TSTP Solution File: SCT135+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SCT135+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 12:33:15 EDT 2023
% Result : Theorem 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.09 % Problem : SCT135+1 : TPTP v8.1.2. Released v5.2.0.
% 0.09/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n026.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue May 30 09:53:13 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.14/0.34 % Drodi V3.5.1
% 0.14/0.44 % Refutation found
% 0.14/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.44 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.44 fof(f4,axiom,(
% 0.14/0.44 v_a____ != v_b____ ),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f5,axiom,(
% 0.14/0.44 v_a____ != v_b_H____ ),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f6,axiom,(
% 0.14/0.44 v_b____ != v_a_H____ ),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f7,axiom,(
% 0.14/0.44 v_a_H____ != v_b_H____ ),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f8,axiom,(
% 0.14/0.44 (! [B_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,v_a____,v_b____),hAPP(v_P____,B_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,v_a_H____,v_b_H____),hAPP(v_P_H____,B_i)) ) )),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f9,axiom,(
% 0.14/0.44 c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P____,c_Arrow__Order__Mirabelle_OProf) ),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f10,axiom,(
% 0.14/0.44 c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P_H____,c_Arrow__Order__Mirabelle_OProf) ),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f14,axiom,(
% 0.14/0.44 (! [V_P_Ha_2,V_Pa_2,V_b_Ha_2,V_a_Ha_2,V_ba_2,V_aa_2] :( V_aa_2 != V_ba_2=> ( V_a_Ha_2 != V_b_Ha_2=> ( V_aa_2 != V_b_Ha_2=> ( V_ba_2 != V_a_Ha_2=> ( c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_Pa_2,c_Arrow__Order__Mirabelle_OProf)=> ( c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_P_Ha_2,c_Arrow__Order__Mirabelle_OProf)=> ( (! [B_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,V_aa_2,V_ba_2),hAPP(V_Pa_2,B_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,V_a_Ha_2,V_b_Ha_2),hAPP(V_P_Ha_2,B_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,V_aa_2,V_ba_2),hAPP(v_F,V_Pa_2))=> 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_Ha_2,V_b_Ha_2),hAPP(v_F,V_P_Ha_2)) ) ) ) ) ) ) ) ) )),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f15,axiom,(
% 0.14/0.44 (! [V_y_2,V_x_2,V_R_2,T_b,T_a] :( hBOOL(hAPP(hAPP(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) ) )),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f24,axiom,(
% 0.14/0.44 (! [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)) ) )),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f521,conjecture,(
% 0.14/0.44 ( 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_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,v_a_H____,v_b_H____),hAPP(v_F,v_P_H____)) ) ),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f522,negated_conjecture,(
% 0.14/0.44 ~(( 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_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,v_a_H____,v_b_H____),hAPP(v_F,v_P_H____)) ) )),
% 0.14/0.44 inference(negated_conjecture,[status(cth)],[f521])).
% 0.14/0.44 fof(f528,plain,(
% 0.14/0.44 ~v_a____=v_b____),
% 0.14/0.44 inference(cnf_transformation,[status(esa)],[f4])).
% 0.14/0.44 fof(f529,plain,(
% 0.14/0.44 ~v_a____=v_b_H____),
% 0.14/0.44 inference(cnf_transformation,[status(esa)],[f5])).
% 0.14/0.44 fof(f530,plain,(
% 0.14/0.44 ~v_b____=v_a_H____),
% 0.14/0.44 inference(cnf_transformation,[status(esa)],[f6])).
% 0.14/0.44 fof(f531,plain,(
% 0.14/0.44 ~v_a_H____=v_b_H____),
% 0.14/0.44 inference(cnf_transformation,[status(esa)],[f7])).
% 0.14/0.44 fof(f532,plain,(
% 0.14/0.44 ![B_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,v_a____,v_b____),hAPP(v_P____,B_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,v_a_H____,v_b_H____),hAPP(v_P_H____,B_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,v_a____,v_b____),hAPP(v_P____,B_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,v_a_H____,v_b_H____),hAPP(v_P_H____,B_i))))),
% 0.14/0.44 inference(NNF_transformation,[status(esa)],[f8])).
% 0.14/0.44 fof(f533,plain,(
% 0.14/0.44 (![B_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,v_a____,v_b____),hAPP(v_P____,B_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,v_a_H____,v_b_H____),hAPP(v_P_H____,B_i))))&(![B_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,v_a____,v_b____),hAPP(v_P____,B_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,v_a_H____,v_b_H____),hAPP(v_P_H____,B_i))))),
% 0.14/0.44 inference(miniscoping,[status(esa)],[f532])).
% 0.14/0.44 fof(f534,plain,(
% 0.14/0.44 ![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,v_a____,v_b____),hAPP(v_P____,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,v_a_H____,v_b_H____),hAPP(v_P_H____,X0)))),
% 0.14/0.44 inference(cnf_transformation,[status(esa)],[f533])).
% 0.14/0.44 fof(f535,plain,(
% 0.14/0.44 ![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,v_a____,v_b____),hAPP(v_P____,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,v_a_H____,v_b_H____),hAPP(v_P_H____,X0)))),
% 0.14/0.44 inference(cnf_transformation,[status(esa)],[f533])).
% 0.14/0.44 fof(f536,plain,(
% 0.14/0.44 c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P____,c_Arrow__Order__Mirabelle_OProf)),
% 0.14/0.44 inference(cnf_transformation,[status(esa)],[f9])).
