TSTP Solution File: SCT022-1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SCT022-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n007.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 12:33:05 EDT 2023
% Result : Unsatisfiable 0.15s 0.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09 % Problem : SCT022-1 : TPTP v8.1.2. Released v4.1.0.
% 0.08/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n007.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 09:23:16 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.15/0.36 % Drodi V3.5.1
% 0.15/0.40 % Refutation found
% 0.15/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.15/0.40 fof(f670,axiom,(
% 0.15/0.40 (![V_x,V_z,T_a,V_r,V_y]: (( hBOOL(c_in(c_Pair(V_x,V_z,T_a,T_a),V_r,tc_prod(T_a,T_a)))| ~ hBOOL(c_in(c_Pair(V_y,V_z,T_a,T_a),V_r,tc_prod(T_a,T_a)))| ~ hBOOL(c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a)))| ~ c_Relation_Otrans(V_r,T_a) ) ))),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f672,axiom,(
% 0.15/0.40 (![V_x,T_a,V_r]: (( ~ hBOOL(c_in(c_Pair(V_x,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)))| ~ c_Relation_Oirrefl(V_r,T_a) ) ))),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f675,axiom,(
% 0.15/0.40 (![V_x,T_a]: (hBOOL(c_in(V_x,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a)) ))),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f676,axiom,(
% 0.15/0.40 (![V_xa,V_x,T_a,V_r,V_A]: (( hBOOL(c_in(c_Pair(V_xa,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)))| hBOOL(c_in(c_Pair(V_x,V_xa,T_a,T_a),V_r,tc_prod(T_a,T_a)))| V_x = V_xa| ~ hBOOL(c_in(V_xa,V_A,T_a))| ~ hBOOL(c_in(V_x,V_A,T_a))| ~ c_Relation_Ototal__on(V_A,V_r,T_a) ) ))),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f677,axiom,(
% 0.15/0.40 (![V_x,V_S,T_a]: (( hBOOL(c_in(V_x,V_S,T_a))| ~ hBOOL(hAPP(V_S,V_x)) ) ))),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f678,axiom,(
% 0.15/0.40 (![V_S,V_x,T_a]: (( hBOOL(hAPP(V_S,V_x))| ~ hBOOL(c_in(V_x,V_S,T_a)) ) ))),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f679,negated_conjecture,(
% 0.15/0.40 (![V_x]: (c_Relation_Otrans(hAPP(v_P,V_x),tc_Arrow__Order__Mirabelle_Oalt) ))),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f680,negated_conjecture,(
% 0.15/0.40 (![V_x]: (c_Relation_Oirrefl(hAPP(v_P,V_x),tc_Arrow__Order__Mirabelle_Oalt) ))),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f681,negated_conjecture,(
% 0.15/0.40 (![V_x]: (c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,V_x),tc_Arrow__Order__Mirabelle_Oalt) ))),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f682,negated_conjecture,(
% 0.15/0.40 hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f683,negated_conjecture,(
% 0.15/0.40 ~ hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f684,negated_conjecture,(
% 0.15/0.40 ( c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)| ~ c_Relation_Oirrefl(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)| ~ c_Relation_Otrans(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt) ) ),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f685,negated_conjecture,(
% 0.15/0.40 ( c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)| ~ c_Relation_Oirrefl(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)| ~ c_Relation_Otrans(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt) ) ),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f687,negated_conjecture,(
% 0.15/0.40 (![V_a,V_b]: (( hBOOL(c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))| ~ hBOOL(c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))| V_a = V_b| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_xa),tc_Arrow__Order__Mirabelle_Oalt)| ~ c_Relation_Oirrefl(hAPP(v_P,v_xa),tc_Arrow__Order__Mirabelle_Oalt)| ~ c_Relation_Otrans(hAPP(v_P,v_xa),tc_Arrow__Order__Mirabelle_Oalt) ) ))),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.41 fof(f1701,plain,(
% 0.15/0.41 ![T_a,V_r]: ((![V_x,V_y]: ((![V_z]: (hBOOL(c_in(c_Pair(V_x,V_z,T_a,T_a),V_r,tc_prod(T_a,T_a)))|~hBOOL(c_in(c_Pair(V_y,V_z,T_a,T_a),V_r,tc_prod(T_a,T_a)))))|~hBOOL(c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a)))))|~c_Relation_Otrans(V_r,T_a))),
% 0.15/0.41 inference(miniscoping,[status(esa)],[f670])).
