(f59530,plain,(
% 156.17/20.12 spl0_435|~spl0_1|~spl0_258|spl0_110|~spl0_250),
% 156.17/20.12 inference(split_clause,[status(thm)],[f59529,f59526,f1723,f54278,f42998,f53730])).
% 156.17/20.12 fof(f59531,plain,(
% 156.17/20.12 spl0_436 <=> ~c_Relation_Osingle__valued(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X2,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f59534,plain,(
% 156.17/20.12 ![X0,X1,X2]: (~c_Relation_Osingle__valued(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=v_b____|~c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X2,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_250)),
% 156.17/20.12 inference(resolution,[status(thm)],[f59508,f1644])).
% 156.17/20.12 fof(f59535,plain,(
% 156.17/20.12 spl0_436|spl0_110|~spl0_250),
% 156.17/20.12 inference(split_clause,[status(thm)],[f59534,f59531,f42998,f53730])).
% 156.17/20.12 fof(f59557,plain,(
% 156.17/20.12 spl0_437 <=> ~c_Wellfounded_Owf(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,X1)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,X1)),c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X0,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X1|v_b____=X1),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f59560,plain,(
% 156.17/20.12 ![X0,X1]: (~c_Wellfounded_Owf(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,X1)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,X1)),c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(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____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,X1)),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____=X1|v_b____=X1|v_a____=v_b____)),
% 156.17/20.12 inference(resolution,[status(thm)],[f42925,f1682])).
% 156.17/20.12 fof(f59561,plain,(
% 156.17/20.12 spl0_437|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.12 inference(split_clause,[status(thm)],[f59560,f59557,f1723,f54278,f42998])).
% 156.17/20.12 fof(f59562,plain,(
% 156.17/20.12 spl0_438 <=> ~c_Wellfounded_Owf(hAPP(v_P_H____,v_sko__CHAINED__1(X0,v_P____,X1,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(X0,v_P____,X1,v_a____,v_b____)),c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X1,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(X1,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,X1,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)))|X1=v_b____|X1=v_a____),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f59565,plain,(
% 156.17/20.12 ![X0,X1]: (~c_Wellfounded_Owf(hAPP(v_P_H____,v_sko__CHAINED__1(X0,v_P____,X1,v_a____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(X0,v_P____,X1,v_a____,v_b____)),c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X1,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),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X1,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,X1,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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)))|X1=v_b____|v_a____=v_b____|X1=v_a____)),
% 156.17/20.12 inference(resolution,[status(thm)],[f42925,f1680])).
% 156.17/20.12 fof(f59566,plain,(
% 156.17/20.12 spl0_438|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.12 inference(split_clause,[status(thm)],[f59565,f59562,f1723,f54278,f42998])).
% 156.17/20.12 fof(f59567,plain,(
% 156.17/20.12 spl0_439 <=> ~c_Wellfounded_Owf(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,X0),c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f59570,plain,(
% 156.17/20.12 ![X0,X1]: (~c_Wellfounded_Owf(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,X0),c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=v_b____|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.12 inference(resolution,[status(thm)],[f42925,f1644])).
% 156.17/20.12 fof(f59571,plain,(
% 156.17/20.12 spl0_439|spl0_110),
% 156.17/20.12 inference(split_clause,[status(thm)],[f59570,f59567,f42998])).
% 156.17/20.12 fof(f59710,plain,(
% 156.17/20.12 spl0_440 <=> hBOOL(hAPP(c_Relation_ORange(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f59713,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4]: (hBOOL(hAPP(c_Relation_ORange(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2))|~c_Wellfounded_Owf(X3,X4))),
% 156.17/20.12 inference(resolution,[status(thm)],[f703,f51303])).
% 156.17/20.12 fof(f59714,plain,(
% 156.17/20.12 spl0_440|spl0_7),
% 156.17/20.12 inference(split_clause,[status(thm)],[f59713,f59710,f1768])).
% 156.17/20.12 fof(f59715,plain,(
% 156.17/20.12 spl0_441 <=> hBOOL(hAPP(c_Relation_ORange(X0,X1,X1),X2))|~c_Nitpick_Orefl_H(X0,X1)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f59718,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4]: (hBOOL(hAPP(c_Relation_ORange(X0,X1,X1),X2))|~c_Wellfounded_Owf(X3,X4)|~c_Nitpick_Orefl_H(X0,X1))),
% 156.17/20.12 inference(resolution,[status(thm)],[f703,f51456])).
% 156.17/20.12 fof(f59719,plain,(
% 156.17/20.12 spl0_441|spl0_7),
% 156.17/20.12 inference(split_clause,[status(thm)],[f59718,f59715,f1768])).
% 156.17/20.12 fof(f59720,plain,(
% 156.17/20.12 spl0_442 <=> hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f59723,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4]: (hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2))|~c_Wellfounded_Owf(X3,X4))),
% 156.17/20.12 inference(resolution,[status(thm)],[f703,f51372])).
% 156.17/20.12 fof(f59724,plain,(
% 156.17/20.12 spl0_442|spl0_7),
% 156.17/20.12 inference(split_clause,[status(thm)],[f59723,f59720,f1768])).
% 156.17/20.12 fof(f59725,plain,(
% 156.17/20.12 spl0_443 <=> hBOOL(hAPP(c_Relation_ODomain(c_Relation_OId(X0),X0,X0),X1))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f59728,plain,(
% 156.17/20.12 ![X0,X1,X2,X3]: (hBOOL(hAPP(c_Relation_ODomain(c_Relation_OId(X0),X0,X0),X1))|~c_Wellfounded_Owf(X2,X3))),
% 156.17/20.12 inference(resolution,[status(thm)],[f703,f50552])).
% 156.17/20.12 fof(f59729,plain,(
% 156.17/20.12 spl0_443|spl0_7),
% 156.17/20.12 inference(split_clause,[status(thm)],[f59728,f59725,f1768])).
% 156.17/20.12 fof(f59742,plain,(
% 156.17/20.12 spl0_445 <=> hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OImage(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X2,X3),X4),X5))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f59745,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6,X7]: (hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OImage(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X2,X3),X4),X5))|~c_Wellfounded_Owf(X6,X7))),
% 156.17/20.12 inference(resolution,[status(thm)],[f703,f47936])).
% 156.17/20.12 fof(f59746,plain,(
% 156.17/20.12 spl0_445|spl0_7),
% 156.17/20.12 inference(split_clause,[status(thm)],[f59745,f59742,f1768])).
% 156.17/20.12 fof(f59747,plain,(
% 156.17/20.12 spl0_446 <=> hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OImage(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X3),X4),X5))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f59750,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6,X7]: (hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OImage(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X3),X4),X5))|~c_Wellfounded_Owf(X6,X7))),
% 156.17/20.12 inference(resolution,[status(thm)],[f703,f47986])).
% 156.17/20.12 fof(f59751,plain,(
% 156.17/20.12 spl0_446|spl0_7),
% 156.17/20.12 inference(split_clause,[status(thm)],[f59750,f59747,f1768])).
% 156.17/20.12 fof(f59752,plain,(
% 156.17/20.12 spl0_447 <=> hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_ORange(c_COMBK(X0,X1,X2),X3,X4),X5),X6))|hBOOL(X0)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f59755,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6,X7,X8]: (hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_ORange(c_COMBK(X0,X1,X2),X3,X4),X5),X6))|~c_Wellfounded_Owf(X7,X8)|hBOOL(X0))),
% 156.17/20.12 inference(resolution,[status(thm)],[f703,f48164])).
% 156.17/20.12 fof(f59756,plain,(
% 156.17/20.12 spl0_447|spl0_7),
% 156.17/20.12 inference(split_clause,[status(thm)],[f59755,f59752,f1768])).
% 156.17/20.12 fof(f59757,plain,(
% 156.17/20.12 spl0_448 <=> hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X2),X3),X4))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f59760,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6]: (hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X2),X3),X4))|~c_Wellfounded_Owf(X5,X6))),
% 156.17/20.12 inference(resolution,[status(thm)],[f703,f47157])).
% 156.17/20.12 fof(f59761,plain,(
% 156.17/20.12 spl0_448|spl0_7),
% 156.17/20.12 inference(split_clause,[status(thm)],[f59760,f59757,f1768])).
% 156.17/20.12 fof(f59762,plain,(
% 156.17/20.12 spl0_449 <=> hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_ODomain(c_COMBK(X0,X1,X2),X3,X4),X5),X6))|hBOOL(X0)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f59765,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6,X7,X8]: (hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_ODomain(c_COMBK(X0,X1,X2),X3,X4),X5),X6))|~c_Wellfounded_Owf(X7,X8)|hBOOL(X0))),
% 156.17/20.12 inference(resolution,[status(thm)],[f703,f47284])).
% 156.17/20.12 fof(f59766,plain,(
% 156.17/20.12 spl0_449|spl0_7),
% 156.17/20.12 inference(split_clause,[status(thm)],[f59765,f59762,f1768])).
% 156.17/20.12 fof(f59767,plain,(
% 156.17/20.12 spl0_450 <=> hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X2),X3),X4))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f59770,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6]: (hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X2),X3),X4))|~c_Wellfounded_Owf(X5,X6))),
% 156.17/20.12 inference(resolution,[status(thm)],[f703,f47110])).
% 156.17/20.12 fof(f59771,plain,(
% 156.17/20.12 spl0_450|spl0_7),
% 156.17/20.12 inference(split_clause,[status(thm)],[f59770,f59767,f1768])).
% 156.17/20.12 fof(f59772,plain,(
% 156.17/20.12 spl0_451 <=> hBOOL(hAPP(c_Wellfounded_Oacc(c_COMBK(X0,X1,X2),X3),X4))|hBOOL(X0)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f59775,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6]: (hBOOL(hAPP(c_Wellfounded_Oacc(c_COMBK(X0,X1,X2),X3),X4))|~c_Wellfounded_Owf(X5,X6)|hBOOL(X0))),
% 156.17/20.12 inference(resolution,[status(thm)],[f703,f35738])).
% 156.17/20.12 fof(f59776,plain,(
% 156.17/20.12 spl0_451|spl0_7),
% 156.17/20.12 inference(split_clause,[status(thm)],[f59775,f59772,f1768])).
% 156.17/20.12 fof(f59777,plain,(
% 156.17/20.12 spl0_452 <=> hBOOL(hAPP(c_Wellfounded_Oacc(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1),X2))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f59780,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4]: (hBOOL(hAPP(c_Wellfounded_Oacc(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1),X2))|~c_Wellfounded_Owf(X3,X4))),
% 156.17/20.12 inference(resolution,[status(thm)],[f703,f31948])).
% 156.17/20.12 fof(f59781,plain,(
% 156.17/20.12 spl0_452|spl0_7),
% 156.17/20.12 inference(split_clause,[status(thm)],[f59780,f59777,f1768])).
% 156.17/20.12 fof(f59883,plain,(
% 156.17/20.12 spl0_475 <=> 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))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f59884,plain,(
% 156.17/20.12 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))|~spl0_475),
% 156.17/20.12 inference(component_clause,[status(thm)],[f59883])).
% 156.17/20.12 fof(f60058,plain,(
% 156.17/20.12 spl0_505 <=> hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,v_b_H____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f60060,plain,(
% 156.17/20.12 ~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,v_b_H____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|spl0_505),
% 156.17/20.12 inference(component_clause,[status(thm)],[f60058])).
% 156.17/20.12 fof(f60069,plain,(
% 156.17/20.12 spl0_508 <=> 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____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f60070,plain,(
% 156.17/20.12 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____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_508),
% 156.17/20.12 inference(component_clause,[status(thm)],[f60069])).
% 156.17/20.12 fof(f60071,plain,(
% 156.17/20.12 ~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____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|spl0_508),
% 156.17/20.12 inference(component_clause,[status(thm)],[f60069])).
% 156.17/20.12 fof(f60072,plain,(
% 156.17/20.12 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))|~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_H____|v_b____=v_b_H____|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,v_b_H____)),c_Pair(v_b____,v_b_H____,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____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_263),
% 156.17/20.12 inference(resolution,[status(thm)],[f54313,f1741])).
% 156.17/20.12 fof(f60073,plain,(
% 156.17/20.12 spl0_239|~spl0_254|spl0_3|spl0_97|~spl0_505|~spl0_508|~spl0_263),
% 156.17/20.12 inference(split_clause,[status(thm)],[f60072,f52976,f54259,f1729,f41290,f60058,f60069,f54312])).
% 156.17/20.12 fof(f60074,plain,(
% 156.17/20.12 spl0_509 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=X0|v_b____=X0|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f60077,plain,(
% 156.17/20.12 ![X0]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~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____=X0|v_b____=X0|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_263)),
% 156.17/20.12 inference(resolution,[status(thm)],[f54313,f40740])).
% 156.17/20.12 fof(f60078,plain,(
% 156.17/20.12 spl0_509|~spl0_254|~spl0_263),
% 156.17/20.12 inference(split_clause,[status(thm)],[f60077,f60074,f54259,f54312])).
% 156.17/20.12 fof(f60090,plain,(
% 156.17/20.12 spl0_513 <=> c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,v_b_H____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f60097,plain,(
% 156.17/20.12 spl0_514 <=> 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))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f60098,plain,(
% 156.17/20.12 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))|~spl0_514),
% 156.17/20.12 inference(component_clause,[status(thm)],[f60097])).
% 156.17/20.12 fof(f60099,plain,(
% 156.17/20.12 ~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))|spl0_514),
% 156.17/20.12 inference(component_clause,[status(thm)],[f60097])).
% 156.17/20.12 fof(f60121,plain,(
% 156.17/20.12 spl0_520 <=> 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)))|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X1,hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f60124,plain,(
% 156.17/20.12 ![X0,X1]: (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)))|v_a____=v_b____|v_b____=v_b____|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X1,hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_263)),
% 156.17/20.12 inference(resolution,[status(thm)],[f54313,f1646])).
% 156.17/20.12 fof(f60125,plain,(
% 156.17/20.12 spl0_520|spl0_110|spl0_175|~spl0_263),
% 156.17/20.12 inference(split_clause,[status(thm)],[f60124,f60121,f42998,f49384,f54312])).
% 156.17/20.12 fof(f60128,plain,(
% 156.17/20.12 spl0_521 <=> 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)))|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~c_Nitpick_Orefl_H(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f60131,plain,(
% 156.17/20.12 ![X0]: (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)))|v_a____=v_b____|v_b____=v_b____|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~c_Nitpick_Orefl_H(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_263)),
% 156.17/20.12 inference(resolution,[status(thm)],[f54313,f1574])).
% 156.17/20.12 fof(f60132,plain,(
% 156.17/20.12 spl0_521|spl0_110|spl0_175|~spl0_263),
% 156.17/20.12 inference(split_clause,[status(thm)],[f60131,f60128,f42998,f49384,f54312])).
% 156.17/20.12 fof(f60136,plain,(
% 156.17/20.12 $false|~spl0_3),
% 156.17/20.12 inference(forward_subsumption_resolution,[status(thm)],[f1730,f1684])).
% 156.17/20.12 fof(f60137,plain,(
% 156.17/20.12 ~spl0_3),
% 156.17/20.12 inference(contradiction_clause,[status(thm)],[f60136])).
% 156.17/20.12 fof(f60170,plain,(
% 156.17/20.12 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))|~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_H____|v_b____=v_b_H____|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,v_b_H____)),v_b____,v_b_H____,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____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_264),
% 156.17/20.12 inference(resolution,[status(thm)],[f54318,f1741])).
% 156.17/20.12 fof(f60171,plain,(
% 156.17/20.12 spl0_239|~spl0_254|spl0_3|spl0_97|~spl0_513|~spl0_508|~spl0_264),
% 156.17/20.12 inference(split_clause,[status(thm)],[f60170,f52976,f54259,f1729,f41290,f60090,f60069,f54317])).
% 156.17/20.12 fof(f60172,plain,(
% 156.17/20.12 spl0_522 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=X0|v_b____=X0|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f60175,plain,(
% 156.17/20.12 ![X0]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~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____=X0|v_b____=X0|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_264)),
% 156.17/20.12 inference(resolution,[status(thm)],[f54318,f40740])).
% 156.17/20.12 fof(f60176,plain,(
% 156.17/20.12 spl0_522|~spl0_254|~spl0_264),
% 156.17/20.12 inference(split_clause,[status(thm)],[f60175,f60172,f54259,f54317])).
% 156.17/20.12 fof(f60192,plain,(
% 156.17/20.12 spl0_524 <=> 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_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X1,hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f60195,plain,(
% 156.17/20.12 ![X0,X1]: (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)))|v_a____=v_b____|v_b____=v_b____|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X1,hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_264)),
% 156.17/20.12 inference(resolution,[status(thm)],[f54318,f1646])).
% 156.17/20.12 fof(f60196,plain,(
% 156.17/20.12 spl0_524|spl0_110|spl0_175|~spl0_264),
% 156.17/20.12 inference(split_clause,[status(thm)],[f60195,f60192,f42998,f49384,f54317])).
% 156.17/20.12 fof(f60199,plain,(
% 156.17/20.12 spl0_525 <=> 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_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_Nitpick_Orefl_H(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f60202,plain,(
% 156.17/20.12 ![X0]: (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)))|v_a____=v_b____|v_b____=v_b____|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_Nitpick_Orefl_H(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_264)),
% 156.17/20.12 inference(resolution,[status(thm)],[f54318,f1574])).
% 156.17/20.12 fof(f60203,plain,(
% 156.17/20.12 spl0_525|spl0_110|spl0_175|~spl0_264),
% 156.17/20.12 inference(split_clause,[status(thm)],[f60202,f60199,f42998,f49384,f54317])).
% 156.17/20.12 fof(f60465,plain,(
% 156.17/20.12 spl0_549 <=> ~c_Nitpick_Orefl_H(X0,X1)|hBOOL(hAPP(c_Relation_ODomain(X0,X1,X1),X2))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f60468,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4]: (~c_Nitpick_Orefl_H(X0,X1)|hBOOL(hAPP(c_Relation_ODomain(X0,X1,X1),X2))|~c_Wellfounded_Owf(X3,X4))),
% 156.17/20.12 inference(resolution,[status(thm)],[f55500,f703])).
% 156.17/20.12 fof(f60469,plain,(
% 156.17/20.12 spl0_549|spl0_7),
% 156.17/20.12 inference(split_clause,[status(thm)],[f60468,f60465,f1768])).
% 156.17/20.12 fof(f60478,plain,(
% 156.17/20.12 ![X0,X1,X2]: (~c_Nitpick_Orefl_H(c_Transitive__Closure_Otrancl(X0,X1),X1)|hBOOL(hAPP(c_Relation_ODomain(X0,X1,X1),X2)))),
% 156.17/20.12 inference(paramodulation,[status(thm)],[f1426,f55500])).
% 156.17/20.12 fof(f61431,plain,(
% 156.17/20.12 spl0_601 <=> c_in(c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f61432,plain,(
% 156.17/20.12 c_in(c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_601),
% 156.17/20.12 inference(component_clause,[status(thm)],[f61431])).
% 156.17/20.12 fof(f61433,plain,(
% 156.17/20.12 ~c_in(c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|spl0_601),
% 156.17/20.12 inference(component_clause,[status(thm)],[f61431])).
% 156.17/20.12 fof(f61434,plain,(
% 156.17/20.12 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))|~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_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~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_H____|v_b____=v_b_H____|v_a____=v_b____|spl0_508),
% 156.17/20.12 inference(resolution,[status(thm)],[f60071,f1682])).
% 156.17/20.12 fof(f61435,plain,(
% 156.17/20.12 spl0_239|~spl0_1|spl0_601|~spl0_254|~spl0_258|spl0_3|spl0_97|spl0_110|spl0_508),
% 156.17/20.12 inference(split_clause,[status(thm)],[f61434,f52976,f1723,f61431,f54259,f54278,f1729,f41290,f42998,f60069])).
% 156.17/20.12 fof(f61738,plain,(
% 156.17/20.12 ![X0]: (c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X0,v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_475)),
% 156.17/20.12 inference(resolution,[status(thm)],[f59884,f1648])).
% 156.17/20.12 fof(f61742,plain,(
% 156.17/20.12 spl0_638 <=> c_in(v_a____,c_Wellfounded_Oacc(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f61744,plain,(
% 156.17/20.12 ~c_in(v_a____,c_Wellfounded_Oacc(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|spl0_638),
% 156.17/20.12 inference(component_clause,[status(thm)],[f61742])).
% 156.17/20.12 fof(f61745,plain,(
% 156.17/20.12 c_in(v_b____,c_Wellfounded_Oacc(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_a____,c_Wellfounded_Oacc(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_475),
% 156.17/20.12 inference(resolution,[status(thm)],[f59884,f1617])).
% 156.17/20.12 fof(f61746,plain,(
% 156.17/20.12 spl0_238|~spl0_638|~spl0_475),
% 156.17/20.12 inference(split_clause,[status(thm)],[f61745,f52971,f61742,f59883])).
% 156.17/20.12 fof(f61754,plain,(
% 156.17/20.12 spl0_640 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f61757,plain,(
% 156.17/20.12 ![X0]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_475)),
% 156.17/20.12 inference(resolution,[status(thm)],[f59884,f1538])).
% 156.17/20.12 fof(f61758,plain,(
% 156.17/20.12 spl0_640|~spl0_90|~spl0_475),
% 156.17/20.12 inference(split_clause,[status(thm)],[f61757,f61754,f40295,f59883])).
% 156.17/20.12 fof(f61759,plain,(
% 156.17/20.12 spl0_641 <=> c_in(c_Pair(X0,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(X0,v_b____,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))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f61762,plain,(
% 156.17/20.12 ![X0]: (c_in(c_Pair(X0,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(X0,v_b____,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_Relation_Otrans(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_475)),
% 156.17/20.12 inference(resolution,[status(thm)],[f59884,f1538])).
% 156.17/20.12 fof(f61763,plain,(
% 156.17/20.12 spl0_641|~spl0_90|~spl0_475),
% 156.17/20.12 inference(split_clause,[status(thm)],[f61762,f61759,f40295,f59883])).
% 156.17/20.12 fof(f61767,plain,(
% 156.17/20.12 ~hBOOL(hAPP(c_Wellfounded_Oacc(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt),v_a____))|spl0_638),
% 156.17/20.12 inference(resolution,[status(thm)],[f61744,f1664])).
% 156.17/20.12 fof(f61845,plain,(
% 156.17/20.12 hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,v_b_H____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_508),
% 156.17/20.12 inference(resolution,[status(thm)],[f60070,f1878])).
