TSTP Solution File: SCT122+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% 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 : n027.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 20:38:20 EDT 2024
% Result : Theorem 3.66s 0.96s
% Output : CNFRefutation 3.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SCT122+1 : TPTP v8.1.2. Released v5.2.0.
% 0.08/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 29 20:39:47 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.21/0.42 % Drodi V3.6.0
% 3.66/0.96 % Refutation found
% 3.66/0.96 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.66/0.96 % SZS output start CNFRefutation for theBenchmark
% 3.66/0.96 fof(f2,axiom,(
% 3.66/0.96 (! [V_x_2,T_a] : c_member(T_a,V_x_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) )),
% 3.66/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.66/0.96 fof(f3,axiom,(
% 3.66/0.96 (! [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) )) )),
% 3.66/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.66/0.96 fof(f4,axiom,(
% 3.66/0.96 (! [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) ) ) ) )) )) )),
% 3.66/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.66/0.96 fof(f5,axiom,(
% 3.66/0.96 (! [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) ) )) )) )),
% 3.66/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.66/0.96 fof(f18,axiom,(
% 3.66/0.96 (! [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)) ) )),
% 3.66/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.66/0.96 fof(f523,hypothesis,(
% 3.66/0.96 (! [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)) ) )),
% 3.66/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.66/0.96 fof(f524,hypothesis,(
% 3.66/0.96 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)) ),
% 3.66/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.66/0.96 fof(f525,hypothesis,(
% 3.66/0.96 ( (! [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)) ) ) ),
% 3.66/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.66/0.96 fof(f526,hypothesis,(
% 3.66/0.96 ( (! [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)) ) ) )) ),
% 3.66/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.66/0.96 fof(f527,conjecture,(
% 3.66/0.96 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)) ),
% 3.66/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.66/0.96 fof(f528,negated_conjecture,(
% 3.66/0.96 ~(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)) )),
% 3.66/0.97 inference(negated_conjecture,[status(cth)],[f527])).
% 3.66/0.97 fof(f532,plain,(
% 3.66/0.97 ![X0,X1]: (c_member(X0,X1,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))))),
% 3.66/0.97 inference(cnf_transformation,[status(esa)],[f2])).
% 3.66/0.97 fof(f533,plain,(
% 3.66/0.97 ![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))))),
% 3.66/0.97 inference(NNF_transformation,[status(esa)],[f3])).
% 3.66/0.97 fof(f534,plain,(
% 3.66/0.97 (![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))))),
% 3.66/0.97 inference(miniscoping,[status(esa)],[f533])).
% 3.66/0.97 fof(f535,plain,(
% 3.66/0.97 (![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)))),
% 3.66/0.97 inference(skolemization,[status(esa)],[f534])).
% 3.66/0.97 fof(f536,plain,(
% 3.66/0.97 ![X0,X1,X2]: (~c_Relation_Oirrefl(X0,X1)|~c_member(tc_prod(X0,X0),c_Product__Type_OPair(X0,X0,X2,X2),X1))),
% 3.66/0.97 inference(cnf_transformation,[status(esa)],[f535])).
% 3.66/0.97 fof(f538,plain,(
% 3.66/0.97 ![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))))))))),
% 3.66/0.97 inference(pre_NNF_transformation,[status(esa)],[f4])).
% 3.66/0.97 fof(f539,plain,(
% 3.66/0.97 ![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)))))))))),
% 3.66/0.97 inference(NNF_transformation,[status(esa)],[f538])).
% 3.66/0.97 fof(f540,plain,(
% 3.66/0.97 (![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)))))))))),
% 3.66/0.97 inference(miniscoping,[status(esa)],[f539])).
% 3.66/0.97 fof(f541,plain,(
% 3.66/0.97 (![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)))))))),
% 3.66/0.97 inference(skolemization,[status(esa)],[f540])).
% 3.66/0.97 fof(f542,plain,(
% 3.66/0.97 ![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))),
% 3.66/0.97 inference(cnf_transformation,[status(esa)],[f541])).
