TSTP Solution File: LCL500+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : LCL500+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 : Wed May 31 12:19:28 EDT 2023
% Result : Theorem 5.67s 1.14s
% Output : CNFRefutation 6.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL500+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue May 30 10:01:21 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.35 % Drodi V3.5.1
% 5.67/1.14 % Refutation found
% 5.67/1.14 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.67/1.14 % SZS output start CNFRefutation for theBenchmark
% 5.67/1.14 fof(f1,axiom,(
% 5.67/1.14 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 5.67/1.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.67/1.14 fof(f17,axiom,(
% 5.67/1.14 ( kn2<=> (! [P,Q] : is_a_theorem(implies(and(P,Q),P)) )) ),
% 5.67/1.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.67/1.14 fof(f23,axiom,(
% 5.67/1.14 ( r2<=> (! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) )) ),
% 5.67/1.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.67/1.14 fof(f24,axiom,(
% 5.67/1.14 ( r3<=> (! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) )) ),
% 5.67/1.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.67/1.14 fof(f26,axiom,(
% 5.67/1.14 ( r5<=> (! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) )) ),
% 5.67/1.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.67/1.14 fof(f27,axiom,(
% 5.67/1.14 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 5.67/1.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.67/1.14 fof(f28,axiom,(
% 5.67/1.14 ( op_and=> (! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) )) ),
% 5.67/1.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.67/1.14 fof(f29,axiom,(
% 5.67/1.14 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 5.67/1.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.67/1.14 fof(f30,axiom,(
% 5.67/1.14 ( op_implies_or=> (! [X,Y] : implies(X,Y) = or(not(X),Y) )) ),
% 5.67/1.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.67/1.14 fof(f32,axiom,(
% 5.67/1.14 op_implies_or ),
% 5.67/1.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.67/1.14 fof(f33,axiom,(
% 5.67/1.14 op_and ),
% 5.67/1.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.67/1.14 fof(f35,axiom,(
% 5.67/1.14 modus_ponens ),
% 5.67/1.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.67/1.14 fof(f37,axiom,(
% 5.67/1.14 r2 ),
% 5.67/1.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.67/1.14 fof(f38,axiom,(
% 5.67/1.14 r3 ),
% 5.67/1.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.67/1.14 fof(f40,axiom,(
% 5.67/1.14 r5 ),
% 5.67/1.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.67/1.14 fof(f42,axiom,(
% 5.67/1.14 op_or ),
% 5.67/1.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.67/1.14 fof(f43,axiom,(
% 5.67/1.14 op_implies_and ),
% 5.67/1.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.67/1.14 fof(f45,conjecture,(
% 5.67/1.14 kn2 ),
% 5.67/1.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.67/1.14 fof(f46,negated_conjecture,(
% 5.67/1.14 ~(kn2 )),
% 5.67/1.14 inference(negated_conjecture,[status(cth)],[f45])).
% 5.67/1.14 fof(f47,plain,(
% 5.67/1.14 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 5.67/1.14 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 5.67/1.14 fof(f48,plain,(
% 5.67/1.14 (~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))))),
% 5.67/1.14 inference(NNF_transformation,[status(esa)],[f47])).
% 5.67/1.14 fof(f49,plain,(
% 5.67/1.14 (~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))))),
% 5.67/1.14 inference(miniscoping,[status(esa)],[f48])).
% 5.67/1.14 fof(f50,plain,(
% 5.67/1.14 (~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)))),
% 5.67/1.14 inference(skolemization,[status(esa)],[f49])).
% 5.67/1.14 fof(f51,plain,(
% 5.67/1.14 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 5.67/1.14 inference(cnf_transformation,[status(esa)],[f50])).
% 5.67/1.14 fof(f117,plain,(
% 5.67/1.14 (~kn2|(![P,Q]: is_a_theorem(implies(and(P,Q),P))))&(kn2|(?[P,Q]: ~is_a_theorem(implies(and(P,Q),P))))),
% 5.67/1.14 inference(NNF_transformation,[status(esa)],[f17])).
% 5.67/1.14 fof(f118,plain,(
% 5.67/1.14 (~kn2|(![P,Q]: is_a_theorem(implies(and(P,Q),P))))&(kn2|~is_a_theorem(implies(and(sk0_33,sk0_34),sk0_33)))),
% 5.67/1.14 inference(skolemization,[status(esa)],[f117])).