% 156.17/20.12 fof(f61846,plain,(
% 156.17/20.12 $false|spl0_505|~spl0_508),
% 156.17/20.12 inference(forward_subsumption_resolution,[status(thm)],[f61845,f60060])).
% 156.17/20.12 fof(f61847,plain,(
% 156.17/20.12 spl0_505|~spl0_508),
% 156.17/20.12 inference(contradiction_clause,[status(thm)],[f61846])).
% 156.17/20.12 fof(f62095,plain,(
% 156.17/20.12 spl0_665 <=> ~c_Relation_Osym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X0,v_b____,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_b____,v_a____,X1)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_b____,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X0,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b____=X1|v_a____=X1),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f62098,plain,(
% 156.17/20.12 ![X0,X1]: (~c_Relation_Osym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X0,v_b____,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_b____,v_a____,X1)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(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_a____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_b____,v_a____,X1)),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____=X1|v_a____=X1|v_b____=v_a____)),
% 156.17/20.12 inference(resolution,[status(thm)],[f44894,f1678])).
% 156.17/20.12 fof(f62099,plain,(
% 156.17/20.12 spl0_665|~spl0_153|~spl0_258|spl0_110),
% 156.17/20.12 inference(split_clause,[status(thm)],[f62098,f62095,f47635,f54278,f42998])).
% 156.17/20.12 fof(f62100,plain,(
% 156.17/20.12 spl0_666 <=> ~c_Relation_Osym(hAPP(v_P____,v_sko__CHAINED__1(X0,v_P____,X1,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(X0,v_P____,X1,v_b____,v_a____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X1,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(X1,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,X1,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)))|X1=v_a____|X1=v_b____),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f62103,plain,(
% 156.17/20.12 ![X0,X1]: (~c_Relation_Osym(hAPP(v_P____,v_sko__CHAINED__1(X0,v_P____,X1,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(X0,v_P____,X1,v_b____,v_a____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|c_in(c_Pair(X1,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_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(X1,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,X1,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~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)))|X1=v_a____|v_b____=v_a____|X1=v_b____)),
% 156.17/20.12 inference(resolution,[status(thm)],[f44894,f1676])).
% 156.17/20.12 fof(f62104,plain,(
% 156.17/20.12 spl0_666|~spl0_153|~spl0_258|spl0_110),
% 156.17/20.12 inference(split_clause,[status(thm)],[f62103,f62100,f47635,f54278,f42998])).
% 156.17/20.12 fof(f62146,plain,(
% 156.17/20.12 spl0_667 <=> ~c_Relation_Osym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X0,v_b____,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_b____,v_a____,X1)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_b____,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X0,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b____=X1|v_a____=X1),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f62149,plain,(
% 156.17/20.12 ![X0,X1]: (~c_Relation_Osym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X0,v_b____,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_b____,v_a____,X1)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(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_a____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_b____,v_a____,X1)),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____=X1|v_a____=X1|v_b____=v_a____)),
% 156.17/20.12 inference(resolution,[status(thm)],[f44895,f1678])).
% 156.17/20.12 fof(f62150,plain,(
% 156.17/20.12 spl0_667|~spl0_153|~spl0_258|spl0_110),
% 156.17/20.12 inference(split_clause,[status(thm)],[f62149,f62146,f47635,f54278,f42998])).
% 156.17/20.12 fof(f62151,plain,(
% 156.17/20.12 spl0_668 <=> ~c_Relation_Osym(hAPP(v_P____,v_sko__CHAINED__1(X0,v_P____,X1,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(X0,v_P____,X1,v_b____,v_a____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X1,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(X1,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,X1,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)))|X1=v_a____|X1=v_b____),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f62154,plain,(
% 156.17/20.12 ![X0,X1]: (~c_Relation_Osym(hAPP(v_P____,v_sko__CHAINED__1(X0,v_P____,X1,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(X0,v_P____,X1,v_b____,v_a____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(X1,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_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(X1,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,X1,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~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)))|X1=v_a____|v_b____=v_a____|X1=v_b____)),
% 156.17/20.12 inference(resolution,[status(thm)],[f44895,f1676])).
% 156.17/20.12 fof(f62155,plain,(
% 156.17/20.12 spl0_668|~spl0_153|~spl0_258|spl0_110),
% 156.17/20.12 inference(split_clause,[status(thm)],[f62154,f62151,f47635,f54278,f42998])).
% 156.17/20.12 fof(f62416,plain,(
% 156.17/20.12 spl0_669 <=> hAPP(hAPP(X0,v_b____),v_a____)=hAPP(hAPP(X0,v_b_H____),v_b____)|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),v_F(v_P____),X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3)|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=X2|v_b____=X2),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f62419,plain,(
% 156.17/20.12 ![X0,X1,X2,X3]: (hAPP(hAPP(X0,v_b____),v_a____)=hAPP(hAPP(X0,v_b_H____),v_b____)|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),v_F(v_P____),X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3)|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~c_in(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____=X2|v_b____=X2|v_a____=v_b____|~spl0_1)),
% 156.17/20.12 inference(resolution,[status(thm)],[f47765,f1682])).
% 156.17/20.12 fof(f62420,plain,(
% 156.17/20.12 spl0_669|~spl0_1|~spl0_258|spl0_110),
% 156.17/20.12 inference(split_clause,[status(thm)],[f62419,f62416,f1723,f54278,f42998])).
% 156.17/20.12 fof(f62470,plain,(
% 156.17/20.12 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____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_601),
% 156.17/20.12 inference(resolution,[status(thm)],[f61432,f1742])).
% 156.17/20.12 fof(f62471,plain,(
% 156.17/20.12 spl0_508|~spl0_601),
% 156.17/20.12 inference(split_clause,[status(thm)],[f62470,f60069,f61431])).
% 156.17/20.12 fof(f62481,plain,(
% 156.17/20.12 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))|~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_H____|v_b____=v_b_H____|~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,v_b_H____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_601|~spl0_263),
% 156.17/20.12 inference(resolution,[status(thm)],[f61432,f54313])).
% 156.17/20.12 fof(f62482,plain,(
% 156.17/20.12 spl0_239|~spl0_254|spl0_3|spl0_97|~spl0_505|~spl0_601|~spl0_263),
% 156.17/20.12 inference(split_clause,[status(thm)],[f62481,f52976,f54259,f1729,f41290,f60058,f61431,f54312])).
% 156.17/20.12 fof(f62483,plain,(
% 156.17/20.12 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_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|~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_H____|v_b____=v_b_H____|v_a____=v_b____|~spl0_601),
% 156.17/20.12 inference(resolution,[status(thm)],[f61432,f1676])).
% 156.17/20.12 fof(f62484,plain,(
% 156.17/20.12 spl0_1|~spl0_239|~spl0_508|~spl0_254|~spl0_258|spl0_3|spl0_97|spl0_110|~spl0_601),
% 156.17/20.12 inference(split_clause,[status(thm)],[f62483,f1723,f52976,f60069,f54259,f54278,f1729,f41290,f42998,f61431])).
% 156.17/20.12 fof(f62527,plain,(
% 156.17/20.12 $false|~spl0_190),
% 156.17/20.12 inference(forward_subsumption_resolution,[status(thm)],[f50312,f878])).
% 156.17/20.12 fof(f62528,plain,(
% 156.17/20.12 ~spl0_190),
% 156.17/20.12 inference(contradiction_clause,[status(thm)],[f62527])).
% 156.17/20.12 fof(f62530,plain,(
% 156.17/20.12 $false|~spl0_32),
% 156.17/20.12 inference(forward_subsumption_resolution,[status(thm)],[f21638,f878])).
% 156.17/20.12 fof(f62531,plain,(
% 156.17/20.12 ~spl0_32),
% 156.17/20.12 inference(contradiction_clause,[status(thm)],[f62530])).
% 156.17/20.12 fof(f62532,plain,(
% 156.17/20.12 $false|~spl0_24),
% 156.17/20.12 inference(forward_subsumption_resolution,[status(thm)],[f6528,f26836])).
% 156.17/20.12 fof(f62533,plain,(
% 156.17/20.12 ~spl0_24),
% 156.17/20.12 inference(contradiction_clause,[status(thm)],[f62532])).
% 156.17/20.12 fof(f62534,plain,(
% 156.17/20.12 $false|~spl0_17),
% 156.17/20.12 inference(forward_subsumption_resolution,[status(thm)],[f3317,f30031])).
% 156.17/20.12 fof(f62535,plain,(
% 156.17/20.12 ~spl0_17),
% 156.17/20.12 inference(contradiction_clause,[status(thm)],[f62534])).
% 156.17/20.12 fof(f62557,plain,(
% 156.17/20.12 spl0_239|~spl0_0),
% 156.17/20.12 inference(split_clause,[status(thm)],[f26539,f52976,f1720])).
% 156.17/20.12 fof(f62560,plain,(
% 156.17/20.12 spl0_676 <=> hBOOL(hAPP(X0,v_a____))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f62561,plain,(
% 156.17/20.12 ![X0]: (hBOOL(hAPP(X0,v_a____))|~spl0_676)),
% 156.17/20.12 inference(component_clause,[status(thm)],[f62560])).
% 156.17/20.12 fof(f62563,plain,(
% 156.17/20.12 spl0_677 <=> c_Nitpick_Orefl_H(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f62566,plain,(
% 156.17/20.12 ![X0]: (hBOOL(hAPP(X0,v_a____))|~c_Nitpick_Orefl_H(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_179)),
% 156.17/20.12 inference(resolution,[status(thm)],[f49600,f30446])).
% 156.17/20.12 fof(f62567,plain,(
% 156.17/20.12 spl0_676|~spl0_677|~spl0_179),
% 156.17/20.12 inference(split_clause,[status(thm)],[f62566,f62560,f62563,f49599])).
% 156.17/20.12 fof(f62574,plain,(
% 156.17/20.12 $false|~spl0_10),
% 156.17/20.12 inference(backward_subsumption_resolution,[status(thm)],[f1711,f2027])).
% 156.17/20.12 fof(f62575,plain,(
% 156.17/20.12 ~spl0_10),
% 156.17/20.12 inference(contradiction_clause,[status(thm)],[f62574])).
% 156.17/20.12 fof(f62580,plain,(
% 156.17/20.12 ~class_Orderings_Opreorder(tc_bool)|~spl0_36),
% 156.17/20.12 inference(resolution,[status(thm)],[f24084,f1698])).
% 156.17/20.12 fof(f62581,plain,(
% 156.17/20.12 $false|~spl0_36),
% 156.17/20.12 inference(forward_subsumption_resolution,[status(thm)],[f62580,f1712])).
% 156.17/20.12 fof(f62582,plain,(
% 156.17/20.12 ~spl0_36),
% 156.17/20.12 inference(contradiction_clause,[status(thm)],[f62581])).
% 156.17/20.12 fof(f62583,plain,(
% 156.17/20.12 ~class_Orderings_Oorder(tc_bool)|~spl0_35),
% 156.17/20.12 inference(resolution,[status(thm)],[f24079,f1702])).
% 156.17/20.12 fof(f62584,plain,(
% 156.17/20.12 $false|~spl0_35),
% 156.17/20.12 inference(forward_subsumption_resolution,[status(thm)],[f62583,f1714])).
% 156.17/20.12 fof(f62585,plain,(
% 156.17/20.12 ~spl0_35),
% 156.17/20.12 inference(contradiction_clause,[status(thm)],[f62584])).
% 156.17/20.12 fof(f62586,plain,(
% 156.17/20.12 ~class_Lattices_Olattice(tc_bool)|~spl0_30),
% 156.17/20.12 inference(resolution,[status(thm)],[f10943,f1700])).
% 156.17/20.12 fof(f62587,plain,(
% 156.17/20.12 $false|~spl0_30),
% 156.17/20.12 inference(forward_subsumption_resolution,[status(thm)],[f62586,f1713])).
% 156.17/20.12 fof(f62588,plain,(
% 156.17/20.12 ~spl0_30),
% 156.17/20.12 inference(contradiction_clause,[status(thm)],[f62587])).
% 156.17/20.12 fof(f62590,plain,(
% 156.17/20.12 $false|~spl0_20),
% 156.17/20.12 inference(backward_subsumption_resolution,[status(thm)],[f51255,f4066])).
% 156.17/20.12 fof(f62591,plain,(
% 156.17/20.12 ~spl0_20),
% 156.17/20.12 inference(contradiction_clause,[status(thm)],[f62590])).
% 156.17/20.12 fof(f62592,plain,(
% 156.17/20.12 ~class_Lattices_Obounded__lattice(tc_bool)|~spl0_14),
% 156.17/20.12 inference(resolution,[status(thm)],[f2429,f1694])).
% 156.17/20.12 fof(f62593,plain,(
% 156.17/20.12 $false|~spl0_14),
% 156.17/20.12 inference(forward_subsumption_resolution,[status(thm)],[f62592,f1710])).
% 156.17/20.12 fof(f62594,plain,(
% 156.17/20.12 ~spl0_14),
% 156.17/20.12 inference(contradiction_clause,[status(thm)],[f62593])).
% 156.17/20.12 fof(f62595,plain,(
% 156.17/20.12 $false|~spl0_676|spl0_638),
% 156.17/20.12 inference(backward_subsumption_resolution,[status(thm)],[f61767,f62561])).
% 156.17/20.12 fof(f62596,plain,(
% 156.17/20.12 ~spl0_676|spl0_638),
% 156.17/20.12 inference(contradiction_clause,[status(thm)],[f62595])).
% 156.17/20.12 fof(f62663,plain,(
% 156.17/20.12 ![X0,X1,X2]: (~c_in(X0,c_Relation_ORange(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2)|~spl0_65)),
% 156.17/20.12 inference(resolution,[status(thm)],[f31089,f50704])).
% 156.17/20.12 fof(f62664,plain,(
% 156.17/20.12 $false|~spl0_65),
% 156.17/20.12 inference(forward_subsumption_resolution,[status(thm)],[f62663,f50704])).
% 156.17/20.12 fof(f62665,plain,(
% 156.17/20.12 ~spl0_65),
% 156.17/20.12 inference(contradiction_clause,[status(thm)],[f62664])).
% 156.17/20.12 fof(f62889,plain,(
% 156.17/20.12 ~class_Lattices_Oboolean__algebra(tc_bool)|~spl0_15),
% 156.17/20.12 inference(resolution,[status(thm)],[f1696,f2516])).
% 156.17/20.12 fof(f62890,plain,(
% 156.17/20.12 $false|~spl0_15),
% 156.17/20.12 inference(forward_subsumption_resolution,[status(thm)],[f62889,f1711])).
% 156.17/20.12 fof(f62891,plain,(
% 156.17/20.12 ~spl0_15),
% 156.17/20.12 inference(contradiction_clause,[status(thm)],[f62890])).
% 156.17/20.12 fof(f63045,plain,(
% 156.17/20.12 spl0_689 <=> hBOOL(hAPP(X0,v_b____))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f63046,plain,(
% 156.17/20.12 ![X0]: (hBOOL(hAPP(X0,v_b____))|~spl0_689)),
% 156.17/20.12 inference(component_clause,[status(thm)],[f63045])).
% 156.17/20.12 fof(f63051,plain,(
% 156.17/20.12 $false|~spl0_689|spl0_180),
% 156.17/20.12 inference(backward_subsumption_resolution,[status(thm)],[f49666,f63046])).
% 156.17/20.12 fof(f63052,plain,(
% 156.17/20.12 ~spl0_689|spl0_180),
% 156.17/20.12 inference(contradiction_clause,[status(thm)],[f63051])).
% 156.17/20.12 fof(f63065,plain,(
% 156.17/20.12 spl0_690 <=> ~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))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f63066,plain,(
% 156.17/20.12 ![X0]: (~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))|~spl0_690)),
% 156.17/20.12 inference(component_clause,[status(thm)],[f63065])).
% 156.17/20.12 fof(f63068,plain,(
% 156.17/20.12 spl0_691 <=> c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X1,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f63069,plain,(
% 156.17/20.12 ![X0]: (c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X0,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_691)),
% 156.17/20.12 inference(component_clause,[status(thm)],[f63068])).
% 156.17/20.12 fof(f63071,plain,(
% 156.17/20.12 ![X0,X1]: (~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(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X1,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_159)),
% 156.17/20.12 inference(resolution,[status(thm)],[f47664,f1648])).
% 156.17/20.12 fof(f63072,plain,(
% 156.17/20.12 spl0_690|spl0_691|~spl0_159),
% 156.17/20.12 inference(split_clause,[status(thm)],[f63071,f63065,f63068,f47663])).
% 156.17/20.12 fof(f63074,plain,(
% 156.17/20.12 spl0_692 <=> 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)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f63076,plain,(
% 156.17/20.12 ~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)|spl0_692),
% 156.17/20.12 inference(component_clause,[status(thm)],[f63074])).
% 156.17/20.12 fof(f63077,plain,(
% 156.17/20.12 ![X0]: (~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(v_b____,c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_159)),
% 156.17/20.12 inference(resolution,[status(thm)],[f47664,f1632])).
% 156.17/20.12 fof(f63078,plain,(
% 156.17/20.12 spl0_690|spl0_692|~spl0_159),
% 156.17/20.12 inference(split_clause,[status(thm)],[f63077,f63065,f63074,f47663])).
% 156.17/20.12 fof(f63080,plain,(
% 156.17/20.12 spl0_693 <=> c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X1,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f63083,plain,(
% 156.17/20.12 ![X0,X1]: (~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(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X1,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_159)),
% 156.17/20.12 inference(resolution,[status(thm)],[f47664,f1628])).
% 156.17/20.12 fof(f63084,plain,(
% 156.17/20.12 spl0_690|spl0_693|~spl0_159),
% 156.17/20.12 inference(split_clause,[status(thm)],[f63083,f63065,f63080,f47663])).
% 156.17/20.12 fof(f63086,plain,(
% 156.17/20.12 spl0_694 <=> c_Relation_Oirrefl(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f63089,plain,(
% 156.17/20.12 ~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_Oirrefl(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_159),
% 156.17/20.12 inference(resolution,[status(thm)],[f47664,f1545])).
% 156.17/20.12 fof(f63090,plain,(
% 156.17/20.12 ~spl0_153|~spl0_694|~spl0_159),
% 156.17/20.12 inference(split_clause,[status(thm)],[f63089,f47635,f63086,f47663])).
% 156.17/20.12 fof(f63091,plain,(
% 156.17/20.12 spl0_695 <=> c_Wellfounded_Oacyclic(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f63094,plain,(
% 156.17/20.12 ~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_Wellfounded_Oacyclic(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_159),
% 156.17/20.12 inference(resolution,[status(thm)],[f47664,f7580])).
% 156.17/20.12 fof(f63095,plain,(
% 156.17/20.12 ~spl0_153|~spl0_695|~spl0_159),
% 156.17/20.12 inference(split_clause,[status(thm)],[f63094,f47635,f63091,f47663])).
% 156.17/20.12 fof(f63096,plain,(
% 156.17/20.12 ~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_Wellfounded_Owf(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_159),
% 156.17/20.12 inference(resolution,[status(thm)],[f47664,f1576])).
% 156.17/20.12 fof(f63097,plain,(
% 156.17/20.12 ~spl0_153|~spl0_156|~spl0_159),
% 156.17/20.12 inference(split_clause,[status(thm)],[f63096,f47635,f47650,f47663])).
% 156.17/20.12 fof(f63098,plain,(
% 156.17/20.12 spl0_696 <=> ~c_Wellfounded_Owf(c_Set_Oinsert(X0,v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f63101,plain,(
% 156.17/20.12 ![X0]: (~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_Wellfounded_Owf(c_Set_Oinsert(X0,v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_159)),
% 156.17/20.12 inference(resolution,[status(thm)],[f47664,f8835])).
% 156.17/20.12 fof(f63102,plain,(
% 156.17/20.12 ~spl0_153|spl0_696|~spl0_159),
% 156.17/20.12 inference(split_clause,[status(thm)],[f63101,f47635,f63098,f47663])).
% 156.17/20.12 fof(f63106,plain,(
% 156.17/20.12 spl0_697 <=> c_in(c_Pair(v_a____,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(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_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f63107,plain,(
% 156.17/20.12 c_in(c_Pair(v_a____,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(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_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_697),
% 156.17/20.12 inference(component_clause,[status(thm)],[f63106])).
% 156.17/20.12 fof(f63109,plain,(
% 156.17/20.12 c_in(c_Pair(v_a____,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(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_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,c_Relation_ODomain(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_157),
% 156.17/20.12 inference(resolution,[status(thm)],[f47656,f1520])).
% 156.17/20.12 fof(f63110,plain,(
% 156.17/20.12 spl0_697|~spl0_186|~spl0_157),
% 156.17/20.12 inference(split_clause,[status(thm)],[f63109,f63106,f50289,f47655])).
% 156.17/20.12 fof(f63111,plain,(
% 156.17/20.12 spl0_698 <=> c_in(c_Pair(v_a____,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(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_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f63112,plain,(
% 156.17/20.12 c_in(c_Pair(v_a____,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(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_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_698),
% 156.17/20.12 inference(component_clause,[status(thm)],[f63111])).
% 156.17/20.12 fof(f63114,plain,(
% 156.17/20.12 c_in(c_Pair(v_a____,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(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_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,c_Relation_ODomain(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_157),
% 156.17/20.12 inference(resolution,[status(thm)],[f47656,f1513])).
% 156.17/20.12 fof(f63115,plain,(
% 156.17/20.12 spl0_698|~spl0_186|~spl0_157),
% 156.17/20.12 inference(split_clause,[status(thm)],[f63114,f63111,f50289,f47655])).
% 156.17/20.12 fof(f63117,plain,(
% 156.17/20.12 spl0_699 <=> ~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X0,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f63118,plain,(
% 156.17/20.12 ![X0]: (~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X0,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_699)),
% 156.17/20.12 inference(component_clause,[status(thm)],[f63117])).
% 156.17/20.12 fof(f63122,plain,(
% 156.17/20.12 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_Nitpick_Orefl_H(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_157),
% 156.17/20.12 inference(resolution,[status(thm)],[f47656,f1574])).
% 156.17/20.12 fof(f63123,plain,(
% 156.17/20.12 spl0_1|~spl0_677|~spl0_157),
% 156.17/20.12 inference(split_clause,[status(thm)],[f63122,f1723,f62563,f47655])).
% 156.17/20.12 fof(f63130,plain,(
% 156.17/20.12 spl0_700 <=> c_in(v_a____,c_Relation_ODomain(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f63133,plain,(
% 156.17/20.12 ![X0]: (c_in(v_a____,c_Relation_ODomain(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X0,v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_475)),
% 156.17/20.12 inference(resolution,[status(thm)],[f61738,f24438])).