% 0.15/0.41 fof(f1702,plain,(
% 0.15/0.41 ![X0,X1,X2,X3,X4]: (hBOOL(c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)))|~hBOOL(c_in(c_Pair(X4,X1,X2,X2),X3,tc_prod(X2,X2)))|~hBOOL(c_in(c_Pair(X0,X4,X2,X2),X3,tc_prod(X2,X2)))|~c_Relation_Otrans(X3,X2))),
% 0.15/0.41 inference(cnf_transformation,[status(esa)],[f1701])).
% 0.15/0.41 fof(f1705,plain,(
% 0.15/0.41 ![T_a,V_r]: ((![V_x]: ~hBOOL(c_in(c_Pair(V_x,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))))|~c_Relation_Oirrefl(V_r,T_a))),
% 0.15/0.41 inference(miniscoping,[status(esa)],[f672])).
% 0.15/0.41 fof(f1706,plain,(
% 0.15/0.41 ![X0,X1,X2]: (~hBOOL(c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1)))|~c_Relation_Oirrefl(X2,X1))),
% 0.15/0.41 inference(cnf_transformation,[status(esa)],[f1705])).
% 0.15/0.41 fof(f1709,plain,(
% 0.15/0.41 ![X0,X1]: (hBOOL(c_in(X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)))),
% 0.15/0.41 inference(cnf_transformation,[status(esa)],[f675])).
% 0.15/0.41 fof(f1710,plain,(
% 0.15/0.41 ![T_a,V_r,V_A]: ((![V_x]: ((![V_xa]: (((hBOOL(c_in(c_Pair(V_xa,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)))|hBOOL(c_in(c_Pair(V_x,V_xa,T_a,T_a),V_r,tc_prod(T_a,T_a))))|V_x=V_xa)|~hBOOL(c_in(V_xa,V_A,T_a))))|~hBOOL(c_in(V_x,V_A,T_a))))|~c_Relation_Ototal__on(V_A,V_r,T_a))),
% 0.15/0.41 inference(miniscoping,[status(esa)],[f676])).
% 0.15/0.41 fof(f1711,plain,(
% 0.15/0.41 ![X0,X1,X2,X3,X4]: (hBOOL(c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)))|hBOOL(c_in(c_Pair(X1,X0,X2,X2),X3,tc_prod(X2,X2)))|X1=X0|~hBOOL(c_in(X0,X4,X2))|~hBOOL(c_in(X1,X4,X2))|~c_Relation_Ototal__on(X4,X3,X2))),
% 0.15/0.41 inference(cnf_transformation,[status(esa)],[f1710])).
% 0.15/0.41 fof(f1712,plain,(
% 0.15/0.41 ![V_x,V_S]: ((![T_a]: hBOOL(c_in(V_x,V_S,T_a)))|~hBOOL(hAPP(V_S,V_x)))),
% 0.15/0.41 inference(miniscoping,[status(esa)],[f677])).
% 0.15/0.41 fof(f1713,plain,(
% 0.15/0.41 ![X0,X1,X2]: (hBOOL(c_in(X0,X1,X2))|~hBOOL(hAPP(X1,X0)))),
% 0.15/0.41 inference(cnf_transformation,[status(esa)],[f1712])).
% 0.15/0.41 fof(f1714,plain,(
% 0.15/0.41 ![V_S,V_x]: (hBOOL(hAPP(V_S,V_x))|(![T_a]: ~hBOOL(c_in(V_x,V_S,T_a))))),
% 0.15/0.41 inference(miniscoping,[status(esa)],[f678])).
% 0.15/0.41 fof(f1715,plain,(
% 0.15/0.41 ![X0,X1,X2]: (hBOOL(hAPP(X0,X1))|~hBOOL(c_in(X1,X0,X2)))),
% 0.15/0.41 inference(cnf_transformation,[status(esa)],[f1714])).
