TSTP Solution File: SCT122+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SCT122+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n026.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 : Wed May 31 12:33:14 EDT 2023
% Result : Theorem 11.19s 1.84s
% Output : CNFRefutation 11.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SCT122+1 : TPTP v8.1.2. Released v5.2.0.
% 0.10/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue May 30 09:52:43 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.39 % Drodi V3.5.1
% 11.19/1.84 % Refutation found
% 11.19/1.84 % SZS status Theorem for theBenchmark: Theorem is valid
% 11.19/1.84 % SZS output start CNFRefutation for theBenchmark
% 11.19/1.84 fof(f3,axiom,(
% 11.19/1.84 (! [V_r_2,T_a] :( c_Relation_Oirrefl(T_a,V_r_2)<=> (! [B_x] : ~ c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_x),V_r_2) )) )),
% 11.19/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.19/1.84 fof(f4,axiom,(
% 11.19/1.84 (! [V_r_2,V_A_2,T_a] :( c_Relation_Ototal__on(T_a,V_A_2,V_r_2)<=> (! [B_x] :( c_member(T_a,B_x,V_A_2)=> (! [B_xa] :( c_member(T_a,B_xa,V_A_2)=> ( B_x != B_xa=> ( c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_xa),V_r_2)| c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_xa,B_x),V_r_2) ) ) ) )) )) )),
% 11.19/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.19/1.84 fof(f5,axiom,(
% 11.19/1.84 (! [V_r_2,T_a] :( c_Relation_Otrans(T_a,V_r_2)<=> (! [B_x,B_y] :( c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_y),V_r_2)=> (! [B_z] :( c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,B_z),V_r_2)=> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_z),V_r_2) ) )) )) )),
% 11.19/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.19/1.84 fof(f7,axiom,(
% 11.19/1.84 (! [V_x_2,T_a] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) )),
% 11.19/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.19/1.84 fof(f17,axiom,(
% 11.19/1.84 (! [V_y_2,V_x_2,T_a] :( c_member(T_a,V_x_2,c_fequal(V_y_2))<=> V_x_2 = V_y_2 ) )),
% 11.19/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.19/1.84 fof(f18,axiom,(
% 11.19/1.84 (! [V_A_2,V_x_2,T_a] :( c_member(T_a,V_x_2,V_A_2)<=> hBOOL(hAPP(V_A_2,V_x_2)) ) )),
% 11.19/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.19/1.84 fof(f19,axiom,(
% 11.19/1.84 (! [V_y_2,V_x_2,V_R_2,T_b,T_a] :( c_FunDef_Oin__rel(T_a,T_b,V_R_2,V_x_2,V_y_2)<=> c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_x_2,V_y_2),V_R_2) ) )),
% 11.19/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.19/1.84 fof(f22,axiom,(
% 11.19/1.84 (! [V_A_2,T_a,V_b_2,V_a_2] :( V_a_2 = V_b_2=> ( c_member(T_a,V_a_2,V_A_2)=> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Relation_OId__on(T_a,V_A_2)) ) ) )),
% 11.19/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.19/1.84 fof(f24,axiom,(
% 11.19/1.84 (! [V_r_2,V_b_2,V_a_2,T_b,T_a] :( c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),V_r_2)=> c_member(T_a,V_a_2,c_Relation_ODomain(T_a,T_b,V_r_2)) ) )),
% 11.19/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.19/1.84 fof(f31,axiom,(
% 11.19/1.84 (! [V_A_2,T_a] : c_Relation_ODomain(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)) = V_A_2 )),
% 11.19/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.19/1.84 fof(f43,axiom,(
% 11.19/1.84 (! [V_A_2,V_c_2,T_a] :( c_member(tc_prod(T_a,T_a),V_c_2,c_Relation_OId__on(T_a,V_A_2))=> ~ (! [B_x] :( c_member(T_a,B_x,V_A_2)=> V_c_2 != c_Product__Type_OPair(T_a,T_a,B_x,B_x) ) )) )),
% 11.19/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.19/1.84 fof(f53,axiom,(
% 11.19/1.84 (! [V_r_2,V_a_2,T_a] :( c_member(T_a,V_a_2,c_Wellfounded_Oacc(T_a,V_r_2))<=> (! [B_x] :( c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,V_a_2),V_r_2)=> c_member(T_a,B_x,c_Wellfounded_Oacc(T_a,V_r_2)) ) )) )),
% 11.19/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.19/1.84 fof(f99,axiom,(
% 11.19/1.84 (! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :( c_Product__Type_OPair(T_a,T_b,V_a,V_b) = c_Product__Type_OPair(T_a,T_b,V_a_H,V_b_H)=> ~ ( V_a = V_a_H=> V_b != V_b_H ) ) )),
% 11.19/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.19/1.84 fof(f225,axiom,(
% 11.19/1.84 (! [V_a_2,T_a] : ~ c_member(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) )),
% 11.19/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.19/1.84 fof(f335,axiom,(
% 11.19/1.84 (! [V_a_2,V_r_2,T_a] :( c_Wellfounded_Owf(T_a,V_r_2)=> ~ c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_a_2),V_r_2) ) )),
% 11.19/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.19/1.84 fof(f345,axiom,(
% 11.19/1.84 (! [V_r_2,T_a] :( c_Wellfounded_Owf(T_a,V_r_2)<=> (! [B_x] : c_member(T_a,B_x,c_Wellfounded_Oacc(T_a,V_r_2)) )) )),
% 11.19/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.19/1.84 fof(f495,axiom,(
% 11.19/1.84 class_Lattices_Obounded__lattice(tc_HOL_Obool) ),
% 11.19/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.19/1.84 fof(f497,axiom,(
% 11.19/1.84 (! [T_2,T_1] :( class_Lattices_Obounded__lattice(T_1)=> class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) )),
% 11.19/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.19/1.84 fof(f498,axiom,(
% 11.19/1.84 (! [T_2,T_1] :( class_Lattices_Obounded__lattice(T_1)=> class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) )),
% 11.19/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.19/1.84 fof(f523,hypothesis,(
% 11.19/1.84 (! [B_x] :( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,B_x))& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,B_x))& c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,B_x)) ) )),
% 11.19/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.19/1.84 fof(f524,hypothesis,(
% 11.19/1.84 c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),v_F(v_P)) ),
% 11.19/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.19/1.84 fof(f525,hypothesis,(
% 11.19/1.84 ( (! [B_x] :( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,B_x))& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,B_x))& c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,B_x)) ))=> ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))& c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),v_F(v_P)) ) ) ),
% 11.19/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.19/1.84 fof(f526,hypothesis,(
% 11.19/1.84 ( (! [B_x] :( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,B_x))& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,B_x))& c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,B_x)) ))=> (! [B_a,B_b] :( B_a != B_b=> ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B_a,B_b),hAPP(v_P,v_i))=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B_a,B_b),v_F(v_P)) ) ) )) ),
% 11.19/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.19/1.84 fof(f527,conjecture,(
% 11.19/1.84 c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),hAPP(v_P,v_i)) ),
% 11.19/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.19/1.84 fof(f528,negated_conjecture,(
% 11.19/1.84 ~(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),hAPP(v_P,v_i)) )),
% 11.19/1.84 inference(negated_conjecture,[status(cth)],[f527])).
% 11.19/1.84 fof(f533,plain,(
% 11.19/1.84 ![V_r_2,T_a]: ((~c_Relation_Oirrefl(T_a,V_r_2)|(![B_x]: ~c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_x),V_r_2)))&(c_Relation_Oirrefl(T_a,V_r_2)|(?[B_x]: c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_x),V_r_2))))),
% 11.19/1.84 inference(NNF_transformation,[status(esa)],[f3])).
% 11.19/1.84 fof(f534,plain,(
% 11.19/1.84 (![V_r_2,T_a]: (~c_Relation_Oirrefl(T_a,V_r_2)|(![B_x]: ~c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_x),V_r_2))))&(![V_r_2,T_a]: (c_Relation_Oirrefl(T_a,V_r_2)|(?[B_x]: c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_x),V_r_2))))),
% 11.19/1.84 inference(miniscoping,[status(esa)],[f533])).
% 11.19/1.84 fof(f535,plain,(
% 11.19/1.84 (![V_r_2,T_a]: (~c_Relation_Oirrefl(T_a,V_r_2)|(![B_x]: ~c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_x),V_r_2))))&(![V_r_2,T_a]: (c_Relation_Oirrefl(T_a,V_r_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,sk0_1(T_a,V_r_2),sk0_1(T_a,V_r_2)),V_r_2)))),
% 11.19/1.84 inference(skolemization,[status(esa)],[f534])).
% 11.19/1.84 fof(f536,plain,(
% 11.19/1.84 ![X0,X1,X2]: (~c_Relation_Oirrefl(X0,X1)|~c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,X2,X2),X1))),
% 11.19/1.84 inference(cnf_transformation,[status(esa)],[f535])).
