TSTP Solution File: LCL494+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : LCL494+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n029.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 20:27:19 EDT 2024
% Result : Theorem 0.16s 0.39s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : LCL494+1 : TPTP v8.1.2. Released v3.3.0.
% 0.09/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.34 % Computer : n029.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8042.1875MB
% 0.10/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Apr 29 20:48:04 EDT 2024
% 0.10/0.35 % CPUTime :
% 0.16/0.36 % Drodi V3.6.0
% 0.16/0.39 % Refutation found
% 0.16/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.16/0.39 fof(f1,axiom,(
% 0.16/0.39 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 0.16/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.39 fof(f14,axiom,(
% 0.16/0.39 ( equivalence_2<=> (! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(Y,X))) )) ),
% 0.16/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.39 fof(f23,axiom,(
% 0.16/0.39 ( r2<=> (! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) )) ),
% 0.16/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.39 fof(f24,axiom,(
% 0.16/0.39 ( r3<=> (! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) )) ),
% 0.16/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.39 fof(f27,axiom,(
% 0.16/0.39 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 0.16/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.39 fof(f28,axiom,(
% 0.16/0.39 ( op_and=> (! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) )) ),
% 0.16/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.39 fof(f29,axiom,(
% 0.16/0.39 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 0.16/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.39 fof(f30,axiom,(
% 0.16/0.39 ( op_implies_or=> (! [X,Y] : implies(X,Y) = or(not(X),Y) )) ),
% 0.16/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.39 fof(f31,axiom,(
% 0.16/0.39 ( op_equiv=> (! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) )) ),
% 0.16/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.39 fof(f32,axiom,(
% 0.16/0.39 op_implies_or ),
% 0.16/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.39 fof(f33,axiom,(
% 0.16/0.39 op_and ),
% 0.16/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.39 fof(f34,axiom,(
% 0.16/0.39 op_equiv ),
% 0.16/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.39 fof(f35,axiom,(
% 0.16/0.39 modus_ponens ),
% 0.16/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.39 fof(f37,axiom,(
% 0.16/0.39 r2 ),
% 0.16/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.39 fof(f38,axiom,(
% 0.16/0.39 r3 ),
% 0.16/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.39 fof(f42,axiom,(
% 0.16/0.39 op_or ),
% 0.16/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.39 fof(f43,axiom,(
% 0.16/0.39 op_implies_and ),
% 0.16/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.39 fof(f45,conjecture,(
% 0.16/0.39 equivalence_2 ),
% 0.16/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.39 fof(f46,negated_conjecture,(
% 0.16/0.39 ~(equivalence_2 )),
% 0.16/0.39 inference(negated_conjecture,[status(cth)],[f45])).
% 0.16/0.39 fof(f47,plain,(
% 0.16/0.39 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 0.16/0.39 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 0.16/0.39 fof(f48,plain,(
% 0.16/0.39 (~modus_ponens|(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y))))&(modus_ponens|(?[X,Y]: ((is_a_theorem(X)&is_a_theorem(implies(X,Y)))&~is_a_theorem(Y))))),
% 0.16/0.39 inference(NNF_transformation,[status(esa)],[f47])).
% 0.16/0.39 fof(f49,plain,(
% 0.16/0.39 (~modus_ponens|(![Y]: ((![X]: (~is_a_theorem(X)|~is_a_theorem(implies(X,Y))))|is_a_theorem(Y))))&(modus_ponens|(?[Y]: ((?[X]: (is_a_theorem(X)&is_a_theorem(implies(X,Y))))&~is_a_theorem(Y))))),
% 0.16/0.39 inference(miniscoping,[status(esa)],[f48])).
% 0.16/0.39 fof(f50,plain,(
% 0.16/0.39 (~modus_ponens|(![Y]: ((![X]: (~is_a_theorem(X)|~is_a_theorem(implies(X,Y))))|is_a_theorem(Y))))&(modus_ponens|((is_a_theorem(sk0_1)&is_a_theorem(implies(sk0_1,sk0_0)))&~is_a_theorem(sk0_0)))),
% 0.16/0.39 inference(skolemization,[status(esa)],[f49])).