% 0.15/0.41 fof(f1716,plain,(
% 0.15/0.41 ![X0]: (c_Relation_Otrans(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt))),
% 0.15/0.41 inference(cnf_transformation,[status(esa)],[f679])).
% 0.15/0.41 fof(f1717,plain,(
% 0.15/0.41 ![X0]: (c_Relation_Oirrefl(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt))),
% 0.15/0.41 inference(cnf_transformation,[status(esa)],[f680])).
% 0.15/0.41 fof(f1718,plain,(
% 0.15/0.41 ![X0]: (c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt))),
% 0.15/0.41 inference(cnf_transformation,[status(esa)],[f681])).
% 0.15/0.41 fof(f1719,plain,(
% 0.15/0.41 hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.15/0.41 inference(cnf_transformation,[status(esa)],[f682])).
% 0.15/0.41 fof(f1720,plain,(
% 0.15/0.41 ~hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.15/0.41 inference(cnf_transformation,[status(esa)],[f683])).
% 0.15/0.41 fof(f1721,plain,(
% 0.15/0.41 c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oirrefl(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Otrans(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)),
% 0.15/0.41 inference(cnf_transformation,[status(esa)],[f684])).
% 0.15/0.41 fof(f1722,plain,(
% 0.15/0.41 c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oirrefl(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Otrans(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)),
% 0.15/0.41 inference(cnf_transformation,[status(esa)],[f685])).
% 0.15/0.41 fof(f1724,plain,(
% 0.15/0.41 (((![V_a,V_b]: ((hBOOL(c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~hBOOL(c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))|V_a=V_b))|~c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_xa),tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Oirrefl(hAPP(v_P,v_xa),tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Otrans(hAPP(v_P,v_xa),tc_Arrow__Order__Mirabelle_Oalt)),
% 0.15/0.41 inference(miniscoping,[status(esa)],[f687])).
% 0.15/0.41 fof(f1725,plain,(
% 0.15/0.41 ![X0,X1]: (hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|X0=X1|~c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_xa),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Oirrefl(hAPP(v_P,v_xa),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Otrans(hAPP(v_P,v_xa),tc_Arrow__Order__Mirabelle_Oalt))),
% 0.15/0.41 inference(cnf_transformation,[status(esa)],[f1724])).
% 0.15/0.41 fof(f1765,plain,(
% 0.15/0.41 spl0_0 <=> c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)),
% 0.15/0.41 introduced(split_symbol_definition)).
% 0.15/0.41 fof(f1768,plain,(
% 0.15/0.41 spl0_1 <=> c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)),
% 0.15/0.41 introduced(split_symbol_definition)).
% 0.15/0.41 fof(f1770,plain,(
% 0.15/0.41 ~c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)|spl0_1),
% 0.15/0.41 inference(component_clause,[status(thm)],[f1768])).
% 0.15/0.41 fof(f1771,plain,(
% 0.15/0.41 spl0_2 <=> c_Relation_Oirrefl(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)),
% 0.15/0.41 introduced(split_symbol_definition)).
% 0.15/0.41 fof(f1773,plain,(
% 0.15/0.41 ~c_Relation_Oirrefl(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)|spl0_2),
% 0.15/0.41 inference(component_clause,[status(thm)],[f1771])).
% 0.15/0.41 fof(f1774,plain,(
% 0.15/0.41 spl0_3 <=> c_Relation_Otrans(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)),
% 0.15/0.41 introduced(split_symbol_definition)).
% 0.15/0.41 fof(f1776,plain,(
% 0.15/0.41 ~c_Relation_Otrans(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)|spl0_3),
% 0.15/0.41 inference(component_clause,[status(thm)],[f1774])).
% 0.15/0.41 fof(f1777,plain,(
% 0.15/0.41 spl0_0|~spl0_1|~spl0_2|~spl0_3),
% 0.15/0.41 inference(split_clause,[status(thm)],[f1721,f1765,f1768,f1771,f1774])).
% 0.15/0.41 fof(f1778,plain,(
% 0.15/0.41 spl0_4 <=> c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)),
% 0.15/0.41 introduced(split_symbol_definition)).
% 0.15/0.41 fof(f1779,plain,(
% 0.15/0.41 c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_4),
% 0.15/0.41 inference(component_clause,[status(thm)],[f1778])).