% 5.67/1.14 fof(f120,plain,(
% 5.67/1.14 kn2|~is_a_theorem(implies(and(sk0_33,sk0_34),sk0_33))),
% 5.67/1.14 inference(cnf_transformation,[status(esa)],[f118])).
% 5.67/1.14 fof(f141,plain,(
% 5.67/1.14 (~r2|(![P,Q]: is_a_theorem(implies(Q,or(P,Q)))))&(r2|(?[P,Q]: ~is_a_theorem(implies(Q,or(P,Q)))))),
% 5.67/1.14 inference(NNF_transformation,[status(esa)],[f23])).
% 5.67/1.14 fof(f142,plain,(
% 5.67/1.14 (~r2|(![P,Q]: is_a_theorem(implies(Q,or(P,Q)))))&(r2|~is_a_theorem(implies(sk0_46,or(sk0_45,sk0_46))))),
% 5.67/1.14 inference(skolemization,[status(esa)],[f141])).
% 5.67/1.14 fof(f143,plain,(
% 5.67/1.14 ![X0,X1]: (~r2|is_a_theorem(implies(X0,or(X1,X0))))),
% 5.67/1.14 inference(cnf_transformation,[status(esa)],[f142])).
% 5.67/1.14 fof(f145,plain,(
% 5.67/1.14 (~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)))))),
% 5.67/1.14 inference(NNF_transformation,[status(esa)],[f24])).
% 5.67/1.14 fof(f146,plain,(
% 5.67/1.14 (~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))))),
% 5.67/1.14 inference(skolemization,[status(esa)],[f145])).
% 5.67/1.14 fof(f147,plain,(
% 5.67/1.14 ![X0,X1]: (~r3|is_a_theorem(implies(or(X0,X1),or(X1,X0))))),
% 5.67/1.14 inference(cnf_transformation,[status(esa)],[f146])).
% 5.67/1.14 fof(f153,plain,(
% 5.67/1.14 (~r5|(![P,Q,R]: is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))))&(r5|(?[P,Q,R]: ~is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))))),
% 5.67/1.14 inference(NNF_transformation,[status(esa)],[f26])).
% 5.67/1.14 fof(f154,plain,(
% 5.67/1.14 (~r5|(![P,Q,R]: is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))))&(r5|~is_a_theorem(implies(implies(sk0_53,sk0_54),implies(or(sk0_52,sk0_53),or(sk0_52,sk0_54)))))),
% 5.67/1.14 inference(skolemization,[status(esa)],[f153])).
% 5.67/1.14 fof(f155,plain,(
% 5.67/1.14 ![X0,X1,X2]: (~r5|is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))))),
% 5.67/1.14 inference(cnf_transformation,[status(esa)],[f154])).
% 5.67/1.14 fof(f157,plain,(
% 5.67/1.14 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 5.67/1.14 inference(pre_NNF_transformation,[status(esa)],[f27])).
% 5.67/1.14 fof(f158,plain,(
% 5.67/1.14 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 5.67/1.14 inference(cnf_transformation,[status(esa)],[f157])).
% 5.67/1.14 fof(f159,plain,(
% 5.67/1.14 ~op_and|(![X,Y]: and(X,Y)=not(or(not(X),not(Y))))),
% 5.67/1.14 inference(pre_NNF_transformation,[status(esa)],[f28])).
% 5.67/1.14 fof(f160,plain,(
% 5.67/1.14 ![X0,X1]: (~op_and|and(X0,X1)=not(or(not(X0),not(X1))))),
% 5.67/1.14 inference(cnf_transformation,[status(esa)],[f159])).
% 5.67/1.14 fof(f161,plain,(
% 5.67/1.14 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 5.67/1.14 inference(pre_NNF_transformation,[status(esa)],[f29])).
% 5.67/1.14 fof(f162,plain,(
% 5.67/1.14 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 5.67/1.14 inference(cnf_transformation,[status(esa)],[f161])).
% 5.67/1.14 fof(f163,plain,(
% 5.67/1.14 ~op_implies_or|(![X,Y]: implies(X,Y)=or(not(X),Y))),
% 5.67/1.14 inference(pre_NNF_transformation,[status(esa)],[f30])).
% 5.67/1.14 fof(f164,plain,(
% 5.67/1.14 ![X0,X1]: (~op_implies_or|implies(X0,X1)=or(not(X0),X1))),
% 5.67/1.14 inference(cnf_transformation,[status(esa)],[f163])).
% 5.67/1.14 fof(f167,plain,(
% 5.67/1.14 op_implies_or),
% 5.67/1.14 inference(cnf_transformation,[status(esa)],[f32])).