% 0.16/0.39 fof(f51,plain,(
% 0.16/0.39 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 0.16/0.39 inference(cnf_transformation,[status(esa)],[f50])).
% 0.16/0.39 fof(f105,plain,(
% 0.16/0.39 (~equivalence_2|(![X,Y]: is_a_theorem(implies(equiv(X,Y),implies(Y,X)))))&(equivalence_2|(?[X,Y]: ~is_a_theorem(implies(equiv(X,Y),implies(Y,X)))))),
% 0.16/0.39 inference(NNF_transformation,[status(esa)],[f14])).
% 0.16/0.39 fof(f106,plain,(
% 0.16/0.39 (~equivalence_2|(![X,Y]: is_a_theorem(implies(equiv(X,Y),implies(Y,X)))))&(equivalence_2|~is_a_theorem(implies(equiv(sk0_28,sk0_29),implies(sk0_29,sk0_28))))),
% 0.16/0.39 inference(skolemization,[status(esa)],[f105])).
% 0.16/0.39 fof(f108,plain,(
% 0.16/0.39 equivalence_2|~is_a_theorem(implies(equiv(sk0_28,sk0_29),implies(sk0_29,sk0_28)))),
% 0.16/0.39 inference(cnf_transformation,[status(esa)],[f106])).
% 0.16/0.39 fof(f141,plain,(
% 0.16/0.39 (~r2|(![P,Q]: is_a_theorem(implies(Q,or(P,Q)))))&(r2|(?[P,Q]: ~is_a_theorem(implies(Q,or(P,Q)))))),
% 0.16/0.39 inference(NNF_transformation,[status(esa)],[f23])).
% 0.16/0.39 fof(f142,plain,(
% 0.16/0.39 (~r2|(![P,Q]: is_a_theorem(implies(Q,or(P,Q)))))&(r2|~is_a_theorem(implies(sk0_46,or(sk0_45,sk0_46))))),
% 0.16/0.39 inference(skolemization,[status(esa)],[f141])).
% 0.16/0.39 fof(f143,plain,(
% 0.16/0.39 ![X0,X1]: (~r2|is_a_theorem(implies(X0,or(X1,X0))))),
% 0.16/0.39 inference(cnf_transformation,[status(esa)],[f142])).
% 0.16/0.39 fof(f145,plain,(
% 0.16/0.39 (~r3|(![P,Q]: is_a_theorem(implies(or(P,Q),or(Q,P)))))&(r3|(?[P,Q]: ~is_a_theorem(implies(or(P,Q),or(Q,P)))))),
% 0.16/0.39 inference(NNF_transformation,[status(esa)],[f24])).
% 0.16/0.39 fof(f146,plain,(
% 0.16/0.39 (~r3|(![P,Q]: is_a_theorem(implies(or(P,Q),or(Q,P)))))&(r3|~is_a_theorem(implies(or(sk0_47,sk0_48),or(sk0_48,sk0_47))))),
% 0.16/0.39 inference(skolemization,[status(esa)],[f145])).
% 0.16/0.39 fof(f147,plain,(
% 0.16/0.39 ![X0,X1]: (~r3|is_a_theorem(implies(or(X0,X1),or(X1,X0))))),
% 0.16/0.39 inference(cnf_transformation,[status(esa)],[f146])).
% 0.16/0.39 fof(f157,plain,(
% 0.16/0.39 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 0.16/0.39 inference(pre_NNF_transformation,[status(esa)],[f27])).
% 0.16/0.39 fof(f158,plain,(
% 0.16/0.39 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 0.16/0.39 inference(cnf_transformation,[status(esa)],[f157])).
% 0.16/0.39 fof(f159,plain,(
% 0.16/0.39 ~op_and|(![X,Y]: and(X,Y)=not(or(not(X),not(Y))))),
% 0.16/0.39 inference(pre_NNF_transformation,[status(esa)],[f28])).
% 0.16/0.39 fof(f160,plain,(
% 0.16/0.39 ![X0,X1]: (~op_and|and(X0,X1)=not(or(not(X0),not(X1))))),
% 0.16/0.39 inference(cnf_transformation,[status(esa)],[f159])).