% 0.14/0.44 fof(f537,plain,(
% 0.14/0.44 c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P_H____,c_Arrow__Order__Mirabelle_OProf)),
% 0.14/0.44 inference(cnf_transformation,[status(esa)],[f10])).
% 0.14/0.44 fof(f564,plain,(
% 0.14/0.44 ![V_P_Ha_2,V_Pa_2,V_b_Ha_2,V_a_Ha_2,V_ba_2,V_aa_2]: (V_aa_2=V_ba_2|(V_a_Ha_2=V_b_Ha_2|(V_aa_2=V_b_Ha_2|(V_ba_2=V_a_Ha_2|(~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_Pa_2,c_Arrow__Order__Mirabelle_OProf)|(~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_P_Ha_2,c_Arrow__Order__Mirabelle_OProf)|((?[B_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,V_aa_2,V_ba_2),hAPP(V_Pa_2,B_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,V_a_Ha_2,V_b_Ha_2),hAPP(V_P_Ha_2,B_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,V_aa_2,V_ba_2),hAPP(v_F,V_Pa_2))|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_Ha_2,V_b_Ha_2),hAPP(v_F,V_P_Ha_2))))))))))),
% 0.14/0.44 inference(pre_NNF_transformation,[status(esa)],[f14])).
% 0.14/0.44 fof(f565,plain,(
% 0.14/0.44 ![V_P_Ha_2,V_Pa_2,V_b_Ha_2,V_a_Ha_2,V_ba_2,V_aa_2]: (V_aa_2=V_ba_2|(V_a_Ha_2=V_b_Ha_2|(V_aa_2=V_b_Ha_2|(V_ba_2=V_a_Ha_2|(~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_Pa_2,c_Arrow__Order__Mirabelle_OProf)|(~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_P_Ha_2,c_Arrow__Order__Mirabelle_OProf)|((?[B_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,V_aa_2,V_ba_2),hAPP(V_Pa_2,B_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,V_a_Ha_2,V_b_Ha_2),hAPP(V_P_Ha_2,B_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,V_aa_2,V_ba_2),hAPP(V_Pa_2,B_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,V_a_Ha_2,V_b_Ha_2),hAPP(V_P_Ha_2,B_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,V_aa_2,V_ba_2),hAPP(v_F,V_Pa_2))|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_Ha_2,V_b_Ha_2),hAPP(v_F,V_P_Ha_2))))))))))),
% 0.14/0.44 inference(NNF_transformation,[status(esa)],[f564])).
% 0.14/0.44 fof(f566,plain,(
% 0.14/0.44 ![V_ba_2,V_aa_2]: (V_aa_2=V_ba_2|(![V_b_Ha_2,V_a_Ha_2]: (V_a_Ha_2=V_b_Ha_2|(V_aa_2=V_b_Ha_2|(V_ba_2=V_a_Ha_2|(![V_Pa_2]: (~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_Pa_2,c_Arrow__Order__Mirabelle_OProf)|(![V_P_Ha_2]: (~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_P_Ha_2,c_Arrow__Order__Mirabelle_OProf)|((?[B_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,V_aa_2,V_ba_2),hAPP(V_Pa_2,B_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,V_a_Ha_2,V_b_Ha_2),hAPP(V_P_Ha_2,B_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,V_aa_2,V_ba_2),hAPP(V_Pa_2,B_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,V_a_Ha_2,V_b_Ha_2),hAPP(V_P_Ha_2,B_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,V_aa_2,V_ba_2),hAPP(v_F,V_Pa_2))|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_Ha_2,V_b_Ha_2),hAPP(v_F,V_P_Ha_2)))))))))))))),
% 0.14/0.44 inference(miniscoping,[status(esa)],[f565])).
% 0.14/0.44 fof(f567,plain,(
% 0.14/0.44 ![V_ba_2,V_aa_2]: (V_aa_2=V_ba_2|(![V_b_Ha_2,V_a_Ha_2]: (V_a_Ha_2=V_b_Ha_2|(V_aa_2=V_b_Ha_2|(V_ba_2=V_a_Ha_2|(![V_Pa_2]: (~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_Pa_2,c_Arrow__Order__Mirabelle_OProf)|(![V_P_Ha_2]: (~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_P_Ha_2,c_Arrow__Order__Mirabelle_OProf)|(((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_aa_2,V_ba_2),hAPP(V_Pa_2,sk0_1(V_P_Ha_2,V_Pa_2,V_a_Ha_2,V_b_Ha_2,V_aa_2,V_ba_2)))|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_Ha_2,V_b_Ha_2),hAPP(V_P_Ha_2,sk0_1(V_P_Ha_2,V_Pa_2,V_a_Ha_2,V_b_Ha_2,V_aa_2,V_ba_2))))&(~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_aa_2,V_ba_2),hAPP(V_Pa_2,sk0_1(V_P_Ha_2,V_Pa_2,V_a_Ha_2,V_b_Ha_2,V_aa_2,V_ba_2)))|~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_Ha_2,V_b_Ha_2),hAPP(V_P_Ha_2,sk0_1(V_P_Ha_2,V_Pa_2,V_a_Ha_2,V_b_Ha_2,V_aa_2,V_ba_2)))))|(~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_aa_2,V_ba_2),hAPP(v_F,V_Pa_2))|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_Ha_2,V_b_Ha_2),hAPP(v_F,V_P_Ha_2)))))))))))))),
% 0.14/0.44 inference(skolemization,[status(esa)],[f566])).