% 5.67/1.14 fof(f168,plain,(
% 5.67/1.14 op_and),
% 5.67/1.14 inference(cnf_transformation,[status(esa)],[f33])).
% 5.67/1.14 fof(f170,plain,(
% 5.67/1.14 modus_ponens),
% 5.67/1.14 inference(cnf_transformation,[status(esa)],[f35])).
% 5.67/1.14 fof(f172,plain,(
% 5.67/1.14 r2),
% 5.67/1.14 inference(cnf_transformation,[status(esa)],[f37])).
% 5.67/1.14 fof(f173,plain,(
% 5.67/1.14 r3),
% 5.67/1.14 inference(cnf_transformation,[status(esa)],[f38])).
% 5.67/1.14 fof(f175,plain,(
% 5.67/1.14 r5),
% 5.67/1.14 inference(cnf_transformation,[status(esa)],[f40])).
% 5.67/1.14 fof(f177,plain,(
% 5.67/1.14 op_or),
% 5.67/1.14 inference(cnf_transformation,[status(esa)],[f42])).
% 5.67/1.14 fof(f178,plain,(
% 5.67/1.14 op_implies_and),
% 5.67/1.14 inference(cnf_transformation,[status(esa)],[f43])).
% 5.67/1.14 fof(f180,plain,(
% 5.67/1.14 ~kn2),
% 5.67/1.14 inference(cnf_transformation,[status(esa)],[f46])).
% 5.67/1.14 fof(f181,plain,(
% 5.67/1.14 spl0_0 <=> modus_ponens),
% 5.67/1.14 introduced(split_symbol_definition)).
% 5.67/1.14 fof(f183,plain,(
% 5.67/1.14 ~modus_ponens|spl0_0),
% 5.67/1.14 inference(component_clause,[status(thm)],[f181])).
% 5.67/1.14 fof(f184,plain,(
% 5.67/1.14 spl0_1 <=> ~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)),
% 5.67/1.14 introduced(split_symbol_definition)).
% 5.67/1.14 fof(f185,plain,(
% 5.67/1.14 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)|~spl0_1)),
% 5.67/1.14 inference(component_clause,[status(thm)],[f184])).
% 5.67/1.14 fof(f187,plain,(
% 5.67/1.14 ~spl0_0|spl0_1),
% 5.67/1.14 inference(split_clause,[status(thm)],[f51,f181,f184])).
% 5.67/1.14 fof(f229,plain,(
% 5.67/1.14 spl0_13 <=> is_a_theorem(implies(X0,implies(X1,X0)))),
% 5.67/1.14 introduced(split_symbol_definition)).
% 5.67/1.14 fof(f230,plain,(
% 5.67/1.14 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0)))|~spl0_13)),
% 5.67/1.14 inference(component_clause,[status(thm)],[f229])).
% 5.67/1.14 fof(f306,plain,(
% 5.67/1.14 spl0_34 <=> is_a_theorem(implies(X0,or(X1,X0)))),
% 5.67/1.14 introduced(split_symbol_definition)).
% 5.67/1.14 fof(f307,plain,(
% 5.67/1.14 ![X0,X1]: (is_a_theorem(implies(X0,or(X1,X0)))|~spl0_34)),
% 5.67/1.14 inference(component_clause,[status(thm)],[f306])).
% 5.67/1.14 fof(f369,plain,(
% 5.67/1.14 spl0_51 <=> kn2),
% 5.67/1.14 introduced(split_symbol_definition)).
% 5.67/1.14 fof(f370,plain,(
% 5.67/1.14 kn2|~spl0_51),
% 5.67/1.14 inference(component_clause,[status(thm)],[f369])).
% 5.67/1.14 fof(f373,plain,(
% 5.67/1.14 spl0_52 <=> is_a_theorem(implies(and(sk0_33,sk0_34),sk0_33))),
% 5.67/1.14 introduced(split_symbol_definition)).
% 5.67/1.14 fof(f375,plain,(
% 5.67/1.14 ~is_a_theorem(implies(and(sk0_33,sk0_34),sk0_33))|spl0_52),
% 5.67/1.14 inference(component_clause,[status(thm)],[f373])).
% 5.67/1.14 fof(f376,plain,(
% 5.67/1.14 spl0_51|~spl0_52),
% 5.67/1.14 inference(split_clause,[status(thm)],[f120,f369,f373])).
% 5.67/1.14 fof(f429,plain,(
% 5.67/1.14 spl0_67 <=> r2),
% 5.67/1.14 introduced(split_symbol_definition)).