% 0.16/0.39 fof(f161,plain,(
% 0.16/0.39 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 0.16/0.39 inference(pre_NNF_transformation,[status(esa)],[f29])).
% 0.16/0.39 fof(f162,plain,(
% 0.16/0.39 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 0.16/0.39 inference(cnf_transformation,[status(esa)],[f161])).
% 0.16/0.39 fof(f163,plain,(
% 0.16/0.39 ~op_implies_or|(![X,Y]: implies(X,Y)=or(not(X),Y))),
% 0.16/0.39 inference(pre_NNF_transformation,[status(esa)],[f30])).
% 0.16/0.39 fof(f164,plain,(
% 0.16/0.39 ![X0,X1]: (~op_implies_or|implies(X0,X1)=or(not(X0),X1))),
% 0.16/0.39 inference(cnf_transformation,[status(esa)],[f163])).
% 0.16/0.39 fof(f165,plain,(
% 0.16/0.39 ~op_equiv|(![X,Y]: equiv(X,Y)=and(implies(X,Y),implies(Y,X)))),
% 0.16/0.39 inference(pre_NNF_transformation,[status(esa)],[f31])).
% 0.16/0.39 fof(f166,plain,(
% 0.16/0.39 ![X0,X1]: (~op_equiv|equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 0.16/0.39 inference(cnf_transformation,[status(esa)],[f165])).
% 0.16/0.39 fof(f167,plain,(
% 0.16/0.39 op_implies_or),
% 0.16/0.39 inference(cnf_transformation,[status(esa)],[f32])).
% 0.16/0.39 fof(f168,plain,(
% 0.16/0.39 op_and),
% 0.16/0.39 inference(cnf_transformation,[status(esa)],[f33])).
% 0.16/0.39 fof(f169,plain,(
% 0.16/0.39 op_equiv),
% 0.16/0.39 inference(cnf_transformation,[status(esa)],[f34])).
% 0.16/0.39 fof(f170,plain,(
% 0.16/0.39 modus_ponens),
% 0.16/0.39 inference(cnf_transformation,[status(esa)],[f35])).
% 0.16/0.39 fof(f172,plain,(
% 0.16/0.39 r2),
% 0.16/0.39 inference(cnf_transformation,[status(esa)],[f37])).
% 0.16/0.39 fof(f173,plain,(
% 0.16/0.39 r3),
% 0.16/0.39 inference(cnf_transformation,[status(esa)],[f38])).
% 0.16/0.39 fof(f177,plain,(
% 0.16/0.39 op_or),
% 0.16/0.39 inference(cnf_transformation,[status(esa)],[f42])).
% 0.16/0.39 fof(f178,plain,(
% 0.16/0.39 op_implies_and),
% 0.16/0.39 inference(cnf_transformation,[status(esa)],[f43])).
% 0.16/0.39 fof(f180,plain,(
% 0.16/0.39 ~equivalence_2),
% 0.16/0.39 inference(cnf_transformation,[status(esa)],[f46])).
% 0.16/0.39 fof(f181,plain,(
% 0.16/0.39 spl0_0 <=> modus_ponens),
% 0.16/0.39 introduced(split_symbol_definition)).
% 0.16/0.39 fof(f183,plain,(
% 0.16/0.39 ~modus_ponens|spl0_0),
% 0.16/0.39 inference(component_clause,[status(thm)],[f181])).
% 0.16/0.39 fof(f184,plain,(
% 0.16/0.39 spl0_1 <=> ~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)),
% 0.16/0.39 introduced(split_symbol_definition)).
% 0.16/0.39 fof(f185,plain,(
% 0.16/0.39 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)|~spl0_1)),
% 0.16/0.39 inference(component_clause,[status(thm)],[f184])).
% 0.16/0.39 fof(f187,plain,(
% 0.16/0.39 ~spl0_0|spl0_1),
% 0.16/0.39 inference(split_clause,[status(thm)],[f51,f181,f184])).
% 0.16/0.39 fof(f229,plain,(
% 0.16/0.39 spl0_13 <=> is_a_theorem(implies(X0,implies(X1,X0)))),
% 0.16/0.39 introduced(split_symbol_definition)).