% 11.19/1.84 fof(f538,plain,(
% 11.19/1.84 ![V_r_2,V_A_2,T_a]: (c_Relation_Ototal__on(T_a,V_A_2,V_r_2)<=>(![B_x]: (~c_member(T_a,B_x,V_A_2)|(![B_xa]: (~c_member(T_a,B_xa,V_A_2)|(B_x=B_xa|(c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_xa),V_r_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_xa,B_x),V_r_2))))))))),
% 11.19/1.84 inference(pre_NNF_transformation,[status(esa)],[f4])).
% 11.19/1.84 fof(f539,plain,(
% 11.19/1.84 ![V_r_2,V_A_2,T_a]: ((~c_Relation_Ototal__on(T_a,V_A_2,V_r_2)|(![B_x]: (~c_member(T_a,B_x,V_A_2)|(![B_xa]: (~c_member(T_a,B_xa,V_A_2)|(B_x=B_xa|(c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_xa),V_r_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_xa,B_x),V_r_2))))))))&(c_Relation_Ototal__on(T_a,V_A_2,V_r_2)|(?[B_x]: (c_member(T_a,B_x,V_A_2)&(?[B_xa]: (c_member(T_a,B_xa,V_A_2)&(~B_x=B_xa&(~c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_xa),V_r_2)&~c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_xa,B_x),V_r_2)))))))))),
% 11.19/1.84 inference(NNF_transformation,[status(esa)],[f538])).
% 11.19/1.84 fof(f540,plain,(
% 11.19/1.84 (![V_r_2,V_A_2,T_a]: (~c_Relation_Ototal__on(T_a,V_A_2,V_r_2)|(![B_x]: (~c_member(T_a,B_x,V_A_2)|(![B_xa]: (~c_member(T_a,B_xa,V_A_2)|(B_x=B_xa|(c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_xa),V_r_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_xa,B_x),V_r_2)))))))))&(![V_r_2,V_A_2,T_a]: (c_Relation_Ototal__on(T_a,V_A_2,V_r_2)|(?[B_x]: (c_member(T_a,B_x,V_A_2)&(?[B_xa]: (c_member(T_a,B_xa,V_A_2)&(~B_x=B_xa&(~c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_xa),V_r_2)&~c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_xa,B_x),V_r_2)))))))))),
% 11.19/1.84 inference(miniscoping,[status(esa)],[f539])).
% 11.19/1.84 fof(f541,plain,(
% 11.19/1.84 (![V_r_2,V_A_2,T_a]: (~c_Relation_Ototal__on(T_a,V_A_2,V_r_2)|(![B_x]: (~c_member(T_a,B_x,V_A_2)|(![B_xa]: (~c_member(T_a,B_xa,V_A_2)|(B_x=B_xa|(c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_xa),V_r_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_xa,B_x),V_r_2)))))))))&(![V_r_2,V_A_2,T_a]: (c_Relation_Ototal__on(T_a,V_A_2,V_r_2)|(c_member(T_a,sk0_2(T_a,V_A_2,V_r_2),V_A_2)&(c_member(T_a,sk0_3(T_a,V_A_2,V_r_2),V_A_2)&(~sk0_2(T_a,V_A_2,V_r_2)=sk0_3(T_a,V_A_2,V_r_2)&(~c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,sk0_2(T_a,V_A_2,V_r_2),sk0_3(T_a,V_A_2,V_r_2)),V_r_2)&~c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,sk0_3(T_a,V_A_2,V_r_2),sk0_2(T_a,V_A_2,V_r_2)),V_r_2)))))))),
% 11.19/1.84 inference(skolemization,[status(esa)],[f540])).
% 11.19/1.84 fof(f542,plain,(
% 11.19/1.84 ![X0,X1,X2,X3,X4]: (~c_Relation_Ototal__on(X0,X1,X2)|~c_member(X0,X3,X1)|~c_member(X0,X4,X1)|X3=X4|c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,X3,X4),X2)|c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,X4,X3),X2))),
% 11.19/1.84 inference(cnf_transformation,[status(esa)],[f541])).
% 11.19/1.84 fof(f548,plain,(
% 11.19/1.84 ![V_r_2,T_a]: (c_Relation_Otrans(T_a,V_r_2)<=>(![B_x,B_y]: (~c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_y),V_r_2)|(![B_z]: (~c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,B_z),V_r_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_z),V_r_2))))))),
% 11.19/1.84 inference(pre_NNF_transformation,[status(esa)],[f5])).
% 11.19/1.84 fof(f549,plain,(
% 11.19/1.84 ![V_r_2,T_a]: ((~c_Relation_Otrans(T_a,V_r_2)|(![B_x,B_y]: (~c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_y),V_r_2)|(![B_z]: (~c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,B_z),V_r_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_z),V_r_2))))))&(c_Relation_Otrans(T_a,V_r_2)|(?[B_x,B_y]: (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_y),V_r_2)&(?[B_z]: (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,B_z),V_r_2)&~c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_z),V_r_2)))))))),
% 11.19/1.84 inference(NNF_transformation,[status(esa)],[f548])).
% 11.19/1.84 fof(f550,plain,(
% 11.19/1.84 (![V_r_2,T_a]: (~c_Relation_Otrans(T_a,V_r_2)|(![B_x,B_y]: (~c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_y),V_r_2)|(![B_z]: (~c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,B_z),V_r_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_z),V_r_2)))))))&(![V_r_2,T_a]: (c_Relation_Otrans(T_a,V_r_2)|(?[B_x,B_y]: (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_y),V_r_2)&(?[B_z]: (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,B_z),V_r_2)&~c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_z),V_r_2)))))))),
% 11.19/1.84 inference(miniscoping,[status(esa)],[f549])).
% 11.19/1.84 fof(f551,plain,(
% 11.19/1.84 (![V_r_2,T_a]: (~c_Relation_Otrans(T_a,V_r_2)|(![B_x,B_y]: (~c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_y),V_r_2)|(![B_z]: (~c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,B_z),V_r_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_z),V_r_2)))))))&(![V_r_2,T_a]: (c_Relation_Otrans(T_a,V_r_2)|(c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,sk0_4(T_a,V_r_2),sk0_5(T_a,V_r_2)),V_r_2)&(c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,sk0_5(T_a,V_r_2),sk0_6(T_a,V_r_2)),V_r_2)&~c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,sk0_4(T_a,V_r_2),sk0_6(T_a,V_r_2)),V_r_2)))))),
% 11.19/1.84 inference(skolemization,[status(esa)],[f550])).
% 11.19/1.84 fof(f552,plain,(
% 11.19/1.84 ![X0,X1,X2,X3,X4]: (~c_Relation_Otrans(X0,X1)|~c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,X2,X3),X1)|~c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,X3,X4),X1)|c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,X2,X4),X1))),
% 11.19/1.84 inference(cnf_transformation,[status(esa)],[f551])).
% 11.19/1.84 fof(f559,plain,(
% 11.19/1.84 ![X0,X1]: (hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)),X1)))),
% 11.19/1.84 inference(cnf_transformation,[status(esa)],[f7])).
% 11.19/1.84 fof(f609,plain,(
% 11.19/1.84 ![V_y_2,V_x_2,T_a]: ((~c_member(T_a,V_x_2,c_fequal(V_y_2))|V_x_2=V_y_2)&(c_member(T_a,V_x_2,c_fequal(V_y_2))|~V_x_2=V_y_2))),
% 11.19/1.84 inference(NNF_transformation,[status(esa)],[f17])).
% 11.19/1.84 fof(f610,plain,(
% 11.19/1.84 (![V_y_2,V_x_2]: ((![T_a]: ~c_member(T_a,V_x_2,c_fequal(V_y_2)))|V_x_2=V_y_2))&(![V_y_2,V_x_2]: ((![T_a]: c_member(T_a,V_x_2,c_fequal(V_y_2)))|~V_x_2=V_y_2))),
% 11.19/1.84 inference(miniscoping,[status(esa)],[f609])).
% 11.19/1.84 fof(f612,plain,(
% 11.19/1.84 ![X0,X1,X2]: (c_member(X0,X1,c_fequal(X2))|~X1=X2)),
% 11.19/1.84 inference(cnf_transformation,[status(esa)],[f610])).
% 11.19/1.84 fof(f613,plain,(
% 11.19/1.84 ![V_A_2,V_x_2,T_a]: ((~c_member(T_a,V_x_2,V_A_2)|hBOOL(hAPP(V_A_2,V_x_2)))&(c_member(T_a,V_x_2,V_A_2)|~hBOOL(hAPP(V_A_2,V_x_2))))),
% 11.19/1.84 inference(NNF_transformation,[status(esa)],[f18])).
% 11.19/1.84 fof(f614,plain,(
% 11.19/1.84 (![V_A_2,V_x_2]: ((![T_a]: ~c_member(T_a,V_x_2,V_A_2))|hBOOL(hAPP(V_A_2,V_x_2))))&(![V_A_2,V_x_2]: ((![T_a]: c_member(T_a,V_x_2,V_A_2))|~hBOOL(hAPP(V_A_2,V_x_2))))),
% 11.19/1.84 inference(miniscoping,[status(esa)],[f613])).