% 5.67/1.14 fof(f431,plain,(
% 5.67/1.14 ~r2|spl0_67),
% 5.67/1.14 inference(component_clause,[status(thm)],[f429])).
% 5.67/1.14 fof(f432,plain,(
% 5.67/1.14 ~spl0_67|spl0_34),
% 5.67/1.14 inference(split_clause,[status(thm)],[f143,f429,f306])).
% 5.67/1.14 fof(f437,plain,(
% 5.67/1.14 spl0_69 <=> r3),
% 5.67/1.14 introduced(split_symbol_definition)).
% 5.67/1.14 fof(f439,plain,(
% 5.67/1.14 ~r3|spl0_69),
% 5.67/1.14 inference(component_clause,[status(thm)],[f437])).
% 5.67/1.14 fof(f440,plain,(
% 5.67/1.14 spl0_70 <=> is_a_theorem(implies(or(X0,X1),or(X1,X0)))),
% 5.67/1.14 introduced(split_symbol_definition)).
% 5.67/1.14 fof(f441,plain,(
% 5.67/1.14 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),or(X1,X0)))|~spl0_70)),
% 5.67/1.14 inference(component_clause,[status(thm)],[f440])).
% 5.67/1.14 fof(f443,plain,(
% 5.67/1.14 ~spl0_69|spl0_70),
% 5.67/1.14 inference(split_clause,[status(thm)],[f147,f437,f440])).
% 5.67/1.14 fof(f459,plain,(
% 5.67/1.14 spl0_75 <=> r5),
% 5.67/1.14 introduced(split_symbol_definition)).
% 5.67/1.14 fof(f461,plain,(
% 5.67/1.14 ~r5|spl0_75),
% 5.67/1.14 inference(component_clause,[status(thm)],[f459])).
% 5.67/1.14 fof(f462,plain,(
% 5.67/1.14 spl0_76 <=> is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1))))),
% 5.67/1.14 introduced(split_symbol_definition)).
% 5.67/1.14 fof(f463,plain,(
% 5.67/1.14 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1))))|~spl0_76)),
% 5.67/1.14 inference(component_clause,[status(thm)],[f462])).
% 5.67/1.14 fof(f465,plain,(
% 5.67/1.14 ~spl0_75|spl0_76),
% 5.67/1.14 inference(split_clause,[status(thm)],[f155,f459,f462])).
% 5.67/1.14 fof(f470,plain,(
% 5.67/1.14 spl0_78 <=> op_or),
% 5.67/1.14 introduced(split_symbol_definition)).
% 5.67/1.14 fof(f472,plain,(
% 5.67/1.14 ~op_or|spl0_78),
% 5.67/1.14 inference(component_clause,[status(thm)],[f470])).
% 5.67/1.14 fof(f473,plain,(
% 5.67/1.14 spl0_79 <=> or(X0,X1)=not(and(not(X0),not(X1)))),
% 5.67/1.14 introduced(split_symbol_definition)).
% 5.67/1.14 fof(f474,plain,(
% 5.67/1.14 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1)))|~spl0_79)),
% 5.67/1.14 inference(component_clause,[status(thm)],[f473])).
% 5.67/1.14 fof(f476,plain,(
% 5.67/1.14 ~spl0_78|spl0_79),
% 5.67/1.14 inference(split_clause,[status(thm)],[f158,f470,f473])).
% 5.67/1.14 fof(f477,plain,(
% 5.67/1.14 spl0_80 <=> op_and),
% 5.67/1.14 introduced(split_symbol_definition)).
% 5.67/1.14 fof(f479,plain,(
% 5.67/1.14 ~op_and|spl0_80),
% 5.67/1.14 inference(component_clause,[status(thm)],[f477])).
% 5.67/1.14 fof(f480,plain,(
% 5.67/1.14 spl0_81 <=> and(X0,X1)=not(or(not(X0),not(X1)))),
% 5.67/1.14 introduced(split_symbol_definition)).
% 5.67/1.14 fof(f481,plain,(
% 5.67/1.14 ![X0,X1]: (and(X0,X1)=not(or(not(X0),not(X1)))|~spl0_81)),
% 5.67/1.14 inference(component_clause,[status(thm)],[f480])).
% 5.67/1.14 fof(f483,plain,(
% 5.67/1.14 ~spl0_80|spl0_81),
% 5.67/1.14 inference(split_clause,[status(thm)],[f160,f477,f480])).