% 0.16/0.39 fof(f230,plain,(
% 0.16/0.39 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0)))|~spl0_13)),
% 0.16/0.39 inference(component_clause,[status(thm)],[f229])).
% 0.16/0.39 fof(f306,plain,(
% 0.16/0.39 spl0_34 <=> is_a_theorem(implies(X0,or(X1,X0)))),
% 0.16/0.39 introduced(split_symbol_definition)).
% 0.16/0.39 fof(f307,plain,(
% 0.16/0.39 ![X0,X1]: (is_a_theorem(implies(X0,or(X1,X0)))|~spl0_34)),
% 0.16/0.39 inference(component_clause,[status(thm)],[f306])).
% 0.16/0.39 fof(f336,plain,(
% 0.16/0.39 spl0_42 <=> equivalence_2),
% 0.16/0.39 introduced(split_symbol_definition)).
% 0.16/0.39 fof(f337,plain,(
% 0.16/0.39 equivalence_2|~spl0_42),
% 0.16/0.39 inference(component_clause,[status(thm)],[f336])).
% 0.16/0.39 fof(f339,plain,(
% 0.16/0.39 spl0_43 <=> is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))),
% 0.16/0.39 introduced(split_symbol_definition)).
% 0.16/0.39 fof(f340,plain,(
% 0.16/0.39 ![X0,X1]: (is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))|~spl0_43)),
% 0.16/0.39 inference(component_clause,[status(thm)],[f339])).
% 0.16/0.39 fof(f343,plain,(
% 0.16/0.39 spl0_44 <=> is_a_theorem(implies(equiv(sk0_28,sk0_29),implies(sk0_29,sk0_28)))),
% 0.16/0.39 introduced(split_symbol_definition)).
% 0.16/0.39 fof(f345,plain,(
% 0.16/0.39 ~is_a_theorem(implies(equiv(sk0_28,sk0_29),implies(sk0_29,sk0_28)))|spl0_44),
% 0.16/0.39 inference(component_clause,[status(thm)],[f343])).
% 0.16/0.39 fof(f346,plain,(
% 0.16/0.39 spl0_42|~spl0_44),
% 0.16/0.39 inference(split_clause,[status(thm)],[f108,f336,f343])).
% 0.16/0.39 fof(f429,plain,(
% 0.16/0.39 spl0_67 <=> r2),
% 0.16/0.39 introduced(split_symbol_definition)).
% 0.16/0.39 fof(f431,plain,(
% 0.16/0.39 ~r2|spl0_67),
% 0.16/0.39 inference(component_clause,[status(thm)],[f429])).
% 0.16/0.39 fof(f432,plain,(
% 0.16/0.39 ~spl0_67|spl0_34),
% 0.16/0.39 inference(split_clause,[status(thm)],[f143,f429,f306])).
% 0.16/0.39 fof(f437,plain,(
% 0.16/0.39 spl0_69 <=> r3),
% 0.16/0.39 introduced(split_symbol_definition)).
% 0.16/0.39 fof(f439,plain,(
% 0.16/0.39 ~r3|spl0_69),
% 0.16/0.39 inference(component_clause,[status(thm)],[f437])).
% 0.16/0.39 fof(f440,plain,(
% 0.16/0.39 spl0_70 <=> is_a_theorem(implies(or(X0,X1),or(X1,X0)))),
% 0.16/0.39 introduced(split_symbol_definition)).
% 0.16/0.39 fof(f441,plain,(
% 0.16/0.39 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),or(X1,X0)))|~spl0_70)),
% 0.16/0.39 inference(component_clause,[status(thm)],[f440])).
% 0.16/0.39 fof(f443,plain,(
% 0.16/0.39 ~spl0_69|spl0_70),
% 0.16/0.39 inference(split_clause,[status(thm)],[f147,f437,f440])).
% 0.16/0.39 fof(f470,plain,(
% 0.16/0.39 spl0_78 <=> op_or),
% 0.16/0.39 introduced(split_symbol_definition)).
% 0.16/0.39 fof(f472,plain,(
% 0.16/0.39 ~op_or|spl0_78),
% 0.16/0.39 inference(component_clause,[status(thm)],[f470])).