% 156.17/20.12 fof(f63134,plain,(
% 156.17/20.12 spl0_700|spl0_243|~spl0_475),
% 156.17/20.12 inference(split_clause,[status(thm)],[f63133,f63130,f53020,f59883])).
% 156.17/20.12 fof(f63137,plain,(
% 156.17/20.12 ![X0]: (c_in(v_b____,c_Relation_ODomain(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X0,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_691)),
% 156.17/20.12 inference(resolution,[status(thm)],[f63069,f24438])).
% 156.17/20.12 fof(f63138,plain,(
% 156.17/20.12 spl0_186|spl0_187|~spl0_691),
% 156.17/20.12 inference(split_clause,[status(thm)],[f63137,f50289,f50292,f63068])).
% 156.17/20.12 fof(f63139,plain,(
% 156.17/20.12 ![X0]: (~c_in(v_b____,c_Relation_ODomain(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X0,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_699)),
% 156.17/20.12 inference(resolution,[status(thm)],[f63118,f24438])).
% 156.17/20.12 fof(f63140,plain,(
% 156.17/20.12 ~spl0_186|spl0_187|~spl0_699),
% 156.17/20.12 inference(split_clause,[status(thm)],[f63139,f50289,f50292,f63117])).
% 156.17/20.12 fof(f63171,plain,(
% 156.17/20.12 spl0_706 <=> c_in(v_b_H____,c_Relation_ORange(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f63173,plain,(
% 156.17/20.12 ~c_in(v_b_H____,c_Relation_ORange(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|spl0_706),
% 156.17/20.12 inference(component_clause,[status(thm)],[f63171])).
% 156.17/20.12 fof(f63193,plain,(
% 156.17/20.12 ~c_in(c_Pair(v_b_H____,v_b____,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_Wellfounded_Owf(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_89),
% 156.17/20.12 inference(resolution,[status(thm)],[f40293,f1576])).
% 156.17/20.12 fof(f63194,plain,(
% 156.17/20.12 ~spl0_106|~spl0_107|~spl0_89),
% 156.17/20.12 inference(split_clause,[status(thm)],[f63193,f42380,f42383,f40292])).
% 156.17/20.12 fof(f63208,plain,(
% 156.17/20.12 spl0_712 <=> c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(v_b____,v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)=v_b_H____),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f63209,plain,(
% 156.17/20.12 c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(v_b____,v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)=v_b_H____|~spl0_712),
% 156.17/20.12 inference(component_clause,[status(thm)],[f63208])).
% 156.17/20.12 fof(f63211,plain,(
% 156.17/20.12 c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(v_b____,v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)=v_b_H____|~c_in(v_b____,c_Relation_ODomain(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_84),
% 156.17/20.12 inference(resolution,[status(thm)],[f39923,f1520])).
% 156.17/20.12 fof(f63212,plain,(
% 156.17/20.12 spl0_712|~spl0_244|~spl0_84),
% 156.17/20.12 inference(split_clause,[status(thm)],[f63211,f63208,f53025,f39922])).
% 156.17/20.12 fof(f63213,plain,(
% 156.17/20.12 spl0_713 <=> c_ATP__Linkup_Osko__Relation__XDomainE__1__1(v_b____,v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)=v_b_H____),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f63214,plain,(
% 156.17/20.12 c_ATP__Linkup_Osko__Relation__XDomainE__1__1(v_b____,v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)=v_b_H____|~spl0_713),
% 156.17/20.12 inference(component_clause,[status(thm)],[f63213])).
% 156.17/20.12 fof(f63289,plain,(
% 156.17/20.12 spl0_715 <=> ~c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Osingle__valued(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f63292,plain,(
% 156.17/20.12 ![X0]: (~c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|v_b____=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.12 inference(resolution,[status(thm)],[f45374,f39703])).
% 156.17/20.12 fof(f63293,plain,(
% 156.17/20.12 spl0_715|spl0_97),
% 156.17/20.12 inference(split_clause,[status(thm)],[f63292,f63289,f41290])).
% 156.17/20.12 fof(f63600,plain,(
% 156.17/20.12 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))|~c_in(v_b____,c_Relation_ODomain(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_713),
% 156.17/20.12 inference(paramodulation,[status(thm)],[f63214,f1513])).
% 156.17/20.12 fof(f63601,plain,(
% 156.17/20.12 spl0_239|~spl0_244|~spl0_713),
% 156.17/20.12 inference(split_clause,[status(thm)],[f63600,f52976,f53025,f63213])).
% 156.17/20.12 fof(f63602,plain,(
% 156.17/20.12 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))|~c_in(v_b____,c_Relation_ODomain(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_712),
% 156.17/20.12 inference(paramodulation,[status(thm)],[f63209,f1520])).
% 156.17/20.12 fof(f63603,plain,(
% 156.17/20.12 spl0_239|~spl0_244|~spl0_712),
% 156.17/20.12 inference(split_clause,[status(thm)],[f63602,f52976,f53025,f63208])).
% 156.17/20.12 fof(f63615,plain,(
% 156.17/20.12 spl0_718 <=> ~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X0,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f63616,plain,(
% 156.17/20.12 ![X0]: (~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X0,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_718)),
% 156.17/20.12 inference(component_clause,[status(thm)],[f63615])).
% 156.17/20.12 fof(f63620,plain,(
% 156.17/20.12 v_a____=v_b____|~c_Nitpick_Orefl_H(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_78),
% 156.17/20.12 inference(resolution,[status(thm)],[f39707,f1574])).
% 156.17/20.12 fof(f63621,plain,(
% 156.17/20.12 spl0_110|~spl0_677|~spl0_78),
% 156.17/20.12 inference(split_clause,[status(thm)],[f63620,f42998,f62563,f39706])).
% 156.17/20.12 fof(f63632,plain,(
% 156.17/20.12 ![X0]: (~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)|~c_Equiv__Relations_Oequiv(X0,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_718)),
% 156.17/20.12 inference(resolution,[status(thm)],[f63616,f24438])).
% 156.17/20.12 fof(f63633,plain,(
% 156.17/20.12 ~spl0_196|spl0_187|~spl0_718),
% 156.17/20.12 inference(split_clause,[status(thm)],[f63632,f50758,f50292,f63615])).
% 156.17/20.12 fof(f63898,plain,(
% 156.17/20.12 spl0_720 <=> ~c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Osingle__valued(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f63901,plain,(
% 156.17/20.12 ![X0]: (~c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_b____=v_b____|~c_Relation_Osingle__valued(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.12 inference(resolution,[status(thm)],[f45391,f44893])).
% 156.17/20.12 fof(f63902,plain,(
% 156.17/20.12 spl0_720|spl0_175),
% 156.17/20.12 inference(split_clause,[status(thm)],[f63901,f63898,f49384])).
% 156.17/20.12 fof(f63913,plain,(
% 156.17/20.12 spl0_722 <=> ~c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Osingle__valued(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f63916,plain,(
% 156.17/20.12 ![X0,X1]: (~c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_b_H____=v_b____|~c_Relation_Osingle__valued(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.12 inference(resolution,[status(thm)],[f45391,f1646])).
% 156.17/20.12 fof(f63917,plain,(
% 156.17/20.12 spl0_722|spl0_97),
% 156.17/20.12 inference(split_clause,[status(thm)],[f63916,f63913,f41290])).
% 156.17/20.12 fof(f63918,plain,(
% 156.17/20.12 spl0_723 <=> ~c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Osingle__valued(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_Nitpick_Orefl_H(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f63921,plain,(
% 156.17/20.12 ![X0]: (~c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_b_H____=v_b____|~c_Relation_Osingle__valued(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_Nitpick_Orefl_H(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.12 inference(resolution,[status(thm)],[f45391,f1574])).
% 156.17/20.12 fof(f63922,plain,(
% 156.17/20.12 spl0_723|spl0_97),
% 156.17/20.12 inference(split_clause,[status(thm)],[f63921,f63918,f41290])).
% 156.17/20.12 fof(f63980,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5]: (~c_Nitpick_Orefl_H(c_Relation_OId__on(X0,X1),X1)|c_FunDef_Oin__rel(X0,X2,X3,X4,X5))),
% 156.17/20.12 inference(paramodulation,[status(thm)],[f1471,f57879])).
% 156.17/20.12 fof(f64063,plain,(
% 156.17/20.12 spl0_724 <=> ~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Relation_OId__on(X0,X1),X2),X2)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f64066,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4]: (~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Relation_OId__on(X0,X1),X2),X2)|X3=X4)),
% 156.17/20.12 inference(resolution,[status(thm)],[f63980,f12916])).
% 156.17/20.12 fof(f64067,plain,(
% 156.17/20.12 spl0_724|spl0_211),
% 156.17/20.12 inference(split_clause,[status(thm)],[f64066,f64063,f51909])).
% 156.17/20.12 fof(f64069,plain,(
% 156.17/20.12 spl0_725 <=> ~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Relation_OId(X0),X1),X1)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f64072,plain,(
% 156.17/20.12 ![X0,X1,X2,X3]: (~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Relation_OId(X0),X1),X1)|X2=X3)),
% 156.17/20.12 inference(resolution,[status(thm)],[f63980,f12917])).
% 156.17/20.12 fof(f64073,plain,(
% 156.17/20.12 spl0_725|spl0_211),
% 156.17/20.12 inference(split_clause,[status(thm)],[f64072,f64069,f51909])).
% 156.17/20.12 fof(f64215,plain,(
% 156.17/20.12 c_in(v_a____,c_Wellfounded_Oacc(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_690),
% 156.17/20.12 inference(resolution,[status(thm)],[f63066,f1502])).
% 156.17/20.12 fof(f64220,plain,(
% 156.17/20.12 ![X0]: (hBOOL(hAPP(X0,v_a____))|~c_Nitpick_Orefl_H(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_690)),
% 156.17/20.12 inference(resolution,[status(thm)],[f64215,f30446])).
% 156.17/20.12 fof(f64221,plain,(
% 156.17/20.12 spl0_676|~spl0_677|~spl0_690),
% 156.17/20.12 inference(split_clause,[status(thm)],[f64220,f62560,f62563,f63065])).
% 156.17/20.12 fof(f64229,plain,(
% 156.17/20.12 spl0_726 <=> ~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Osym(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Osingle__valued(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f64232,plain,(
% 156.17/20.12 ![X0,X1]: (~c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Osym(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_b____=v_b____|~c_Relation_Osingle__valued(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~spl0_235)),
% 156.17/20.12 inference(resolution,[status(thm)],[f52757,f45391])).
% 156.17/20.12 fof(f64233,plain,(
% 156.17/20.12 spl0_726|spl0_175|~spl0_235),
% 156.17/20.12 inference(split_clause,[status(thm)],[f64232,f64229,f49384,f52756])).
% 156.17/20.12 fof(f64444,plain,(
% 156.17/20.12 c_in(v_b____,c_Relation_ODomain(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_514),
% 156.17/20.12 inference(resolution,[status(thm)],[f60098,f1636])).
% 156.17/20.12 fof(f64445,plain,(
% 156.17/20.12 spl0_186|~spl0_514),
% 156.17/20.12 inference(split_clause,[status(thm)],[f64444,f50289,f60097])).
% 156.17/20.12 fof(f64476,plain,(
% 156.17/20.12 spl0_731 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=X0|v_b____=X0|hAPP(X1,v_b____)=hAPP(X1,v_b_H____)|~c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),X1,tc_Arrow__Order__Mirabelle_Oalt,X2)|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f64479,plain,(
% 156.17/20.12 ![X0,X1,X2]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~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____=X0|v_b____=X0|hAPP(X1,v_b____)=hAPP(X1,v_b_H____)|~c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),X1,tc_Arrow__Order__Mirabelle_Oalt,X2)|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_305)),
% 156.17/20.12 inference(resolution,[status(thm)],[f54985,f45389])).
% 156.17/20.12 fof(f64480,plain,(
% 156.17/20.12 spl0_731|~spl0_254|~spl0_305),
% 156.17/20.12 inference(split_clause,[status(thm)],[f64479,f64476,f54259,f54984])).
% 156.17/20.12 fof(f64481,plain,(
% 156.17/20.12 spl0_732 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=X0|v_b____=X0|hAPP(X1,v_b____)=hAPP(X1,v_b_H____)|~c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),X1,tc_Arrow__Order__Mirabelle_Oalt,X2)|X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f64484,plain,(
% 156.17/20.12 ![X0,X1,X2]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~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____=X0|v_b____=X0|hAPP(X1,v_b____)=hAPP(X1,v_b_H____)|~c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),X1,tc_Arrow__Order__Mirabelle_Oalt,X2)|X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_305)),
% 156.17/20.12 inference(resolution,[status(thm)],[f54985,f39703])).
% 156.17/20.12 fof(f64485,plain,(
% 156.17/20.12 spl0_732|~spl0_254|~spl0_305),
% 156.17/20.12 inference(split_clause,[status(thm)],[f64484,f64481,f54259,f54984])).
% 156.17/20.12 fof(f64495,plain,(
% 156.17/20.12 spl0_733 <=> 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)))|hAPP(X1,v_b____)=hAPP(X1,v_b_H____)|~c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X1,tc_Arrow__Order__Mirabelle_Oalt,X2)|~c_Relation_Oirrefl(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f64498,plain,(
% 156.17/20.12 ![X0,X1,X2]: (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)))|v_a____=v_b____|v_b____=v_b____|hAPP(X1,v_b____)=hAPP(X1,v_b_H____)|~c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X1,tc_Arrow__Order__Mirabelle_Oalt,X2)|~c_Relation_Oirrefl(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_305)),
% 156.17/20.12 inference(resolution,[status(thm)],[f54985,f1545])).
% 156.17/20.12 fof(f64499,plain,(
% 156.17/20.12 spl0_733|spl0_110|spl0_175|~spl0_305),
% 156.17/20.12 inference(split_clause,[status(thm)],[f64498,f64495,f42998,f49384,f54984])).
% 156.17/20.12 fof(f64500,plain,(
% 156.17/20.12 spl0_734 <=> 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)))|hAPP(X1,v_b____)=hAPP(X1,v_b_H____)|~c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X1,tc_Arrow__Order__Mirabelle_Oalt,X2)|~c_Wellfounded_Oacyclic(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f64503,plain,(
% 156.17/20.12 ![X0,X1,X2]: (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)))|v_a____=v_b____|v_b____=v_b____|hAPP(X1,v_b____)=hAPP(X1,v_b_H____)|~c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X1,tc_Arrow__Order__Mirabelle_Oalt,X2)|~c_Wellfounded_Oacyclic(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_305)),
% 156.17/20.12 inference(resolution,[status(thm)],[f54985,f7580])).
% 156.17/20.12 fof(f64504,plain,(
% 156.17/20.12 spl0_734|spl0_110|spl0_175|~spl0_305),
% 156.17/20.12 inference(split_clause,[status(thm)],[f64503,f64500,f42998,f49384,f54984])).
% 156.17/20.12 fof(f64505,plain,(
% 156.17/20.12 spl0_735 <=> 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)))|hAPP(X1,v_b____)=hAPP(X1,v_b_H____)|~c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X1,tc_Arrow__Order__Mirabelle_Oalt,X2)|~c_Wellfounded_Owf(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f64508,plain,(
% 156.17/20.12 ![X0,X1,X2]: (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)))|v_a____=v_b____|v_b____=v_b____|hAPP(X1,v_b____)=hAPP(X1,v_b_H____)|~c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X1,tc_Arrow__Order__Mirabelle_Oalt,X2)|~c_Wellfounded_Owf(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_305)),
% 156.17/20.12 inference(resolution,[status(thm)],[f54985,f1576])).
% 156.17/20.12 fof(f64509,plain,(
% 156.17/20.12 spl0_735|spl0_110|spl0_175|~spl0_305),
% 156.17/20.12 inference(split_clause,[status(thm)],[f64508,f64505,f42998,f49384,f54984])).
% 156.17/20.12 fof(f64510,plain,(
% 156.17/20.12 spl0_736 <=> 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)))|hAPP(X1,v_b____)=hAPP(X1,v_b_H____)|~c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X1,tc_Arrow__Order__Mirabelle_Oalt,X2)|~c_Wellfounded_Owf(c_Set_Oinsert(X3,hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f64513,plain,(
% 156.17/20.12 ![X0,X1,X2,X3]: (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)))|v_a____=v_b____|v_b____=v_b____|hAPP(X1,v_b____)=hAPP(X1,v_b_H____)|~c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X1,tc_Arrow__Order__Mirabelle_Oalt,X2)|~c_Wellfounded_Owf(c_Set_Oinsert(X3,hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_305)),
% 156.17/20.12 inference(resolution,[status(thm)],[f54985,f8835])).
% 156.17/20.12 fof(f64514,plain,(
% 156.17/20.12 spl0_736|spl0_110|spl0_175|~spl0_305),
% 156.17/20.12 inference(split_clause,[status(thm)],[f64513,f64510,f42998,f49384,f54984])).
% 156.17/20.12 fof(f64551,plain,(
% 156.17/20.12 spl0_738 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=X0|v_b____=X0|hAPP(hAPP(X1,X2),v_b____)=hAPP(hAPP(X1,X3),v_b_H____)|~c_in(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4))|~c_Equiv__Relations_Ocongruent2(X5,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),X1,X4,tc_Arrow__Order__Mirabelle_Oalt,X6)|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f64554,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~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____=X0|v_b____=X0|hAPP(hAPP(X1,X2),v_b____)=hAPP(hAPP(X1,X3),v_b_H____)|~c_in(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4))|~c_Equiv__Relations_Ocongruent2(X5,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),X1,X4,tc_Arrow__Order__Mirabelle_Oalt,X6)|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_306)),
% 156.17/20.12 inference(resolution,[status(thm)],[f54990,f45389])).
% 156.17/20.12 fof(f64555,plain,(
% 156.17/20.12 spl0_738|~spl0_254|~spl0_306),
% 156.17/20.12 inference(split_clause,[status(thm)],[f64554,f64551,f54259,f54989])).
% 156.17/20.12 fof(f64556,plain,(
% 156.17/20.12 spl0_739 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=X0|v_b____=X0|hAPP(hAPP(X1,X2),v_b____)=hAPP(hAPP(X1,X3),v_b_H____)|~c_in(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4))|~c_Equiv__Relations_Ocongruent2(X5,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),X1,X4,tc_Arrow__Order__Mirabelle_Oalt,X6)|X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f64559,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~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____=X0|v_b____=X0|hAPP(hAPP(X1,X2),v_b____)=hAPP(hAPP(X1,X3),v_b_H____)|~c_in(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4))|~c_Equiv__Relations_Ocongruent2(X5,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),X1,X4,tc_Arrow__Order__Mirabelle_Oalt,X6)|X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_306)),
% 156.17/20.12 inference(resolution,[status(thm)],[f54990,f39703])).
% 156.17/20.12 fof(f64560,plain,(
% 156.17/20.12 spl0_739|~spl0_254|~spl0_306),
% 156.17/20.12 inference(split_clause,[status(thm)],[f64559,f64556,f54259,f54989])).
% 156.17/20.12 fof(f64570,plain,(
% 156.17/20.12 spl0_740 <=> 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)))|hAPP(hAPP(X1,X2),v_b____)=hAPP(hAPP(X1,X3),v_b_H____)|~c_in(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4))|~c_Equiv__Relations_Ocongruent2(X5,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X1,X4,tc_Arrow__Order__Mirabelle_Oalt,X6)|~c_Relation_Oirrefl(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f64573,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6]: (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)))|v_a____=v_b____|v_b____=v_b____|hAPP(hAPP(X1,X2),v_b____)=hAPP(hAPP(X1,X3),v_b_H____)|~c_in(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4))|~c_Equiv__Relations_Ocongruent2(X5,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X1,X4,tc_Arrow__Order__Mirabelle_Oalt,X6)|~c_Relation_Oirrefl(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_306)),
% 156.17/20.12 inference(resolution,[status(thm)],[f54990,f1545])).
% 156.17/20.12 fof(f64574,plain,(
% 156.17/20.12 spl0_740|spl0_110|spl0_175|~spl0_306),
% 156.17/20.12 inference(split_clause,[status(thm)],[f64573,f64570,f42998,f49384,f54989])).
% 156.17/20.12 fof(f64575,plain,(
% 156.17/20.12 spl0_741 <=> 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)))|hAPP(hAPP(X1,X2),v_b____)=hAPP(hAPP(X1,X3),v_b_H____)|~c_in(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4))|~c_Equiv__Relations_Ocongruent2(X5,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X1,X4,tc_Arrow__Order__Mirabelle_Oalt,X6)|~c_Wellfounded_Oacyclic(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f64578,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6]: (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)))|v_a____=v_b____|v_b____=v_b____|hAPP(hAPP(X1,X2),v_b____)=hAPP(hAPP(X1,X3),v_b_H____)|~c_in(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4))|~c_Equiv__Relations_Ocongruent2(X5,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X1,X4,tc_Arrow__Order__Mirabelle_Oalt,X6)|~c_Wellfounded_Oacyclic(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_306)),
% 156.17/20.12 inference(resolution,[status(thm)],[f54990,f7580])).
% 156.17/20.12 fof(f64579,plain,(
% 156.17/20.12 spl0_741|spl0_110|spl0_175|~spl0_306),
% 156.17/20.12 inference(split_clause,[status(thm)],[f64578,f64575,f42998,f49384,f54989])).
% 156.17/20.12 fof(f64580,plain,(
% 156.17/20.12 spl0_742 <=> 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)))|hAPP(hAPP(X1,X2),v_b____)=hAPP(hAPP(X1,X3),v_b_H____)|~c_in(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4))|~c_Equiv__Relations_Ocongruent2(X5,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X1,X4,tc_Arrow__Order__Mirabelle_Oalt,X6)|~c_Wellfounded_Owf(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f64583,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6]: (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)))|v_a____=v_b____|v_b____=v_b____|hAPP(hAPP(X1,X2),v_b____)=hAPP(hAPP(X1,X3),v_b_H____)|~c_in(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4))|~c_Equiv__Relations_Ocongruent2(X5,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X1,X4,tc_Arrow__Order__Mirabelle_Oalt,X6)|~c_Wellfounded_Owf(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_306)),
% 156.17/20.12 inference(resolution,[status(thm)],[f54990,f1576])).
% 156.17/20.12 fof(f64584,plain,(
% 156.17/20.12 spl0_742|spl0_110|spl0_175|~spl0_306),
% 156.17/20.12 inference(split_clause,[status(thm)],[f64583,f64580,f42998,f49384,f54989])).