% 0.15/0.41 fof(f1781,plain,(
% 0.15/0.41 spl0_4|~spl0_1|~spl0_2|~spl0_3),
% 0.15/0.41 inference(split_clause,[status(thm)],[f1722,f1778,f1768,f1771,f1774])).
% 0.15/0.41 fof(f1786,plain,(
% 0.15/0.41 spl0_6 <=> hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|X0=X1),
% 0.15/0.41 introduced(split_symbol_definition)).
% 0.15/0.41 fof(f1787,plain,(
% 0.15/0.41 ![X0,X1]: (hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|X0=X1|~spl0_6)),
% 0.15/0.41 inference(component_clause,[status(thm)],[f1786])).
% 0.15/0.41 fof(f1789,plain,(
% 0.15/0.41 spl0_7 <=> c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_xa),tc_Arrow__Order__Mirabelle_Oalt)),
% 0.15/0.41 introduced(split_symbol_definition)).
% 0.15/0.41 fof(f1791,plain,(
% 0.15/0.41 ~c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_xa),tc_Arrow__Order__Mirabelle_Oalt)|spl0_7),
% 0.15/0.41 inference(component_clause,[status(thm)],[f1789])).
% 0.15/0.41 fof(f1792,plain,(
% 0.15/0.41 spl0_8 <=> c_Relation_Oirrefl(hAPP(v_P,v_xa),tc_Arrow__Order__Mirabelle_Oalt)),
% 0.15/0.41 introduced(split_symbol_definition)).
% 0.15/0.41 fof(f1794,plain,(
% 0.15/0.41 ~c_Relation_Oirrefl(hAPP(v_P,v_xa),tc_Arrow__Order__Mirabelle_Oalt)|spl0_8),
% 0.15/0.41 inference(component_clause,[status(thm)],[f1792])).
% 0.15/0.41 fof(f1795,plain,(
% 0.15/0.41 spl0_9 <=> c_Relation_Otrans(hAPP(v_P,v_xa),tc_Arrow__Order__Mirabelle_Oalt)),
% 0.15/0.41 introduced(split_symbol_definition)).
% 0.15/0.41 fof(f1797,plain,(
% 0.15/0.41 ~c_Relation_Otrans(hAPP(v_P,v_xa),tc_Arrow__Order__Mirabelle_Oalt)|spl0_9),
% 0.15/0.41 inference(component_clause,[status(thm)],[f1795])).
% 0.15/0.41 fof(f1798,plain,(
% 0.15/0.41 spl0_6|~spl0_7|~spl0_8|~spl0_9),
% 0.15/0.41 inference(split_clause,[status(thm)],[f1725,f1786,f1789,f1792,f1795])).
% 0.15/0.41 fof(f1802,plain,(
% 0.15/0.41 hBOOL(hAPP(v_F(v_P),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.15/0.41 inference(resolution,[status(thm)],[f1715,f1719])).
% 0.15/0.41 fof(f1804,plain,(
% 0.15/0.41 $false|spl0_9),
% 0.15/0.41 inference(forward_subsumption_resolution,[status(thm)],[f1797,f1716])).
% 0.15/0.41 fof(f1805,plain,(
% 0.15/0.41 spl0_9),
% 0.15/0.41 inference(contradiction_clause,[status(thm)],[f1804])).
% 0.15/0.41 fof(f1806,plain,(
% 0.15/0.41 $false|spl0_8),
% 0.15/0.41 inference(forward_subsumption_resolution,[status(thm)],[f1794,f1717])).
% 0.15/0.41 fof(f1807,plain,(
% 0.15/0.41 spl0_8),
% 0.15/0.41 inference(contradiction_clause,[status(thm)],[f1806])).
% 0.15/0.41 fof(f1808,plain,(
% 0.15/0.41 $false|spl0_3),
% 0.15/0.41 inference(forward_subsumption_resolution,[status(thm)],[f1776,f1716])).
% 0.15/0.41 fof(f1809,plain,(
% 0.15/0.41 spl0_3),
% 0.15/0.41 inference(contradiction_clause,[status(thm)],[f1808])).