% 11.19/1.84 fof(f615,plain,(
% 11.19/1.84 ![X0,X1,X2]: (~c_member(X0,X1,X2)|hBOOL(hAPP(X2,X1)))),
% 11.19/1.84 inference(cnf_transformation,[status(esa)],[f614])).
% 11.19/1.84 fof(f616,plain,(
% 11.19/1.84 ![X0,X1,X2]: (c_member(X0,X1,X2)|~hBOOL(hAPP(X2,X1)))),
% 11.19/1.84 inference(cnf_transformation,[status(esa)],[f614])).
% 11.19/1.84 fof(f617,plain,(
% 11.19/1.84 ![V_y_2,V_x_2,V_R_2,T_b,T_a]: ((~c_FunDef_Oin__rel(T_a,T_b,V_R_2,V_x_2,V_y_2)|c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_x_2,V_y_2),V_R_2))&(c_FunDef_Oin__rel(T_a,T_b,V_R_2,V_x_2,V_y_2)|~c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_x_2,V_y_2),V_R_2)))),
% 11.19/1.84 inference(NNF_transformation,[status(esa)],[f19])).
% 11.19/1.84 fof(f618,plain,(
% 11.19/1.84 (![V_y_2,V_x_2,V_R_2,T_b,T_a]: (~c_FunDef_Oin__rel(T_a,T_b,V_R_2,V_x_2,V_y_2)|c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_x_2,V_y_2),V_R_2)))&(![V_y_2,V_x_2,V_R_2,T_b,T_a]: (c_FunDef_Oin__rel(T_a,T_b,V_R_2,V_x_2,V_y_2)|~c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_x_2,V_y_2),V_R_2)))),
% 11.19/1.84 inference(miniscoping,[status(esa)],[f617])).
% 11.19/1.84 fof(f619,plain,(
% 11.19/1.84 ![X0,X1,X2,X3,X4]: (~c_FunDef_Oin__rel(X0,X1,X2,X3,X4)|c_member(tc_prod(X0,X1),c_Product__Type_OPair(X0,X1,X3,X4),X2))),
% 11.19/1.84 inference(cnf_transformation,[status(esa)],[f618])).
% 11.19/1.84 fof(f620,plain,(
% 11.19/1.84 ![X0,X1,X2,X3,X4]: (c_FunDef_Oin__rel(X0,X1,X2,X3,X4)|~c_member(tc_prod(X0,X1),c_Product__Type_OPair(X0,X1,X3,X4),X2))),
% 11.19/1.84 inference(cnf_transformation,[status(esa)],[f618])).
% 11.19/1.84 fof(f627,plain,(
% 11.19/1.84 ![V_A_2,T_a,V_b_2,V_a_2]: (~V_a_2=V_b_2|(~c_member(T_a,V_a_2,V_A_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Relation_OId__on(T_a,V_A_2))))),
% 11.19/1.84 inference(pre_NNF_transformation,[status(esa)],[f22])).
% 11.19/1.84 fof(f628,plain,(
% 11.19/1.84 ![V_b_2,V_a_2]: (~V_a_2=V_b_2|(![V_A_2,T_a]: (~c_member(T_a,V_a_2,V_A_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Relation_OId__on(T_a,V_A_2)))))),
% 11.19/1.84 inference(miniscoping,[status(esa)],[f627])).
% 11.19/1.84 fof(f629,plain,(
% 11.19/1.84 ![X0,X1,X2,X3]: (~X0=X1|~c_member(X2,X0,X3)|c_member(tc_prod(X2,X2),c_Product__Type_OPair(X2,X2,X0,X1),c_Relation_OId__on(X2,X3)))),
% 11.19/1.84 inference(cnf_transformation,[status(esa)],[f628])).
% 11.19/1.84 fof(f635,plain,(
% 11.19/1.84 ![V_r_2,V_b_2,V_a_2,T_b,T_a]: (~c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),V_r_2)|c_member(T_a,V_a_2,c_Relation_ODomain(T_a,T_b,V_r_2)))),
% 11.19/1.84 inference(pre_NNF_transformation,[status(esa)],[f24])).
% 11.19/1.84 fof(f636,plain,(
% 11.19/1.84 ![V_r_2,V_a_2,T_b,T_a]: ((![V_b_2]: ~c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),V_r_2))|c_member(T_a,V_a_2,c_Relation_ODomain(T_a,T_b,V_r_2)))),
% 11.19/1.84 inference(miniscoping,[status(esa)],[f635])).
% 11.19/1.84 fof(f637,plain,(
% 11.19/1.84 ![X0,X1,X2,X3,X4]: (~c_member(tc_prod(X0,X1),c_Product__Type_OPair(X0,X1,X2,X3),X4)|c_member(X0,X2,c_Relation_ODomain(X0,X1,X4)))),
% 11.19/1.84 inference(cnf_transformation,[status(esa)],[f636])).
% 11.19/1.84 fof(f661,plain,(
% 11.19/1.84 ![X0,X1]: (c_Relation_ODomain(X0,X0,c_Relation_OId__on(X0,X1))=X1)),
% 11.19/1.84 inference(cnf_transformation,[status(esa)],[f31])).
% 11.19/1.84 fof(f736,plain,(
% 11.19/1.84 ![V_A_2,V_c_2,T_a]: (~c_member(tc_prod(T_a,T_a),V_c_2,c_Relation_OId__on(T_a,V_A_2))|(?[B_x]: (c_member(T_a,B_x,V_A_2)&V_c_2=c_Product__Type_OPair(T_a,T_a,B_x,B_x))))),
% 11.19/1.84 inference(pre_NNF_transformation,[status(esa)],[f43])).
% 11.19/1.84 fof(f737,plain,(
% 11.19/1.84 ![V_A_2,V_c_2,T_a]: (~c_member(tc_prod(T_a,T_a),V_c_2,c_Relation_OId__on(T_a,V_A_2))|(c_member(T_a,sk0_13(T_a,V_c_2,V_A_2),V_A_2)&V_c_2=c_Product__Type_OPair(T_a,T_a,sk0_13(T_a,V_c_2,V_A_2),sk0_13(T_a,V_c_2,V_A_2))))),
% 11.19/1.84 inference(skolemization,[status(esa)],[f736])).
% 11.19/1.84 fof(f739,plain,(
% 11.19/1.84 ![X0,X1,X2]: (~c_member(tc_prod(X0,X0),X1,c_Relation_OId__on(X0,X2))|X1=c_Product__Type_OPair(X0,X0,sk0_13(X0,X1,X2),sk0_13(X0,X1,X2)))),
% 11.19/1.84 inference(cnf_transformation,[status(esa)],[f737])).
% 11.19/1.84 fof(f767,plain,(
% 11.19/1.84 ![V_r_2,V_a_2,T_a]: (c_member(T_a,V_a_2,c_Wellfounded_Oacc(T_a,V_r_2))<=>(![B_x]: (~c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,V_a_2),V_r_2)|c_member(T_a,B_x,c_Wellfounded_Oacc(T_a,V_r_2)))))),
% 11.19/1.84 inference(pre_NNF_transformation,[status(esa)],[f53])).
% 11.19/1.84 fof(f768,plain,(
% 11.19/1.84 ![V_r_2,V_a_2,T_a]: ((~c_member(T_a,V_a_2,c_Wellfounded_Oacc(T_a,V_r_2))|(![B_x]: (~c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,V_a_2),V_r_2)|c_member(T_a,B_x,c_Wellfounded_Oacc(T_a,V_r_2)))))&(c_member(T_a,V_a_2,c_Wellfounded_Oacc(T_a,V_r_2))|(?[B_x]: (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,V_a_2),V_r_2)&~c_member(T_a,B_x,c_Wellfounded_Oacc(T_a,V_r_2))))))),
% 11.19/1.84 inference(NNF_transformation,[status(esa)],[f767])).
% 11.19/1.84 fof(f769,plain,(
% 11.19/1.84 (![V_r_2,V_a_2,T_a]: (~c_member(T_a,V_a_2,c_Wellfounded_Oacc(T_a,V_r_2))|(![B_x]: (~c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,V_a_2),V_r_2)|c_member(T_a,B_x,c_Wellfounded_Oacc(T_a,V_r_2))))))&(![V_r_2,V_a_2,T_a]: (c_member(T_a,V_a_2,c_Wellfounded_Oacc(T_a,V_r_2))|(?[B_x]: (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,V_a_2),V_r_2)&~c_member(T_a,B_x,c_Wellfounded_Oacc(T_a,V_r_2))))))),
% 11.19/1.84 inference(miniscoping,[status(esa)],[f768])).
% 11.19/1.84 fof(f770,plain,(
% 11.19/1.84 (![V_r_2,V_a_2,T_a]: (~c_member(T_a,V_a_2,c_Wellfounded_Oacc(T_a,V_r_2))|(![B_x]: (~c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,V_a_2),V_r_2)|c_member(T_a,B_x,c_Wellfounded_Oacc(T_a,V_r_2))))))&(![V_r_2,V_a_2,T_a]: (c_member(T_a,V_a_2,c_Wellfounded_Oacc(T_a,V_r_2))|(c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,sk0_16(T_a,V_a_2,V_r_2),V_a_2),V_r_2)&~c_member(T_a,sk0_16(T_a,V_a_2,V_r_2),c_Wellfounded_Oacc(T_a,V_r_2)))))),
% 11.19/1.84 inference(skolemization,[status(esa)],[f769])).