% 156.17/20.12 fof(f64585,plain,(
% 156.17/20.12 spl0_743 <=> 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)))|hAPP(hAPP(X1,X2),v_b____)=hAPP(hAPP(X1,X3),v_b_H____)|~c_in(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4))|~c_Equiv__Relations_Ocongruent2(X5,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X1,X4,tc_Arrow__Order__Mirabelle_Oalt,X6)|~c_Wellfounded_Owf(c_Set_Oinsert(X7,hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f64588,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6,X7]: (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)))|v_a____=v_b____|v_b____=v_b____|hAPP(hAPP(X1,X2),v_b____)=hAPP(hAPP(X1,X3),v_b_H____)|~c_in(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4))|~c_Equiv__Relations_Ocongruent2(X5,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X1,X4,tc_Arrow__Order__Mirabelle_Oalt,X6)|~c_Wellfounded_Owf(c_Set_Oinsert(X7,hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_306)),
% 156.17/20.12 inference(resolution,[status(thm)],[f54990,f8835])).
% 156.17/20.12 fof(f64589,plain,(
% 156.17/20.12 spl0_743|spl0_110|spl0_175|~spl0_306),
% 156.17/20.12 inference(split_clause,[status(thm)],[f64588,f64585,f42998,f49384,f54989])).
% 156.17/20.12 fof(f64611,plain,(
% 156.17/20.12 spl0_745 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=X0|v_b____=X0|hAPP(hAPP(X1,v_b____),X2)=hAPP(hAPP(X1,v_b_H____),X3)|~c_in(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4))|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),X5,X1,tc_Arrow__Order__Mirabelle_Oalt,X4,X6)|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f64614,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~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____=X0|v_b____=X0|hAPP(hAPP(X1,v_b____),X2)=hAPP(hAPP(X1,v_b_H____),X3)|~c_in(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4))|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),X5,X1,tc_Arrow__Order__Mirabelle_Oalt,X4,X6)|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_307)),
% 156.17/20.12 inference(resolution,[status(thm)],[f54995,f45389])).
% 156.17/20.12 fof(f64615,plain,(
% 156.17/20.12 spl0_745|~spl0_254|~spl0_307),
% 156.17/20.12 inference(split_clause,[status(thm)],[f64614,f64611,f54259,f54994])).
% 156.17/20.12 fof(f64616,plain,(
% 156.17/20.12 spl0_746 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=X0|v_b____=X0|hAPP(hAPP(X1,v_b____),X2)=hAPP(hAPP(X1,v_b_H____),X3)|~c_in(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4))|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),X5,X1,tc_Arrow__Order__Mirabelle_Oalt,X4,X6)|X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f64619,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~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____=X0|v_b____=X0|hAPP(hAPP(X1,v_b____),X2)=hAPP(hAPP(X1,v_b_H____),X3)|~c_in(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4))|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),X5,X1,tc_Arrow__Order__Mirabelle_Oalt,X4,X6)|X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_307)),
% 156.17/20.12 inference(resolution,[status(thm)],[f54995,f39703])).
% 156.17/20.12 fof(f64620,plain,(
% 156.17/20.12 spl0_746|~spl0_254|~spl0_307),
% 156.17/20.12 inference(split_clause,[status(thm)],[f64619,f64616,f54259,f54994])).
% 156.17/20.12 fof(f64630,plain,(
% 156.17/20.12 spl0_747 <=> 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)))|hAPP(hAPP(X1,v_b____),X2)=hAPP(hAPP(X1,v_b_H____),X3)|~c_in(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4))|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X5,X1,tc_Arrow__Order__Mirabelle_Oalt,X4,X6)|~c_Relation_Oirrefl(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f64633,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6]: (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)))|v_a____=v_b____|v_b____=v_b____|hAPP(hAPP(X1,v_b____),X2)=hAPP(hAPP(X1,v_b_H____),X3)|~c_in(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4))|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X5,X1,tc_Arrow__Order__Mirabelle_Oalt,X4,X6)|~c_Relation_Oirrefl(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_307)),
% 156.17/20.12 inference(resolution,[status(thm)],[f54995,f1545])).
% 156.17/20.12 fof(f64634,plain,(
% 156.17/20.12 spl0_747|spl0_110|spl0_175|~spl0_307),
% 156.17/20.12 inference(split_clause,[status(thm)],[f64633,f64630,f42998,f49384,f54994])).
% 156.17/20.12 fof(f64635,plain,(
% 156.17/20.12 spl0_748 <=> 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)))|hAPP(hAPP(X1,v_b____),X2)=hAPP(hAPP(X1,v_b_H____),X3)|~c_in(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4))|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X5,X1,tc_Arrow__Order__Mirabelle_Oalt,X4,X6)|~c_Wellfounded_Oacyclic(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f64638,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6]: (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)))|v_a____=v_b____|v_b____=v_b____|hAPP(hAPP(X1,v_b____),X2)=hAPP(hAPP(X1,v_b_H____),X3)|~c_in(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4))|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X5,X1,tc_Arrow__Order__Mirabelle_Oalt,X4,X6)|~c_Wellfounded_Oacyclic(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_307)),
% 156.17/20.12 inference(resolution,[status(thm)],[f54995,f7580])).
% 156.17/20.12 fof(f64639,plain,(
% 156.17/20.12 spl0_748|spl0_110|spl0_175|~spl0_307),
% 156.17/20.12 inference(split_clause,[status(thm)],[f64638,f64635,f42998,f49384,f54994])).
% 156.17/20.12 fof(f64640,plain,(
% 156.17/20.12 spl0_749 <=> 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)))|hAPP(hAPP(X1,v_b____),X2)=hAPP(hAPP(X1,v_b_H____),X3)|~c_in(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4))|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X5,X1,tc_Arrow__Order__Mirabelle_Oalt,X4,X6)|~c_Wellfounded_Owf(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f64643,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6]: (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)))|v_a____=v_b____|v_b____=v_b____|hAPP(hAPP(X1,v_b____),X2)=hAPP(hAPP(X1,v_b_H____),X3)|~c_in(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4))|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X5,X1,tc_Arrow__Order__Mirabelle_Oalt,X4,X6)|~c_Wellfounded_Owf(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_307)),
% 156.17/20.12 inference(resolution,[status(thm)],[f54995,f1576])).
% 156.17/20.12 fof(f64644,plain,(
% 156.17/20.12 spl0_749|spl0_110|spl0_175|~spl0_307),
% 156.17/20.12 inference(split_clause,[status(thm)],[f64643,f64640,f42998,f49384,f54994])).
% 156.17/20.12 fof(f64645,plain,(
% 156.17/20.12 spl0_750 <=> 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)))|hAPP(hAPP(X1,v_b____),X2)=hAPP(hAPP(X1,v_b_H____),X3)|~c_in(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4))|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X5,X1,tc_Arrow__Order__Mirabelle_Oalt,X4,X6)|~c_Wellfounded_Owf(c_Set_Oinsert(X7,hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f64648,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6,X7]: (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)))|v_a____=v_b____|v_b____=v_b____|hAPP(hAPP(X1,v_b____),X2)=hAPP(hAPP(X1,v_b_H____),X3)|~c_in(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4))|~c_Equiv__Relations_Ocongruent2(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X5,X1,tc_Arrow__Order__Mirabelle_Oalt,X4,X6)|~c_Wellfounded_Owf(c_Set_Oinsert(X7,hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_307)),
% 156.17/20.12 inference(resolution,[status(thm)],[f54995,f8835])).
% 156.17/20.12 fof(f64649,plain,(
% 156.17/20.12 spl0_750|spl0_110|spl0_175|~spl0_307),
% 156.17/20.12 inference(split_clause,[status(thm)],[f64648,f64645,f42998,f49384,f54994])).
% 156.17/20.12 fof(f64659,plain,(
% 156.17/20.12 spl0_751 <=> hBOOL(X0)|hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OImage(X1,c_COMBK(X0,X2,X3),X4,X5),X6),X7))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f64662,plain,(
% 156.17/20.12 ![X0,X1,X2,X3,X4,X5,X6,X7,X8,X9]: (hBOOL(X0)|hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OImage(X1,c_COMBK(X0,X2,X3),X4,X5),X6),X7))|~c_Wellfounded_Owf(X8,X9))),
% 156.17/20.12 inference(resolution,[status(thm)],[f54756,f984])).
% 156.17/20.12 fof(f64663,plain,(
% 156.17/20.12 spl0_751|spl0_7),
% 156.17/20.12 inference(split_clause,[status(thm)],[f64662,f64659,f1768])).
% 156.17/20.12 fof(f64984,plain,(
% 156.17/20.12 spl0_753 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=X0|v_b____=X0|c_in(v_b____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f64987,plain,(
% 156.17/20.12 ![X0]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~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____=X0|v_b____=X0|c_in(v_b____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_309)),
% 156.17/20.12 inference(resolution,[status(thm)],[f55005,f45389])).
% 156.17/20.12 fof(f64988,plain,(
% 156.17/20.12 spl0_753|~spl0_254|~spl0_309),
% 156.17/20.12 inference(split_clause,[status(thm)],[f64987,f64984,f54259,f55004])).
% 156.17/20.12 fof(f64989,plain,(
% 156.17/20.12 spl0_754 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=X0|v_b____=X0|c_in(v_b____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f64992,plain,(
% 156.17/20.12 ![X0]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~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____=X0|v_b____=X0|c_in(v_b____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_309)),
% 156.17/20.12 inference(resolution,[status(thm)],[f55005,f39703])).
% 156.17/20.12 fof(f64993,plain,(
% 156.17/20.12 spl0_754|~spl0_254|~spl0_309),
% 156.17/20.12 inference(split_clause,[status(thm)],[f64992,f64989,f54259,f55004])).
% 156.17/20.12 fof(f65003,plain,(
% 156.17/20.12 spl0_755 <=> 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_b____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oirrefl(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f65006,plain,(
% 156.17/20.12 ![X0]: (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)))|v_a____=v_b____|v_b____=v_b____|c_in(v_b____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oirrefl(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_309)),
% 156.17/20.12 inference(resolution,[status(thm)],[f55005,f1545])).
% 156.17/20.12 fof(f65007,plain,(
% 156.17/20.12 spl0_755|spl0_110|spl0_175|~spl0_309),
% 156.17/20.12 inference(split_clause,[status(thm)],[f65006,f65003,f42998,f49384,f55004])).
% 156.17/20.12 fof(f65008,plain,(
% 156.17/20.12 spl0_756 <=> 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_b____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Oacyclic(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f65011,plain,(
% 156.17/20.12 ![X0]: (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)))|v_a____=v_b____|v_b____=v_b____|c_in(v_b____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Oacyclic(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_309)),
% 156.17/20.12 inference(resolution,[status(thm)],[f55005,f7580])).
% 156.17/20.12 fof(f65012,plain,(
% 156.17/20.12 spl0_756|spl0_110|spl0_175|~spl0_309),
% 156.17/20.12 inference(split_clause,[status(thm)],[f65011,f65008,f42998,f49384,f55004])).
% 156.17/20.12 fof(f65013,plain,(
% 156.17/20.12 spl0_757 <=> 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_b____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f65016,plain,(
% 156.17/20.12 ![X0]: (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)))|v_a____=v_b____|v_b____=v_b____|c_in(v_b____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_309)),
% 156.17/20.12 inference(resolution,[status(thm)],[f55005,f1576])).
% 156.17/20.12 fof(f65017,plain,(
% 156.17/20.12 spl0_757|spl0_110|spl0_175|~spl0_309),
% 156.17/20.12 inference(split_clause,[status(thm)],[f65016,f65013,f42998,f49384,f55004])).
% 156.17/20.12 fof(f65018,plain,(
% 156.17/20.12 spl0_758 <=> 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_b____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(c_Set_Oinsert(X1,hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f65021,plain,(
% 156.17/20.12 ![X0,X1]: (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)))|v_a____=v_b____|v_b____=v_b____|c_in(v_b____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(c_Set_Oinsert(X1,hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_309)),
% 156.17/20.12 inference(resolution,[status(thm)],[f55005,f8835])).
% 156.17/20.12 fof(f65022,plain,(
% 156.17/20.12 spl0_758|spl0_110|spl0_175|~spl0_309),
% 156.17/20.12 inference(split_clause,[status(thm)],[f65021,f65018,f42998,f49384,f55004])).
% 156.17/20.12 fof(f65027,plain,(
% 156.17/20.12 ![X0]: (~c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X0,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|spl0_514)),
% 156.17/20.12 inference(resolution,[status(thm)],[f60099,f1646])).
% 156.17/20.12 fof(f65029,plain,(
% 156.17/20.12 ![X0]: (~c_in(v_b____,c_Relation_ODomain(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X0,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|spl0_514)),
% 156.17/20.12 inference(resolution,[status(thm)],[f65027,f24438])).
% 156.17/20.12 fof(f65030,plain,(
% 156.17/20.12 ~spl0_186|spl0_187|spl0_514),
% 156.17/20.12 inference(split_clause,[status(thm)],[f65029,f50289,f50292,f60097])).
% 156.17/20.12 fof(f65032,plain,(
% 156.17/20.12 spl0_759 <=> c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)=v_a____),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f65033,plain,(
% 156.17/20.12 c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)=v_a____|~spl0_759),
% 156.17/20.12 inference(component_clause,[status(thm)],[f65032])).
% 156.17/20.12 fof(f65037,plain,(
% 156.17/20.12 spl0_760 <=> c_ATP__Linkup_Osko__Relation__XDomainE__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)=v_a____),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f65038,plain,(
% 156.17/20.12 c_ATP__Linkup_Osko__Relation__XDomainE__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)=v_a____|~spl0_760),
% 156.17/20.12 inference(component_clause,[status(thm)],[f65037])).
% 156.17/20.12 fof(f65045,plain,(
% 156.17/20.12 v_b____=v_a____|~c_Nitpick_Orefl_H(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_162),
% 156.17/20.12 inference(resolution,[status(thm)],[f47708,f1574])).
% 156.17/20.12 fof(f65046,plain,(
% 156.17/20.12 spl0_110|~spl0_677|~spl0_162),
% 156.17/20.12 inference(split_clause,[status(thm)],[f65045,f42998,f62563,f47707])).
% 156.17/20.12 fof(f65048,plain,(
% 156.17/20.12 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(v_b____,c_Relation_ODomain(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_760),
% 156.17/20.12 inference(paramodulation,[status(thm)],[f65038,f1513])).
% 156.17/20.12 fof(f65049,plain,(
% 156.17/20.12 spl0_153|~spl0_186|~spl0_760),
% 156.17/20.12 inference(split_clause,[status(thm)],[f65048,f47635,f50289,f65037])).
% 156.17/20.12 fof(f65067,plain,(
% 156.17/20.12 spl0_762 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=X0|v_b____=X0|c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f65070,plain,(
% 156.17/20.12 ![X0]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~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____=X0|v_b____=X0|c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_310)),
% 156.17/20.12 inference(resolution,[status(thm)],[f55010,f45389])).
% 156.17/20.12 fof(f65071,plain,(
% 156.17/20.12 spl0_762|~spl0_254|~spl0_310),
% 156.17/20.12 inference(split_clause,[status(thm)],[f65070,f65067,f54259,f55009])).
% 156.17/20.12 fof(f65072,plain,(
% 156.17/20.12 spl0_763 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=X0|v_b____=X0|c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.12 introduced(split_symbol_definition)).
% 156.17/20.12 fof(f65075,plain,(
% 156.17/20.12 ![X0]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~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____=X0|v_b____=X0|c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_310)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55010,f39703])).
% 156.17/20.13 fof(f65076,plain,(
% 156.17/20.13 spl0_763|~spl0_254|~spl0_310),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65075,f65072,f54259,f55009])).
% 156.17/20.13 fof(f65086,plain,(
% 156.17/20.13 spl0_764 <=> 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_b_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oirrefl(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65089,plain,(
% 156.17/20.13 ![X0]: (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)))|v_a____=v_b____|v_b____=v_b____|c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oirrefl(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_310)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55010,f1545])).
% 156.17/20.13 fof(f65090,plain,(
% 156.17/20.13 spl0_764|spl0_110|spl0_175|~spl0_310),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65089,f65086,f42998,f49384,f55009])).
% 156.17/20.13 fof(f65091,plain,(
% 156.17/20.13 spl0_765 <=> 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_b_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Oacyclic(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65094,plain,(
% 156.17/20.13 ![X0]: (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)))|v_a____=v_b____|v_b____=v_b____|c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Oacyclic(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_310)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55010,f7580])).
% 156.17/20.13 fof(f65095,plain,(
% 156.17/20.13 spl0_765|spl0_110|spl0_175|~spl0_310),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65094,f65091,f42998,f49384,f55009])).
% 156.17/20.13 fof(f65096,plain,(
% 156.17/20.13 spl0_766 <=> 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_b_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65099,plain,(
% 156.17/20.13 ![X0]: (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)))|v_a____=v_b____|v_b____=v_b____|c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_310)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55010,f1576])).
% 156.17/20.13 fof(f65100,plain,(
% 156.17/20.13 spl0_766|spl0_110|spl0_175|~spl0_310),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65099,f65096,f42998,f49384,f55009])).
% 156.17/20.13 fof(f65101,plain,(
% 156.17/20.13 spl0_767 <=> 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_b_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(c_Set_Oinsert(X1,hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65104,plain,(
% 156.17/20.13 ![X0,X1]: (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)))|v_a____=v_b____|v_b____=v_b____|c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(c_Set_Oinsert(X1,hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_310)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55010,f8835])).
% 156.17/20.13 fof(f65105,plain,(
% 156.17/20.13 spl0_767|spl0_110|spl0_175|~spl0_310),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65104,f65101,f42998,f49384,f55009])).
% 156.17/20.13 fof(f65127,plain,(
% 156.17/20.13 spl0_769 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=X0|v_b____=X0|c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65130,plain,(
% 156.17/20.13 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~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____=X0|v_b____=X0|c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_311)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55015,f45389])).
% 156.17/20.13 fof(f65131,plain,(
% 156.17/20.13 spl0_769|~spl0_254|~spl0_311),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65130,f65127,f54259,f55014])).
% 156.17/20.13 fof(f65132,plain,(
% 156.17/20.13 spl0_770 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=X0|v_b____=X0|c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65135,plain,(
% 156.17/20.13 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~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____=X0|v_b____=X0|c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_311)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55015,f39703])).
% 156.17/20.13 fof(f65136,plain,(
% 156.17/20.13 spl0_770|~spl0_254|~spl0_311),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65135,f65132,f54259,f55014])).
% 156.17/20.13 fof(f65146,plain,(
% 156.17/20.13 spl0_771 <=> 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_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oirrefl(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65149,plain,(
% 156.17/20.13 ![X0,X1]: (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)))|v_a____=v_b____|v_b____=v_b____|c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oirrefl(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_311)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55015,f1545])).
% 156.17/20.13 fof(f65150,plain,(
% 156.17/20.13 spl0_771|spl0_110|spl0_175|~spl0_311),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65149,f65146,f42998,f49384,f55014])).
% 156.17/20.13 fof(f65151,plain,(
% 156.17/20.13 spl0_772 <=> 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_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Oacyclic(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65154,plain,(
% 156.17/20.13 ![X0,X1]: (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)))|v_a____=v_b____|v_b____=v_b____|c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Oacyclic(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_311)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55015,f7580])).
% 156.17/20.13 fof(f65155,plain,(
% 156.17/20.13 spl0_772|spl0_110|spl0_175|~spl0_311),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65154,f65151,f42998,f49384,f55014])).
% 156.17/20.13 fof(f65156,plain,(
% 156.17/20.13 spl0_773 <=> 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_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65159,plain,(
% 156.17/20.13 ![X0,X1]: (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)))|v_a____=v_b____|v_b____=v_b____|c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_311)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55015,f1576])).
% 156.17/20.13 fof(f65160,plain,(
% 156.17/20.13 spl0_773|spl0_110|spl0_175|~spl0_311),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65159,f65156,f42998,f49384,f55014])).
% 156.17/20.13 fof(f65161,plain,(
% 156.17/20.13 spl0_774 <=> 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_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(c_Set_Oinsert(X2,hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65164,plain,(
% 156.17/20.13 ![X0,X1,X2]: (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)))|v_a____=v_b____|v_b____=v_b____|c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(c_Set_Oinsert(X2,hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_311)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55015,f8835])).
% 156.17/20.13 fof(f65165,plain,(
% 156.17/20.13 spl0_774|spl0_110|spl0_175|~spl0_311),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65164,f65161,f42998,f49384,f55014])).
% 156.17/20.13 fof(f65170,plain,(
% 156.17/20.13 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(v_b____,c_Relation_ODomain(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_759),
% 156.17/20.13 inference(paramodulation,[status(thm)],[f65033,f1520])).
% 156.17/20.13 fof(f65171,plain,(
% 156.17/20.13 spl0_153|~spl0_186|~spl0_759),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65170,f47635,f50289,f65032])).
% 156.17/20.13 fof(f65221,plain,(
% 156.17/20.13 spl0_776 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=X0|v_b____=X0|c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65224,plain,(
% 156.17/20.13 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~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____=X0|v_b____=X0|c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_312)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55020,f45389])).
% 156.17/20.13 fof(f65225,plain,(
% 156.17/20.13 spl0_776|~spl0_254|~spl0_312),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65224,f65221,f54259,f55019])).
% 156.17/20.13 fof(f65226,plain,(
% 156.17/20.13 spl0_777 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=X0|v_b____=X0|c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65229,plain,(
% 156.17/20.13 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~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____=X0|v_b____=X0|c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_312)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55020,f39703])).
% 156.17/20.13 fof(f65230,plain,(
% 156.17/20.13 spl0_777|~spl0_254|~spl0_312),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65229,f65226,f54259,f55019])).
% 156.17/20.13 fof(f65240,plain,(
% 156.17/20.13 spl0_778 <=> 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_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oirrefl(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65243,plain,(
% 156.17/20.13 ![X0,X1]: (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)))|v_a____=v_b____|v_b____=v_b____|c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oirrefl(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_312)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55020,f1545])).
% 156.17/20.13 fof(f65244,plain,(
% 156.17/20.13 spl0_778|spl0_110|spl0_175|~spl0_312),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65243,f65240,f42998,f49384,f55019])).
% 156.17/20.13 fof(f65245,plain,(
% 156.17/20.13 spl0_779 <=> 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_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Oacyclic(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65248,plain,(
% 156.17/20.13 ![X0,X1]: (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)))|v_a____=v_b____|v_b____=v_b____|c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Oacyclic(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_312)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55020,f7580])).