% 0.15/0.41 fof(f1810,plain,(
% 0.15/0.41 $false|spl0_2),
% 0.15/0.41 inference(forward_subsumption_resolution,[status(thm)],[f1773,f1717])).
% 0.15/0.41 fof(f1811,plain,(
% 0.15/0.41 spl0_2),
% 0.15/0.41 inference(contradiction_clause,[status(thm)],[f1810])).
% 0.15/0.41 fof(f1812,plain,(
% 0.15/0.41 $false|spl0_1),
% 0.15/0.41 inference(forward_subsumption_resolution,[status(thm)],[f1770,f1718])).
% 0.15/0.41 fof(f1813,plain,(
% 0.15/0.41 spl0_1),
% 0.15/0.41 inference(contradiction_clause,[status(thm)],[f1812])).
% 0.15/0.41 fof(f1814,plain,(
% 0.15/0.41 $false|spl0_7),
% 0.15/0.41 inference(forward_subsumption_resolution,[status(thm)],[f1791,f1718])).
% 0.15/0.41 fof(f1815,plain,(
% 0.15/0.41 spl0_7),
% 0.15/0.41 inference(contradiction_clause,[status(thm)],[f1814])).
% 0.15/0.41 fof(f1816,plain,(
% 0.15/0.41 ![X0,X1]: (hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|X0=X1|~hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_6)),
% 0.15/0.41 inference(resolution,[status(thm)],[f1787,f1713])).
% 0.15/0.41 fof(f1817,plain,(
% 0.15/0.41 ![X0,X1]: (X0=X1|~hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|hBOOL(hAPP(v_F(v_P),c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_6)),
% 0.15/0.41 inference(resolution,[status(thm)],[f1816,f1715])).
% 0.15/0.41 fof(f1836,plain,(
% 0.15/0.41 ![X0,X1,X2]: (~c_Relation_Oirrefl(X0,X1)|~hBOOL(hAPP(X0,c_Pair(X2,X2,X1,X1))))),
% 0.15/0.41 inference(resolution,[status(thm)],[f1706,f1713])).
% 0.15/0.41 fof(f1891,plain,(
% 0.15/0.41 ![X0,X1,X2,X3,X4]: (hBOOL(c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)))|~hBOOL(c_in(c_Pair(X0,X4,X2,X2),X3,tc_prod(X2,X2)))|~c_Relation_Otrans(X3,X2)|~hBOOL(hAPP(X3,c_Pair(X4,X1,X2,X2))))),
% 0.15/0.41 inference(resolution,[status(thm)],[f1702,f1713])).
% 0.15/0.41 fof(f1903,plain,(
% 0.15/0.41 ![X0,X1,X2,X3,X4]: (hBOOL(c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)))|~c_Relation_Otrans(X3,X2)|~hBOOL(hAPP(X3,c_Pair(X4,X1,X2,X2)))|~hBOOL(hAPP(X3,c_Pair(X0,X4,X2,X2))))),
% 0.15/0.41 inference(resolution,[status(thm)],[f1891,f1713])).
% 0.15/0.41 fof(f1921,plain,(
% 0.15/0.41 ![X0,X1,X2,X3]: (~c_Relation_Otrans(X0,X1)|~hBOOL(hAPP(X0,c_Pair(X2,X3,X1,X1)))|~hBOOL(hAPP(X0,c_Pair(X3,X2,X1,X1)))|~c_Relation_Oirrefl(X0,X1))),
% 0.15/0.41 inference(resolution,[status(thm)],[f1903,f1706])).
% 0.15/0.41 fof(f1925,plain,(
% 0.15/0.41 spl0_24 <=> hBOOL(hAPP(v_F(v_P),c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.15/0.41 introduced(split_symbol_definition)).
% 0.15/0.41 fof(f1928,plain,(
% 0.15/0.41 ~c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)|~hBOOL(hAPP(v_F(v_P),c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)),
% 0.15/0.41 inference(resolution,[status(thm)],[f1921,f1802])).
% 0.15/0.41 fof(f1929,plain,(
% 0.15/0.41 ~spl0_0|~spl0_24|~spl0_4),
% 0.15/0.41 inference(split_clause,[status(thm)],[f1928,f1765,f1925,f1778])).