% 3.66/0.97 fof(f548,plain,(
% 3.66/0.97 ![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))))))),
% 3.66/0.97 inference(pre_NNF_transformation,[status(esa)],[f5])).
% 3.66/0.97 fof(f549,plain,(
% 3.66/0.97 ![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)))))))),
% 3.66/0.97 inference(NNF_transformation,[status(esa)],[f548])).
% 3.66/0.97 fof(f550,plain,(
% 3.66/0.97 (![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)))))))),
% 3.66/0.97 inference(miniscoping,[status(esa)],[f549])).
% 3.66/0.97 fof(f551,plain,(
% 3.66/0.97 (![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)))))),
% 3.66/0.97 inference(skolemization,[status(esa)],[f550])).
% 3.66/0.97 fof(f552,plain,(
% 3.66/0.97 ![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))),
% 3.66/0.97 inference(cnf_transformation,[status(esa)],[f551])).
% 3.66/0.97 fof(f613,plain,(
% 3.66/0.97 ![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))))),
% 3.66/0.97 inference(NNF_transformation,[status(esa)],[f18])).
% 3.66/0.97 fof(f614,plain,(
% 3.66/0.97 (![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))))),
% 3.66/0.97 inference(miniscoping,[status(esa)],[f613])).
% 3.66/0.97 fof(f615,plain,(
% 3.66/0.97 ![X0,X1,X2]: (~c_member(X0,X1,X2)|hBOOL(hAPP(X2,X1)))),
% 3.66/0.97 inference(cnf_transformation,[status(esa)],[f614])).
% 3.66/0.97 fof(f616,plain,(
% 3.66/0.97 ![X0,X1,X2]: (c_member(X0,X1,X2)|~hBOOL(hAPP(X2,X1)))),
% 3.66/0.97 inference(cnf_transformation,[status(esa)],[f614])).
% 3.66/0.97 fof(f2077,plain,(
% 3.66/0.97 ((![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)))),
% 3.66/0.97 inference(miniscoping,[status(esa)],[f523])).
% 3.66/0.97 fof(f2078,plain,(
% 3.66/0.97 ![X0]: (c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X0)))),
% 3.66/0.97 inference(cnf_transformation,[status(esa)],[f2077])).
% 3.66/0.97 fof(f2079,plain,(
% 3.66/0.97 ![X0]: (c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X0)))),
% 3.66/0.97 inference(cnf_transformation,[status(esa)],[f2077])).
% 3.66/0.97 fof(f2080,plain,(
% 3.66/0.97 ![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)))),
% 3.66/0.97 inference(cnf_transformation,[status(esa)],[f2077])).
% 3.66/0.97 fof(f2081,plain,(
% 3.66/0.97 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))),
% 3.66/0.97 inference(cnf_transformation,[status(esa)],[f524])).
% 3.66/0.97 fof(f2082,plain,(
% 3.66/0.97 (?[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)))),
% 3.66/0.97 inference(pre_NNF_transformation,[status(esa)],[f525])).
% 3.66/0.97 fof(f2083,plain,(
% 3.66/0.97 (((?[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)))),
% 3.66/0.97 inference(miniscoping,[status(esa)],[f2082])).
% 3.66/0.97 fof(f2084,plain,(
% 3.66/0.97 ((~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)))),
% 3.66/0.97 inference(skolemization,[status(esa)],[f2083])).
% 3.66/0.97 fof(f2085,plain,(
% 3.66/0.97 ~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))),
% 3.66/0.97 inference(cnf_transformation,[status(esa)],[f2084])).
% 3.66/0.97 fof(f2086,plain,(
% 3.66/0.97 ~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))),
% 3.66/0.97 inference(cnf_transformation,[status(esa)],[f2084])).
% 3.66/0.97 fof(f2088,plain,(
% 3.66/0.97 (?[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)))))),
% 3.66/0.97 inference(pre_NNF_transformation,[status(esa)],[f526])).