% 156.17/20.13 fof(f65249,plain,(
% 156.17/20.13 spl0_779|spl0_110|spl0_175|~spl0_312),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65248,f65245,f42998,f49384,f55019])).
% 156.17/20.13 fof(f65250,plain,(
% 156.17/20.13 spl0_780 <=> 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_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65253,plain,(
% 156.17/20.13 ![X0,X1]: (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)))|v_a____=v_b____|v_b____=v_b____|c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_312)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55020,f1576])).
% 156.17/20.13 fof(f65254,plain,(
% 156.17/20.13 spl0_780|spl0_110|spl0_175|~spl0_312),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65253,f65250,f42998,f49384,f55019])).
% 156.17/20.13 fof(f65255,plain,(
% 156.17/20.13 spl0_781 <=> 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_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(c_Set_Oinsert(X2,hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65258,plain,(
% 156.17/20.13 ![X0,X1,X2]: (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)))|v_a____=v_b____|v_b____=v_b____|c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(c_Set_Oinsert(X2,hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_312)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55020,f8835])).
% 156.17/20.13 fof(f65259,plain,(
% 156.17/20.13 spl0_781|spl0_110|spl0_175|~spl0_312),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65258,f65255,f42998,f49384,f55019])).
% 156.17/20.13 fof(f65281,plain,(
% 156.17/20.13 spl0_783 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=X0|v_b____=X0|c_in(v_b_H____,c_Relation_OImage(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),X1,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)|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65284,plain,(
% 156.17/20.13 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~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____=X0|v_b____=X0|c_in(v_b_H____,c_Relation_OImage(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),X1,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)|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_313)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55025,f45389])).
% 156.17/20.13 fof(f65285,plain,(
% 156.17/20.13 spl0_783|~spl0_254|~spl0_313),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65284,f65281,f54259,f55024])).
% 156.17/20.13 fof(f65286,plain,(
% 156.17/20.13 spl0_784 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=X0|v_b____=X0|c_in(v_b_H____,c_Relation_OImage(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),X1,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_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65289,plain,(
% 156.17/20.13 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~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____=X0|v_b____=X0|c_in(v_b_H____,c_Relation_OImage(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),X1,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_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_313)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55025,f39703])).
% 156.17/20.13 fof(f65290,plain,(
% 156.17/20.13 spl0_784|~spl0_254|~spl0_313),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65289,f65286,f54259,f55024])).
% 156.17/20.13 fof(f65300,plain,(
% 156.17/20.13 spl0_785 <=> 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_b_H____,c_Relation_OImage(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X1,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)|~c_Relation_Oirrefl(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65303,plain,(
% 156.17/20.13 ![X0,X1]: (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)))|v_a____=v_b____|v_b____=v_b____|c_in(v_b_H____,c_Relation_OImage(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X1,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)|~c_Relation_Oirrefl(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_313)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55025,f1545])).
% 156.17/20.13 fof(f65304,plain,(
% 156.17/20.13 spl0_785|spl0_110|spl0_175|~spl0_313),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65303,f65300,f42998,f49384,f55024])).
% 156.17/20.13 fof(f65305,plain,(
% 156.17/20.13 spl0_786 <=> 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_b_H____,c_Relation_OImage(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X1,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)|~c_Wellfounded_Oacyclic(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65308,plain,(
% 156.17/20.13 ![X0,X1]: (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)))|v_a____=v_b____|v_b____=v_b____|c_in(v_b_H____,c_Relation_OImage(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X1,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)|~c_Wellfounded_Oacyclic(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_313)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55025,f7580])).
% 156.17/20.13 fof(f65309,plain,(
% 156.17/20.13 spl0_786|spl0_110|spl0_175|~spl0_313),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65308,f65305,f42998,f49384,f55024])).
% 156.17/20.13 fof(f65310,plain,(
% 156.17/20.13 spl0_787 <=> 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_b_H____,c_Relation_OImage(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X1,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)|~c_Wellfounded_Owf(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65313,plain,(
% 156.17/20.13 ![X0,X1]: (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)))|v_a____=v_b____|v_b____=v_b____|c_in(v_b_H____,c_Relation_OImage(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X1,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)|~c_Wellfounded_Owf(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_313)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55025,f1576])).
% 156.17/20.13 fof(f65314,plain,(
% 156.17/20.13 spl0_787|spl0_110|spl0_175|~spl0_313),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65313,f65310,f42998,f49384,f55024])).
% 156.17/20.13 fof(f65315,plain,(
% 156.17/20.13 spl0_788 <=> 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_b_H____,c_Relation_OImage(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X1,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)|~c_Wellfounded_Owf(c_Set_Oinsert(X2,hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65318,plain,(
% 156.17/20.13 ![X0,X1,X2]: (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)))|v_a____=v_b____|v_b____=v_b____|c_in(v_b_H____,c_Relation_OImage(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),X1,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)|~c_Wellfounded_Owf(c_Set_Oinsert(X2,hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_313)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55025,f8835])).
% 156.17/20.13 fof(f65319,plain,(
% 156.17/20.13 spl0_788|spl0_110|spl0_175|~spl0_313),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65318,f65315,f42998,f49384,f55024])).
% 156.17/20.13 fof(f65338,plain,(
% 156.17/20.13 spl0_789 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=X0|v_b____=X0|c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65341,plain,(
% 156.17/20.13 ![X0]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~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____=X0|v_b____=X0|c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_314)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55030,f45389])).
% 156.17/20.13 fof(f65342,plain,(
% 156.17/20.13 spl0_789|~spl0_254|~spl0_314),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65341,f65338,f54259,f55029])).
% 156.17/20.13 fof(f65343,plain,(
% 156.17/20.13 spl0_790 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=X0|v_b____=X0|c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65346,plain,(
% 156.17/20.13 ![X0]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~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____=X0|v_b____=X0|c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_314)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55030,f39703])).
% 156.17/20.13 fof(f65347,plain,(
% 156.17/20.13 spl0_790|~spl0_254|~spl0_314),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65346,f65343,f54259,f55029])).
% 156.17/20.13 fof(f65357,plain,(
% 156.17/20.13 spl0_791 <=> 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_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oirrefl(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65360,plain,(
% 156.17/20.13 ![X0]: (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)))|v_a____=v_b____|v_b____=v_b____|c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oirrefl(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_314)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55030,f1545])).
% 156.17/20.13 fof(f65361,plain,(
% 156.17/20.13 spl0_791|spl0_110|spl0_175|~spl0_314),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65360,f65357,f42998,f49384,f55029])).
% 156.17/20.13 fof(f65362,plain,(
% 156.17/20.13 spl0_792 <=> 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_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Oacyclic(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65365,plain,(
% 156.17/20.13 ![X0]: (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)))|v_a____=v_b____|v_b____=v_b____|c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Oacyclic(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_314)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55030,f7580])).
% 156.17/20.13 fof(f65366,plain,(
% 156.17/20.13 spl0_792|spl0_110|spl0_175|~spl0_314),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65365,f65362,f42998,f49384,f55029])).
% 156.17/20.13 fof(f65367,plain,(
% 156.17/20.13 spl0_793 <=> 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_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65370,plain,(
% 156.17/20.13 ![X0]: (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)))|v_a____=v_b____|v_b____=v_b____|c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_314)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55030,f1576])).
% 156.17/20.13 fof(f65371,plain,(
% 156.17/20.13 spl0_793|spl0_110|spl0_175|~spl0_314),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65370,f65367,f42998,f49384,f55029])).
% 156.17/20.13 fof(f65372,plain,(
% 156.17/20.13 spl0_794 <=> 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_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(c_Set_Oinsert(X1,hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65375,plain,(
% 156.17/20.13 ![X0,X1]: (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)))|v_a____=v_b____|v_b____=v_b____|c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(c_Set_Oinsert(X1,hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_314)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55030,f8835])).
% 156.17/20.13 fof(f65376,plain,(
% 156.17/20.13 spl0_794|spl0_110|spl0_175|~spl0_314),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65375,f65372,f42998,f49384,f55029])).
% 156.17/20.13 fof(f65741,plain,(
% 156.17/20.13 spl0_799 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=X0|v_b____=X0|c_in(c_Pair(X1,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X1,v_b____,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____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65744,plain,(
% 156.17/20.13 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~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____=X0|v_b____=X0|c_in(c_Pair(X1,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X1,v_b____,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____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_318)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55050,f45389])).
% 156.17/20.13 fof(f65745,plain,(
% 156.17/20.13 spl0_799|~spl0_254|~spl0_318),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65744,f65741,f54259,f55049])).
% 156.17/20.13 fof(f65746,plain,(
% 156.17/20.13 spl0_800 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=X0|v_b____=X0|c_in(c_Pair(X1,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X1,v_b____,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____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65749,plain,(
% 156.17/20.13 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~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____=X0|v_b____=X0|c_in(c_Pair(X1,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X1,v_b____,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____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_318)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55050,f39703])).
% 156.17/20.13 fof(f65750,plain,(
% 156.17/20.13 spl0_800|~spl0_254|~spl0_318),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65749,f65746,f54259,f55049])).
% 156.17/20.13 fof(f65760,plain,(
% 156.17/20.13 spl0_801 <=> 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(c_Pair(X1,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X1,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oirrefl(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65763,plain,(
% 156.17/20.13 ![X0,X1]: (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)))|v_a____=v_b____|v_b____=v_b____|c_in(c_Pair(X1,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X1,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oirrefl(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_318)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55050,f1545])).
% 156.17/20.13 fof(f65764,plain,(
% 156.17/20.13 spl0_801|spl0_110|spl0_175|~spl0_318),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65763,f65760,f42998,f49384,f55049])).
% 156.17/20.13 fof(f65765,plain,(
% 156.17/20.13 spl0_802 <=> 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(c_Pair(X1,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X1,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Oacyclic(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65768,plain,(
% 156.17/20.13 ![X0,X1]: (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)))|v_a____=v_b____|v_b____=v_b____|c_in(c_Pair(X1,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X1,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Oacyclic(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_318)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55050,f7580])).
% 156.17/20.13 fof(f65769,plain,(
% 156.17/20.13 spl0_802|spl0_110|spl0_175|~spl0_318),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65768,f65765,f42998,f49384,f55049])).
% 156.17/20.13 fof(f65770,plain,(
% 156.17/20.13 spl0_803 <=> 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(c_Pair(X1,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X1,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65773,plain,(
% 156.17/20.13 ![X0,X1]: (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)))|v_a____=v_b____|v_b____=v_b____|c_in(c_Pair(X1,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X1,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_318)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55050,f1576])).
% 156.17/20.13 fof(f65774,plain,(
% 156.17/20.13 spl0_803|spl0_110|spl0_175|~spl0_318),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65773,f65770,f42998,f49384,f55049])).
% 156.17/20.13 fof(f65775,plain,(
% 156.17/20.13 spl0_804 <=> 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(c_Pair(X1,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X1,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(c_Set_Oinsert(X2,hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65778,plain,(
% 156.17/20.13 ![X0,X1,X2]: (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)))|v_a____=v_b____|v_b____=v_b____|c_in(c_Pair(X1,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(X1,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(c_Set_Oinsert(X2,hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_318)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55050,f8835])).
% 156.17/20.13 fof(f65779,plain,(
% 156.17/20.13 spl0_804|spl0_110|spl0_175|~spl0_318),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65778,f65775,f42998,f49384,f55049])).
% 156.17/20.13 fof(f65797,plain,(
% 156.17/20.13 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))|~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_H____|v_b____=v_b_H____|hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,v_b_H____)),c_Pair(v_b____,v_b_H____,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____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_321),
% 156.17/20.13 inference(resolution,[status(thm)],[f55065,f1742])).
% 156.17/20.13 fof(f65798,plain,(
% 156.17/20.13 spl0_239|~spl0_254|spl0_3|spl0_97|spl0_505|spl0_508|~spl0_321),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65797,f52976,f54259,f1729,f41290,f60058,f60069,f55064])).
% 156.17/20.13 fof(f65799,plain,(
% 156.17/20.13 spl0_805 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=X0|v_b____=X0|hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65802,plain,(
% 156.17/20.13 ![X0]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~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____=X0|v_b____=X0|hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_321)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55065,f45389])).
% 156.17/20.13 fof(f65803,plain,(
% 156.17/20.13 spl0_805|~spl0_254|~spl0_321),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65802,f65799,f54259,f55064])).
% 156.17/20.13 fof(f65804,plain,(
% 156.17/20.13 spl0_806 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=X0|v_b____=X0|hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65807,plain,(
% 156.17/20.13 ![X0]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~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____=X0|v_b____=X0|hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_321)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55065,f39703])).
% 156.17/20.13 fof(f65808,plain,(
% 156.17/20.13 spl0_806|~spl0_254|~spl0_321),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65807,f65804,f54259,f55064])).
% 156.17/20.13 fof(f65818,plain,(
% 156.17/20.13 spl0_807 <=> 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)))|hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~c_Relation_Oirrefl(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65821,plain,(
% 156.17/20.13 ![X0]: (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)))|v_a____=v_b____|v_b____=v_b____|hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~c_Relation_Oirrefl(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_321)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55065,f1545])).
% 156.17/20.13 fof(f65822,plain,(
% 156.17/20.13 spl0_807|spl0_110|spl0_175|~spl0_321),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65821,f65818,f42998,f49384,f55064])).
% 156.17/20.13 fof(f65823,plain,(
% 156.17/20.13 spl0_808 <=> 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)))|hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~c_Wellfounded_Oacyclic(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65826,plain,(
% 156.17/20.13 ![X0]: (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)))|v_a____=v_b____|v_b____=v_b____|hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~c_Wellfounded_Oacyclic(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_321)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55065,f7580])).
% 156.17/20.13 fof(f65827,plain,(
% 156.17/20.13 spl0_808|spl0_110|spl0_175|~spl0_321),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65826,f65823,f42998,f49384,f55064])).
% 156.17/20.13 fof(f65828,plain,(
% 156.17/20.13 spl0_809 <=> 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)))|hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~c_Wellfounded_Owf(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65831,plain,(
% 156.17/20.13 ![X0]: (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)))|v_a____=v_b____|v_b____=v_b____|hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~c_Wellfounded_Owf(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_321)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55065,f1576])).
% 156.17/20.13 fof(f65832,plain,(
% 156.17/20.13 spl0_809|spl0_110|spl0_175|~spl0_321),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65831,f65828,f42998,f49384,f55064])).
% 156.17/20.13 fof(f65833,plain,(
% 156.17/20.13 spl0_810 <=> 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)))|hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~c_Wellfounded_Owf(c_Set_Oinsert(X1,hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65836,plain,(
% 156.17/20.13 ![X0,X1]: (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)))|v_a____=v_b____|v_b____=v_b____|hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~c_Wellfounded_Owf(c_Set_Oinsert(X1,hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_321)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55065,f8835])).
% 156.17/20.13 fof(f65837,plain,(
% 156.17/20.13 spl0_810|spl0_110|spl0_175|~spl0_321),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65836,f65833,f42998,f49384,f55064])).
% 156.17/20.13 fof(f65873,plain,(
% 156.17/20.13 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))|~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_H____|v_b____=v_b_H____|c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,v_b_H____)),v_b____,v_b_H____,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____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_322),
% 156.17/20.13 inference(resolution,[status(thm)],[f55070,f1742])).
% 156.17/20.13 fof(f65874,plain,(
% 156.17/20.13 spl0_239|~spl0_254|spl0_3|spl0_97|spl0_513|spl0_508|~spl0_322),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65873,f52976,f54259,f1729,f41290,f60090,f60069,f55069])).
% 156.17/20.13 fof(f65875,plain,(
% 156.17/20.13 spl0_813 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=X0|v_b____=X0|c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65878,plain,(
% 156.17/20.13 ![X0]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~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____=X0|v_b____=X0|c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_322)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55070,f45389])).
% 156.17/20.13 fof(f65879,plain,(
% 156.17/20.13 spl0_813|~spl0_254|~spl0_322),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65878,f65875,f54259,f55069])).
% 156.17/20.13 fof(f65880,plain,(
% 156.17/20.13 spl0_814 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_a____=X0|v_b____=X0|c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65883,plain,(
% 156.17/20.13 ![X0]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~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____=X0|v_b____=X0|c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_322)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55070,f39703])).
% 156.17/20.13 fof(f65884,plain,(
% 156.17/20.13 spl0_814|~spl0_254|~spl0_322),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65883,f65880,f54259,f55069])).
% 156.17/20.13 fof(f65894,plain,(
% 156.17/20.13 spl0_815 <=> 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_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oirrefl(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65897,plain,(
% 156.17/20.13 ![X0]: (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)))|v_a____=v_b____|v_b____=v_b____|c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oirrefl(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_322)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55070,f1545])).
% 156.17/20.13 fof(f65898,plain,(
% 156.17/20.13 spl0_815|spl0_110|spl0_175|~spl0_322),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65897,f65894,f42998,f49384,f55069])).
% 156.17/20.13 fof(f65899,plain,(
% 156.17/20.13 spl0_816 <=> 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_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Oacyclic(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65902,plain,(
% 156.17/20.13 ![X0]: (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)))|v_a____=v_b____|v_b____=v_b____|c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Oacyclic(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_322)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55070,f7580])).
% 156.17/20.13 fof(f65903,plain,(
% 156.17/20.13 spl0_816|spl0_110|spl0_175|~spl0_322),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65902,f65899,f42998,f49384,f55069])).
% 156.17/20.13 fof(f65904,plain,(
% 156.17/20.13 spl0_817 <=> 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_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65907,plain,(
% 156.17/20.13 ![X0]: (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)))|v_a____=v_b____|v_b____=v_b____|c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_322)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55070,f1576])).
% 156.17/20.13 fof(f65908,plain,(
% 156.17/20.13 spl0_817|spl0_110|spl0_175|~spl0_322),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65907,f65904,f42998,f49384,f55069])).
% 156.17/20.13 fof(f65909,plain,(
% 156.17/20.13 spl0_818 <=> 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_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(c_Set_Oinsert(X1,hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65912,plain,(
% 156.17/20.13 ![X0,X1]: (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)))|v_a____=v_b____|v_b____=v_b____|c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_Wellfounded_Owf(c_Set_Oinsert(X1,hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_322)),
% 156.17/20.13 inference(resolution,[status(thm)],[f55070,f8835])).
% 156.17/20.13 fof(f65913,plain,(
% 156.17/20.13 spl0_818|spl0_110|spl0_175|~spl0_322),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65912,f65909,f42998,f49384,f55069])).
% 156.17/20.13 fof(f65941,plain,(
% 156.17/20.13 spl0_819 <=> ~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Relation_OId__on(c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X5),X6),tc_prod(X7,X7)),X7)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65944,plain,(
% 156.17/20.13 ![X0,X1,X2,X3,X4,X5,X6,X7]: (hBOOL(hAPP(X0,X1))|hBOOL(hAPP(X0,X2))|~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Relation_OId__on(c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X5),X6),tc_prod(X7,X7)),X7))),
% 156.17/20.13 inference(resolution,[status(thm)],[f55344,f1242])).
% 156.17/20.13 fof(f65945,plain,(
% 156.17/20.13 spl0_381|spl0_819),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65944,f58069,f65941])).
% 156.17/20.13 fof(f65963,plain,(
% 156.17/20.13 spl0_820 <=> ~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X4),X5),X6)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f65966,plain,(
% 156.17/20.13 ![X0,X1,X2,X3,X4,X5,X6]: (hBOOL(hAPP(X0,X1))|~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X4),X5),X6))),
% 156.17/20.13 inference(resolution,[status(thm)],[f55344,f30446])).
% 156.17/20.13 fof(f65967,plain,(
% 156.17/20.13 spl0_75|spl0_820),
% 156.17/20.13 inference(split_clause,[status(thm)],[f65966,f37252,f65963])).
% 156.17/20.13 fof(f66378,plain,(
% 156.17/20.13 spl0_825 <=> c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_b_H____|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),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(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Oirrefl(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f66381,plain,(
% 156.17/20.13 ![X0,X1]: (c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_b_H____=v_b____|X0=v_b_H____|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),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(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Oirrefl(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_267)),
% 156.17/20.13 inference(resolution,[status(thm)],[f54338,f1545])).
% 156.17/20.13 fof(f66382,plain,(
% 156.17/20.13 spl0_825|~spl0_106|spl0_97|~spl0_267),
% 156.17/20.13 inference(split_clause,[status(thm)],[f66381,f66378,f42380,f41290,f54337])).
% 156.17/20.13 fof(f66383,plain,(
% 156.17/20.13 spl0_826 <=> c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_b_H____|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),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(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Wellfounded_Oacyclic(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f66386,plain,(
% 156.17/20.13 ![X0,X1]: (c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_b_H____=v_b____|X0=v_b_H____|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),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(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Wellfounded_Oacyclic(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_267)),
% 156.17/20.13 inference(resolution,[status(thm)],[f54338,f7580])).
% 156.17/20.13 fof(f66387,plain,(
% 156.17/20.13 spl0_826|~spl0_106|spl0_97|~spl0_267),
% 156.17/20.13 inference(split_clause,[status(thm)],[f66386,f66383,f42380,f41290,f54337])).
% 156.17/20.13 fof(f66388,plain,(
% 156.17/20.13 spl0_827 <=> c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_b_H____|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),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(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Wellfounded_Owf(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f66391,plain,(
% 156.17/20.13 ![X0,X1]: (c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_b_H____=v_b____|X0=v_b_H____|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),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(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Wellfounded_Owf(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_267)),
% 156.17/20.13 inference(resolution,[status(thm)],[f54338,f1576])).
% 156.17/20.13 fof(f66392,plain,(
% 156.17/20.13 spl0_827|~spl0_106|spl0_97|~spl0_267),
% 156.17/20.13 inference(split_clause,[status(thm)],[f66391,f66388,f42380,f41290,f54337])).
% 156.17/20.13 fof(f66393,plain,(
% 156.17/20.13 spl0_828 <=> c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|X0=v_b_H____|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),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(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Wellfounded_Owf(c_Set_Oinsert(X2,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f66396,plain,(
% 156.17/20.13 ![X0,X1,X2]: (c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b_H____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(X0,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|X0=v_b____|v_b_H____=v_b____|X0=v_b_H____|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),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(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Wellfounded_Owf(c_Set_Oinsert(X2,hAPP(v_P_H____,v_sko__CHAINED__1(X1,v_P_H____,X0,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_267)),
% 156.17/20.13 inference(resolution,[status(thm)],[f54338,f8835])).
% 156.17/20.13 fof(f66397,plain,(
% 156.17/20.13 spl0_828|~spl0_106|spl0_97|~spl0_267),
% 156.17/20.13 inference(split_clause,[status(thm)],[f66396,f66393,f42380,f41290,f54337])).