% 0.15/0.41 fof(f1950,plain,(
% 0.15/0.41 spl0_27 <=> v_a=v_b),
% 0.15/0.41 introduced(split_symbol_definition)).
% 0.15/0.41 fof(f1951,plain,(
% 0.15/0.41 v_a=v_b|~spl0_27),
% 0.15/0.41 inference(component_clause,[status(thm)],[f1950])).
% 0.15/0.41 fof(f1953,plain,(
% 0.15/0.41 spl0_28 <=> ~hBOOL(c_in(v_b,X0,tc_Arrow__Order__Mirabelle_Oalt))|~hBOOL(c_in(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Ototal__on(X0,hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt)),
% 0.15/0.41 introduced(split_symbol_definition)).
% 0.15/0.41 fof(f1954,plain,(
% 0.15/0.41 ![X0]: (~hBOOL(c_in(v_b,X0,tc_Arrow__Order__Mirabelle_Oalt))|~hBOOL(c_in(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Ototal__on(X0,hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_28)),
% 0.15/0.41 inference(component_clause,[status(thm)],[f1953])).
% 0.15/0.41 fof(f1962,plain,(
% 0.15/0.41 ![X0,X1,X2,X3,X4]: (hBOOL(c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)))|X1=X0|~hBOOL(c_in(X0,X4,X2))|~hBOOL(c_in(X1,X4,X2))|~c_Relation_Ototal__on(X4,X3,X2)|hBOOL(hAPP(X3,c_Pair(X1,X0,X2,X2))))),
% 0.15/0.41 inference(resolution,[status(thm)],[f1711,f1715])).
% 0.15/0.41 fof(f1963,plain,(
% 0.15/0.41 spl0_29 <=> hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.15/0.41 introduced(split_symbol_definition)).
% 0.15/0.41 fof(f1964,plain,(
% 0.15/0.41 hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_29),
% 0.15/0.42 inference(component_clause,[status(thm)],[f1963])).
% 0.15/0.42 fof(f1966,plain,(
% 0.15/0.42 ![X0]: (v_b=v_a|~hBOOL(c_in(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt))|~hBOOL(c_in(v_b,X0,tc_Arrow__Order__Mirabelle_Oalt))|~c_Relation_Ototal__on(X0,hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt)|hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))),
% 0.15/0.42 inference(resolution,[status(thm)],[f1962,f1720])).
% 0.15/0.42 fof(f1967,plain,(
% 0.15/0.42 spl0_27|spl0_28|spl0_29),
% 0.15/0.42 inference(split_clause,[status(thm)],[f1966,f1950,f1953,f1963])).
% 0.15/0.42 fof(f2043,plain,(
% 0.15/0.42 hBOOL(hAPP(v_F(v_P),c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_27),
% 0.15/0.42 inference(backward_demodulation,[status(thm)],[f1951,f1802])).
% 0.15/0.42 fof(f2052,plain,(
% 0.15/0.42 spl0_38 <=> hBOOL(hAPP(v_F(v_P),c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.15/0.42 introduced(split_symbol_definition)).
% 0.15/0.42 fof(f2053,plain,(
% 0.15/0.42 hBOOL(hAPP(v_F(v_P),c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_38),
% 0.15/0.42 inference(component_clause,[status(thm)],[f2052])).
% 0.15/0.42 fof(f2065,plain,(
% 0.15/0.42 ~c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)|~spl0_38),
% 0.15/0.42 inference(resolution,[status(thm)],[f2053,f1836])).
% 0.15/0.42 fof(f2066,plain,(
% 0.15/0.42 $false|~spl0_4|~spl0_38),
% 0.15/0.42 inference(forward_subsumption_resolution,[status(thm)],[f2065,f1779])).
% 0.15/0.42 fof(f2067,plain,(
% 0.15/0.42 ~spl0_4|~spl0_38),
% 0.15/0.42 inference(contradiction_clause,[status(thm)],[f2066])).
% 0.15/0.42 fof(f2118,plain,(
% 0.15/0.42 spl0_46 <=> hBOOL(c_in(v_b,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt))),
% 0.15/0.42 introduced(split_symbol_definition)).