% 11.19/1.84 fof(f772,plain,(
% 11.19/1.84 ![X0,X1,X2]: (c_member(X0,X1,c_Wellfounded_Oacc(X0,X2))|c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,sk0_16(X0,X1,X2),X1),X2))),
% 11.19/1.84 inference(cnf_transformation,[status(esa)],[f770])).
% 11.19/1.84 fof(f921,plain,(
% 11.19/1.84 ![V_b_H,V_a_H,V_b,V_a,T_b,T_a]: (~c_Product__Type_OPair(T_a,T_b,V_a,V_b)=c_Product__Type_OPair(T_a,T_b,V_a_H,V_b_H)|(V_a=V_a_H&V_b=V_b_H))),
% 11.19/1.84 inference(pre_NNF_transformation,[status(esa)],[f99])).
% 11.19/1.84 fof(f922,plain,(
% 11.19/1.84 ![V_b_H,V_a_H,V_b,V_a]: ((![T_b,T_a]: ~c_Product__Type_OPair(T_a,T_b,V_a,V_b)=c_Product__Type_OPair(T_a,T_b,V_a_H,V_b_H))|(V_a=V_a_H&V_b=V_b_H))),
% 11.19/1.84 inference(miniscoping,[status(esa)],[f921])).
% 11.19/1.84 fof(f924,plain,(
% 11.19/1.84 ![X0,X1,X2,X3,X4,X5]: (~c_Product__Type_OPair(X0,X1,X2,X3)=c_Product__Type_OPair(X0,X1,X4,X5)|X3=X5)),
% 11.19/1.84 inference(cnf_transformation,[status(esa)],[f922])).
% 11.19/1.84 fof(f1268,plain,(
% 11.19/1.84 ![X0,X1]: (~c_member(X0,X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))))),
% 11.19/1.84 inference(cnf_transformation,[status(esa)],[f225])).
% 11.19/1.84 fof(f1569,plain,(
% 11.19/1.84 ![V_a_2,V_r_2,T_a]: (~c_Wellfounded_Owf(T_a,V_r_2)|~c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_a_2),V_r_2))),
% 11.19/1.84 inference(pre_NNF_transformation,[status(esa)],[f335])).
% 11.19/1.84 fof(f1570,plain,(
% 11.19/1.84 ![V_r_2,T_a]: (~c_Wellfounded_Owf(T_a,V_r_2)|(![V_a_2]: ~c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_a_2),V_r_2)))),
% 11.19/1.84 inference(miniscoping,[status(esa)],[f1569])).
% 11.19/1.84 fof(f1571,plain,(
% 11.19/1.84 ![X0,X1,X2]: (~c_Wellfounded_Owf(X0,X1)|~c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,X2,X2),X1))),
% 11.19/1.84 inference(cnf_transformation,[status(esa)],[f1570])).
% 11.19/1.84 fof(f1604,plain,(
% 11.19/1.84 ![V_r_2,T_a]: ((~c_Wellfounded_Owf(T_a,V_r_2)|(![B_x]: c_member(T_a,B_x,c_Wellfounded_Oacc(T_a,V_r_2))))&(c_Wellfounded_Owf(T_a,V_r_2)|(?[B_x]: ~c_member(T_a,B_x,c_Wellfounded_Oacc(T_a,V_r_2)))))),
% 11.19/1.84 inference(NNF_transformation,[status(esa)],[f345])).
% 11.19/1.84 fof(f1605,plain,(
% 11.19/1.84 (![V_r_2,T_a]: (~c_Wellfounded_Owf(T_a,V_r_2)|(![B_x]: c_member(T_a,B_x,c_Wellfounded_Oacc(T_a,V_r_2)))))&(![V_r_2,T_a]: (c_Wellfounded_Owf(T_a,V_r_2)|(?[B_x]: ~c_member(T_a,B_x,c_Wellfounded_Oacc(T_a,V_r_2)))))),
% 11.19/1.84 inference(miniscoping,[status(esa)],[f1604])).
% 11.19/1.84 fof(f1606,plain,(
% 11.19/1.84 (![V_r_2,T_a]: (~c_Wellfounded_Owf(T_a,V_r_2)|(![B_x]: c_member(T_a,B_x,c_Wellfounded_Oacc(T_a,V_r_2)))))&(![V_r_2,T_a]: (c_Wellfounded_Owf(T_a,V_r_2)|~c_member(T_a,sk0_74(T_a,V_r_2),c_Wellfounded_Oacc(T_a,V_r_2))))),
% 11.19/1.84 inference(skolemization,[status(esa)],[f1605])).
% 11.19/1.84 fof(f1608,plain,(
% 11.19/1.84 ![X0,X1]: (c_Wellfounded_Owf(X0,X1)|~c_member(X0,sk0_74(X0,X1),c_Wellfounded_Oacc(X0,X1)))),
% 11.19/1.84 inference(cnf_transformation,[status(esa)],[f1606])).
% 11.19/1.84 fof(f2023,plain,(
% 11.19/1.84 class_Lattices_Obounded__lattice(tc_HOL_Obool)),
% 11.19/1.84 inference(cnf_transformation,[status(esa)],[f495])).
% 11.19/1.84 fof(f2027,plain,(
% 11.19/1.84 ![T_2,T_1]: (~class_Lattices_Obounded__lattice(T_1)|class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)))),
% 11.19/1.84 inference(pre_NNF_transformation,[status(esa)],[f497])).
% 11.19/1.84 fof(f2028,plain,(
% 11.19/1.84 ![T_1]: (~class_Lattices_Obounded__lattice(T_1)|(![T_2]: class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1))))),
% 11.19/1.84 inference(miniscoping,[status(esa)],[f2027])).
% 11.19/1.84 fof(f2029,plain,(
% 11.19/1.84 ![X0,X1]: (~class_Lattices_Obounded__lattice(X0)|class_Lattices_Obounded__lattice__top(tc_fun(X1,X0)))),
% 11.19/1.84 inference(cnf_transformation,[status(esa)],[f2028])).
% 11.19/1.84 fof(f2030,plain,(
% 11.19/1.84 ![T_2,T_1]: (~class_Lattices_Obounded__lattice(T_1)|class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)))),
% 11.19/1.84 inference(pre_NNF_transformation,[status(esa)],[f498])).
% 11.19/1.84 fof(f2031,plain,(
% 11.19/1.84 ![T_1]: (~class_Lattices_Obounded__lattice(T_1)|(![T_2]: class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1))))),
% 11.19/1.84 inference(miniscoping,[status(esa)],[f2030])).
% 11.19/1.84 fof(f2032,plain,(
% 11.19/1.84 ![X0,X1]: (~class_Lattices_Obounded__lattice(X0)|class_Lattices_Obounded__lattice__bot(tc_fun(X1,X0)))),
% 11.19/1.84 inference(cnf_transformation,[status(esa)],[f2031])).
% 11.19/1.84 fof(f2077,plain,(
% 11.19/1.84 ((![B_x]: c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,B_x)))&(![B_x]: c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,B_x))))&(![B_x]: c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,B_x)))),
% 11.19/1.84 inference(miniscoping,[status(esa)],[f523])).
% 11.19/1.84 fof(f2078,plain,(
% 11.19/1.84 ![X0]: (c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X0)))),
% 11.19/1.84 inference(cnf_transformation,[status(esa)],[f2077])).
% 11.19/1.84 fof(f2079,plain,(
% 11.19/1.84 ![X0]: (c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X0)))),
% 11.19/1.84 inference(cnf_transformation,[status(esa)],[f2077])).
% 11.19/1.84 fof(f2080,plain,(
% 11.19/1.84 ![X0]: (c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,X0)))),
% 11.19/1.84 inference(cnf_transformation,[status(esa)],[f2077])).
% 11.19/1.84 fof(f2081,plain,(
% 11.19/1.84 c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),v_F(v_P))),
% 11.19/1.84 inference(cnf_transformation,[status(esa)],[f524])).
% 11.19/1.84 fof(f2082,plain,(
% 11.19/1.84 (?[B_x]: ((~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,B_x))|~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,B_x)))|~c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,B_x))))|((c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))&c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)))&c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),v_F(v_P)))),
% 11.19/1.84 inference(pre_NNF_transformation,[status(esa)],[f525])).
% 11.19/1.84 fof(f2083,plain,(
% 11.19/1.84 (((?[B_x]: ~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,B_x)))|(?[B_x]: ~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,B_x))))|(?[B_x]: ~c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,B_x))))|((c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))&c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)))&c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),v_F(v_P)))),
% 11.19/1.84 inference(miniscoping,[status(esa)],[f2082])).