% 156.17/20.13 fof(f66411,plain,(
% 156.17/20.13 ![X0]: (c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X0,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_153)),
% 156.17/20.13 inference(resolution,[status(thm)],[f47636,f1648])).
% 156.17/20.13 fof(f66421,plain,(
% 156.17/20.13 ![X0]: (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)|~c_Equiv__Relations_Oequiv(X0,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_153)),
% 156.17/20.13 inference(resolution,[status(thm)],[f66411,f24438])).
% 156.17/20.13 fof(f66422,plain,(
% 156.17/20.13 spl0_196|spl0_187|~spl0_153),
% 156.17/20.13 inference(split_clause,[status(thm)],[f66421,f50758,f50292,f47635])).
% 156.17/20.13 fof(f66465,plain,(
% 156.17/20.13 spl0_833 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b_H____=X0|v_b____=X0|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Oirrefl(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f66468,plain,(
% 156.17/20.13 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b_H____,v_b____,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____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b_H____=X0|v_b____=X0|v_b_H____=v_b____|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Oirrefl(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_303)),
% 156.17/20.13 inference(resolution,[status(thm)],[f54975,f1545])).
% 156.17/20.13 fof(f66469,plain,(
% 156.17/20.13 spl0_833|~spl0_106|spl0_97|~spl0_303),
% 156.17/20.13 inference(split_clause,[status(thm)],[f66468,f66465,f42380,f41290,f54974])).
% 156.17/20.13 fof(f66470,plain,(
% 156.17/20.13 spl0_834 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b_H____=X0|v_b____=X0|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Wellfounded_Oacyclic(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f66473,plain,(
% 156.17/20.13 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b_H____,v_b____,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____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b_H____=X0|v_b____=X0|v_b_H____=v_b____|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Wellfounded_Oacyclic(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_303)),
% 156.17/20.13 inference(resolution,[status(thm)],[f54975,f7580])).
% 156.17/20.13 fof(f66474,plain,(
% 156.17/20.13 spl0_834|~spl0_106|spl0_97|~spl0_303),
% 156.17/20.13 inference(split_clause,[status(thm)],[f66473,f66470,f42380,f41290,f54974])).
% 156.17/20.13 fof(f66475,plain,(
% 156.17/20.13 spl0_835 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b_H____=X0|v_b____=X0|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Wellfounded_Owf(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f66478,plain,(
% 156.17/20.13 ![X0,X1]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b_H____,v_b____,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____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b_H____=X0|v_b____=X0|v_b_H____=v_b____|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Wellfounded_Owf(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_303)),
% 156.17/20.13 inference(resolution,[status(thm)],[f54975,f1576])).
% 156.17/20.13 fof(f66479,plain,(
% 156.17/20.13 spl0_835|~spl0_106|spl0_97|~spl0_303),
% 156.17/20.13 inference(split_clause,[status(thm)],[f66478,f66475,f42380,f41290,f54974])).
% 156.17/20.13 fof(f66480,plain,(
% 156.17/20.13 spl0_836 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b_H____=X0|v_b____=X0|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Wellfounded_Owf(c_Set_Oinsert(X2,hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f66483,plain,(
% 156.17/20.13 ![X0,X1,X2]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(c_Pair(v_b_H____,v_b____,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____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b_H____=X0|v_b____=X0|v_b_H____=v_b____|~c_Relation_Otrans(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Wellfounded_Owf(c_Set_Oinsert(X2,hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X1,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_303)),
% 156.17/20.13 inference(resolution,[status(thm)],[f54975,f8835])).
% 156.17/20.13 fof(f66484,plain,(
% 156.17/20.13 spl0_836|~spl0_106|spl0_97|~spl0_303),
% 156.17/20.13 inference(split_clause,[status(thm)],[f66483,f66480,f42380,f41290,f54974])).
% 156.17/20.13 fof(f66524,plain,(
% 156.17/20.13 spl0_844 <=> ~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Relation_OId__on(c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X5),X6),tc_prod(X7,X7)),X7)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f66527,plain,(
% 156.17/20.13 ![X0,X1,X2,X3,X4,X5,X6,X7]: (hBOOL(hAPP(X0,X1))|hBOOL(hAPP(X0,X2))|~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Relation_OId__on(c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X5),X6),tc_prod(X7,X7)),X7))),
% 156.17/20.13 inference(resolution,[status(thm)],[f55373,f1242])).
% 156.17/20.13 fof(f66528,plain,(
% 156.17/20.13 spl0_381|spl0_844),
% 156.17/20.13 inference(split_clause,[status(thm)],[f66527,f58069,f66524])).
% 156.17/20.13 fof(f66546,plain,(
% 156.17/20.13 spl0_845 <=> ~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X4),X5),X6)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f66549,plain,(
% 156.17/20.13 ![X0,X1,X2,X3,X4,X5,X6]: (hBOOL(hAPP(X0,X1))|~c_Nitpick_Orefl_H(c_Relation_OId__on(c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X4),X5),X6))),
% 156.17/20.13 inference(resolution,[status(thm)],[f55373,f30446])).
% 156.17/20.13 fof(f66550,plain,(
% 156.17/20.13 spl0_75|spl0_845),
% 156.17/20.13 inference(split_clause,[status(thm)],[f66549,f37252,f66546])).
% 156.17/20.13 fof(f66559,plain,(
% 156.17/20.13 spl0_846 <=> hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1),X2),X3),X4))),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f66562,plain,(
% 156.17/20.13 ![X0,X1,X2,X3,X4,X5,X6]: (hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1),X2),X3),X4))|~c_Wellfounded_Owf(X5,X6))),
% 156.17/20.13 inference(resolution,[status(thm)],[f56162,f984])).
% 156.17/20.13 fof(f66563,plain,(
% 156.17/20.13 spl0_846|spl0_7),
% 156.17/20.13 inference(split_clause,[status(thm)],[f66562,f66559,f1768])).
% 156.17/20.13 fof(f66883,plain,(
% 156.17/20.13 spl0_855 <=> ~c_Nitpick_Orefl_H(c_Transitive__Closure_Otrancl(X0,tc_prod(X1,X1)),tc_prod(X1,X1))|~c_Wellfounded_Owf(c_Relation_ORange(X0,tc_prod(X1,X1),tc_prod(X1,X1)),X1)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f66886,plain,(
% 156.17/20.13 ![X0,X1,X2,X3,X4]: (~c_Nitpick_Orefl_H(c_Transitive__Closure_Otrancl(X0,tc_prod(X1,X1)),tc_prod(X1,X1))|hBOOL(hAPP(X2,X3))|hBOOL(hAPP(X2,X4))|~c_Wellfounded_Owf(c_Relation_ORange(X0,tc_prod(X1,X1),tc_prod(X1,X1)),X1))),
% 156.17/20.13 inference(resolution,[status(thm)],[f51461,f1242])).
% 156.17/20.13 fof(f66887,plain,(
% 156.17/20.13 spl0_855|spl0_381),
% 156.17/20.13 inference(split_clause,[status(thm)],[f66886,f66883,f58069])).
% 156.17/20.13 fof(f68490,plain,(
% 156.17/20.13 spl0_860 <=> ~c_Nitpick_Orefl_H(c_Transitive__Closure_Otrancl(X0,tc_prod(X1,X1)),tc_prod(X1,X1))|~c_Wellfounded_Owf(c_Relation_ODomain(X0,tc_prod(X1,X1),tc_prod(X1,X1)),X1)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f68493,plain,(
% 156.17/20.13 ![X0,X1,X2,X3,X4]: (~c_Nitpick_Orefl_H(c_Transitive__Closure_Otrancl(X0,tc_prod(X1,X1)),tc_prod(X1,X1))|hBOOL(hAPP(X2,X3))|hBOOL(hAPP(X2,X4))|~c_Wellfounded_Owf(c_Relation_ODomain(X0,tc_prod(X1,X1),tc_prod(X1,X1)),X1))),
% 156.17/20.13 inference(resolution,[status(thm)],[f55523,f1242])).
% 156.17/20.13 fof(f68494,plain,(
% 156.17/20.13 spl0_860|spl0_381),
% 156.17/20.13 inference(split_clause,[status(thm)],[f68493,f68490,f58069])).
% 156.17/20.13 fof(f68799,plain,(
% 156.17/20.13 spl0_867 <=> 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_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),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____,X0,v_b_H____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X2,hAPP(X0,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f68802,plain,(
% 156.17/20.13 ![X0,X1,X2]: (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)))|v_b_H____=v_b____|v_b____=v_b____|~c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),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____,X0,v_b_H____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X2,hAPP(X0,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_260)),
% 156.17/20.13 inference(resolution,[status(thm)],[f54297,f1646])).
% 156.17/20.13 fof(f68803,plain,(
% 156.17/20.13 spl0_867|spl0_97|spl0_175|~spl0_260),
% 156.17/20.13 inference(split_clause,[status(thm)],[f68802,f68799,f41290,f49384,f54296])).
% 156.17/20.13 fof(f68804,plain,(
% 156.17/20.13 spl0_868 <=> 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_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),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____,X0,v_b_H____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Nitpick_Orefl_H(hAPP(X0,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f68807,plain,(
% 156.17/20.13 ![X0,X1]: (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)))|v_b_H____=v_b____|v_b____=v_b____|~c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(X1,hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),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____,X0,v_b_H____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Nitpick_Orefl_H(hAPP(X0,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_260)),
% 156.17/20.13 inference(resolution,[status(thm)],[f54297,f1574])).
% 156.17/20.13 fof(f68808,plain,(
% 156.17/20.13 spl0_868|spl0_97|spl0_175|~spl0_260),
% 156.17/20.13 inference(split_clause,[status(thm)],[f68807,f68804,f41290,f49384,f54296])).
% 156.17/20.13 fof(f68828,plain,(
% 156.17/20.13 spl0_871 <=> 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_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),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____,X0,v_b_H____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X1,hAPP(X0,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f68831,plain,(
% 156.17/20.13 ![X0,X1]: (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)))|v_b_H____=v_b____|v_b____=v_b____|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),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____,X0,v_b_H____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X1,hAPP(X0,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_261)),
% 156.17/20.13 inference(resolution,[status(thm)],[f54302,f1646])).
% 156.17/20.13 fof(f68832,plain,(
% 156.17/20.13 spl0_871|spl0_97|spl0_175|~spl0_261),
% 156.17/20.13 inference(split_clause,[status(thm)],[f68831,f68828,f41290,f49384,f54301])).
% 156.17/20.13 fof(f68833,plain,(
% 156.17/20.13 spl0_872 <=> 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_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),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____,X0,v_b_H____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Nitpick_Orefl_H(hAPP(X0,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f68836,plain,(
% 156.17/20.13 ![X0]: (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)))|v_b_H____=v_b____|v_b____=v_b____|~c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),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____,X0,v_b_H____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Nitpick_Orefl_H(hAPP(X0,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_261)),
% 156.17/20.13 inference(resolution,[status(thm)],[f54302,f1574])).
% 156.17/20.13 fof(f68837,plain,(
% 156.17/20.13 spl0_872|spl0_97|spl0_175|~spl0_261),
% 156.17/20.13 inference(split_clause,[status(thm)],[f68836,f68833,f41290,f49384,f54301])).
% 156.17/20.13 fof(f68877,plain,(
% 156.17/20.13 spl0_879 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_b_H____=X0|v_b____=X0|~c_Relation_Oantisym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f68880,plain,(
% 156.17/20.13 ![X0]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b_H____=X0|v_b____=X0|~c_Relation_Oantisym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_301)),
% 156.17/20.13 inference(resolution,[status(thm)],[f54965,f39703])).
% 156.17/20.13 fof(f68881,plain,(
% 156.17/20.13 spl0_879|~spl0_254|~spl0_301),
% 156.17/20.13 inference(split_clause,[status(thm)],[f68880,f68877,f54259,f54964])).
% 156.17/20.13 fof(f68891,plain,(
% 156.17/20.13 spl0_880 <=> 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_Relation_Oantisym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),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____,X0,v_b_H____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Oirrefl(hAPP(X0,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f68894,plain,(
% 156.17/20.13 ![X0]: (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)))|v_b_H____=v_b____|v_b____=v_b____|~c_Relation_Oantisym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),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____,X0,v_b_H____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Oirrefl(hAPP(X0,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_301)),
% 156.17/20.13 inference(resolution,[status(thm)],[f54965,f1545])).
% 156.17/20.13 fof(f68895,plain,(
% 156.17/20.13 spl0_880|spl0_97|spl0_175|~spl0_301),
% 156.17/20.13 inference(split_clause,[status(thm)],[f68894,f68891,f41290,f49384,f54964])).
% 156.17/20.13 fof(f68896,plain,(
% 156.17/20.13 spl0_881 <=> 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_Relation_Oantisym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),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____,X0,v_b_H____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Wellfounded_Oacyclic(hAPP(X0,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f68899,plain,(
% 156.17/20.13 ![X0]: (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)))|v_b_H____=v_b____|v_b____=v_b____|~c_Relation_Oantisym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),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____,X0,v_b_H____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Wellfounded_Oacyclic(hAPP(X0,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_301)),
% 156.17/20.13 inference(resolution,[status(thm)],[f54965,f7580])).
% 156.17/20.13 fof(f68900,plain,(
% 156.17/20.13 spl0_881|spl0_97|spl0_175|~spl0_301),
% 156.17/20.13 inference(split_clause,[status(thm)],[f68899,f68896,f41290,f49384,f54964])).
% 156.17/20.13 fof(f68901,plain,(
% 156.17/20.13 spl0_882 <=> 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_Relation_Oantisym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),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____,X0,v_b_H____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Wellfounded_Owf(hAPP(X0,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f68904,plain,(
% 156.17/20.13 ![X0]: (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)))|v_b_H____=v_b____|v_b____=v_b____|~c_Relation_Oantisym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),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____,X0,v_b_H____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Wellfounded_Owf(hAPP(X0,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_301)),
% 156.17/20.13 inference(resolution,[status(thm)],[f54965,f1576])).
% 156.17/20.13 fof(f68905,plain,(
% 156.17/20.13 spl0_882|spl0_97|spl0_175|~spl0_301),
% 156.17/20.13 inference(split_clause,[status(thm)],[f68904,f68901,f41290,f49384,f54964])).
% 156.17/20.13 fof(f68906,plain,(
% 156.17/20.13 spl0_883 <=> 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_Relation_Oantisym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),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____,X0,v_b_H____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Wellfounded_Owf(c_Set_Oinsert(X1,hAPP(X0,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f68909,plain,(
% 156.17/20.13 ![X0,X1]: (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)))|v_b_H____=v_b____|v_b____=v_b____|~c_Relation_Oantisym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),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____,X0,v_b_H____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Wellfounded_Owf(c_Set_Oinsert(X1,hAPP(X0,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_301)),
% 156.17/20.13 inference(resolution,[status(thm)],[f54965,f8835])).
% 156.17/20.13 fof(f68910,plain,(
% 156.17/20.13 spl0_883|spl0_97|spl0_175|~spl0_301),
% 156.17/20.13 inference(split_clause,[status(thm)],[f68909,f68906,f41290,f49384,f54964])).
% 156.17/20.13 fof(f68921,plain,(
% 156.17/20.13 spl0_885 <=> c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|v_b_H____=X0|v_b____=X0|~c_Wellfounded_Owf(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f68924,plain,(
% 156.17/20.13 ![X0]: (c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_b_H____=X0|v_b____=X0|~c_Wellfounded_Owf(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|X0=v_b_H____|~c_Relation_Osingle__valued(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_b_H____,v_b____,X0)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_b_H____,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_302)),
% 156.17/20.13 inference(resolution,[status(thm)],[f54970,f39703])).
% 156.17/20.13 fof(f68925,plain,(
% 156.17/20.13 spl0_885|~spl0_254|~spl0_302),
% 156.17/20.13 inference(split_clause,[status(thm)],[f68924,f68921,f54259,f54969])).
% 156.17/20.13 fof(f68935,plain,(
% 156.17/20.13 spl0_886 <=> 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_Wellfounded_Owf(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),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____,X0,v_b_H____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Oirrefl(hAPP(X0,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f68938,plain,(
% 156.17/20.13 ![X0]: (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)))|v_b_H____=v_b____|v_b____=v_b____|~c_Wellfounded_Owf(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),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____,X0,v_b_H____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Oirrefl(hAPP(X0,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_302)),
% 156.17/20.13 inference(resolution,[status(thm)],[f54970,f1545])).
% 156.17/20.13 fof(f68939,plain,(
% 156.17/20.13 spl0_886|spl0_97|spl0_175|~spl0_302),
% 156.17/20.13 inference(split_clause,[status(thm)],[f68938,f68935,f41290,f49384,f54969])).
% 156.17/20.13 fof(f68940,plain,(
% 156.17/20.13 spl0_887 <=> 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_Wellfounded_Owf(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),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____,X0,v_b_H____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Wellfounded_Oacyclic(hAPP(X0,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f68943,plain,(
% 156.17/20.13 ![X0]: (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)))|v_b_H____=v_b____|v_b____=v_b____|~c_Wellfounded_Owf(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),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____,X0,v_b_H____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Wellfounded_Oacyclic(hAPP(X0,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_302)),
% 156.17/20.13 inference(resolution,[status(thm)],[f54970,f7580])).
% 156.17/20.13 fof(f68944,plain,(
% 156.17/20.13 spl0_887|spl0_97|spl0_175|~spl0_302),
% 156.17/20.13 inference(split_clause,[status(thm)],[f68943,f68940,f41290,f49384,f54969])).
% 156.17/20.13 fof(f68945,plain,(
% 156.17/20.13 spl0_888 <=> 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_Wellfounded_Owf(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),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____,X0,v_b_H____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Wellfounded_Owf(hAPP(X0,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f68948,plain,(
% 156.17/20.13 ![X0]: (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)))|v_b_H____=v_b____|v_b____=v_b____|~c_Wellfounded_Owf(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),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____,X0,v_b_H____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Wellfounded_Owf(hAPP(X0,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_302)),
% 156.17/20.13 inference(resolution,[status(thm)],[f54970,f1576])).
% 156.17/20.13 fof(f68949,plain,(
% 156.17/20.13 spl0_888|spl0_97|spl0_175|~spl0_302),
% 156.17/20.13 inference(split_clause,[status(thm)],[f68948,f68945,f41290,f49384,f54969])).
% 156.17/20.13 fof(f68950,plain,(
% 156.17/20.13 spl0_889 <=> 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_Wellfounded_Owf(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),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____,X0,v_b_H____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Wellfounded_Owf(c_Set_Oinsert(X1,hAPP(X0,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f68953,plain,(
% 156.17/20.13 ![X0,X1]: (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)))|v_b_H____=v_b____|v_b____=v_b____|~c_Wellfounded_Owf(hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),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____,X0,v_b_H____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Wellfounded_Owf(c_Set_Oinsert(X1,hAPP(X0,v_sko__CHAINED__1(v_P_H____,X0,v_b_H____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_302)),
% 156.17/20.13 inference(resolution,[status(thm)],[f54970,f8835])).
% 156.17/20.13 fof(f68954,plain,(
% 156.17/20.13 spl0_889|spl0_97|spl0_175|~spl0_302),
% 156.17/20.13 inference(split_clause,[status(thm)],[f68953,f68950,f41290,f49384,f54969])).
% 156.17/20.13 fof(f69211,plain,(
% 156.17/20.13 spl0_890 <=> c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(v_b_H____,v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____,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))),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f69214,plain,(
% 156.17/20.13 c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(v_b_H____,v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____,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(v_b_H____,c_Relation_ORange(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_241),
% 156.17/20.13 inference(resolution,[status(thm)],[f52989,f1524])).
% 156.17/20.13 fof(f69215,plain,(
% 156.17/20.13 spl0_890|~spl0_706|~spl0_241),
% 156.17/20.13 inference(split_clause,[status(thm)],[f69214,f69211,f63171,f52988])).
% 156.17/20.13 fof(f69217,plain,(
% 156.17/20.13 spl0_891 <=> c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(v_F(v_P_H____),v_b_H____,tc_Arrow__Order__Mirabelle_Oalt),v_b____,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))),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f69220,plain,(
% 156.17/20.13 c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(v_F(v_P_H____),v_b_H____,tc_Arrow__Order__Mirabelle_Oalt),v_b____,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(v_b_H____,c_Wellfounded_Oacc(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_241),
% 156.17/20.13 inference(resolution,[status(thm)],[f52989,f1502])).
% 156.17/20.13 fof(f69221,plain,(
% 156.17/20.13 spl0_891|spl0_237|~spl0_241),
% 156.17/20.13 inference(split_clause,[status(thm)],[f69220,f69217,f52968,f52988])).
% 156.17/20.13 fof(f69222,plain,(
% 156.17/20.13 spl0_892 <=> c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(v_b_H____,v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____,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))),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f69225,plain,(
% 156.17/20.13 c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(v_b_H____,v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____,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(v_b_H____,c_Relation_ORange(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_241),
% 156.17/20.13 inference(resolution,[status(thm)],[f52989,f1376])).
% 156.17/20.13 fof(f69226,plain,(
% 156.17/20.13 spl0_892|~spl0_706|~spl0_241),
% 156.17/20.13 inference(split_clause,[status(thm)],[f69225,f69222,f63171,f52988])).
% 156.17/20.13 fof(f69231,plain,(
% 156.17/20.13 $false|~spl0_0|spl0_706),
% 156.17/20.13 inference(forward_subsumption_resolution,[status(thm)],[f63173,f54597])).
% 156.17/20.13 fof(f69232,plain,(
% 156.17/20.13 ~spl0_0|spl0_706),
% 156.17/20.13 inference(contradiction_clause,[status(thm)],[f69231])).
% 156.17/20.13 fof(f69290,plain,(
% 156.17/20.13 spl0_897 <=> c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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))),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f69291,plain,(
% 156.17/20.13 c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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))|~spl0_897),
% 156.17/20.13 inference(component_clause,[status(thm)],[f69290])).
% 156.17/20.13 fof(f69293,plain,(
% 156.17/20.13 c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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(v_b____,c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_161),
% 156.17/20.13 inference(resolution,[status(thm)],[f47703,f1524])).
% 156.17/20.13 fof(f69294,plain,(
% 156.17/20.13 spl0_897|~spl0_692|~spl0_161),
% 156.17/20.13 inference(split_clause,[status(thm)],[f69293,f69290,f63074,f47702])).