% 3.66/0.97 fof(f2089,plain,(
% 3.66/0.97 (((?[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)))))),
% 3.66/0.97 inference(miniscoping,[status(esa)],[f2088])).
% 3.66/0.97 fof(f2090,plain,(
% 3.66/0.97 ((~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)))))),
% 3.66/0.97 inference(skolemization,[status(esa)],[f2089])).
% 3.66/0.97 fof(f2091,plain,(
% 3.66/0.97 ![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)))),
% 3.66/0.97 inference(cnf_transformation,[status(esa)],[f2090])).
% 3.66/0.97 fof(f2092,plain,(
% 3.66/0.97 ~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))),
% 3.66/0.97 inference(cnf_transformation,[status(esa)],[f528])).
% 3.66/0.97 fof(f2110,plain,(
% 3.66/0.97 spl0_0 <=> c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sk0_84))),
% 3.66/0.97 introduced(split_symbol_definition)).
% 3.66/0.97 fof(f2112,plain,(
% 3.66/0.97 ~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sk0_84))|spl0_0),
% 3.66/0.97 inference(component_clause,[status(thm)],[f2110])).
% 3.66/0.97 fof(f2113,plain,(
% 3.66/0.97 spl0_1 <=> c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sk0_85))),
% 3.66/0.97 introduced(split_symbol_definition)).
% 3.66/0.97 fof(f2115,plain,(
% 3.66/0.97 ~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sk0_85))|spl0_1),
% 3.66/0.97 inference(component_clause,[status(thm)],[f2113])).
% 3.66/0.97 fof(f2116,plain,(
% 3.66/0.97 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))),
% 3.66/0.97 introduced(split_symbol_definition)).
% 3.66/0.97 fof(f2118,plain,(
% 3.66/0.97 ~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),
% 3.66/0.97 inference(component_clause,[status(thm)],[f2116])).
% 3.66/0.97 fof(f2119,plain,(
% 3.66/0.97 spl0_3 <=> c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))),
% 3.66/0.97 introduced(split_symbol_definition)).
% 3.66/0.97 fof(f2122,plain,(
% 3.66/0.97 ~spl0_0|~spl0_1|~spl0_2|spl0_3),
% 3.66/0.97 inference(split_clause,[status(thm)],[f2085,f2110,f2113,f2116,f2119])).
% 3.66/0.97 fof(f2123,plain,(
% 3.66/0.97 spl0_4 <=> c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))),
% 3.66/0.97 introduced(split_symbol_definition)).
% 3.66/0.97 fof(f2124,plain,(
% 3.66/0.97 c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|~spl0_4),
% 3.66/0.97 inference(component_clause,[status(thm)],[f2123])).
% 3.66/0.97 fof(f2126,plain,(
% 3.66/0.97 ~spl0_0|~spl0_1|~spl0_2|spl0_4),
% 3.66/0.97 inference(split_clause,[status(thm)],[f2086,f2110,f2113,f2116,f2123])).
% 3.66/0.97 fof(f2131,plain,(
% 3.66/0.97 spl0_6 <=> c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sk0_87))),
% 3.66/0.97 introduced(split_symbol_definition)).
% 3.66/0.97 fof(f2133,plain,(
% 3.66/0.97 ~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sk0_87))|spl0_6),
% 3.66/0.97 inference(component_clause,[status(thm)],[f2131])).
% 3.66/0.97 fof(f2134,plain,(
% 3.66/0.97 spl0_7 <=> c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sk0_88))),
% 3.66/0.97 introduced(split_symbol_definition)).
% 3.66/0.97 fof(f2136,plain,(
% 3.66/0.97 ~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,sk0_88))|spl0_7),
% 3.66/0.97 inference(component_clause,[status(thm)],[f2134])).
% 3.66/0.97 fof(f2137,plain,(
% 3.66/0.97 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))),
% 3.66/0.97 introduced(split_symbol_definition)).