% 11.19/1.84 fof(f2084,plain,(
% 11.19/1.84 ((~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sk0_84))|~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sk0_85)))|~c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,sk0_86)))|((c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))&c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)))&c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),v_F(v_P)))),
% 11.19/1.84 inference(skolemization,[status(esa)],[f2083])).
% 11.19/1.84 fof(f2085,plain,(
% 11.19/1.84 ~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sk0_84))|~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sk0_85))|~c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,sk0_86))|c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))),
% 11.19/1.84 inference(cnf_transformation,[status(esa)],[f2084])).
% 11.19/1.84 fof(f2086,plain,(
% 11.19/1.84 ~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sk0_84))|~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sk0_85))|~c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,sk0_86))|c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))),
% 11.19/1.84 inference(cnf_transformation,[status(esa)],[f2084])).
% 11.19/1.84 fof(f2088,plain,(
% 11.19/1.84 (?[B_x]: ((~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,B_x))|~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,B_x)))|~c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,B_x))))|(![B_a,B_b]: (B_a=B_b|(~c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B_a,B_b),hAPP(v_P,v_i))|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B_a,B_b),v_F(v_P)))))),
% 11.19/1.84 inference(pre_NNF_transformation,[status(esa)],[f526])).
% 11.19/1.84 fof(f2089,plain,(
% 11.19/1.84 (((?[B_x]: ~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,B_x)))|(?[B_x]: ~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,B_x))))|(?[B_x]: ~c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,B_x))))|(![B_a,B_b]: (B_a=B_b|(~c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B_a,B_b),hAPP(v_P,v_i))|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B_a,B_b),v_F(v_P)))))),
% 11.19/1.84 inference(miniscoping,[status(esa)],[f2088])).
% 11.19/1.84 fof(f2090,plain,(
% 11.19/1.84 ((~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sk0_87))|~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sk0_88)))|~c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,sk0_89)))|(![B_a,B_b]: (B_a=B_b|(~c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B_a,B_b),hAPP(v_P,v_i))|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B_a,B_b),v_F(v_P)))))),
% 11.19/1.84 inference(skolemization,[status(esa)],[f2089])).
% 11.19/1.84 fof(f2091,plain,(
% 11.19/1.84 ![X0,X1]: (~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sk0_87))|~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sk0_88))|~c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,sk0_89))|X0=X1|~c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(v_P,v_i))|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_F(v_P)))),
% 11.19/1.84 inference(cnf_transformation,[status(esa)],[f2090])).
% 11.19/1.84 fof(f2092,plain,(
% 11.19/1.84 ~c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),hAPP(v_P,v_i))),
% 11.19/1.84 inference(cnf_transformation,[status(esa)],[f528])).
% 11.19/1.84 fof(f2110,plain,(
% 11.19/1.84 spl0_0 <=> c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sk0_84))),
% 11.19/1.84 introduced(split_symbol_definition)).
% 11.19/1.84 fof(f2112,plain,(
% 11.19/1.84 ~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sk0_84))|spl0_0),
% 11.19/1.84 inference(component_clause,[status(thm)],[f2110])).
% 11.19/1.84 fof(f2113,plain,(
% 11.19/1.84 spl0_1 <=> c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sk0_85))),
% 11.19/1.84 introduced(split_symbol_definition)).
% 11.19/1.84 fof(f2115,plain,(
% 11.19/1.84 ~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sk0_85))|spl0_1),
% 11.19/1.84 inference(component_clause,[status(thm)],[f2113])).
% 11.19/1.84 fof(f2116,plain,(
% 11.19/1.84 spl0_2 <=> c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,sk0_86))),
% 11.19/1.84 introduced(split_symbol_definition)).
% 11.19/1.84 fof(f2118,plain,(
% 11.19/1.84 ~c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,sk0_86))|spl0_2),
% 11.19/1.84 inference(component_clause,[status(thm)],[f2116])).
% 11.19/1.84 fof(f2119,plain,(
% 11.19/1.84 spl0_3 <=> c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))),
% 11.19/1.84 introduced(split_symbol_definition)).
% 11.19/1.84 fof(f2122,plain,(
% 11.19/1.84 ~spl0_0|~spl0_1|~spl0_2|spl0_3),
% 11.19/1.84 inference(split_clause,[status(thm)],[f2085,f2110,f2113,f2116,f2119])).
% 11.19/1.84 fof(f2123,plain,(
% 11.19/1.84 spl0_4 <=> c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))),
% 11.19/1.84 introduced(split_symbol_definition)).
% 11.19/1.84 fof(f2126,plain,(
% 11.19/1.84 ~spl0_0|~spl0_1|~spl0_2|spl0_4),
% 11.19/1.84 inference(split_clause,[status(thm)],[f2086,f2110,f2113,f2116,f2123])).
% 11.19/1.84 fof(f2131,plain,(
% 11.19/1.84 spl0_6 <=> c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sk0_87))),
% 11.19/1.84 introduced(split_symbol_definition)).
% 11.19/1.84 fof(f2133,plain,(
% 11.19/1.84 ~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sk0_87))|spl0_6),
% 11.19/1.84 inference(component_clause,[status(thm)],[f2131])).
% 11.19/1.84 fof(f2134,plain,(
% 11.19/1.84 spl0_7 <=> c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sk0_88))),
% 11.19/1.84 introduced(split_symbol_definition)).
% 11.19/1.84 fof(f2136,plain,(
% 11.19/1.84 ~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sk0_88))|spl0_7),
% 11.19/1.84 inference(component_clause,[status(thm)],[f2134])).
% 11.19/1.84 fof(f2137,plain,(
% 11.19/1.84 spl0_8 <=> c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,sk0_89))),
% 11.19/1.84 introduced(split_symbol_definition)).
% 11.19/1.84 fof(f2139,plain,(
% 11.19/1.84 ~c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,sk0_89))|spl0_8),
% 11.19/1.84 inference(component_clause,[status(thm)],[f2137])).
% 11.19/1.84 fof(f2140,plain,(
% 11.19/1.84 spl0_9 <=> X0=X1|~c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(v_P,v_i))|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_F(v_P))),
% 11.19/1.84 introduced(split_symbol_definition)).
% 11.19/1.84 fof(f2141,plain,(
% 11.19/1.84 ![X0,X1]: (X0=X1|~c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(v_P,v_i))|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_F(v_P))|~spl0_9)),
% 11.19/1.84 inference(component_clause,[status(thm)],[f2140])).
% 11.19/1.84 fof(f2143,plain,(
% 11.19/1.84 ~spl0_6|~spl0_7|~spl0_8|spl0_9),
% 11.19/1.84 inference(split_clause,[status(thm)],[f2091,f2131,f2134,f2137,f2140])).
% 11.19/1.84 fof(f2154,plain,(
% 11.19/1.84 ![X0,X1]: (c_member(X0,X1,c_fequal(X1)))),
% 11.19/1.84 inference(destructive_equality_resolution,[status(esa)],[f612])).
% 11.19/1.84 fof(f2155,plain,(
% 11.19/1.84 ![X0,X1,X2]: (~c_member(X0,X1,X2)|c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,X1,X1),c_Relation_OId__on(X0,X2)))),
% 11.19/1.84 inference(destructive_equality_resolution,[status(esa)],[f629])).
% 11.19/1.84 fof(f2228,plain,(
% 11.19/1.84 spl0_10 <=> ~c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,X0,hAPP(v_P,v_i))|~c_member(tc_Arrow__Order__Mirabelle_Oalt,v_b,X0)|~c_member(tc_Arrow__Order__Mirabelle_Oalt,v_a,X0)),
% 11.19/1.84 introduced(split_symbol_definition)).
% 11.19/1.84 fof(f2229,plain,(
% 11.19/1.84 ![X0]: (~c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,X0,hAPP(v_P,v_i))|~c_member(tc_Arrow__Order__Mirabelle_Oalt,v_b,X0)|~c_member(tc_Arrow__Order__Mirabelle_Oalt,v_a,X0)|~spl0_10)),
% 11.19/1.84 inference(component_clause,[status(thm)],[f2228])).
% 11.19/1.84 fof(f2231,plain,(
% 11.19/1.84 spl0_11 <=> v_b=v_a),
% 11.19/1.84 introduced(split_symbol_definition)).
% 11.19/1.84 fof(f2232,plain,(
% 11.19/1.84 v_b=v_a|~spl0_11),
% 11.19/1.84 inference(component_clause,[status(thm)],[f2231])).
% 11.19/1.84 fof(f2234,plain,(
% 11.19/1.84 spl0_12 <=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_a),hAPP(v_P,v_i))),
% 11.19/1.84 introduced(split_symbol_definition)).
% 11.19/1.84 fof(f2235,plain,(
% 11.19/1.84 c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_a),hAPP(v_P,v_i))|~spl0_12),
% 11.19/1.84 inference(component_clause,[status(thm)],[f2234])).
% 11.19/1.84 fof(f2237,plain,(
% 11.19/1.84 ![X0]: (~c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,X0,hAPP(v_P,v_i))|~c_member(tc_Arrow__Order__Mirabelle_Oalt,v_b,X0)|~c_member(tc_Arrow__Order__Mirabelle_Oalt,v_a,X0)|v_b=v_a|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_a),hAPP(v_P,v_i)))),
% 11.19/1.84 inference(resolution,[status(thm)],[f542,f2092])).