% 0.14/0.44 fof(f568,plain,(
% 0.14/0.44 ![X0,X1,X2,X3,X4,X5]: (X0=X1|X2=X3|X0=X3|X1=X2|~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4,c_Arrow__Order__Mirabelle_OProf)|~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5,c_Arrow__Order__Mirabelle_OProf)|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(X4,sk0_1(X5,X4,X2,X3,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,X2,X3),hAPP(X5,sk0_1(X5,X4,X2,X3,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_F,X4))|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,X2,X3),hAPP(v_F,X5)))),
% 0.14/0.44 inference(cnf_transformation,[status(esa)],[f567])).
% 0.14/0.44 fof(f569,plain,(
% 0.14/0.44 ![X0,X1,X2,X3,X4,X5]: (X0=X1|X2=X3|X0=X3|X1=X2|~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4,c_Arrow__Order__Mirabelle_OProf)|~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5,c_Arrow__Order__Mirabelle_OProf)|~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(X4,sk0_1(X5,X4,X2,X3,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,X2,X3),hAPP(X5,sk0_1(X5,X4,X2,X3,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_F,X4))|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,X2,X3),hAPP(v_F,X5)))),
% 0.14/0.44 inference(cnf_transformation,[status(esa)],[f567])).
% 0.14/0.44 fof(f570,plain,(
% 0.14/0.44 ![V_y_2,V_x_2,V_R_2,T_b,T_a]: ((~hBOOL(hAPP(hAPP(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))&(hBOOL(hAPP(hAPP(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)))),
% 0.14/0.44 inference(NNF_transformation,[status(esa)],[f15])).
% 0.14/0.44 fof(f571,plain,(
% 0.14/0.44 (![V_y_2,V_x_2,V_R_2,T_b,T_a]: (~hBOOL(hAPP(hAPP(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]: (hBOOL(hAPP(hAPP(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)))),
% 0.14/0.44 inference(miniscoping,[status(esa)],[f570])).
% 0.14/0.44 fof(f572,plain,(
% 0.14/0.44 ![X0,X1,X2,X3,X4]: (~hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X0,X1,X2),X3),X4))|c_member(tc_prod(X0,X1),c_Product__Type_OPair(X0,X1,X3,X4),X2))),
% 0.14/0.44 inference(cnf_transformation,[status(esa)],[f571])).
% 0.14/0.44 fof(f609,plain,(
% 0.14/0.44 ![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))))),
% 0.14/0.44 inference(NNF_transformation,[status(esa)],[f24])).
% 0.14/0.44 fof(f610,plain,(
% 0.14/0.44 (![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))))),
% 0.14/0.44 inference(miniscoping,[status(esa)],[f609])).
% 0.14/0.44 fof(f611,plain,(
% 0.14/0.44 ![X0,X1,X2]: (~c_member(X0,X1,X2)|hBOOL(hAPP(X2,X1)))),
% 0.14/0.44 inference(cnf_transformation,[status(esa)],[f610])).
% 0.14/0.44 fof(f612,plain,(
% 0.14/0.44 ![X0,X1,X2]: (c_member(X0,X1,X2)|~hBOOL(hAPP(X2,X1)))),
% 0.14/0.44 inference(cnf_transformation,[status(esa)],[f610])).
% 0.14/0.44 fof(f2079,plain,(
% 0.14/0.44 (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_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,v_a_H____,v_b_H____),hAPP(v_F,v_P_H____)))),
% 0.14/0.44 inference(pre_NNF_transformation,[status(esa)],[f522])).
% 0.14/0.44 fof(f2080,plain,(
% 0.14/0.44 (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_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,v_a_H____,v_b_H____),hAPP(v_F,v_P_H____)))&(~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_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,v_a_H____,v_b_H____),hAPP(v_F,v_P_H____)))),
% 0.14/0.44 inference(NNF_transformation,[status(esa)],[f2079])).
% 0.14/0.44 fof(f2081,plain,(
% 0.14/0.44 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_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,v_a_H____,v_b_H____),hAPP(v_F,v_P_H____))),
% 0.14/0.44 inference(cnf_transformation,[status(esa)],[f2080])).
% 0.14/0.44 fof(f2082,plain,(
% 0.14/0.44 ~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_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,v_a_H____,v_b_H____),hAPP(v_F,v_P_H____))),
% 0.14/0.44 inference(cnf_transformation,[status(esa)],[f2080])).
% 0.14/0.44 fof(f2095,plain,(
% 0.14/0.44 spl0_0 <=> 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_F,v_P____))),
% 0.14/0.44 introduced(split_symbol_definition)).
% 0.14/0.44 fof(f2098,plain,(
% 0.14/0.44 spl0_1 <=> 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_H____,v_b_H____),hAPP(v_F,v_P_H____))),
% 0.14/0.44 introduced(split_symbol_definition)).
% 0.14/0.44 fof(f2101,plain,(
% 0.14/0.44 spl0_0|spl0_1),
% 0.14/0.44 inference(split_clause,[status(thm)],[f2081,f2095,f2098])).
% 0.14/0.44 fof(f2102,plain,(
% 0.14/0.44 ~spl0_0|~spl0_1),
% 0.14/0.44 inference(split_clause,[status(thm)],[f2082,f2095,f2098])).