% 0.16/0.39 fof(f473,plain,(
% 0.16/0.39 spl0_79 <=> or(X0,X1)=not(and(not(X0),not(X1)))),
% 0.16/0.39 introduced(split_symbol_definition)).
% 0.16/0.39 fof(f474,plain,(
% 0.16/0.39 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1)))|~spl0_79)),
% 0.16/0.39 inference(component_clause,[status(thm)],[f473])).
% 0.16/0.39 fof(f476,plain,(
% 0.16/0.39 ~spl0_78|spl0_79),
% 0.16/0.39 inference(split_clause,[status(thm)],[f158,f470,f473])).
% 0.16/0.39 fof(f477,plain,(
% 0.16/0.39 spl0_80 <=> op_and),
% 0.16/0.39 introduced(split_symbol_definition)).
% 0.16/0.39 fof(f479,plain,(
% 0.16/0.39 ~op_and|spl0_80),
% 0.16/0.39 inference(component_clause,[status(thm)],[f477])).
% 0.16/0.39 fof(f480,plain,(
% 0.16/0.39 spl0_81 <=> and(X0,X1)=not(or(not(X0),not(X1)))),
% 0.16/0.39 introduced(split_symbol_definition)).
% 0.16/0.39 fof(f481,plain,(
% 0.16/0.39 ![X0,X1]: (and(X0,X1)=not(or(not(X0),not(X1)))|~spl0_81)),
% 0.16/0.39 inference(component_clause,[status(thm)],[f480])).
% 0.16/0.39 fof(f483,plain,(
% 0.16/0.39 ~spl0_80|spl0_81),
% 0.16/0.39 inference(split_clause,[status(thm)],[f160,f477,f480])).
% 0.16/0.39 fof(f484,plain,(
% 0.16/0.39 spl0_82 <=> op_implies_and),
% 0.16/0.39 introduced(split_symbol_definition)).
% 0.16/0.39 fof(f486,plain,(
% 0.16/0.39 ~op_implies_and|spl0_82),
% 0.16/0.39 inference(component_clause,[status(thm)],[f484])).
% 0.16/0.39 fof(f487,plain,(
% 0.16/0.39 spl0_83 <=> implies(X0,X1)=not(and(X0,not(X1)))),
% 0.16/0.39 introduced(split_symbol_definition)).
% 0.16/0.39 fof(f488,plain,(
% 0.16/0.39 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1)))|~spl0_83)),
% 0.16/0.39 inference(component_clause,[status(thm)],[f487])).
% 0.16/0.39 fof(f490,plain,(
% 0.16/0.39 ~spl0_82|spl0_83),
% 0.16/0.39 inference(split_clause,[status(thm)],[f162,f484,f487])).
% 0.16/0.39 fof(f491,plain,(
% 0.16/0.39 spl0_84 <=> op_implies_or),
% 0.16/0.39 introduced(split_symbol_definition)).
% 0.16/0.39 fof(f493,plain,(
% 0.16/0.39 ~op_implies_or|spl0_84),
% 0.16/0.39 inference(component_clause,[status(thm)],[f491])).
% 0.16/0.39 fof(f494,plain,(
% 0.16/0.39 spl0_85 <=> implies(X0,X1)=or(not(X0),X1)),
% 0.16/0.39 introduced(split_symbol_definition)).
% 0.16/0.39 fof(f495,plain,(
% 0.16/0.39 ![X0,X1]: (implies(X0,X1)=or(not(X0),X1)|~spl0_85)),
% 0.16/0.39 inference(component_clause,[status(thm)],[f494])).
% 0.16/0.39 fof(f497,plain,(
% 0.16/0.39 ~spl0_84|spl0_85),
% 0.16/0.39 inference(split_clause,[status(thm)],[f164,f491,f494])).
% 0.16/0.39 fof(f498,plain,(
% 0.16/0.39 spl0_86 <=> op_equiv),
% 0.16/0.39 introduced(split_symbol_definition)).
% 0.16/0.39 fof(f500,plain,(
% 0.16/0.39 ~op_equiv|spl0_86),
% 0.16/0.39 inference(component_clause,[status(thm)],[f498])).
% 0.16/0.39 fof(f501,plain,(
% 0.16/0.39 spl0_87 <=> equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))),
% 0.16/0.39 introduced(split_symbol_definition)).