% 11.19/1.84 fof(f2238,plain,(
% 11.19/1.84 spl0_10|spl0_11|spl0_12),
% 11.19/1.84 inference(split_clause,[status(thm)],[f2237,f2228,f2231,f2234])).
% 11.19/1.84 fof(f2239,plain,(
% 11.19/1.84 $false|spl0_0),
% 11.19/1.84 inference(forward_subsumption_resolution,[status(thm)],[f2112,f2078])).
% 11.19/1.84 fof(f2240,plain,(
% 11.19/1.84 spl0_0),
% 11.19/1.84 inference(contradiction_clause,[status(thm)],[f2239])).
% 11.19/1.84 fof(f2241,plain,(
% 11.19/1.84 $false|spl0_6),
% 11.19/1.84 inference(forward_subsumption_resolution,[status(thm)],[f2133,f2078])).
% 11.19/1.84 fof(f2242,plain,(
% 11.19/1.84 spl0_6),
% 11.19/1.84 inference(contradiction_clause,[status(thm)],[f2241])).
% 11.19/1.84 fof(f2263,plain,(
% 11.19/1.84 spl0_15 <=> ~c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_a),v_F(v_P))|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_b),v_F(v_P))),
% 11.19/1.84 introduced(split_symbol_definition)).
% 11.19/1.84 fof(f2264,plain,(
% 11.19/1.84 ![X0]: (~c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_a),v_F(v_P))|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_b),v_F(v_P))|~spl0_15)),
% 11.19/1.84 inference(component_clause,[status(thm)],[f2263])).
% 11.19/1.84 fof(f2266,plain,(
% 11.19/1.84 ![X0]: (~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|~c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_a),v_F(v_P))|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_b),v_F(v_P)))),
% 11.19/1.84 inference(resolution,[status(thm)],[f552,f2081])).
% 11.19/1.84 fof(f2267,plain,(
% 11.19/1.84 ~spl0_3|spl0_15),
% 11.19/1.84 inference(split_clause,[status(thm)],[f2266,f2119,f2263])).
% 11.19/1.84 fof(f2276,plain,(
% 11.19/1.84 $false|spl0_1),
% 11.19/1.84 inference(backward_subsumption_resolution,[status(thm)],[f2115,f2079])).
% 11.19/1.84 fof(f2277,plain,(
% 11.19/1.84 spl0_1),
% 11.19/1.84 inference(contradiction_clause,[status(thm)],[f2276])).
% 11.19/1.84 fof(f2278,plain,(
% 11.19/1.84 $false|spl0_7),
% 11.19/1.84 inference(backward_subsumption_resolution,[status(thm)],[f2136,f2079])).
% 11.19/1.84 fof(f2279,plain,(
% 11.19/1.84 spl0_7),
% 11.19/1.84 inference(contradiction_clause,[status(thm)],[f2278])).
% 11.19/1.84 fof(f2370,plain,(
% 11.19/1.84 ![X0,X1,X2]: (c_member(X0,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))),
% 11.19/1.84 inference(resolution,[status(thm)],[f616,f559])).
% 11.19/1.84 fof(f2471,plain,(
% 11.19/1.84 ![X0]: (~c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P),X0,v_a)|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_b),v_F(v_P))|~spl0_15)),
% 11.19/1.84 inference(resolution,[status(thm)],[f619,f2264])).
% 11.19/1.84 fof(f2481,plain,(
% 11.19/1.84 ![X0,X1,X2]: (~c_FunDef_Oin__rel(X0,X0,X1,X2,X2)|~c_Relation_Oirrefl(X0,X1))),
% 11.19/1.84 inference(resolution,[status(thm)],[f619,f536])).
% 11.19/1.84 fof(f2565,plain,(
% 11.19/1.84 ![X0,X1,X2]: (~c_member(X0,X1,X2)|c_FunDef_Oin__rel(X0,X0,c_Relation_OId__on(X0,X2),X1,X1))),
% 11.19/1.84 inference(resolution,[status(thm)],[f2155,f620])).
% 11.19/1.84 fof(f2622,plain,(
% 11.19/1.84 spl0_36 <=> c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P),v_b,v_a)),
% 11.19/1.84 introduced(split_symbol_definition)).
% 11.19/1.84 fof(f2624,plain,(
% 11.19/1.84 ~c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P),v_b,v_a)|spl0_36),
% 11.19/1.84 inference(component_clause,[status(thm)],[f2622])).
% 11.19/1.84 fof(f2625,plain,(
% 11.19/1.84 ~c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P),v_b,v_a)|~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|~spl0_15),
% 11.19/1.84 inference(resolution,[status(thm)],[f2471,f536])).
% 11.19/1.84 fof(f2626,plain,(
% 11.19/1.84 ~spl0_36|~spl0_4|~spl0_15),
% 11.19/1.84 inference(split_clause,[status(thm)],[f2625,f2622,f2123,f2263])).
% 11.19/1.84 fof(f2856,plain,(
% 11.19/1.84 spl0_40 <=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_a),v_F(v_P))),
% 11.19/1.84 introduced(split_symbol_definition)).
% 11.19/1.84 fof(f2857,plain,(
% 11.19/1.84 c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_a),v_F(v_P))|~spl0_40),
% 11.19/1.84 inference(component_clause,[status(thm)],[f2856])).
% 11.19/1.84 fof(f2883,plain,(
% 11.19/1.84 c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P),v_a,v_b)),
% 11.19/1.84 inference(resolution,[status(thm)],[f2081,f620])).
% 11.19/1.84 fof(f3148,plain,(
% 11.19/1.84 c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P),v_a,v_a)|~spl0_11),
% 11.19/1.84 inference(backward_demodulation,[status(thm)],[f2232,f2883])).
% 11.19/1.84 fof(f3278,plain,(
% 11.19/1.84 hBOOL(hAPP(hAPP(v_P,v_i),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_a)))|~spl0_12),
% 11.19/1.84 inference(resolution,[status(thm)],[f2235,f615])).
% 11.19/1.84 fof(f4906,plain,(
% 11.19/1.84 spl0_131 <=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X6),X7)),
% 11.19/1.84 introduced(split_symbol_definition)).
% 11.19/1.84 fof(f4907,plain,(
% 11.19/1.84 ![X0,X1,X2,X3]: (c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,X1,X2),X3)|~spl0_131)),
% 11.19/1.84 inference(component_clause,[status(thm)],[f4906])).
% 11.19/1.84 fof(f4917,plain,(
% 11.19/1.84 spl0_132 <=> c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X5,X5),X6)),
% 11.19/1.84 introduced(split_symbol_definition)).
% 11.19/1.84 fof(f4918,plain,(
% 11.19/1.84 ![X0,X1,X2]: (c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,X1,X1),X2)|~spl0_132)),
% 11.19/1.84 inference(component_clause,[status(thm)],[f4917])).
% 11.19/1.84 fof(f5032,plain,(
% 11.19/1.84 ![X0,X1,X2,X3]: (~c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,X1,X2),c_Relation_OId__on(X0,X3))|X2=sk0_13(X0,c_Product__Type_OPair(X0,X0,X1,X2),X3))),
% 11.19/1.84 inference(resolution,[status(thm)],[f739,f924])).
% 11.19/1.84 fof(f5475,plain,(
% 11.19/1.84 ![X0,X1,X2]: (c_member(X0,X1,c_Wellfounded_Oacc(X0,c_Relation_OId__on(X0,X2)))|X1=sk0_13(X0,c_Product__Type_OPair(X0,X0,sk0_16(X0,X1,c_Relation_OId__on(X0,X2)),X1),X2))),
% 11.19/1.84 inference(resolution,[status(thm)],[f772,f5032])).
% 11.19/1.84 fof(f5621,plain,(
% 11.19/1.84 ![X0,X1,X2]: (~c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,sk0_16(X0,X1,c_Relation_OId__on(X0,X2)),X1),c_Relation_OId__on(X0,X2))|c_Product__Type_OPair(X0,X0,sk0_16(X0,X1,c_Relation_OId__on(X0,X2)),X1)=c_Product__Type_OPair(X0,X0,sk0_13(X0,c_Product__Type_OPair(X0,X0,sk0_16(X0,X1,c_Relation_OId__on(X0,X2)),X1),X2),X1)|c_member(X0,X1,c_Wellfounded_Oacc(X0,c_Relation_OId__on(X0,X2))))),
% 11.19/1.84 inference(paramodulation,[status(thm)],[f5475,f739])).
% 11.19/1.84 fof(f5622,plain,(
% 11.19/1.84 ![X0,X1,X2]: (c_Product__Type_OPair(X0,X0,sk0_16(X0,X1,c_Relation_OId__on(X0,X2)),X1)=c_Product__Type_OPair(X0,X0,sk0_13(X0,c_Product__Type_OPair(X0,X0,sk0_16(X0,X1,c_Relation_OId__on(X0,X2)),X1),X2),X1)|c_member(X0,X1,c_Wellfounded_Oacc(X0,c_Relation_OId__on(X0,X2))))),
% 11.19/1.84 inference(forward_subsumption_resolution,[status(thm)],[f5621,f772])).