% 0.14/0.44 fof(f2202,plain,(
% 0.14/0.44 ![X0,X1,X2,X3]: (c_member(X0,X1,X2)|~c_member(X3,X1,X2))),
% 0.14/0.44 inference(resolution,[status(thm)],[f612,f611])).
% 0.14/0.44 fof(f2203,plain,(
% 0.14/0.44 ![X0]: (c_member(X0,v_P_H____,c_Arrow__Order__Mirabelle_OProf))),
% 0.14/0.44 inference(resolution,[status(thm)],[f2202,f537])).
% 0.14/0.44 fof(f2204,plain,(
% 0.14/0.44 ![X0]: (c_member(X0,v_P____,c_Arrow__Order__Mirabelle_OProf))),
% 0.14/0.44 inference(resolution,[status(thm)],[f2202,f536])).
% 0.14/0.44 fof(f2205,plain,(
% 0.14/0.44 ![X0,X1]: (c_member(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,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,v_a____,v_b____),hAPP(v_P____,X1)))),
% 0.14/0.44 inference(resolution,[status(thm)],[f2202,f534])).
% 0.14/0.44 fof(f2216,plain,(
% 0.14/0.44 spl0_5 <=> X0=X1|X0=v_b_H____|X1=v_a_H____|~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2,c_Arrow__Order__Mirabelle_OProf)|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(X2,sk0_1(v_P_H____,X2,v_a_H____,v_b_H____,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_F,X2))|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____,sk0_1(v_P_H____,X2,v_a_H____,v_b_H____,X0,X1)))),
% 0.14/0.44 introduced(split_symbol_definition)).
% 0.14/0.44 fof(f2217,plain,(
% 0.14/0.44 ![X0,X1,X2]: (X0=X1|X0=v_b_H____|X1=v_a_H____|~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2,c_Arrow__Order__Mirabelle_OProf)|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(X2,sk0_1(v_P_H____,X2,v_a_H____,v_b_H____,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_F,X2))|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____,sk0_1(v_P_H____,X2,v_a_H____,v_b_H____,X0,X1)))|~spl0_5)),
% 0.14/0.44 inference(component_clause,[status(thm)],[f2216])).
% 0.14/0.44 fof(f2219,plain,(
% 0.14/0.44 spl0_6 <=> v_a_H____=v_b_H____),
% 0.14/0.44 introduced(split_symbol_definition)).
% 0.14/0.44 fof(f2220,plain,(
% 0.14/0.44 v_a_H____=v_b_H____|~spl0_6),
% 0.14/0.44 inference(component_clause,[status(thm)],[f2219])).
% 0.14/0.44 fof(f2222,plain,(
% 0.14/0.44 spl0_7 <=> c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P_H____,c_Arrow__Order__Mirabelle_OProf)),
% 0.14/0.44 introduced(split_symbol_definition)).
% 0.14/0.44 fof(f2224,plain,(
% 0.14/0.44 ~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P_H____,c_Arrow__Order__Mirabelle_OProf)|spl0_7),
% 0.14/0.44 inference(component_clause,[status(thm)],[f2222])).
% 0.14/0.44 fof(f2225,plain,(
% 0.14/0.44 ![X0,X1,X2]: (X0=X1|v_a_H____=v_b_H____|X0=v_b_H____|X1=v_a_H____|~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2,c_Arrow__Order__Mirabelle_OProf)|~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P_H____,c_Arrow__Order__Mirabelle_OProf)|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(X2,sk0_1(v_P_H____,X2,v_a_H____,v_b_H____,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_F,X2))|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_H____,v_b_H____),hAPP(v_F,v_P_H____))|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____,sk0_1(v_P_H____,X2,v_a_H____,v_b_H____,X0,X1))))),
% 0.14/0.44 inference(resolution,[status(thm)],[f568,f535])).
% 0.14/0.44 fof(f2226,plain,(
% 0.14/0.44 spl0_5|spl0_6|~spl0_7|spl0_1),
% 0.14/0.44 inference(split_clause,[status(thm)],[f2225,f2216,f2219,f2222,f2098])).
% 0.14/0.44 fof(f2235,plain,(
% 0.14/0.44 spl0_9 <=> c_member(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,sk0_1(v_P____,X1,v_a____,v_b____,X2,X3)))|X2=X3|X2=v_b____|X3=v_a____|~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)|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,X2,X3),hAPP(X1,sk0_1(v_P____,X1,v_a____,v_b____,X2,X3)))|~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,X2,X3),hAPP(v_F,X1))),
% 0.14/0.44 introduced(split_symbol_definition)).
% 0.14/0.44 fof(f2236,plain,(
% 0.14/0.44 ![X0,X1,X2,X3]: (c_member(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,sk0_1(v_P____,X1,v_a____,v_b____,X2,X3)))|X2=X3|X2=v_b____|X3=v_a____|~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)|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,X2,X3),hAPP(X1,sk0_1(v_P____,X1,v_a____,v_b____,X2,X3)))|~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,X2,X3),hAPP(v_F,X1))|~spl0_9)),
% 0.14/0.44 inference(component_clause,[status(thm)],[f2235])).
% 0.14/0.44 fof(f2238,plain,(
% 0.14/0.44 spl0_10 <=> v_a____=v_b____),
% 0.14/0.44 introduced(split_symbol_definition)).