% 3.66/0.97 fof(f2139,plain,(
% 3.66/0.97 ~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),
% 3.66/0.97 inference(component_clause,[status(thm)],[f2137])).
% 3.66/0.97 fof(f2140,plain,(
% 3.66/0.97 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))),
% 3.66/0.97 introduced(split_symbol_definition)).
% 3.66/0.97 fof(f2141,plain,(
% 3.66/0.97 ![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)),
% 3.66/0.97 inference(component_clause,[status(thm)],[f2140])).
% 3.66/0.97 fof(f2143,plain,(
% 3.66/0.97 ~spl0_6|~spl0_7|~spl0_8|spl0_9),
% 3.66/0.97 inference(split_clause,[status(thm)],[f2091,f2131,f2134,f2137,f2140])).
% 3.66/0.97 fof(f2249,plain,(
% 3.66/0.97 $false|spl0_8),
% 3.66/0.97 inference(forward_subsumption_resolution,[status(thm)],[f2139,f2080])).
% 3.66/0.97 fof(f2250,plain,(
% 3.66/0.97 spl0_8),
% 3.66/0.97 inference(contradiction_clause,[status(thm)],[f2249])).
% 3.66/0.97 fof(f2251,plain,(
% 3.66/0.97 $false|spl0_7),
% 3.66/0.97 inference(forward_subsumption_resolution,[status(thm)],[f2136,f2079])).
% 3.66/0.97 fof(f2252,plain,(
% 3.66/0.97 spl0_7),
% 3.66/0.97 inference(contradiction_clause,[status(thm)],[f2251])).
% 3.66/0.97 fof(f2253,plain,(
% 3.66/0.97 $false|spl0_6),
% 3.66/0.97 inference(forward_subsumption_resolution,[status(thm)],[f2133,f2078])).
% 3.66/0.97 fof(f2254,plain,(
% 3.66/0.97 spl0_6),
% 3.66/0.97 inference(contradiction_clause,[status(thm)],[f2253])).
% 3.66/0.97 fof(f2255,plain,(
% 3.66/0.97 $false|spl0_2),
% 3.66/0.97 inference(forward_subsumption_resolution,[status(thm)],[f2118,f2080])).
% 3.66/0.97 fof(f2256,plain,(
% 3.66/0.97 spl0_2),
% 3.66/0.97 inference(contradiction_clause,[status(thm)],[f2255])).
% 3.66/0.97 fof(f2268,plain,(
% 3.66/0.97 $false|spl0_1),
% 3.66/0.97 inference(forward_subsumption_resolution,[status(thm)],[f2115,f2079])).
% 3.66/0.97 fof(f2269,plain,(
% 3.66/0.97 spl0_1),
% 3.66/0.97 inference(contradiction_clause,[status(thm)],[f2268])).
% 3.66/0.97 fof(f2274,plain,(
% 3.66/0.97 $false|spl0_0),
% 3.66/0.97 inference(forward_subsumption_resolution,[status(thm)],[f2112,f2078])).
% 3.66/0.97 fof(f2275,plain,(
% 3.66/0.97 spl0_0),
% 3.66/0.97 inference(contradiction_clause,[status(thm)],[f2274])).
% 3.66/0.97 fof(f2279,plain,(
% 3.66/0.97 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)),
% 3.66/0.97 introduced(split_symbol_definition)).
% 3.66/0.97 fof(f2280,plain,(
% 3.66/0.97 ![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)),
% 3.66/0.97 inference(component_clause,[status(thm)],[f2279])).
% 3.66/0.97 fof(f2282,plain,(
% 3.66/0.97 spl0_11 <=> v_b=v_a),
% 3.66/0.97 introduced(split_symbol_definition)).
% 3.66/0.97 fof(f2283,plain,(
% 3.66/0.97 v_b=v_a|~spl0_11),
% 3.66/0.97 inference(component_clause,[status(thm)],[f2282])).