% 156.17/20.13 fof(f69296,plain,(
% 156.17/20.13 spl0_898 <=> c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(v_F(v_P____),v_b____,tc_Arrow__Order__Mirabelle_Oalt),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))),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f69297,plain,(
% 156.17/20.13 c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(v_F(v_P____),v_b____,tc_Arrow__Order__Mirabelle_Oalt),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))|~spl0_898),
% 156.17/20.13 inference(component_clause,[status(thm)],[f69296])).
% 156.17/20.13 fof(f69299,plain,(
% 156.17/20.13 c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(v_F(v_P____),v_b____,tc_Arrow__Order__Mirabelle_Oalt),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(v_b____,c_Wellfounded_Oacc(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_161),
% 156.17/20.13 inference(resolution,[status(thm)],[f47703,f1502])).
% 156.17/20.13 fof(f69300,plain,(
% 156.17/20.13 spl0_898|spl0_180|~spl0_161),
% 156.17/20.13 inference(split_clause,[status(thm)],[f69299,f69296,f49602,f47702])).
% 156.17/20.13 fof(f69301,plain,(
% 156.17/20.13 spl0_899 <=> c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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))),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f69302,plain,(
% 156.17/20.13 c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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))|~spl0_899),
% 156.17/20.13 inference(component_clause,[status(thm)],[f69301])).
% 156.17/20.13 fof(f69304,plain,(
% 156.17/20.13 c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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(v_b____,c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_161),
% 156.17/20.13 inference(resolution,[status(thm)],[f47703,f1376])).
% 156.17/20.13 fof(f69305,plain,(
% 156.17/20.13 spl0_899|~spl0_692|~spl0_161),
% 156.17/20.13 inference(split_clause,[status(thm)],[f69304,f69301,f63074,f47702])).
% 156.17/20.13 fof(f69309,plain,(
% 156.17/20.13 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_Nitpick_Orefl_H(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_161),
% 156.17/20.13 inference(resolution,[status(thm)],[f47703,f1574])).
% 156.17/20.13 fof(f69310,plain,(
% 156.17/20.13 spl0_153|~spl0_677|~spl0_161),
% 156.17/20.13 inference(split_clause,[status(thm)],[f69309,f47635,f62563,f47702])).
% 156.17/20.13 fof(f69330,plain,(
% 156.17/20.13 spl0_903 <=> ~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))),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f69331,plain,(
% 156.17/20.13 ![X0]: (~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))|~spl0_903)),
% 156.17/20.13 inference(component_clause,[status(thm)],[f69330])).
% 156.17/20.13 fof(f69336,plain,(
% 156.17/20.13 ![X0]: (~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(v_b____,c_Relation_ODomain(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_160)),
% 156.17/20.13 inference(resolution,[status(thm)],[f47698,f1636])).
% 156.17/20.13 fof(f69337,plain,(
% 156.17/20.13 spl0_903|spl0_186|~spl0_160),
% 156.17/20.13 inference(split_clause,[status(thm)],[f69336,f69330,f50289,f47697])).
% 156.17/20.13 fof(f69343,plain,(
% 156.17/20.13 ~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_Oirrefl(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_160),
% 156.17/20.13 inference(resolution,[status(thm)],[f47698,f1545])).
% 156.17/20.13 fof(f69344,plain,(
% 156.17/20.13 ~spl0_1|~spl0_694|~spl0_160),
% 156.17/20.13 inference(split_clause,[status(thm)],[f69343,f1723,f63086,f47697])).
% 156.17/20.13 fof(f69345,plain,(
% 156.17/20.13 ~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_Wellfounded_Oacyclic(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_160),
% 156.17/20.13 inference(resolution,[status(thm)],[f47698,f7580])).
% 156.17/20.13 fof(f69346,plain,(
% 156.17/20.13 ~spl0_1|~spl0_695|~spl0_160),
% 156.17/20.13 inference(split_clause,[status(thm)],[f69345,f1723,f63091,f47697])).
% 156.17/20.13 fof(f69347,plain,(
% 156.17/20.13 ~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_Wellfounded_Owf(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_160),
% 156.17/20.13 inference(resolution,[status(thm)],[f47698,f1576])).
% 156.17/20.13 fof(f69348,plain,(
% 156.17/20.13 ~spl0_1|~spl0_156|~spl0_160),
% 156.17/20.13 inference(split_clause,[status(thm)],[f69347,f1723,f47650,f47697])).
% 156.17/20.13 fof(f69349,plain,(
% 156.17/20.13 ![X0]: (~c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_Wellfounded_Owf(c_Set_Oinsert(X0,v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_160)),
% 156.17/20.13 inference(resolution,[status(thm)],[f47698,f8835])).
% 156.17/20.13 fof(f69350,plain,(
% 156.17/20.13 ~spl0_1|spl0_696|~spl0_160),
% 156.17/20.13 inference(split_clause,[status(thm)],[f69349,f1723,f63098,f47697])).
% 156.17/20.13 fof(f69527,plain,(
% 156.17/20.13 ~c_Nitpick_Orefl_H(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|spl0_196),
% 156.17/20.13 inference(resolution,[status(thm)],[f51460,f50760])).
% 156.17/20.13 fof(f69530,plain,(
% 156.17/20.13 spl0_904 <=> ~c_Nitpick_Orefl_H(c_Relation_Oconverse(X0,tc_prod(X1,X1),tc_prod(X1,X1)),tc_prod(X1,X1))|~c_Wellfounded_Owf(c_Relation_ODomain(X0,tc_prod(X1,X1),tc_prod(X1,X1)),X1)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f69533,plain,(
% 156.17/20.13 ![X0,X1,X2,X3,X4]: (~c_Nitpick_Orefl_H(c_Relation_Oconverse(X0,tc_prod(X1,X1),tc_prod(X1,X1)),tc_prod(X1,X1))|hBOOL(hAPP(X2,X3))|hBOOL(hAPP(X2,X4))|~c_Wellfounded_Owf(c_Relation_ODomain(X0,tc_prod(X1,X1),tc_prod(X1,X1)),X1))),
% 156.17/20.13 inference(resolution,[status(thm)],[f51460,f1242])).
% 156.17/20.13 fof(f69534,plain,(
% 156.17/20.13 spl0_904|spl0_381),
% 156.17/20.13 inference(split_clause,[status(thm)],[f69533,f69530,f58069])).
% 156.17/20.13 fof(f69689,plain,(
% 156.17/20.13 c_in(v_b____,c_Wellfounded_Oacc(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|spl0_692),
% 156.17/20.13 inference(resolution,[status(thm)],[f63076,f50680])).
% 156.17/20.13 fof(f69691,plain,(
% 156.17/20.13 ![X0]: (hBOOL(hAPP(X0,v_b____))|~c_Nitpick_Orefl_H(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|spl0_692)),
% 156.17/20.13 inference(resolution,[status(thm)],[f69689,f30446])).
% 156.17/20.13 fof(f69692,plain,(
% 156.17/20.13 spl0_689|~spl0_677|spl0_692),
% 156.17/20.13 inference(split_clause,[status(thm)],[f69691,f63045,f62563,f63074])).
% 156.17/20.13 fof(f69696,plain,(
% 156.17/20.13 ![X0]: (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),c_Transitive__Closure_Otrancl(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_903)),
% 156.17/20.13 inference(resolution,[status(thm)],[f69331,f1257])).
% 156.17/20.13 fof(f69697,plain,(
% 156.17/20.13 ![X0]: (~c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Transitive__Closure_Otrancl(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~spl0_903)),
% 156.17/20.13 inference(forward_subsumption_resolution,[status(thm)],[f69696,f69331])).
% 156.17/20.13 fof(f69715,plain,(
% 156.17/20.13 ![X0]: (~c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_903)),
% 156.17/20.13 inference(resolution,[status(thm)],[f69697,f1646])).
% 156.17/20.13 fof(f69719,plain,(
% 156.17/20.13 spl0_905 <=> ~c_Equiv__Relations_Oequiv(X0,c_Transitive__Closure_Otrancl(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f69722,plain,(
% 156.17/20.13 ![X0]: (~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)|~c_Equiv__Relations_Oequiv(X0,c_Transitive__Closure_Otrancl(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_903)),
% 156.17/20.13 inference(resolution,[status(thm)],[f69715,f24453])).
% 156.17/20.13 fof(f69723,plain,(
% 156.17/20.13 ~spl0_196|spl0_905|~spl0_903),
% 156.17/20.13 inference(split_clause,[status(thm)],[f69722,f50758,f69719,f69330])).
% 156.17/20.13 fof(f69724,plain,(
% 156.17/20.13 spl0_906 <=> c_in(v_a____,c_Relation_ODomain(c_Transitive__Closure_Otrancl(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f69727,plain,(
% 156.17/20.13 ![X0]: (~c_in(v_a____,c_Relation_ODomain(c_Transitive__Closure_Otrancl(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_Equiv__Relations_Oequiv(X0,c_Transitive__Closure_Otrancl(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_903)),
% 156.17/20.13 inference(resolution,[status(thm)],[f69715,f24438])).
% 156.17/20.13 fof(f69728,plain,(
% 156.17/20.13 ~spl0_906|spl0_905|~spl0_903),
% 156.17/20.13 inference(split_clause,[status(thm)],[f69727,f69724,f69719,f69330])).
% 156.17/20.13 fof(f70146,plain,(
% 156.17/20.13 ~c_FunDef_Oin__rel(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,v_b_H____)),v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)|spl0_508),
% 156.17/20.13 inference(resolution,[status(thm)],[f60071,f12914])).
% 156.17/20.13 fof(f70218,plain,(
% 156.17/20.13 spl0_907 <=> c_Set_Oinsert(X2,X3,X4)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f70219,plain,(
% 156.17/20.13 ![X0,X1,X2]: (c_Set_Oinsert(X0,X1,X2)=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))|~spl0_907)),
% 156.17/20.13 inference(component_clause,[status(thm)],[f70218])).
% 156.17/20.13 fof(f70224,plain,(
% 156.17/20.13 $false|~spl0_907),
% 156.17/20.13 inference(forward_subsumption_resolution,[status(thm)],[f70219,f823])).
% 156.17/20.13 fof(f70225,plain,(
% 156.17/20.13 ~spl0_907),
% 156.17/20.13 inference(contradiction_clause,[status(thm)],[f70224])).
% 156.17/20.13 fof(f70226,plain,(
% 156.17/20.13 ~spl0_513|spl0_508),
% 156.17/20.13 inference(split_clause,[status(thm)],[f70146,f60090,f60069])).
% 156.17/20.13 fof(f70239,plain,(
% 156.17/20.13 spl0_908 <=> ~c_Nitpick_Orefl_H(c_Transitive__Closure_Otrancl(X0,X1),X1)|hBOOL(hAPP(c_Relation_ORange(X0,X1,X1),X2))),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f70242,plain,(
% 156.17/20.13 ![X0,X1,X2,X3,X4]: (~c_Nitpick_Orefl_H(c_Transitive__Closure_Otrancl(X0,X1),X1)|hBOOL(hAPP(c_Relation_ORange(X0,X1,X1),X2))|~c_Wellfounded_Owf(X3,X4))),
% 156.17/20.13 inference(resolution,[status(thm)],[f57886,f984])).
% 156.17/20.13 fof(f70243,plain,(
% 156.17/20.13 spl0_908|spl0_7),
% 156.17/20.13 inference(split_clause,[status(thm)],[f70242,f70239,f1768])).
% 156.17/20.13 fof(f70266,plain,(
% 156.17/20.13 spl0_909 <=> ~c_Nitpick_Orefl_H(c_Relation_Oconverse(X0,tc_prod(X1,X1),tc_prod(X1,X1)),tc_prod(X1,X1))|~c_Wellfounded_Owf(c_Relation_ORange(X0,tc_prod(X1,X1),tc_prod(X1,X1)),X1)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f70269,plain,(
% 156.17/20.13 ![X0,X1,X2,X3,X4]: (~c_Nitpick_Orefl_H(c_Relation_Oconverse(X0,tc_prod(X1,X1),tc_prod(X1,X1)),tc_prod(X1,X1))|hBOOL(hAPP(X2,X3))|hBOOL(hAPP(X2,X4))|~c_Wellfounded_Owf(c_Relation_ORange(X0,tc_prod(X1,X1),tc_prod(X1,X1)),X1))),
% 156.17/20.13 inference(resolution,[status(thm)],[f58651,f1242])).
% 156.17/20.13 fof(f70270,plain,(
% 156.17/20.13 spl0_909|spl0_381),
% 156.17/20.13 inference(split_clause,[status(thm)],[f70269,f70266,f58069])).
% 156.17/20.13 fof(f70311,plain,(
% 156.17/20.13 spl0_910 <=> c_in(v_a____,c_Wellfounded_Oacc(hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,v_b_H____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f70312,plain,(
% 156.17/20.13 c_in(v_a____,c_Wellfounded_Oacc(hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,v_b_H____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_910),
% 156.17/20.13 inference(component_clause,[status(thm)],[f70311])).
% 156.17/20.13 fof(f70314,plain,(
% 156.17/20.13 spl0_911 <=> c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,v_b_H____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f70317,plain,(
% 156.17/20.13 c_in(v_a____,c_Wellfounded_Oacc(hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,v_b_H____)),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_H____,v_a____,v_b____,v_b_H____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_508),
% 156.17/20.13 inference(resolution,[status(thm)],[f60070,f1617])).
% 156.17/20.13 fof(f70318,plain,(
% 156.17/20.13 spl0_910|~spl0_911|~spl0_508),
% 156.17/20.13 inference(split_clause,[status(thm)],[f70317,f70311,f70314,f60069])).
% 156.17/20.13 fof(f70353,plain,(
% 156.17/20.13 spl0_916 <=> ~c_Nitpick_Orefl_H(c_Transitive__Closure_Otrancl(X0,X1),X1)|hBOOL(hAPP(c_Relation_ODomain(X0,X1,X1),X2))),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f70356,plain,(
% 156.17/20.13 ![X0,X1,X2,X3,X4]: (~c_Nitpick_Orefl_H(c_Transitive__Closure_Otrancl(X0,X1),X1)|hBOOL(hAPP(c_Relation_ODomain(X0,X1,X1),X2))|~c_Wellfounded_Owf(X3,X4))),
% 156.17/20.13 inference(resolution,[status(thm)],[f60478,f984])).
% 156.17/20.13 fof(f70357,plain,(
% 156.17/20.13 spl0_916|spl0_7),
% 156.17/20.13 inference(split_clause,[status(thm)],[f70356,f70353,f1768])).
% 156.17/20.13 fof(f70446,plain,(
% 156.17/20.13 spl0_917 <=> c_Nitpick_Orefl_H(hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,v_b_H____)),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f70449,plain,(
% 156.17/20.13 ![X0]: (hBOOL(hAPP(X0,v_a____))|~c_Nitpick_Orefl_H(hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,v_b_H____)),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_910)),
% 156.17/20.13 inference(resolution,[status(thm)],[f70312,f30446])).
% 156.17/20.13 fof(f70450,plain,(
% 156.17/20.13 spl0_676|~spl0_917|~spl0_910),
% 156.17/20.13 inference(split_clause,[status(thm)],[f70449,f62560,f70446,f70311])).
% 156.17/20.13 fof(f71026,plain,(
% 156.17/20.13 ![X0]: (c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(v_F(v_P____),v_b____,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X0,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_898)),
% 156.17/20.13 inference(resolution,[status(thm)],[f69297,f1650])).
% 156.17/20.13 fof(f71052,plain,(
% 156.17/20.13 spl0_919 <=> ~c_Relation_Orefl__on(c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X0,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f71055,plain,(
% 156.17/20.13 spl0_920 <=> hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(v_F(v_P____),v_b____,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f71056,plain,(
% 156.17/20.13 ![X0]: (hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(v_F(v_P____),v_b____,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_920)),
% 156.17/20.13 inference(component_clause,[status(thm)],[f71055])).
% 156.17/20.13 fof(f71058,plain,(
% 156.17/20.13 ![X0,X1]: (~c_Relation_Orefl__on(c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X0,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(v_F(v_P____),v_b____,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_898)),
% 156.17/20.13 inference(resolution,[status(thm)],[f71026,f30441])).
% 156.17/20.13 fof(f71059,plain,(
% 156.17/20.13 spl0_919|spl0_920|~spl0_898),
% 156.17/20.13 inference(split_clause,[status(thm)],[f71058,f71052,f71055,f69296])).
% 156.17/20.13 fof(f71060,plain,(
% 156.17/20.13 spl0_921 <=> c_Relation_Orefl__on(c_Wellfounded_Oacc(c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f71063,plain,(
% 156.17/20.13 ![X0]: (~c_Relation_Orefl__on(c_Wellfounded_Oacc(c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(v_F(v_P____),v_b____,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_898)),
% 156.17/20.13 inference(resolution,[status(thm)],[f71026,f30443])).
% 156.17/20.13 fof(f71064,plain,(
% 156.17/20.13 ~spl0_921|spl0_920|~spl0_898),
% 156.17/20.13 inference(split_clause,[status(thm)],[f71063,f71060,f71055,f69296])).
% 156.17/20.13 fof(f71065,plain,(
% 156.17/20.13 spl0_922 <=> ~c_Relation_Orefl__on(c_Wellfounded_Oacc(X0,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~c_Nitpick_Orefl_H(X0,tc_Arrow__Order__Mirabelle_Oalt)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f71068,plain,(
% 156.17/20.13 ![X0,X1]: (~c_Relation_Orefl__on(c_Wellfounded_Oacc(X0,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(v_F(v_P____),v_b____,tc_Arrow__Order__Mirabelle_Oalt)))|~c_Nitpick_Orefl_H(X0,tc_Arrow__Order__Mirabelle_Oalt)|~spl0_898)),
% 156.17/20.13 inference(resolution,[status(thm)],[f71026,f30446])).
% 156.17/20.13 fof(f71069,plain,(
% 156.17/20.13 spl0_922|spl0_920|~spl0_898),
% 156.17/20.13 inference(split_clause,[status(thm)],[f71068,f71065,f71055,f69296])).
% 156.17/20.13 fof(f71112,plain,(
% 156.17/20.13 spl0_923 <=> c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(v_F(v_P____),v_b____,tc_Arrow__Order__Mirabelle_Oalt),X0,X1)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f71113,plain,(
% 156.17/20.13 ![X0,X1]: (c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(v_F(v_P____),v_b____,tc_Arrow__Order__Mirabelle_Oalt),X0,X1)|~spl0_923)),
% 156.17/20.13 inference(component_clause,[status(thm)],[f71112])).
% 156.17/20.13 fof(f71115,plain,(
% 156.17/20.13 spl0_924 <=> c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(v_F(v_P____),v_b____,tc_Arrow__Order__Mirabelle_Oalt)=X2),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f71116,plain,(
% 156.17/20.13 ![X0]: (c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(v_F(v_P____),v_b____,tc_Arrow__Order__Mirabelle_Oalt)=X0|~spl0_924)),
% 156.17/20.13 inference(component_clause,[status(thm)],[f71115])).
% 156.17/20.13 fof(f71123,plain,(
% 156.17/20.13 $false|~spl0_920),
% 156.17/20.13 inference(resolution,[status(thm)],[f71056,f49080])).
% 156.17/20.13 fof(f71124,plain,(
% 156.17/20.13 ~spl0_920),
% 156.17/20.13 inference(contradiction_clause,[status(thm)],[f71123])).
% 156.17/20.13 fof(f71132,plain,(
% 156.17/20.13 ![X0,X1]: (X0=X1|~spl0_924)),
% 156.17/20.13 inference(paramodulation,[status(thm)],[f71116,f71116])).
% 156.17/20.13 fof(f71133,plain,(
% 156.17/20.13 spl0_211|~spl0_924),
% 156.17/20.13 inference(split_clause,[status(thm)],[f71132,f51909,f71115])).
% 156.17/20.13 fof(f71153,plain,(
% 156.17/20.13 $false|~spl0_923),
% 156.17/20.13 inference(resolution,[status(thm)],[f71113,f49089])).
% 156.17/20.13 fof(f71154,plain,(
% 156.17/20.13 ~spl0_923),
% 156.17/20.13 inference(contradiction_clause,[status(thm)],[f71153])).
% 156.17/20.13 fof(f71247,plain,(
% 156.17/20.13 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)|~spl0_698),
% 156.17/20.13 inference(resolution,[status(thm)],[f63112,f1636])).
% 156.17/20.13 fof(f71248,plain,(
% 156.17/20.13 spl0_196|~spl0_698),
% 156.17/20.13 inference(split_clause,[status(thm)],[f71247,f50758,f63111])).
% 156.17/20.13 fof(f71261,plain,(
% 156.17/20.13 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)|~spl0_697),
% 156.17/20.13 inference(resolution,[status(thm)],[f63107,f1636])).
% 156.17/20.13 fof(f71262,plain,(
% 156.17/20.13 spl0_196|~spl0_697),
% 156.17/20.13 inference(split_clause,[status(thm)],[f71261,f50758,f63106])).
% 156.17/20.13 fof(f71291,plain,(
% 156.17/20.13 ![X0,X1,X2,X3,X4,X5]: (X0=X1|~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X4),tc_prod(X5,X5)),X5))),
% 156.17/20.13 inference(resolution,[status(thm)],[f47086,f28696])).
% 156.17/20.13 fof(f71292,plain,(
% 156.17/20.13 spl0_211|spl0_394),
% 156.17/20.13 inference(split_clause,[status(thm)],[f71291,f51909,f58139])).
% 156.17/20.13 fof(f71293,plain,(
% 156.17/20.13 spl0_928 <=> ~c_Wellfounded_Oacyclic(c_Wellfounded_Oacc(c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X4),tc_prod(X5,X5)),X5)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f71296,plain,(
% 156.17/20.13 ![X0,X1,X2,X3,X4,X5]: (X0=X1|~c_Wellfounded_Oacyclic(c_Wellfounded_Oacc(c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X4),tc_prod(X5,X5)),X5))),
% 156.17/20.13 inference(resolution,[status(thm)],[f47086,f24366])).
% 156.17/20.13 fof(f71297,plain,(
% 156.17/20.13 spl0_211|spl0_928),
% 156.17/20.13 inference(split_clause,[status(thm)],[f71296,f51909,f71293])).
% 156.17/20.13 fof(f71298,plain,(
% 156.17/20.13 ![X0,X1,X2,X3,X4,X5]: (X0=X1|~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X4),tc_prod(X5,X5)),X5))),
% 156.17/20.13 inference(resolution,[status(thm)],[f47133,f28696])).
% 156.17/20.13 fof(f71299,plain,(
% 156.17/20.13 spl0_211|spl0_392),
% 156.17/20.13 inference(split_clause,[status(thm)],[f71298,f51909,f58129])).