% 0.14/0.44 fof(f2239,plain,(
% 0.14/0.44 v_a____=v_b____|~spl0_10),
% 0.14/0.44 inference(component_clause,[status(thm)],[f2238])).
% 0.14/0.44 fof(f2241,plain,(
% 0.14/0.44 spl0_11 <=> c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P____,c_Arrow__Order__Mirabelle_OProf)),
% 0.14/0.44 introduced(split_symbol_definition)).
% 0.14/0.44 fof(f2243,plain,(
% 0.14/0.44 ~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P____,c_Arrow__Order__Mirabelle_OProf)|spl0_11),
% 0.14/0.44 inference(component_clause,[status(thm)],[f2241])).
% 0.14/0.44 fof(f2244,plain,(
% 0.14/0.44 ![X0,X1,X2,X3]: (c_member(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,sk0_1(v_P____,X1,v_a____,v_b____,X2,X3)))|X2=X3|v_a____=v_b____|X2=v_b____|X3=v_a____|~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)|~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P____,c_Arrow__Order__Mirabelle_OProf)|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,X2,X3),hAPP(X1,sk0_1(v_P____,X1,v_a____,v_b____,X2,X3)))|~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,X2,X3),hAPP(v_F,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,v_a____,v_b____),hAPP(v_F,v_P____)))),
% 0.14/0.44 inference(resolution,[status(thm)],[f2205,f568])).
% 0.14/0.44 fof(f2245,plain,(
% 0.14/0.44 spl0_9|spl0_10|~spl0_11|spl0_0),
% 0.14/0.44 inference(split_clause,[status(thm)],[f2244,f2235,f2238,f2241,f2095])).
% 0.14/0.44 fof(f2246,plain,(
% 0.14/0.44 $false|spl0_11),
% 0.14/0.44 inference(forward_subsumption_resolution,[status(thm)],[f2243,f2204])).
% 0.14/0.44 fof(f2247,plain,(
% 0.14/0.44 spl0_11),
% 0.14/0.44 inference(contradiction_clause,[status(thm)],[f2246])).
% 0.14/0.44 fof(f2248,plain,(
% 0.14/0.44 spl0_12 <=> c_member(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,sk0_1(v_P____,v_P____,v_a____,v_b____,v_a____,v_b____)))),
% 0.14/0.44 introduced(split_symbol_definition)).
% 0.14/0.44 fof(f2251,plain,(
% 0.14/0.44 ![X0,X1]: (c_member(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,sk0_1(v_P____,v_P____,v_a____,v_b____,v_a____,v_b____)))|v_a____=v_b____|v_a____=v_b____|v_b____=v_a____|~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P____,c_Arrow__Order__Mirabelle_OProf)|~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_F,v_P____))|c_member(X1,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,sk0_1(v_P____,v_P____,v_a____,v_b____,v_a____,v_b____)))|~spl0_9)),
% 0.14/0.44 inference(resolution,[status(thm)],[f2236,f2205])).
% 0.14/0.44 fof(f2252,plain,(
% 0.14/0.44 spl0_12|spl0_10|~spl0_11|~spl0_0|~spl0_9),
% 0.14/0.44 inference(split_clause,[status(thm)],[f2251,f2248,f2238,f2241,f2095,f2235])).
% 0.14/0.44 fof(f2253,plain,(
% 0.14/0.44 spl0_13 <=> c_member(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,sk0_1(v_P____,v_P_H____,v_a____,v_b____,v_a_H____,v_b_H____)))),
% 0.14/0.44 introduced(split_symbol_definition)).
% 0.14/0.44 fof(f2254,plain,(
% 0.14/0.44 ![X0]: (c_member(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,sk0_1(v_P____,v_P_H____,v_a____,v_b____,v_a_H____,v_b_H____)))|~spl0_13)),
% 0.14/0.44 inference(component_clause,[status(thm)],[f2253])).
% 0.14/0.44 fof(f2256,plain,(
% 0.14/0.44 spl0_14 <=> v_a_H____=v_b____),
% 0.14/0.44 introduced(split_symbol_definition)).
% 0.14/0.44 fof(f2257,plain,(
% 0.14/0.44 v_a_H____=v_b____|~spl0_14),
% 0.14/0.44 inference(component_clause,[status(thm)],[f2256])).
% 0.14/0.44 fof(f2259,plain,(
% 0.14/0.44 spl0_15 <=> v_b_H____=v_a____),
% 0.14/0.44 introduced(split_symbol_definition)).
% 0.14/0.44 fof(f2260,plain,(
% 0.14/0.44 v_b_H____=v_a____|~spl0_15),
% 0.14/0.44 inference(component_clause,[status(thm)],[f2259])).
% 0.14/0.44 fof(f2262,plain,(
% 0.14/0.44 spl0_16 <=> 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____,sk0_1(v_P____,v_P_H____,v_a____,v_b____,v_a_H____,v_b_H____)))),
% 0.14/0.44 introduced(split_symbol_definition)).
% 0.14/0.44 fof(f2263,plain,(
% 0.14/0.44 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____,sk0_1(v_P____,v_P_H____,v_a____,v_b____,v_a_H____,v_b_H____)))|~spl0_16),
% 0.14/0.44 inference(component_clause,[status(thm)],[f2262])).