% 5.67/1.14 fof(f484,plain,(
% 5.67/1.14 spl0_82 <=> op_implies_and),
% 5.67/1.14 introduced(split_symbol_definition)).
% 5.67/1.14 fof(f486,plain,(
% 5.67/1.14 ~op_implies_and|spl0_82),
% 5.67/1.14 inference(component_clause,[status(thm)],[f484])).
% 5.67/1.14 fof(f487,plain,(
% 5.67/1.14 spl0_83 <=> implies(X0,X1)=not(and(X0,not(X1)))),
% 5.67/1.14 introduced(split_symbol_definition)).
% 5.67/1.14 fof(f488,plain,(
% 5.67/1.14 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1)))|~spl0_83)),
% 5.67/1.14 inference(component_clause,[status(thm)],[f487])).
% 5.67/1.14 fof(f490,plain,(
% 5.67/1.14 ~spl0_82|spl0_83),
% 5.67/1.14 inference(split_clause,[status(thm)],[f162,f484,f487])).
% 5.67/1.14 fof(f491,plain,(
% 5.67/1.14 spl0_84 <=> op_implies_or),
% 5.67/1.14 introduced(split_symbol_definition)).
% 5.67/1.14 fof(f493,plain,(
% 5.67/1.14 ~op_implies_or|spl0_84),
% 5.67/1.14 inference(component_clause,[status(thm)],[f491])).
% 5.67/1.14 fof(f494,plain,(
% 5.67/1.14 spl0_85 <=> implies(X0,X1)=or(not(X0),X1)),
% 5.67/1.14 introduced(split_symbol_definition)).
% 5.67/1.14 fof(f495,plain,(
% 5.67/1.14 ![X0,X1]: (implies(X0,X1)=or(not(X0),X1)|~spl0_85)),
% 5.67/1.14 inference(component_clause,[status(thm)],[f494])).
% 5.67/1.14 fof(f497,plain,(
% 5.67/1.14 ~spl0_84|spl0_85),
% 5.67/1.14 inference(split_clause,[status(thm)],[f164,f491,f494])).
% 5.67/1.14 fof(f507,plain,(
% 5.67/1.14 $false|spl0_84),
% 5.67/1.14 inference(forward_subsumption_resolution,[status(thm)],[f493,f167])).
% 5.67/1.14 fof(f508,plain,(
% 5.67/1.14 spl0_84),
% 5.67/1.14 inference(contradiction_clause,[status(thm)],[f507])).
% 5.67/1.14 fof(f509,plain,(
% 5.67/1.14 $false|spl0_82),
% 5.67/1.14 inference(forward_subsumption_resolution,[status(thm)],[f486,f178])).
% 5.67/1.14 fof(f510,plain,(
% 5.67/1.14 spl0_82),
% 5.67/1.14 inference(contradiction_clause,[status(thm)],[f509])).
% 5.67/1.14 fof(f511,plain,(
% 5.67/1.14 $false|spl0_80),
% 5.67/1.14 inference(forward_subsumption_resolution,[status(thm)],[f479,f168])).
% 5.67/1.14 fof(f512,plain,(
% 5.67/1.14 spl0_80),
% 5.67/1.14 inference(contradiction_clause,[status(thm)],[f511])).
% 5.67/1.14 fof(f513,plain,(
% 5.67/1.14 $false|spl0_78),
% 5.67/1.14 inference(forward_subsumption_resolution,[status(thm)],[f472,f177])).
% 5.67/1.14 fof(f514,plain,(
% 5.67/1.14 spl0_78),
% 5.67/1.14 inference(contradiction_clause,[status(thm)],[f513])).
% 5.67/1.14 fof(f515,plain,(
% 5.67/1.14 $false|spl0_0),
% 5.67/1.14 inference(forward_subsumption_resolution,[status(thm)],[f183,f170])).
% 5.67/1.14 fof(f516,plain,(
% 5.67/1.14 spl0_0),
% 5.67/1.14 inference(contradiction_clause,[status(thm)],[f515])).
% 5.67/1.14 fof(f519,plain,(
% 5.67/1.14 ![X0,X1]: (and(X0,X1)=not(implies(X0,not(X1)))|~spl0_85|~spl0_81)),
% 5.67/1.14 inference(forward_demodulation,[status(thm)],[f495,f481])).
% 5.67/1.14 fof(f520,plain,(
% 5.67/1.14 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1)|~spl0_83|~spl0_79)),
% 5.67/1.14 inference(forward_demodulation,[status(thm)],[f488,f474])).