% 3.66/0.97 fof(f2285,plain,(
% 3.66/0.97 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))),
% 3.66/0.97 introduced(split_symbol_definition)).
% 3.66/0.97 fof(f2286,plain,(
% 3.66/0.97 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),
% 3.66/0.97 inference(component_clause,[status(thm)],[f2285])).
% 3.66/0.97 fof(f2288,plain,(
% 3.66/0.97 ![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)))),
% 3.66/0.97 inference(resolution,[status(thm)],[f542,f2092])).
% 3.66/0.97 fof(f2289,plain,(
% 3.66/0.97 spl0_10|spl0_11|spl0_12),
% 3.66/0.97 inference(split_clause,[status(thm)],[f2288,f2279,f2282,f2285])).
% 3.66/0.97 fof(f2290,plain,(
% 3.66/0.97 spl0_13 <=> 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))),
% 3.66/0.97 introduced(split_symbol_definition)).
% 3.66/0.97 fof(f2291,plain,(
% 3.66/0.97 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_13),
% 3.66/0.97 inference(component_clause,[status(thm)],[f2290])).
% 3.66/0.97 fof(f2293,plain,(
% 3.66/0.97 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),
% 3.66/0.97 inference(resolution,[status(thm)],[f2141,f2286])).
% 3.66/0.97 fof(f2294,plain,(
% 3.66/0.97 spl0_11|spl0_13|~spl0_9|~spl0_12),
% 3.66/0.97 inference(split_clause,[status(thm)],[f2293,f2282,f2290,f2140,f2285])).
% 3.66/0.97 fof(f2308,plain,(
% 3.66/0.97 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_a),v_F(v_P))|~spl0_11),
% 3.66/0.97 inference(backward_demodulation,[status(thm)],[f2283,f2081])).
% 3.66/0.97 fof(f2310,plain,(
% 3.66/0.97 ~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|~spl0_11),
% 3.66/0.97 inference(resolution,[status(thm)],[f2308,f536])).
% 3.66/0.97 fof(f2311,plain,(
% 3.66/0.97 $false|~spl0_4|~spl0_11),
% 3.66/0.97 inference(forward_subsumption_resolution,[status(thm)],[f2310,f2124])).
% 3.66/0.97 fof(f2312,plain,(
% 3.66/0.97 ~spl0_4|~spl0_11),
% 3.66/0.97 inference(contradiction_clause,[status(thm)],[f2311])).
% 3.66/0.97 fof(f2346,plain,(
% 3.66/0.97 ![X0,X1,X2,X3]: (c_member(X0,X1,X2)|~c_member(X3,X1,X2))),
% 3.66/0.97 inference(resolution,[status(thm)],[f616,f615])).
% 3.66/0.97 fof(f2347,plain,(
% 3.66/0.97 ![X0]: (c_member(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),v_F(v_P)))),
% 3.66/0.97 inference(resolution,[status(thm)],[f2346,f2081])).
% 3.66/0.97 fof(f2348,plain,(
% 3.66/0.97 ![X0]: (c_member(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_a),v_F(v_P))|~spl0_13)),
% 3.66/0.97 inference(resolution,[status(thm)],[f2346,f2291])).
% 3.66/0.97 fof(f2357,plain,(
% 3.66/0.97 ![X0,X1,X2]: (c_member(X0,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))),
% 3.66/0.97 inference(resolution,[status(thm)],[f2346,f532])).
% 3.66/0.97 fof(f2431,plain,(
% 3.66/0.97 spl0_25 <=> ~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))|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))),
% 3.66/0.97 introduced(split_symbol_definition)).
% 3.66/0.97 fof(f2432,plain,(
% 3.66/0.97 ![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_b),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))|~spl0_25)),
% 3.66/0.97 inference(component_clause,[status(thm)],[f2431])).
% 3.66/0.97 fof(f2434,plain,(
% 3.66/0.97 ![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_b),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))|~spl0_13)),
% 3.66/0.97 inference(resolution,[status(thm)],[f552,f2348])).