% 0.14/0.44 fof(f2265,plain,(
% 0.14/0.44 ![X0]: (c_member(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,sk0_1(v_P____,v_P_H____,v_a____,v_b____,v_a_H____,v_b_H____)))|v_a_H____=v_b_H____|v_a_H____=v_b____|v_b_H____=v_a____|~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P_H____,c_Arrow__Order__Mirabelle_OProf)|~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_H____,v_b_H____),hAPP(v_F,v_P_H____))|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____,sk0_1(v_P____,v_P_H____,v_a____,v_b____,v_a_H____,v_b_H____)))|~spl0_9)),
% 0.14/0.44 inference(resolution,[status(thm)],[f2236,f535])).
% 0.14/0.44 fof(f2266,plain,(
% 0.14/0.44 spl0_13|spl0_6|spl0_14|spl0_15|~spl0_7|~spl0_1|spl0_16|~spl0_9),
% 0.14/0.44 inference(split_clause,[status(thm)],[f2265,f2253,f2219,f2256,f2259,f2222,f2098,f2262,f2235])).
% 0.14/0.44 fof(f2273,plain,(
% 0.14/0.44 $false|spl0_7),
% 0.14/0.44 inference(forward_subsumption_resolution,[status(thm)],[f2224,f2203])).
% 0.14/0.44 fof(f2274,plain,(
% 0.14/0.44 spl0_7),
% 0.14/0.44 inference(contradiction_clause,[status(thm)],[f2273])).
% 0.14/0.44 fof(f2275,plain,(
% 0.14/0.44 $false|~spl0_6),
% 0.14/0.44 inference(forward_subsumption_resolution,[status(thm)],[f2220,f531])).
% 0.14/0.44 fof(f2276,plain,(
% 0.14/0.44 ~spl0_6),
% 0.14/0.44 inference(contradiction_clause,[status(thm)],[f2275])).
% 0.14/0.44 fof(f2277,plain,(
% 0.14/0.44 $false|~spl0_10),
% 0.14/0.44 inference(forward_subsumption_resolution,[status(thm)],[f2239,f528])).
% 0.14/0.44 fof(f2278,plain,(
% 0.14/0.44 ~spl0_10),
% 0.14/0.44 inference(contradiction_clause,[status(thm)],[f2277])).
% 0.14/0.44 fof(f2279,plain,(
% 0.14/0.44 ![X0,X1,X2,X3]: (X0=X1|X0=v_b_H____|X1=v_a_H____|~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2,c_Arrow__Order__Mirabelle_OProf)|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(X2,sk0_1(v_P_H____,X2,v_a_H____,v_b_H____,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_F,X2))|c_member(X3,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,sk0_1(v_P_H____,X2,v_a_H____,v_b_H____,X0,X1)))|~spl0_5)),
% 0.14/0.44 inference(resolution,[status(thm)],[f2217,f2205])).
% 0.14/0.44 fof(f2280,plain,(
% 0.14/0.44 ![X0,X1,X2,X3]: (X0=X1|X0=v_b_H____|X1=v_a_H____|~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2,c_Arrow__Order__Mirabelle_OProf)|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(X2,sk0_1(v_P_H____,X2,v_a_H____,v_b_H____,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_F,X2))|c_member(X3,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,sk0_1(v_P_H____,X2,v_a_H____,v_b_H____,X0,X1)))|~spl0_5)),
% 0.14/0.44 inference(resolution,[status(thm)],[f2217,f2202])).
% 0.14/0.44 fof(f2283,plain,(
% 0.14/0.44 ![X0]: (c_member(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,sk0_1(v_P____,v_P_H____,v_a____,v_b____,v_a_H____,v_b_H____)))|~spl0_16)),
% 0.14/0.44 inference(resolution,[status(thm)],[f2263,f2205])).
% 0.14/0.44 fof(f2284,plain,(
% 0.14/0.44 spl0_18 <=> 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_H____,v_b_H____),hAPP(v_P_H____,sk0_1(v_P____,v_P_H____,v_a____,v_b____,v_a_H____,v_b_H____)))),
% 0.14/0.44 introduced(split_symbol_definition)).
% 0.14/0.44 fof(f2286,plain,(
% 0.14/0.44 ~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_H____,v_b_H____),hAPP(v_P_H____,sk0_1(v_P____,v_P_H____,v_a____,v_b____,v_a_H____,v_b_H____)))|spl0_18),
% 0.14/0.44 inference(component_clause,[status(thm)],[f2284])).
% 0.14/0.44 fof(f2287,plain,(
% 0.14/0.44 v_a_H____=v_b_H____|v_a____=v_b____|v_a_H____=v_b____|v_b_H____=v_a____|~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P_H____,c_Arrow__Order__Mirabelle_OProf)|~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P____,c_Arrow__Order__Mirabelle_OProf)|~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_H____,v_b_H____),hAPP(v_P_H____,sk0_1(v_P____,v_P_H____,v_a____,v_b____,v_a_H____,v_b_H____)))|~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_H____,v_b_H____),hAPP(v_F,v_P_H____))|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_F,v_P____))|~spl0_16),
% 0.14/0.44 inference(resolution,[status(thm)],[f2263,f569])).
% 0.14/0.44 fof(f2288,plain,(
% 0.14/0.44 spl0_6|spl0_10|spl0_14|spl0_15|~spl0_7|~spl0_11|~spl0_18|~spl0_1|spl0_0|~spl0_16),
% 0.14/0.44 inference(split_clause,[status(thm)],[f2287,f2219,f2238,f2256,f2259,f2222,f2241,f2284,f2098,f2095,f2262])).