% 5.67/1.14 fof(f569,plain,(
% 5.67/1.14 $false|spl0_75),
% 5.67/1.14 inference(forward_subsumption_resolution,[status(thm)],[f461,f175])).
% 5.67/1.14 fof(f570,plain,(
% 5.67/1.14 spl0_75),
% 5.67/1.14 inference(contradiction_clause,[status(thm)],[f569])).
% 5.67/1.14 fof(f573,plain,(
% 5.67/1.14 $false|spl0_69),
% 5.67/1.14 inference(forward_subsumption_resolution,[status(thm)],[f439,f173])).
% 5.67/1.14 fof(f574,plain,(
% 5.67/1.14 spl0_69),
% 5.67/1.14 inference(contradiction_clause,[status(thm)],[f573])).
% 5.67/1.14 fof(f581,plain,(
% 5.67/1.14 $false|spl0_67),
% 5.67/1.14 inference(forward_subsumption_resolution,[status(thm)],[f431,f172])).
% 5.67/1.14 fof(f582,plain,(
% 5.67/1.14 spl0_67),
% 5.67/1.14 inference(contradiction_clause,[status(thm)],[f581])).
% 5.67/1.14 fof(f586,plain,(
% 5.67/1.14 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0)))|~spl0_34|~spl0_85)),
% 5.67/1.14 inference(paramodulation,[status(thm)],[f495,f307])).
% 5.67/1.14 fof(f587,plain,(
% 5.67/1.14 spl0_13|~spl0_34|~spl0_85),
% 5.67/1.14 inference(split_clause,[status(thm)],[f586,f229,f306,f494])).
% 5.67/1.14 fof(f593,plain,(
% 5.67/1.14 ![X0,X1,X2]: (or(and(X0,not(X1)),X2)=implies(implies(X0,X1),X2)|~spl0_79|~spl0_83)),
% 5.67/1.14 inference(paramodulation,[status(thm)],[f488,f520])).
% 5.67/1.14 fof(f595,plain,(
% 5.67/1.14 ![X0,X1]: (and(not(X0),X1)=not(or(X0,not(X1)))|~spl0_85|~spl0_81|~spl0_83|~spl0_79)),
% 5.67/1.14 inference(paramodulation,[status(thm)],[f520,f519])).
% 5.67/1.14 fof(f611,plain,(
% 5.67/1.14 spl0_89 <=> ~is_a_theorem(X1)),
% 5.67/1.14 introduced(split_symbol_definition)).
% 5.67/1.14 fof(f612,plain,(
% 5.67/1.14 ![X0]: (~is_a_theorem(X0)|~spl0_89)),
% 5.67/1.14 inference(component_clause,[status(thm)],[f611])).
% 5.67/1.14 fof(f622,plain,(
% 5.67/1.14 ![X0,X1]: (and(not(not(X0)),X1)=not(implies(X0,not(X1)))|~spl0_81|~spl0_83|~spl0_79|~spl0_85)),
% 5.67/1.14 inference(paramodulation,[status(thm)],[f495,f595])).
% 5.67/1.14 fof(f623,plain,(
% 5.67/1.14 ![X0,X1]: (and(not(not(X0)),X1)=and(X0,X1)|~spl0_81|~spl0_83|~spl0_79|~spl0_85)),
% 5.67/1.14 inference(forward_demodulation,[status(thm)],[f519,f622])).
% 5.67/1.14 fof(f635,plain,(
% 5.67/1.14 ![X0,X1,X2]: (and(not(and(X0,X1)),X2)=and(implies(X0,not(X1)),X2)|~spl0_83|~spl0_79|~spl0_85|~spl0_81)),
% 5.67/1.14 inference(paramodulation,[status(thm)],[f519,f623])).
% 5.67/1.14 fof(f649,plain,(
% 5.67/1.14 ![X0,X1,X2]: (and(not(and(X0,not(X1))),X2)=not(implies(implies(X0,X1),not(X2)))|~spl0_85|~spl0_81|~spl0_79|~spl0_83)),
% 5.67/1.14 inference(paramodulation,[status(thm)],[f593,f595])).
% 5.67/1.14 fof(f650,plain,(
% 5.67/1.14 ![X0,X1,X2]: (and(implies(X0,not(not(X1))),X2)=not(implies(implies(X0,X1),not(X2)))|~spl0_85|~spl0_81|~spl0_79|~spl0_83)),
% 5.67/1.14 inference(forward_demodulation,[status(thm)],[f635,f649])).