% 0.15/0.42 fof(f2120,plain,(
% 0.15/0.42 ~hBOOL(c_in(v_b,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt))|spl0_46),
% 0.15/0.42 inference(component_clause,[status(thm)],[f2118])).
% 0.15/0.42 fof(f2121,plain,(
% 0.15/0.42 spl0_47 <=> hBOOL(c_in(v_a,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt))),
% 0.15/0.43 introduced(split_symbol_definition)).
% 0.15/0.43 fof(f2123,plain,(
% 0.15/0.43 ~hBOOL(c_in(v_a,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt))|spl0_47),
% 0.15/0.43 inference(component_clause,[status(thm)],[f2121])).
% 0.15/0.43 fof(f2126,plain,(
% 0.15/0.43 $false|spl0_47),
% 0.15/0.43 inference(forward_subsumption_resolution,[status(thm)],[f2123,f1709])).
% 0.15/0.43 fof(f2127,plain,(
% 0.15/0.43 spl0_47),
% 0.15/0.43 inference(contradiction_clause,[status(thm)],[f2126])).
% 0.15/0.43 fof(f2128,plain,(
% 0.15/0.43 $false|spl0_46),
% 0.15/0.43 inference(forward_subsumption_resolution,[status(thm)],[f2120,f1709])).
% 0.15/0.43 fof(f2129,plain,(
% 0.15/0.43 spl0_46),
% 0.15/0.43 inference(contradiction_clause,[status(thm)],[f2128])).
% 0.15/0.43 fof(f2130,plain,(
% 0.15/0.43 spl0_38|~spl0_27),
% 0.15/0.43 inference(split_clause,[status(thm)],[f2043,f2052,f1950])).
% 0.15/0.43 fof(f2155,plain,(
% 0.15/0.43 spl0_52 <=> c_Relation_Oirrefl(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt)),
% 0.15/0.43 introduced(split_symbol_definition)).
% 0.15/0.43 fof(f2157,plain,(
% 0.15/0.43 ~c_Relation_Oirrefl(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt)|spl0_52),
% 0.15/0.43 inference(component_clause,[status(thm)],[f2155])).
% 0.15/0.43 fof(f2161,plain,(
% 0.15/0.43 $false|spl0_52),
% 0.15/0.43 inference(forward_subsumption_resolution,[status(thm)],[f2157,f1717])).
% 0.15/0.43 fof(f2162,plain,(
% 0.15/0.43 spl0_52),
% 0.15/0.43 inference(contradiction_clause,[status(thm)],[f2161])).
% 0.15/0.43 fof(f2165,plain,(
% 0.15/0.43 ~hBOOL(c_in(v_b,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt))|~hBOOL(c_in(v_a,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt))|~spl0_28),
% 0.15/0.43 inference(resolution,[status(thm)],[f1954,f1718])).
% 0.15/0.43 fof(f2166,plain,(
% 0.15/0.43 ~spl0_46|~spl0_47|~spl0_28),
% 0.15/0.43 inference(split_clause,[status(thm)],[f2165,f2118,f2121,f1953])).
% 0.15/0.43 fof(f2167,plain,(
% 0.15/0.43 v_b=v_a|hBOOL(hAPP(v_F(v_P),c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))|~spl0_29|~spl0_6),
% 0.15/0.43 inference(resolution,[status(thm)],[f1964,f1817])).
% 0.15/0.43 fof(f2168,plain,(
% 0.15/0.43 spl0_27|spl0_24|~spl0_29|~spl0_6),
% 0.15/0.43 inference(split_clause,[status(thm)],[f2167,f1950,f1925,f1963,f1786])).
% 0.15/0.43 fof(f2179,plain,(
% 0.15/0.43 $false),
% 0.15/0.43 inference(sat_refutation,[status(thm)],[f1777,f1781,f1798,f1805,f1807,f1809,f1811,f1813,f1815,f1929,f1967,f2067,f2127,f2129,f2130,f2162,f2166,f2168])).
% 0.15/0.43 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/0.43 % Elapsed time: 0.118033 seconds
% 0.15/0.43 % CPU time: 0.441654 seconds
% 0.15/0.43 % Memory used: 59.598 MB
%------------------------------------------------------------------------------