% 0.14/0.44 fof(f2302,plain,(
% 0.14/0.44 spl0_19 <=> c_member(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,sk0_1(v_P_H____,v_P____,v_a_H____,v_b_H____,v_a____,v_b____)))),
% 0.14/0.44 introduced(split_symbol_definition)).
% 0.14/0.44 fof(f2303,plain,(
% 0.14/0.44 ![X0]: (c_member(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,sk0_1(v_P_H____,v_P____,v_a_H____,v_b_H____,v_a____,v_b____)))|~spl0_19)),
% 0.14/0.44 inference(component_clause,[status(thm)],[f2302])).
% 0.14/0.44 fof(f2305,plain,(
% 0.14/0.44 ![X0,X1]: (v_a____=v_b____|v_a____=v_b_H____|v_b____=v_a_H____|~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P____,c_Arrow__Order__Mirabelle_OProf)|~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_F,v_P____))|c_member(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,sk0_1(v_P_H____,v_P____,v_a_H____,v_b_H____,v_a____,v_b____)))|c_member(X1,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,sk0_1(v_P_H____,v_P____,v_a_H____,v_b_H____,v_a____,v_b____)))|~spl0_5)),
% 0.14/0.44 inference(resolution,[status(thm)],[f2279,f2205])).
% 0.14/0.44 fof(f2306,plain,(
% 0.14/0.44 spl0_10|spl0_15|spl0_14|~spl0_11|~spl0_0|spl0_19|~spl0_5),
% 0.14/0.44 inference(split_clause,[status(thm)],[f2305,f2238,f2259,f2256,f2241,f2095,f2302,f2216])).
% 0.14/0.44 fof(f2321,plain,(
% 0.14/0.44 $false|~spl0_14),
% 0.14/0.44 inference(forward_subsumption_resolution,[status(thm)],[f2257,f530])).
% 0.14/0.44 fof(f2322,plain,(
% 0.14/0.44 ~spl0_14),
% 0.14/0.44 inference(contradiction_clause,[status(thm)],[f2321])).
% 0.14/0.44 fof(f2323,plain,(
% 0.14/0.44 $false|~spl0_15),
% 0.14/0.44 inference(forward_subsumption_resolution,[status(thm)],[f2260,f529])).
% 0.14/0.44 fof(f2324,plain,(
% 0.14/0.44 ~spl0_15),
% 0.14/0.44 inference(contradiction_clause,[status(thm)],[f2323])).
% 0.14/0.44 fof(f2326,plain,(
% 0.14/0.44 spl0_23 <=> c_member(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,sk0_1(v_P_H____,v_P____,v_a_H____,v_b_H____,v_a____,v_b____)))),
% 0.14/0.44 introduced(split_symbol_definition)).
% 0.14/0.44 fof(f2327,plain,(
% 0.14/0.44 ![X0]: (c_member(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,sk0_1(v_P_H____,v_P____,v_a_H____,v_b_H____,v_a____,v_b____)))|~spl0_23)),
% 0.14/0.44 inference(component_clause,[status(thm)],[f2326])).
% 0.14/0.44 fof(f2340,plain,(
% 0.14/0.44 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,v_a____,v_b____),hAPP(v_P____,sk0_1(v_P_H____,v_P____,v_a_H____,v_b_H____,v_a____,v_b____)))),
% 0.14/0.44 introduced(split_symbol_definition)).
% 0.14/0.44 fof(f2342,plain,(
% 0.14/0.44 ~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____,sk0_1(v_P_H____,v_P____,v_a_H____,v_b_H____,v_a____,v_b____)))|spl0_25),
% 0.14/0.44 inference(component_clause,[status(thm)],[f2340])).
% 0.14/0.44 fof(f2343,plain,(
% 0.14/0.44 v_a____=v_b____|v_a_H____=v_b_H____|v_a____=v_b_H____|v_b____=v_a_H____|~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P____,c_Arrow__Order__Mirabelle_OProf)|~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P_H____,c_Arrow__Order__Mirabelle_OProf)|~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____,sk0_1(v_P_H____,v_P____,v_a_H____,v_b_H____,v_a____,v_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,v_a____,v_b____),hAPP(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,v_a_H____,v_b_H____),hAPP(v_F,v_P_H____))|~spl0_19),
% 0.14/0.44 inference(resolution,[status(thm)],[f2303,f569])).
% 0.14/0.44 fof(f2344,plain,(
% 0.14/0.44 spl0_10|spl0_6|spl0_15|spl0_14|~spl0_11|~spl0_7|~spl0_25|~spl0_0|spl0_1|~spl0_19),
% 0.14/0.44 inference(split_clause,[status(thm)],[f2343,f2238,f2219,f2259,f2256,f2241,f2222,f2340,f2095,f2098,f2302])).
% 0.14/0.44 fof(f2346,plain,(
% 0.14/0.44 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____,sk0_1(v_P____,v_P_H____,v_a____,v_b____,v_a_H____,v_b_H____)))|~spl0_13),
% 0.14/0.44 inference(resolution,[status(thm)],[f2254,f535])).
% 0.14/0.44 fof(f2348,plain,(
% 0.14/0.44 $false|~spl0_13|spl0_18),
% 0.14/0.44 inference(forward_subsumption_resolution,[status(thm)],[f2286,f2254])).