% 11.19/1.84 fof(f5644,plain,(
% 11.19/1.84 ![X0,X1,X2]: (c_Product__Type_OPair(X0,X0,sk0_16(X0,X1,c_Relation_OId__on(X0,X2)),X1)=c_Product__Type_OPair(X0,X0,X1,X1)|c_member(X0,X1,c_Wellfounded_Oacc(X0,c_Relation_OId__on(X0,X2)))|c_member(X0,X1,c_Wellfounded_Oacc(X0,c_Relation_OId__on(X0,X2))))),
% 11.19/1.84 inference(paramodulation,[status(thm)],[f5475,f5622])).
% 11.19/1.84 fof(f5645,plain,(
% 11.19/1.84 ![X0,X1,X2]: (c_Product__Type_OPair(X0,X0,sk0_16(X0,X1,c_Relation_OId__on(X0,X2)),X1)=c_Product__Type_OPair(X0,X0,X1,X1)|c_member(X0,X1,c_Wellfounded_Oacc(X0,c_Relation_OId__on(X0,X2))))),
% 11.19/1.84 inference(duplicate_literals_removal,[status(esa)],[f5644])).
% 11.19/1.84 fof(f5696,plain,(
% 11.19/1.84 spl0_187 <=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_b),v_F(v_P))),
% 11.19/1.84 introduced(split_symbol_definition)).
% 11.19/1.84 fof(f5697,plain,(
% 11.19/1.84 c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_b),v_F(v_P))|~spl0_187),
% 11.19/1.84 inference(component_clause,[status(thm)],[f5696])).
% 11.19/1.84 fof(f5717,plain,(
% 11.19/1.84 spl0_192 <=> c_member(X1,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_b),v_F(v_P))),
% 11.19/1.84 introduced(split_symbol_definition)).
% 11.19/1.84 fof(f5718,plain,(
% 11.19/1.84 ![X0]: (c_member(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_b),v_F(v_P))|~spl0_192)),
% 11.19/1.84 inference(component_clause,[status(thm)],[f5717])).
% 11.19/1.84 fof(f5744,plain,(
% 11.19/1.84 ![X0,X1,X2]: (c_member(X0,X1,c_Wellfounded_Oacc(X0,c_Relation_OId__on(X0,X2)))|c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,X1,X1),c_Relation_OId__on(X0,X2))|c_member(X0,X1,c_Wellfounded_Oacc(X0,c_Relation_OId__on(X0,X2))))),
% 11.19/1.84 inference(paramodulation,[status(thm)],[f5645,f772])).
% 11.19/1.84 fof(f5745,plain,(
% 11.19/1.84 ![X0,X1,X2]: (c_member(X0,X1,c_Wellfounded_Oacc(X0,c_Relation_OId__on(X0,X2)))|c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,X1,X1),c_Relation_OId__on(X0,X2)))),
% 11.19/1.84 inference(duplicate_literals_removal,[status(esa)],[f5744])).
% 11.19/1.84 fof(f5775,plain,(
% 11.19/1.84 ![X0,X1,X2]: (c_member(X0,X1,c_Wellfounded_Oacc(X0,c_Relation_OId__on(X0,X2)))|c_member(X0,X1,c_Relation_ODomain(X0,X0,c_Relation_OId__on(X0,X2))))),
% 11.19/1.84 inference(resolution,[status(thm)],[f5745,f637])).
% 11.19/1.84 fof(f5776,plain,(
% 11.19/1.84 ![X0,X1,X2]: (c_member(X0,X1,c_Wellfounded_Oacc(X0,c_Relation_OId__on(X0,X2)))|c_member(X0,X1,X2))),
% 11.19/1.84 inference(forward_demodulation,[status(thm)],[f661,f5775])).
% 11.19/1.84 fof(f5788,plain,(
% 11.19/1.84 ![X0,X1]: (c_member(X0,sk0_74(X0,c_Relation_OId__on(X0,X1)),X1)|c_Wellfounded_Owf(X0,c_Relation_OId__on(X0,X1)))),
% 11.19/1.84 inference(resolution,[status(thm)],[f5776,f1608])).
% 11.19/1.84 fof(f5938,plain,(
% 11.19/1.84 hBOOL(hAPP(v_F(v_P),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_b)))|~spl0_187),
% 11.19/1.84 inference(resolution,[status(thm)],[f5697,f615])).
% 11.19/1.84 fof(f5943,plain,(
% 11.19/1.84 ![X0]: (c_member(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_b),v_F(v_P))|~spl0_187)),
% 11.19/1.84 inference(resolution,[status(thm)],[f5938,f616])).
% 11.19/1.84 fof(f6006,plain,(
% 11.19/1.84 ![X0,X1]: (c_Wellfounded_Owf(X0,c_Relation_OId__on(X0,X1))|hBOOL(hAPP(X1,sk0_74(X0,c_Relation_OId__on(X0,X1)))))),
% 11.19/1.84 inference(resolution,[status(thm)],[f5788,f615])).
% 11.19/1.84 fof(f6048,plain,(
% 11.19/1.84 ![X0,X1,X2]: (c_Wellfounded_Owf(X0,c_Relation_OId__on(X0,X1))|c_member(X2,sk0_74(X0,c_Relation_OId__on(X0,X1)),X1))),
% 11.19/1.84 inference(resolution,[status(thm)],[f6006,f616])).
% 11.19/1.84 fof(f6053,plain,(
% 11.19/1.84 ![X0,X1]: (c_Wellfounded_Owf(X0,c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),
% 11.19/1.84 inference(resolution,[status(thm)],[f6048,f1268])).
% 11.19/1.84 fof(f6121,plain,(
% 11.19/1.84 spl0_201 <=> ~class_Lattices_Obounded__lattice__bot(tc_fun(X0,tc_HOL_Obool))),
% 11.19/1.84 introduced(split_symbol_definition)).
% 11.19/1.84 fof(f6122,plain,(
% 11.19/1.84 ![X0]: (~class_Lattices_Obounded__lattice__bot(tc_fun(X0,tc_HOL_Obool))|~spl0_201)),
% 11.19/1.84 inference(component_clause,[status(thm)],[f6121])).
% 11.19/1.84 fof(f6207,plain,(
% 11.19/1.84 spl0_203 <=> ~class_Lattices_Obounded__lattice__top(tc_fun(X0,tc_HOL_Obool))),
% 11.19/1.84 introduced(split_symbol_definition)).
% 11.19/1.84 fof(f6208,plain,(
% 11.19/1.84 ![X0]: (~class_Lattices_Obounded__lattice__top(tc_fun(X0,tc_HOL_Obool))|~spl0_203)),
% 11.19/1.84 inference(component_clause,[status(thm)],[f6207])).
% 11.19/1.84 fof(f6347,plain,(
% 11.19/1.84 c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P),v_b,v_b)|~spl0_192),
% 11.19/1.84 inference(resolution,[status(thm)],[f5718,f620])).
% 11.19/1.84 fof(f6526,plain,(
% 11.19/1.84 ![X0]: (c_member(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_a),hAPP(v_P,v_i))|~spl0_12)),
% 11.19/1.84 inference(resolution,[status(thm)],[f3278,f616])).
% 11.19/1.84 fof(f6544,plain,(
% 11.19/1.84 spl0_232 <=> c_Wellfounded_Owf(tc_Arrow__Order__Mirabelle_Oalt,c_Relation_OId__on(tc_Arrow__Order__Mirabelle_Oalt,c_fequal(v_b)))),
% 11.19/1.84 introduced(split_symbol_definition)).
% 11.19/1.84 fof(f6545,plain,(
% 11.19/1.84 c_Wellfounded_Owf(tc_Arrow__Order__Mirabelle_Oalt,c_Relation_OId__on(tc_Arrow__Order__Mirabelle_Oalt,c_fequal(v_b)))|~spl0_232),
% 11.19/1.84 inference(component_clause,[status(thm)],[f6544])).
% 11.19/1.84 fof(f6779,plain,(
% 11.19/1.84 ~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|~spl0_192),
% 11.19/1.84 inference(resolution,[status(thm)],[f6347,f2481])).
% 11.19/1.84 fof(f7432,plain,(
% 11.19/1.84 ~c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P),v_a,v_a)|~spl0_11|spl0_36),
% 11.19/1.84 inference(forward_demodulation,[status(thm)],[f2232,f2624])).
% 11.19/1.84 fof(f7433,plain,(
% 11.19/1.84 $false|~spl0_11|spl0_36),
% 11.19/1.84 inference(forward_subsumption_resolution,[status(thm)],[f7432,f3148])).
% 11.19/1.84 fof(f7434,plain,(
% 11.19/1.84 ~spl0_11|spl0_36),
% 11.19/1.84 inference(contradiction_clause,[status(thm)],[f7433])).