% 0.16/0.39 fof(f502,plain,(
% 0.16/0.39 ![X0,X1]: (equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))|~spl0_87)),
% 0.16/0.39 inference(component_clause,[status(thm)],[f501])).
% 0.16/0.39 fof(f504,plain,(
% 0.16/0.39 ~spl0_86|spl0_87),
% 0.16/0.39 inference(split_clause,[status(thm)],[f166,f498,f501])).
% 0.16/0.39 fof(f505,plain,(
% 0.16/0.39 $false|spl0_86),
% 0.16/0.39 inference(forward_subsumption_resolution,[status(thm)],[f500,f169])).
% 0.16/0.39 fof(f506,plain,(
% 0.16/0.39 spl0_86),
% 0.16/0.39 inference(contradiction_clause,[status(thm)],[f505])).
% 0.16/0.39 fof(f507,plain,(
% 0.16/0.39 $false|spl0_84),
% 0.16/0.39 inference(forward_subsumption_resolution,[status(thm)],[f493,f167])).
% 0.16/0.39 fof(f508,plain,(
% 0.16/0.39 spl0_84),
% 0.16/0.39 inference(contradiction_clause,[status(thm)],[f507])).
% 0.16/0.39 fof(f509,plain,(
% 0.16/0.39 $false|spl0_82),
% 0.16/0.39 inference(forward_subsumption_resolution,[status(thm)],[f486,f178])).
% 0.16/0.39 fof(f510,plain,(
% 0.16/0.39 spl0_82),
% 0.16/0.39 inference(contradiction_clause,[status(thm)],[f509])).
% 0.16/0.39 fof(f511,plain,(
% 0.16/0.39 $false|spl0_80),
% 0.16/0.39 inference(forward_subsumption_resolution,[status(thm)],[f479,f168])).
% 0.16/0.39 fof(f512,plain,(
% 0.16/0.39 spl0_80),
% 0.16/0.39 inference(contradiction_clause,[status(thm)],[f511])).
% 0.16/0.39 fof(f513,plain,(
% 0.16/0.39 $false|spl0_78),
% 0.16/0.39 inference(forward_subsumption_resolution,[status(thm)],[f472,f177])).
% 0.16/0.39 fof(f514,plain,(
% 0.16/0.39 spl0_78),
% 0.16/0.39 inference(contradiction_clause,[status(thm)],[f513])).
% 0.16/0.39 fof(f515,plain,(
% 0.16/0.39 $false|spl0_0),
% 0.16/0.39 inference(forward_subsumption_resolution,[status(thm)],[f183,f170])).
% 0.16/0.39 fof(f516,plain,(
% 0.16/0.39 spl0_0),
% 0.16/0.39 inference(contradiction_clause,[status(thm)],[f515])).
% 0.16/0.39 fof(f519,plain,(
% 0.16/0.39 ![X0,X1]: (and(X0,X1)=not(implies(X0,not(X1)))|~spl0_85|~spl0_81)),
% 0.16/0.39 inference(forward_demodulation,[status(thm)],[f495,f481])).
% 0.16/0.39 fof(f544,plain,(
% 0.16/0.39 $false|~spl0_43|spl0_44),
% 0.16/0.39 inference(backward_subsumption_resolution,[status(thm)],[f345,f340])).
% 0.16/0.39 fof(f545,plain,(
% 0.16/0.39 ~spl0_43|spl0_44),
% 0.16/0.39 inference(contradiction_clause,[status(thm)],[f544])).
% 0.16/0.39 fof(f572,plain,(
% 0.16/0.39 $false|spl0_69),
% 0.16/0.39 inference(forward_subsumption_resolution,[status(thm)],[f439,f173])).
% 0.16/0.39 fof(f573,plain,(
% 0.16/0.39 spl0_69),
% 0.16/0.39 inference(contradiction_clause,[status(thm)],[f572])).
% 0.16/0.39 fof(f576,plain,(
% 0.16/0.39 $false|spl0_67),
% 0.16/0.39 inference(forward_subsumption_resolution,[status(thm)],[f431,f172])).