% 0.14/0.44 fof(f2349,plain,(
% 0.14/0.44 ~spl0_13|spl0_18),
% 0.14/0.44 inference(contradiction_clause,[status(thm)],[f2348])).
% 0.14/0.44 fof(f2359,plain,(
% 0.14/0.44 v_a_H____=v_b_H____|v_a____=v_b____|v_a_H____=v_b____|v_b_H____=v_a____|~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P_H____,c_Arrow__Order__Mirabelle_OProf)|~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P____,c_Arrow__Order__Mirabelle_OProf)|~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_H____,v_b_H____),hAPP(v_P_H____,sk0_1(v_P____,v_P_H____,v_a____,v_b____,v_a_H____,v_b_H____)))|~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_H____,v_b_H____),hAPP(v_F,v_P_H____))|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_F,v_P____))|~spl0_13),
% 0.14/0.44 inference(resolution,[status(thm)],[f2346,f569])).
% 0.14/0.44 fof(f2360,plain,(
% 0.14/0.44 spl0_6|spl0_10|spl0_14|spl0_15|~spl0_7|~spl0_11|~spl0_18|~spl0_1|spl0_0|~spl0_13),
% 0.14/0.44 inference(split_clause,[status(thm)],[f2359,f2219,f2238,f2256,f2259,f2222,f2241,f2284,f2098,f2095,f2253])).
% 0.14/0.44 fof(f2362,plain,(
% 0.14/0.44 spl0_13|~spl0_16),
% 0.14/0.44 inference(split_clause,[status(thm)],[f2283,f2253,f2262])).
% 0.14/0.44 fof(f2376,plain,(
% 0.14/0.44 ![X0]: (v_a____=v_b____|v_a____=v_b_H____|v_b____=v_a_H____|~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P____,c_Arrow__Order__Mirabelle_OProf)|~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_F,v_P____))|c_member(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,sk0_1(v_P_H____,v_P____,v_a_H____,v_b_H____,v_a____,v_b____)))|~spl0_5|spl0_25)),
% 0.14/0.44 inference(resolution,[status(thm)],[f2280,f2342])).
% 0.14/0.44 fof(f2377,plain,(
% 0.14/0.44 spl0_10|spl0_15|spl0_14|~spl0_11|~spl0_0|spl0_23|~spl0_5|spl0_25),
% 0.14/0.44 inference(split_clause,[status(thm)],[f2376,f2238,f2259,f2256,f2241,f2095,f2326,f2216,f2340])).
% 0.14/0.44 fof(f2412,plain,(
% 0.14/0.44 ![X0]: (~hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P_H____,X0)),v_a_H____),v_b_H____))|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____,X0)))),
% 0.14/0.44 inference(resolution,[status(thm)],[f572,f535])).
% 0.14/0.44 fof(f2425,plain,(
% 0.14/0.44 spl0_26 <=> ~hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P_H____,sk0_1(v_P____,X0,v_a____,v_b____,X1,X2))),v_a_H____),v_b_H____))|X1=X2|X1=v_b____|X2=v_a____|~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)|~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,X1,X2),hAPP(X0,sk0_1(v_P____,X0,v_a____,v_b____,X1,X2)))|~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,X1,X2),hAPP(v_F,X0))),
% 0.14/0.44 introduced(split_symbol_definition)).
% 0.14/0.44 fof(f2428,plain,(
% 0.14/0.44 ![X0,X1,X2]: (~hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P_H____,sk0_1(v_P____,X0,v_a____,v_b____,X1,X2))),v_a_H____),v_b_H____))|X1=X2|v_a____=v_b____|X1=v_b____|X2=v_a____|~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)|~c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P____,c_Arrow__Order__Mirabelle_OProf)|~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,X1,X2),hAPP(X0,sk0_1(v_P____,X0,v_a____,v_b____,X1,X2)))|~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,X1,X2),hAPP(v_F,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,v_a____,v_b____),hAPP(v_F,v_P____)))),
% 0.14/0.44 inference(resolution,[status(thm)],[f2412,f569])).
% 0.14/0.44 fof(f2429,plain,(
% 0.14/0.44 spl0_26|spl0_10|~spl0_11|spl0_0),
% 0.14/0.44 inference(split_clause,[status(thm)],[f2428,f2425,f2238,f2241,f2095])).
% 0.14/0.44 fof(f2477,plain,(
% 0.14/0.44 $false|~spl0_23|spl0_25),
% 0.14/0.44 inference(backward_subsumption_resolution,[status(thm)],[f2342,f2327])).
% 0.14/0.44 fof(f2478,plain,(
% 0.14/0.44 ~spl0_23|spl0_25),
% 0.14/0.44 inference(contradiction_clause,[status(thm)],[f2477])).
% 0.14/0.44 fof(f2479,plain,(
% 0.14/0.44 $false),
% 0.14/0.44 inference(sat_refutation,[status(thm)],[f2101,f2102,f2226,f2245,f2247,f2252,f2266,f2274,f2276,f2278,f2288,f2306,f2322,f2324,f2344,f2349,f2360,f2362,f2377,f2429,f2478])).
% 0.14/0.44 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.47 % Elapsed time: 0.162059 seconds
% 0.14/0.47 % CPU time: 0.531538 seconds
% 0.14/0.47 % Memory used: 100.332 MB
%------------------------------------------------------------------------------