% 11.19/1.84 fof(f9771,plain,(
% 11.19/1.84 ![X0,X1,X2]: (~c_Wellfounded_Owf(X0,X1)|~c_FunDef_Oin__rel(X0,X0,X1,X2,X2))),
% 11.19/1.84 inference(resolution,[status(thm)],[f1571,f619])).
% 11.19/1.84 fof(f10441,plain,(
% 11.19/1.84 ![X0,X1,X2]: (~c_Wellfounded_Owf(X0,c_Relation_OId__on(X0,X1))|~c_member(X0,X2,X1))),
% 11.19/1.84 inference(resolution,[status(thm)],[f9771,f2565])).
% 11.19/1.84 fof(f10958,plain,(
% 11.19/1.84 ![X0,X1,X2]: (~c_member(X0,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))),
% 11.19/1.84 inference(resolution,[status(thm)],[f10441,f6053])).
% 11.19/1.84 fof(f14042,plain,(
% 11.19/1.84 v_b=v_a|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_a),v_F(v_P))|~spl0_9|~spl0_12),
% 11.19/1.84 inference(resolution,[status(thm)],[f2141,f6526])).
% 11.19/1.84 fof(f14043,plain,(
% 11.19/1.84 spl0_11|spl0_40|~spl0_9|~spl0_12),
% 11.19/1.84 inference(split_clause,[status(thm)],[f14042,f2231,f2856,f2140,f2234])).
% 11.19/1.84 fof(f14053,plain,(
% 11.19/1.84 spl0_420 <=> c_member(tc_Arrow__Order__Mirabelle_Oalt,v_a,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)))),
% 11.19/1.84 introduced(split_symbol_definition)).
% 11.19/1.84 fof(f14055,plain,(
% 11.19/1.84 ~c_member(tc_Arrow__Order__Mirabelle_Oalt,v_a,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)))|spl0_420),
% 11.19/1.84 inference(component_clause,[status(thm)],[f14053])).
% 11.19/1.84 fof(f14066,plain,(
% 11.19/1.84 $false|spl0_420),
% 11.19/1.84 inference(forward_subsumption_resolution,[status(thm)],[f14055,f2370])).
% 11.19/1.84 fof(f14067,plain,(
% 11.19/1.84 spl0_420),
% 11.19/1.84 inference(contradiction_clause,[status(thm)],[f14066])).
% 11.19/1.84 fof(f14156,plain,(
% 11.19/1.84 $false|spl0_2),
% 11.19/1.84 inference(backward_subsumption_resolution,[status(thm)],[f2118,f2080])).
% 11.19/1.84 fof(f14157,plain,(
% 11.19/1.84 spl0_2),
% 11.19/1.84 inference(contradiction_clause,[status(thm)],[f14156])).
% 11.19/1.84 fof(f14158,plain,(
% 11.19/1.84 $false|spl0_8),
% 11.19/1.84 inference(backward_subsumption_resolution,[status(thm)],[f2139,f2080])).
% 11.19/1.84 fof(f14159,plain,(
% 11.19/1.84 spl0_8),
% 11.19/1.84 inference(contradiction_clause,[status(thm)],[f14158])).
% 11.19/1.84 fof(f14160,plain,(
% 11.19/1.84 spl0_423 <=> c_member(tc_Arrow__Order__Mirabelle_Oalt,v_b,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)))),
% 11.19/1.84 introduced(split_symbol_definition)).
% 11.19/1.84 fof(f14162,plain,(
% 11.19/1.84 ~c_member(tc_Arrow__Order__Mirabelle_Oalt,v_b,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)))|spl0_423),
% 11.19/1.84 inference(component_clause,[status(thm)],[f14160])).
% 11.19/1.84 fof(f14178,plain,(
% 11.19/1.84 ~spl0_4|~spl0_192),
% 11.19/1.84 inference(split_clause,[status(thm)],[f6779,f2123,f5717])).
% 11.19/1.84 fof(f14182,plain,(
% 11.19/1.84 $false|spl0_423),
% 11.19/1.84 inference(forward_subsumption_resolution,[status(thm)],[f14162,f2370])).
% 11.19/1.84 fof(f14183,plain,(
% 11.19/1.84 spl0_423),
% 11.19/1.84 inference(contradiction_clause,[status(thm)],[f14182])).
% 11.19/1.84 fof(f14382,plain,(
% 11.19/1.84 ~c_member(tc_Arrow__Order__Mirabelle_Oalt,v_b,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)))|~c_member(tc_Arrow__Order__Mirabelle_Oalt,v_a,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)))|~spl0_10),
% 11.19/1.84 inference(resolution,[status(thm)],[f2229,f2080])).
% 11.19/1.84 fof(f14383,plain,(
% 11.19/1.84 ~spl0_423|~spl0_420|~spl0_10),
% 11.19/1.84 inference(split_clause,[status(thm)],[f14382,f14160,f14053,f2228])).
% 11.81/2.06 fof(f14917,plain,(
% 11.81/2.06 spl0_192|~spl0_187),
% 11.81/2.06 inference(split_clause,[status(thm)],[f5943,f5717,f5696])).
% 11.81/2.06 fof(f15039,plain,(
% 11.81/2.06 ![X0]: (~c_member(tc_Arrow__Order__Mirabelle_Oalt,X0,c_fequal(v_b))|~spl0_232)),
% 11.81/2.06 inference(resolution,[status(thm)],[f6545,f10441])).
% 11.81/2.06 fof(f15046,plain,(
% 11.81/2.06 $false|~spl0_232),
% 11.81/2.06 inference(resolution,[status(thm)],[f15039,f2154])).
% 11.81/2.06 fof(f15047,plain,(
% 11.81/2.06 ~spl0_232),
% 11.81/2.06 inference(contradiction_clause,[status(thm)],[f15046])).
% 11.81/2.06 fof(f15059,plain,(
% 11.81/2.06 ~class_Lattices_Obounded__lattice(tc_HOL_Obool)|~spl0_203),
% 11.81/2.06 inference(resolution,[status(thm)],[f6208,f2029])).
% 11.81/2.06 fof(f15060,plain,(
% 11.81/2.06 $false|~spl0_203),
% 11.81/2.06 inference(forward_subsumption_resolution,[status(thm)],[f15059,f2023])).
% 11.81/2.06 fof(f15061,plain,(
% 11.81/2.06 ~spl0_203),
% 11.81/2.06 inference(contradiction_clause,[status(thm)],[f15060])).
% 11.81/2.06 fof(f15062,plain,(
% 11.81/2.06 ~class_Lattices_Obounded__lattice(tc_HOL_Obool)|~spl0_201),
% 11.81/2.06 inference(resolution,[status(thm)],[f6122,f2032])).
% 11.81/2.06 fof(f15063,plain,(
% 11.81/2.06 $false|~spl0_201),
% 11.81/2.06 inference(forward_subsumption_resolution,[status(thm)],[f15062,f2023])).
% 11.81/2.06 fof(f15064,plain,(
% 11.81/2.06 ~spl0_201),
% 11.81/2.06 inference(contradiction_clause,[status(thm)],[f15063])).
% 11.81/2.06 fof(f15080,plain,(
% 11.81/2.06 $false|~spl0_132),
% 11.81/2.06 inference(resolution,[status(thm)],[f4918,f10958])).
% 11.81/2.06 fof(f15081,plain,(
% 11.81/2.06 ~spl0_132),
% 11.81/2.06 inference(contradiction_clause,[status(thm)],[f15080])).
% 11.81/2.06 fof(f15090,plain,(
% 11.81/2.06 $false|~spl0_131),
% 11.81/2.06 inference(backward_subsumption_resolution,[status(thm)],[f2092,f4907])).
% 11.81/2.06 fof(f15091,plain,(
% 11.81/2.06 ~spl0_131),
% 11.81/2.06 inference(contradiction_clause,[status(thm)],[f15090])).
% 11.81/2.06 fof(f15176,plain,(
% 11.81/2.06 c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_b),v_F(v_P))|~spl0_40|~spl0_15),
% 11.81/2.06 inference(resolution,[status(thm)],[f2857,f2264])).
% 11.81/2.06 fof(f15177,plain,(
% 11.81/2.06 spl0_187|~spl0_40|~spl0_15),
% 11.81/2.06 inference(split_clause,[status(thm)],[f15176,f5696,f2856,f2263])).
% 11.81/2.06 fof(f15179,plain,(
% 11.81/2.06 $false),
% 11.81/2.06 inference(sat_refutation,[status(thm)],[f2122,f2126,f2143,f2238,f2240,f2242,f2267,f2277,f2279,f2626,f7434,f14043,f14067,f14157,f14159,f14178,f14183,f14383,f14917,f15047,f15061,f15064,f15081,f15091,f15177])).
% 11.81/2.06 % SZS output end CNFRefutation for theBenchmark.p
% 11.81/2.06 % Elapsed time: 1.708775 seconds
% 11.81/2.06 % CPU time: 11.854006 seconds
% 11.81/2.06 % Memory used: 224.924 MB
%------------------------------------------------------------------------------