% 5.67/1.14 fof(f651,plain,(
% 5.67/1.14 ![X0,X1,X2]: (and(implies(X0,not(not(X1))),X2)=and(implies(X0,X1),X2)|~spl0_85|~spl0_81|~spl0_79|~spl0_83)),
% 5.67/1.14 inference(forward_demodulation,[status(thm)],[f519,f650])).
% 5.67/1.14 fof(f708,plain,(
% 5.67/1.14 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),or(not(X2),X1))))|~spl0_76|~spl0_85)),
% 5.67/1.14 inference(paramodulation,[status(thm)],[f495,f463])).
% 5.67/1.14 fof(f709,plain,(
% 5.67/1.14 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1))))|~spl0_76|~spl0_85)),
% 5.67/1.14 inference(forward_demodulation,[status(thm)],[f495,f708])).
% 5.67/1.14 fof(f958,plain,(
% 5.67/1.14 ![X0,X1,X2]: (and(or(X0,not(not(X1))),X2)=and(implies(not(X0),X1),X2)|~spl0_85|~spl0_81|~spl0_83|~spl0_79)),
% 5.67/1.14 inference(paramodulation,[status(thm)],[f520,f651])).
% 5.67/1.14 fof(f959,plain,(
% 5.67/1.14 ![X0,X1,X2]: (and(or(X0,not(not(X1))),X2)=and(or(X0,X1),X2)|~spl0_85|~spl0_81|~spl0_83|~spl0_79)),
% 5.67/1.14 inference(forward_demodulation,[status(thm)],[f520,f958])).
% 5.67/1.14 fof(f1006,plain,(
% 5.67/1.14 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(implies(X2,X0),implies(X2,X1)))|~spl0_76|~spl0_85|~spl0_1)),
% 5.67/1.14 inference(resolution,[status(thm)],[f709,f185])).
% 5.67/1.14 fof(f1109,plain,(
% 5.67/1.14 ![X0,X1,X2]: (implies(or(X0,not(not(X1))),X2)=not(and(or(X0,X1),not(X2)))|~spl0_85|~spl0_81|~spl0_83|~spl0_79)),
% 5.67/1.14 inference(paramodulation,[status(thm)],[f959,f488])).
% 5.67/1.14 fof(f1110,plain,(
% 5.67/1.14 ![X0,X1,X2]: (implies(or(X0,not(not(X1))),X2)=implies(or(X0,X1),X2)|~spl0_85|~spl0_81|~spl0_83|~spl0_79)),
% 5.67/1.14 inference(forward_demodulation,[status(thm)],[f488,f1109])).
% 5.67/1.14 fof(f1118,plain,(
% 5.67/1.14 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X2,X0))|is_a_theorem(implies(X2,X1))|~spl0_76|~spl0_85|~spl0_1)),
% 5.67/1.14 inference(resolution,[status(thm)],[f1006,f185])).
% 5.67/1.14 fof(f1184,plain,(
% 5.67/1.14 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),implies(X2,or(X0,not(not(X1))))))|~spl0_13|~spl0_85|~spl0_81|~spl0_83|~spl0_79)),
% 5.67/1.14 inference(paramodulation,[status(thm)],[f1110,f230])).
% 5.67/1.14 fof(f1211,plain,(
% 5.67/1.14 ![X0,X1,X2]: (~is_a_theorem(implies(implies(X0,X1),X2))|is_a_theorem(implies(X1,X2))|~spl0_76|~spl0_85|~spl0_1|~spl0_13)),
% 5.67/1.14 inference(resolution,[status(thm)],[f1118,f230])).
% 5.67/1.14 fof(f1290,plain,(
% 5.67/1.14 $false|~spl0_89|~spl0_76|~spl0_85),
% 5.67/1.14 inference(backward_subsumption_resolution,[status(thm)],[f709,f612])).
% 5.67/1.14 fof(f1291,plain,(
% 5.67/1.14 ~spl0_89|~spl0_76|~spl0_85),
% 5.67/1.14 inference(contradiction_clause,[status(thm)],[f1290])).
% 5.67/1.14 fof(f2030,plain,(
% 5.67/1.14 ![X0,X1,X2]: (~is_a_theorem(or(X0,X1))|is_a_theorem(implies(X2,or(X0,not(not(X1)))))|~spl0_13|~spl0_85|~spl0_81|~spl0_83|~spl0_79|~spl0_1)),
% 5.67/1.14 inference(resolution,[status(thm)],[f1184,f185])).