% 156.17/20.13 fof(f71300,plain,(
% 156.17/20.13 spl0_929 <=> ~c_Wellfounded_Oacyclic(c_Wellfounded_Oacc(c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X4),tc_prod(X5,X5)),X5)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f71303,plain,(
% 156.17/20.13 ![X0,X1,X2,X3,X4,X5]: (X0=X1|~c_Wellfounded_Oacyclic(c_Wellfounded_Oacc(c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X4),tc_prod(X5,X5)),X5))),
% 156.17/20.13 inference(resolution,[status(thm)],[f47133,f24366])).
% 156.17/20.13 fof(f71304,plain,(
% 156.17/20.13 spl0_211|spl0_929),
% 156.17/20.13 inference(split_clause,[status(thm)],[f71303,f51909,f71300])).
% 156.17/20.13 fof(f71311,plain,(
% 156.17/20.13 spl0_930 <=> ~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Lattices_Olower__semilattice__class_Oinf(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),tc_fun(X5,tc_bool)),tc_prod(X6,X6)),X6)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f71314,plain,(
% 156.17/20.13 ![X0,X1,X2,X3,X4,X5,X6]: (hBOOL(hAPP(X0,X1))|hBOOL(hAPP(X0,X2))|~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Lattices_Olower__semilattice__class_Oinf(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),tc_fun(X5,tc_bool)),tc_prod(X6,X6)),X6))),
% 156.17/20.13 inference(resolution,[status(thm)],[f47987,f1242])).
% 156.17/20.13 fof(f71315,plain,(
% 156.17/20.13 spl0_381|spl0_930),
% 156.17/20.13 inference(split_clause,[status(thm)],[f71314,f58069,f71311])).
% 156.17/20.13 fof(f71333,plain,(
% 156.17/20.13 spl0_931 <=> ~c_Nitpick_Orefl_H(c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X4,tc_bool)),X5)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f71336,plain,(
% 156.17/20.13 ![X0,X1,X2,X3,X4,X5]: (hBOOL(hAPP(X0,X1))|~c_Nitpick_Orefl_H(c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X4,tc_bool)),X5))),
% 156.17/20.13 inference(resolution,[status(thm)],[f47987,f30446])).
% 156.17/20.13 fof(f71337,plain,(
% 156.17/20.13 spl0_75|spl0_931),
% 156.17/20.13 inference(split_clause,[status(thm)],[f71336,f37252,f71333])).
% 156.17/20.13 fof(f71354,plain,(
% 156.17/20.13 spl0_932 <=> ~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,tc_fun(X5,tc_bool)),tc_prod(X6,X6)),X6)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f71357,plain,(
% 156.17/20.13 ![X0,X1,X2,X3,X4,X5,X6]: (hBOOL(hAPP(X0,X1))|hBOOL(hAPP(X0,X2))|~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,tc_fun(X5,tc_bool)),tc_prod(X6,X6)),X6))),
% 156.17/20.13 inference(resolution,[status(thm)],[f49073,f1242])).
% 156.17/20.13 fof(f71358,plain,(
% 156.17/20.13 spl0_381|spl0_932),
% 156.17/20.13 inference(split_clause,[status(thm)],[f71357,f58069,f71354])).
% 156.17/20.13 fof(f71376,plain,(
% 156.17/20.13 spl0_933 <=> ~c_Nitpick_Orefl_H(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,tc_fun(X4,tc_bool)),X5)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f71379,plain,(
% 156.17/20.13 ![X0,X1,X2,X3,X4,X5]: (hBOOL(hAPP(X0,X1))|~c_Nitpick_Orefl_H(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,tc_fun(X4,tc_bool)),X5))),
% 156.17/20.13 inference(resolution,[status(thm)],[f49073,f30446])).
% 156.17/20.13 fof(f71380,plain,(
% 156.17/20.13 spl0_75|spl0_933),
% 156.17/20.13 inference(split_clause,[status(thm)],[f71379,f37252,f71376])).
% 156.17/20.13 fof(f71394,plain,(
% 156.17/20.13 spl0_934 <=> c_Relation_Oirrefl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2),X2)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f71397,plain,(
% 156.17/20.13 ![X0,X1,X2]: (hBOOL(X0)|c_Relation_Oirrefl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2),X2))),
% 156.17/20.13 inference(paramodulation,[status(thm)],[f806,f49183])).
% 156.17/20.13 fof(f71398,plain,(
% 156.17/20.13 spl0_62|spl0_934),
% 156.17/20.13 inference(split_clause,[status(thm)],[f71397,f29892,f71394])).
% 156.17/20.13 fof(f71439,plain,(
% 156.17/20.13 spl0_935 <=> ~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,tc_fun(X5,tc_bool)),tc_prod(X6,X6)),X6)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f71442,plain,(
% 156.17/20.13 ![X0,X1,X2,X3,X4,X5,X6]: (hBOOL(hAPP(X0,X1))|hBOOL(hAPP(X0,X2))|~c_Wellfounded_Owf(c_Wellfounded_Oacc(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,tc_fun(X5,tc_bool)),tc_prod(X6,X6)),X6))),
% 156.17/20.13 inference(resolution,[status(thm)],[f49219,f1242])).
% 156.17/20.13 fof(f71443,plain,(
% 156.17/20.13 spl0_381|spl0_935),
% 156.17/20.13 inference(split_clause,[status(thm)],[f71442,f58069,f71439])).
% 156.17/20.13 fof(f71461,plain,(
% 156.17/20.13 spl0_936 <=> ~c_Nitpick_Orefl_H(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,tc_fun(X4,tc_bool)),X5)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f71464,plain,(
% 156.17/20.13 ![X0,X1,X2,X3,X4,X5]: (hBOOL(hAPP(X0,X1))|~c_Nitpick_Orefl_H(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,tc_fun(X4,tc_bool)),X5))),
% 156.17/20.13 inference(resolution,[status(thm)],[f49219,f30446])).
% 156.17/20.13 fof(f71465,plain,(
% 156.17/20.13 spl0_75|spl0_936),
% 156.17/20.13 inference(split_clause,[status(thm)],[f71464,f37252,f71461])).
% 156.17/20.13 fof(f71911,plain,(
% 156.17/20.13 ![X0]: (c_in(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X0,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_899)),
% 156.17/20.13 inference(resolution,[status(thm)],[f69302,f1650])).
% 156.17/20.13 fof(f71938,plain,(
% 156.17/20.13 spl0_939 <=> hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Relation__XRangeE__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f71939,plain,(
% 156.17/20.13 ![X0]: (hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Relation__XRangeE__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_939)),
% 156.17/20.13 inference(component_clause,[status(thm)],[f71938])).
% 156.17/20.13 fof(f71941,plain,(
% 156.17/20.13 ![X0,X1]: (~c_Relation_Orefl__on(c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X0,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Relation__XRangeE__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_899)),
% 156.17/20.13 inference(resolution,[status(thm)],[f71911,f30441])).
% 156.17/20.13 fof(f71942,plain,(
% 156.17/20.13 spl0_919|spl0_939|~spl0_899),
% 156.17/20.13 inference(split_clause,[status(thm)],[f71941,f71052,f71938,f69301])).
% 156.17/20.13 fof(f71943,plain,(
% 156.17/20.13 ![X0]: (~c_Relation_Orefl__on(c_Wellfounded_Oacc(c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Relation__XRangeE__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_899)),
% 156.17/20.13 inference(resolution,[status(thm)],[f71911,f30443])).
% 156.17/20.13 fof(f71944,plain,(
% 156.17/20.13 ~spl0_921|spl0_939|~spl0_899),
% 156.17/20.13 inference(split_clause,[status(thm)],[f71943,f71060,f71938,f69301])).
% 156.17/20.13 fof(f71945,plain,(
% 156.17/20.13 ![X0,X1]: (~c_Relation_Orefl__on(c_Wellfounded_Oacc(X0,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Relation__XRangeE__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~c_Nitpick_Orefl_H(X0,tc_Arrow__Order__Mirabelle_Oalt)|~spl0_899)),
% 156.17/20.13 inference(resolution,[status(thm)],[f71911,f30446])).
% 156.17/20.13 fof(f71946,plain,(
% 156.17/20.13 spl0_922|spl0_939|~spl0_899),
% 156.17/20.13 inference(split_clause,[status(thm)],[f71945,f71065,f71938,f69301])).
% 156.17/20.13 fof(f71991,plain,(
% 156.17/20.13 spl0_940 <=> c_in(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,X1)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f71992,plain,(
% 156.17/20.13 ![X0,X1]: (c_in(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,X1)|~spl0_940)),
% 156.17/20.13 inference(component_clause,[status(thm)],[f71991])).
% 156.17/20.13 fof(f71994,plain,(
% 156.17/20.13 spl0_941 <=> c_ATP__Linkup_Osko__Relation__XRangeE__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)=X2),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f71995,plain,(
% 156.17/20.13 ![X0]: (c_ATP__Linkup_Osko__Relation__XRangeE__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)=X0|~spl0_941)),
% 156.17/20.13 inference(component_clause,[status(thm)],[f71994])).
% 156.17/20.13 fof(f72002,plain,(
% 156.17/20.13 $false|~spl0_939),
% 156.17/20.13 inference(resolution,[status(thm)],[f71939,f49080])).
% 156.17/20.13 fof(f72003,plain,(
% 156.17/20.13 ~spl0_939),
% 156.17/20.13 inference(contradiction_clause,[status(thm)],[f72002])).
% 156.17/20.13 fof(f72012,plain,(
% 156.17/20.13 ![X0,X1]: (X0=X1|~spl0_941)),
% 156.17/20.13 inference(paramodulation,[status(thm)],[f71995,f71995])).
% 156.17/20.13 fof(f72013,plain,(
% 156.17/20.13 spl0_211|~spl0_941),
% 156.17/20.13 inference(split_clause,[status(thm)],[f72012,f51909,f71994])).
% 156.17/20.13 fof(f72024,plain,(
% 156.17/20.13 $false|~spl0_940),
% 156.17/20.13 inference(resolution,[status(thm)],[f71992,f49089])).
% 156.17/20.13 fof(f72025,plain,(
% 156.17/20.13 ~spl0_940),
% 156.17/20.13 inference(contradiction_clause,[status(thm)],[f72024])).
% 156.17/20.13 fof(f72029,plain,(
% 156.17/20.13 ![X0]: (c_in(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Orefl__on(X0,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_897)),
% 156.17/20.13 inference(resolution,[status(thm)],[f69291,f1650])).
% 156.17/20.13 fof(f72056,plain,(
% 156.17/20.13 spl0_942 <=> hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f72057,plain,(
% 156.17/20.13 ![X0]: (hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_942)),
% 156.17/20.13 inference(component_clause,[status(thm)],[f72056])).
% 156.17/20.13 fof(f72059,plain,(
% 156.17/20.13 ![X0,X1]: (~c_Relation_Orefl__on(c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X0,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_897)),
% 156.17/20.13 inference(resolution,[status(thm)],[f72029,f30441])).
% 156.17/20.13 fof(f72060,plain,(
% 156.17/20.13 spl0_919|spl0_942|~spl0_897),
% 156.17/20.13 inference(split_clause,[status(thm)],[f72059,f71052,f72056,f69290])).
% 156.17/20.13 fof(f72061,plain,(
% 156.17/20.13 ![X0]: (~c_Relation_Orefl__on(c_Wellfounded_Oacc(c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_897)),
% 156.17/20.13 inference(resolution,[status(thm)],[f72029,f30443])).
% 156.17/20.13 fof(f72062,plain,(
% 156.17/20.13 ~spl0_921|spl0_942|~spl0_897),
% 156.17/20.13 inference(split_clause,[status(thm)],[f72061,f71060,f72056,f69290])).
% 156.17/20.13 fof(f72063,plain,(
% 156.17/20.13 ![X0,X1]: (~c_Relation_Orefl__on(c_Wellfounded_Oacc(X0,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~c_Nitpick_Orefl_H(X0,tc_Arrow__Order__Mirabelle_Oalt)|~spl0_897)),
% 156.17/20.13 inference(resolution,[status(thm)],[f72029,f30446])).
% 156.17/20.13 fof(f72064,plain,(
% 156.17/20.13 spl0_922|spl0_942|~spl0_897),
% 156.17/20.13 inference(split_clause,[status(thm)],[f72063,f71065,f72056,f69290])).
% 156.17/20.13 fof(f72109,plain,(
% 156.17/20.13 spl0_943 <=> c_in(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,X1)),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f72110,plain,(
% 156.17/20.13 ![X0,X1]: (c_in(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,X1)|~spl0_943)),
% 156.17/20.13 inference(component_clause,[status(thm)],[f72109])).
% 156.17/20.13 fof(f72112,plain,(
% 156.17/20.13 spl0_944 <=> c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)=X2),
% 156.17/20.13 introduced(split_symbol_definition)).
% 156.17/20.13 fof(f72113,plain,(
% 156.17/20.13 ![X0]: (c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(v_b____,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)=X0|~spl0_944)),
% 156.17/20.13 inference(component_clause,[status(thm)],[f72112])).
% 156.17/20.13 fof(f72120,plain,(
% 156.17/20.13 $false|~spl0_942),
% 156.17/20.13 inference(resolution,[status(thm)],[f72057,f49080])).
% 156.17/20.13 fof(f72121,plain,(
% 156.17/20.13 ~spl0_942),
% 156.17/20.13 inference(contradiction_clause,[status(thm)],[f72120])).
% 156.17/20.13 fof(f72130,plain,(
% 156.17/20.13 ![X0,X1]: (X0=X1|~spl0_944)),
% 156.17/20.13 inference(paramodulation,[status(thm)],[f72113,f72113])).
% 156.17/20.13 fof(f72131,plain,(
% 156.17/20.13 spl0_211|~spl0_944),
% 156.17/20.13 inference(split_clause,[status(thm)],[f72130,f51909,f72112])).
% 156.17/20.13 fof(f72142,plain,(
% 156.17/20.13 $false|~spl0_943),
% 156.17/20.13 inference(resolution,[status(thm)],[f72110,f49089])).
% 156.17/20.13 fof(f72143,plain,(
% 156.17/20.13 ~spl0_943),
% 156.17/20.13 inference(contradiction_clause,[status(thm)],[f72142])).
% 156.17/20.13 fof(f73266,plain,(
% 156.17/20.13 ![X0,X1,X2]: (c_Nitpick_Orefl_H(X0,X1)|~c_in(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X0,X1),X2,X1)|~c_Relation_Orefl__on(X2,X0,X1))),
% 156.17/20.13 inference(resolution,[status(thm)],[f1294,f1646])).
% 156.17/20.13 fof(f73824,plain,(
% 156.17/20.13 ![X0,X1,X2]: (c_Nitpick_Orefl_H(X0,X1)|~c_Relation_Orefl__on(c_Relation_ODomain(X2,X1,X1),X0,X1)|~c_Nitpick_Orefl_H(X2,X1))),
% 156.17/20.13 inference(resolution,[status(thm)],[f73266,f51612])).
% 156.17/20.13 fof(f73929,plain,(
% 156.17/20.13 ![X0,X1,X2]: (c_Nitpick_Orefl_H(c_Relation_Oconverse(X0,X1,X1),X1)|~c_Nitpick_Orefl_H(X0,X1)|~c_Equiv__Relations_Oequiv(X2,X0,X1))),
% 156.17/20.13 inference(resolution,[status(thm)],[f73824,f25064])).
% 156.17/20.13 fof(f74068,plain,(
% 156.17/20.13 ~hBOOL(hAPP(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____,v_b_H____)),c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|spl0_601),
% 156.17/20.13 inference(resolution,[status(thm)],[f61433,f1664])).
% 156.17/20.13 fof(f74069,plain,(
% 156.17/20.13 ~spl0_505|spl0_601),
% 156.17/20.13 inference(split_clause,[status(thm)],[f74068,f60058,f61431])).
% 156.17/20.13 fof(f74198,plain,(
% 156.17/20.13 ![X0]: (~c_Nitpick_Orefl_H(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|~c_Equiv__Relations_Oequiv(X0,v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)|spl0_196)),
% 156.17/20.13 inference(resolution,[status(thm)],[f73929,f69527])).
% 156.17/20.13 fof(f74199,plain,(
% 156.17/20.13 ~spl0_677|spl0_187|spl0_196),
% 156.17/20.13 inference(split_clause,[status(thm)],[f74198,f62563,f50292,f50758])).
% 156.17/20.13 fof(f74806,plain,(
% 156.17/20.13 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____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))|~c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))|v_a____=v_b_H____|v_a____=v_b____|spl0_508|~spl0_291),
% 156.17/20.13 inference(resolution,[status(thm)],[f60071,f54458])).
% 156.17/20.13 fof(f74807,plain,(
% 156.17/20.13 spl0_1|spl0_508|~spl0_258|spl0_3|spl0_110|~spl0_291),
% 156.17/20.13 inference(split_clause,[status(thm)],[f74806,f1723,f60069,f54278,f1729,f42998,f54457])).
% 156.17/20.13 fof(f74808,plain,(
% 156.17/20.13 $false),
% 156.17/20.13 inference(sat_refutation,[status(thm)],[f1732,f1736,f1737,f1753,f1772,f1787,f2098,f3443,f3445,f4330,f7955,f7957,f7965,f7981,f8064,f8067,f12091,f24074,f27197,f29896,f30546,f30858,f31092,f31099,f31205,f31329,f35924,f37259,f37322,f37923,f39713,f39929,f40136,f41112,f41294,f41562,f42387,f42992,f42997,f43005,f43010,f43054,f44486,f44892,f45383,f47440,f47445,f47450,f47460,f47473,f47478,f47485,f47642,f47649,f47662,f47667,f47691,f47701,f47706,f47933,f47983,f48161,f49391,f49396,f49404,f49606,f50074,f50082,f50308,f50511,f51060,f51066,f51193,f51887,f51891,f51940,f52654,f52659,f52665,f52670,f52675,f52680,f52685,f52690,f52695,f52700,f52705,f52710,f52715,f52720,f52725,f52730,f52735,f52740,f52745,f52750,f52755,f52760,f52975,f52980,f52987,f52992,f53024,f53029,f53078,f53127,f53150,f53158,f53640,f53734,f54263,f54268,f54282,f54287,f54293,f54300,f54305,f54316,f54321,f54331,f54336,f54341,f54346,f54351,f54356,f54361,f54366,f54371,f54376,f54381,f54386,f54391,f54396,f54401,f54406,f54411,f54416,f54421,f54426,f54431,f54436,f54441,f54446,f54451,f54461,f54466,f54487,f54753,f54861,f54866,f54968,f54973,f54978,f54983,f54988,f54993,f54998,f55003,f55008,f55013,f55018,f55023,f55028,f55033,f55038,f55043,f55048,f55053,f55058,f55063,f55068,f55073,f55078,f55083,f55098,f55314,f55319,f55324,f55390,f55395,f55400,f55426,f55431,f55642,f55647,f55974,f55998,f56003,f56037,f56042,f56067,f56072,f56097,f56102,f56159,f56189,f56194,f56319,f56324,f56344,f56349,f56631,f56636,f56724,f56729,f56756,f56761,f56792,f56797,f56822,f56827,f56852,f56857,f56899,f56904,f56958,f56963,f57004,f57009,f57475,f57480,f57551,f57556,f57632,f57637,f57679,f57684,f58076,f58081,f58086,f58091,f58096,f58113,f58118,f58123,f58128,f58138,f58148,f58153,f58158,f58163,f58168,f58175,f58245,f58250,f58293,f58298,f58330,f58335,f58362,f58417,f58422,f58465,f58470,f58512,f58517,f58544,f58549,f58607,f58612,f58617,f58632,f58637,f58642,f59339,f59344,f59373,f59378,f59407,f59412,f59501,f59525,f59530,f59535,f59561,f59566,f59571,f59714,f59719,f59724,f59729,f59746,f59751,f59756,f59761,f59766,f59771,f59776,f59781,f60073,f60078,f60125,f60132,f60137,f60171,f60176,f60196,f60203,f60469,f61435,f61746,f61758,f61763,f61847,f62099,f62104,f62150,f62155,f62420,f62471,f62482,f62484,f62528,f62531,f62533,f62535,f62557,f62567,f62575,f62582,f62585,f62588,f62591,f62594,f62596,f62665,f62891,f63052,f63072,f63078,f63084,f63090,f63095,f63097,f63102,f63110,f63115,f63123,f63134,f63138,f63140,f63194,f63212,f63293,f63601,f63603,f63621,f63633,f63902,f63917,f63922,f64067,f64073,f64221,f64233,f64445,f64480,f64485,f64499,f64504,f64509,f64514,f64555,f64560,f64574,f64579,f64584,f64589,f64615,f64620,f64634,f64639,f64644,f64649,f64663,f64988,f64993,f65007,f65012,f65017,f65022,f65030,f65046,f65049,f65071,f65076,f65090,f65095,f65100,f65105,f65131,f65136,f65150,f65155,f65160,f65165,f65171,f65225,f65230,f65244,f65249,f65254,f65259,f65285,f65290,f65304,f65309,f65314,f65319,f65342,f65347,f65361,f65366,f65371,f65376,f65745,f65750,f65764,f65769,f65774,f65779,f65798,f65803,f65808,f65822,f65827,f65832,f65837,f65874,f65879,f65884,f65898,f65903,f65908,f65913,f65945,f65967,f66382,f66387,f66392,f66397,f66422,f66469,f66474,f66479,f66484,f66528,f66550,f66563,f66887,f68494,f68803,f68808,f68832,f68837,f68881,f68895,f68900,f68905,f68910,f68925,f68939,f68944,f68949,f68954,f69215,f69221,f69226,f69232,f69294,f69300,f69305,f69310,f69337,f69344,f69346,f69348,f69350,f69534,f69692,f69723,f69728,f70225,f70226,f70243,f70270,f70318,f70357,f70450,f71059,f71064,f71069,f71124,f71133,f71154,f71248,f71262,f71292,f71297,f71299,f71304,f71315,f71337,f71358,f71380,f71398,f71443,f71465,f71942,f71944,f71946,f72003,f72013,f72025,f72060,f72062,f72064,f72121,f72131,f72143,f74069,f74199,f74807])).
% 157.18/20.26 % SZS output end CNFRefutation for theBenchmark.p
% 158.44/20.77 % Elapsed time: 20.391282 seconds
% 158.44/20.77 % CPU time: 157.600072 seconds
% 158.44/20.77 % Total memory used: 1.409 GB
% 158.44/20.77 % Net memory used: 1.382 GB
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