% 3.66/0.97 fof(f2435,plain,(
% 3.66/0.97 ~spl0_3|spl0_25|~spl0_13),
% 3.66/0.97 inference(split_clause,[status(thm)],[f2434,f2119,f2431,f2290])).
% 3.66/0.97 fof(f2527,plain,(
% 3.66/0.97 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_a),v_F(v_P))|~spl0_25),
% 3.66/0.97 inference(resolution,[status(thm)],[f2432,f2347])).
% 3.66/0.97 fof(f2530,plain,(
% 3.66/0.97 ~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|~spl0_25),
% 3.66/0.97 inference(resolution,[status(thm)],[f2527,f536])).
% 3.66/0.97 fof(f2531,plain,(
% 3.66/0.97 $false|~spl0_4|~spl0_25),
% 3.66/0.97 inference(forward_subsumption_resolution,[status(thm)],[f2530,f2124])).
% 3.66/0.97 fof(f2532,plain,(
% 3.66/0.97 ~spl0_4|~spl0_25),
% 3.66/0.97 inference(contradiction_clause,[status(thm)],[f2531])).
% 3.66/0.97 fof(f2821,plain,(
% 3.66/0.97 spl0_64 <=> c_member(tc_Arrow__Order__Mirabelle_Oalt,v_b,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)))),
% 3.66/0.97 introduced(split_symbol_definition)).
% 3.66/0.97 fof(f2823,plain,(
% 3.66/0.97 ~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_64),
% 3.66/0.97 inference(component_clause,[status(thm)],[f2821])).
% 3.66/0.97 fof(f2824,plain,(
% 3.66/0.97 spl0_65 <=> c_member(tc_Arrow__Order__Mirabelle_Oalt,v_a,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)))),
% 3.66/0.97 introduced(split_symbol_definition)).
% 3.66/0.97 fof(f2826,plain,(
% 3.66/0.97 ~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_65),
% 3.66/0.97 inference(component_clause,[status(thm)],[f2824])).
% 3.66/0.97 fof(f2827,plain,(
% 3.66/0.97 ~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),
% 3.66/0.97 inference(resolution,[status(thm)],[f2080,f2280])).
% 3.66/0.97 fof(f2828,plain,(
% 3.66/0.97 ~spl0_64|~spl0_65|~spl0_10),
% 3.66/0.97 inference(split_clause,[status(thm)],[f2827,f2821,f2824,f2279])).
% 3.66/0.97 fof(f2829,plain,(
% 3.66/0.97 $false|spl0_64),
% 3.66/0.97 inference(forward_subsumption_resolution,[status(thm)],[f2823,f2357])).
% 3.66/0.97 fof(f2830,plain,(
% 3.66/0.97 spl0_64),
% 3.66/0.97 inference(contradiction_clause,[status(thm)],[f2829])).
% 3.66/0.97 fof(f2831,plain,(
% 3.66/0.97 $false|spl0_65),
% 3.66/0.97 inference(forward_subsumption_resolution,[status(thm)],[f2826,f2357])).
% 3.66/0.97 fof(f2832,plain,(
% 3.66/0.97 spl0_65),
% 3.66/0.97 inference(contradiction_clause,[status(thm)],[f2831])).
% 3.66/0.97 fof(f2833,plain,(
% 3.66/0.97 $false),
% 3.66/0.97 inference(sat_refutation,[status(thm)],[f2122,f2126,f2143,f2250,f2252,f2254,f2256,f2269,f2275,f2289,f2294,f2312,f2435,f2532,f2828,f2830,f2832])).
% 3.66/0.97 % SZS output end CNFRefutation for theBenchmark.p
% 4.41/1.02 % Elapsed time: 0.643234 seconds
% 4.41/1.02 % CPU time: 4.398592 seconds
% 4.41/1.02 % Total memory used: 158.022 MB
% 4.41/1.02 % Net memory used: 156.628 MB
%------------------------------------------------------------------------------