% 0.16/0.39 fof(f577,plain,(
% 0.16/0.39 spl0_67),
% 0.16/0.39 inference(contradiction_clause,[status(thm)],[f576])).
% 0.16/0.39 fof(f585,plain,(
% 0.16/0.39 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1)|~spl0_79|~spl0_83)),
% 0.16/0.39 inference(paramodulation,[status(thm)],[f488,f474])).
% 0.16/0.39 fof(f603,plain,(
% 0.16/0.39 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0)))|~spl0_34|~spl0_85)),
% 0.16/0.39 inference(paramodulation,[status(thm)],[f495,f307])).
% 0.16/0.39 fof(f604,plain,(
% 0.16/0.39 spl0_13|~spl0_34|~spl0_85),
% 0.16/0.39 inference(split_clause,[status(thm)],[f603,f229,f306,f494])).
% 0.16/0.39 fof(f617,plain,(
% 0.16/0.39 ![X0,X1,X2]: (or(implies(X0,not(X1)),X2)=implies(and(X0,X1),X2)|~spl0_79|~spl0_83|~spl0_85|~spl0_81)),
% 0.16/0.39 inference(paramodulation,[status(thm)],[f519,f585])).
% 0.16/0.39 fof(f620,plain,(
% 0.16/0.39 ![X0,X1]: (is_a_theorem(or(X0,implies(X1,not(X0))))|~spl0_13|~spl0_79|~spl0_83)),
% 0.16/0.39 inference(paramodulation,[status(thm)],[f585,f230])).
% 0.16/0.39 fof(f660,plain,(
% 0.16/0.39 ![X0,X1]: (~is_a_theorem(or(X0,X1))|is_a_theorem(or(X1,X0))|~spl0_70|~spl0_1)),
% 0.16/0.39 inference(resolution,[status(thm)],[f441,f185])).
% 0.16/0.39 fof(f775,plain,(
% 0.16/0.39 ![X0,X1]: (is_a_theorem(or(implies(X0,not(X1)),X1))|~spl0_70|~spl0_1|~spl0_13|~spl0_79|~spl0_83)),
% 0.16/0.39 inference(resolution,[status(thm)],[f660,f620])).
% 0.16/0.39 fof(f776,plain,(
% 0.16/0.39 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X1))|~spl0_85|~spl0_81|~spl0_70|~spl0_1|~spl0_13|~spl0_79|~spl0_83)),
% 0.16/0.39 inference(forward_demodulation,[status(thm)],[f617,f775])).
% 0.16/0.39 fof(f794,plain,(
% 0.16/0.39 ![X0,X1]: (is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))|~spl0_85|~spl0_81|~spl0_70|~spl0_1|~spl0_13|~spl0_79|~spl0_83|~spl0_87)),
% 0.16/0.39 inference(paramodulation,[status(thm)],[f502,f776])).
% 0.16/0.39 fof(f795,plain,(
% 0.16/0.39 spl0_43|~spl0_85|~spl0_81|~spl0_70|~spl0_1|~spl0_13|~spl0_79|~spl0_83|~spl0_87),
% 0.16/0.39 inference(split_clause,[status(thm)],[f794,f339,f494,f480,f440,f184,f229,f473,f487,f501])).
% 0.16/0.39 fof(f796,plain,(
% 0.16/0.39 $false|~spl0_42),
% 0.16/0.39 inference(forward_subsumption_resolution,[status(thm)],[f337,f180])).
% 0.16/0.39 fof(f797,plain,(
% 0.16/0.39 ~spl0_42),
% 0.16/0.39 inference(contradiction_clause,[status(thm)],[f796])).
% 0.16/0.39 fof(f798,plain,(
% 0.16/0.39 $false),
% 0.16/0.39 inference(sat_refutation,[status(thm)],[f187,f346,f432,f443,f476,f483,f490,f497,f504,f506,f508,f510,f512,f514,f516,f545,f573,f577,f604,f795,f797])).
% 0.16/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.16/0.40 % Elapsed time: 0.051153 seconds
% 0.16/0.40 % CPU time: 0.251406 seconds
% 0.16/0.40 % Total memory used: 55.995 MB
% 0.16/0.40 % Net memory used: 55.637 MB
%------------------------------------------------------------------------------