% 5.67/1.14 fof(f2126,plain,(
% 5.67/1.14 spl0_94 <=> ~is_a_theorem(or(X0,X1))|is_a_theorem(or(X0,not(not(X1))))),
% 5.67/1.14 introduced(split_symbol_definition)).
% 5.67/1.14 fof(f2127,plain,(
% 5.67/1.14 ![X0,X1]: (~is_a_theorem(or(X0,X1))|is_a_theorem(or(X0,not(not(X1))))|~spl0_94)),
% 5.67/1.14 inference(component_clause,[status(thm)],[f2126])).
% 5.67/1.14 fof(f2129,plain,(
% 5.67/1.14 ![X0,X1,X2]: (~is_a_theorem(or(X0,X1))|~is_a_theorem(X2)|is_a_theorem(or(X0,not(not(X1))))|~spl0_13|~spl0_85|~spl0_81|~spl0_83|~spl0_79|~spl0_1)),
% 5.67/1.14 inference(resolution,[status(thm)],[f2030,f185])).
% 5.67/1.14 fof(f2130,plain,(
% 5.67/1.14 spl0_94|spl0_89|~spl0_13|~spl0_85|~spl0_81|~spl0_83|~spl0_79|~spl0_1),
% 5.67/1.14 inference(split_clause,[status(thm)],[f2129,f2126,f611,f229,f494,f480,f487,f473,f184])).
% 5.67/1.14 fof(f2185,plain,(
% 5.67/1.14 ![X0,X1]: (~is_a_theorem(or(not(X0),X1))|is_a_theorem(implies(X0,not(not(X1))))|~spl0_94|~spl0_85)),
% 5.67/1.14 inference(paramodulation,[status(thm)],[f495,f2127])).
% 5.67/1.14 fof(f2186,plain,(
% 5.67/1.14 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(X0,not(not(X1))))|~spl0_94|~spl0_85)),
% 5.67/1.14 inference(forward_demodulation,[status(thm)],[f495,f2185])).
% 5.67/1.14 fof(f2264,plain,(
% 5.67/1.14 ![X0,X1,X2]: (~is_a_theorem(implies(implies(X0,X1),X2))|is_a_theorem(implies(X1,not(not(X2))))|~spl0_94|~spl0_76|~spl0_85|~spl0_1|~spl0_13)),
% 5.67/1.14 inference(resolution,[status(thm)],[f2186,f1211])).
% 5.67/1.14 fof(f3321,plain,(
% 5.67/1.14 ![X0,X1]: (~is_a_theorem(or(X0,X1))|is_a_theorem(or(X1,X0))|~spl0_70|~spl0_1)),
% 5.67/1.14 inference(resolution,[status(thm)],[f441,f185])).
% 5.67/1.14 fof(f3327,plain,(
% 5.67/1.14 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),or(X1,not(X0))))|~spl0_70|~spl0_85)),
% 5.67/1.14 inference(paramodulation,[status(thm)],[f495,f441])).
% 5.67/1.14 fof(f3498,plain,(
% 5.67/1.14 ![X0,X1]: (is_a_theorem(implies(X0,not(not(or(X0,not(X1))))))|~spl0_70|~spl0_94|~spl0_76|~spl0_85|~spl0_1|~spl0_13)),
% 5.67/1.14 inference(resolution,[status(thm)],[f3327,f2264])).
% 5.67/1.14 fof(f3499,plain,(
% 5.67/1.14 ![X0,X1]: (is_a_theorem(implies(X0,not(and(not(X0),X1))))|~spl0_81|~spl0_83|~spl0_79|~spl0_70|~spl0_94|~spl0_76|~spl0_85|~spl0_1|~spl0_13)),
% 5.67/1.14 inference(forward_demodulation,[status(thm)],[f595,f3498])).
% 5.67/1.14 fof(f3584,plain,(
% 6.22/1.16 ![X0,X1]: (is_a_theorem(or(X0,not(and(not(not(X0)),X1))))|~spl0_81|~spl0_70|~spl0_94|~spl0_76|~spl0_85|~spl0_1|~spl0_13|~spl0_83|~spl0_79)),
% 6.22/1.16 inference(paramodulation,[status(thm)],[f520,f3499])).
% 6.22/1.16 fof(f3585,plain,(
% 6.22/1.16 ![X0,X1]: (is_a_theorem(or(X0,not(and(X0,X1))))|~spl0_81|~spl0_70|~spl0_94|~spl0_76|~spl0_85|~spl0_1|~spl0_13|~spl0_83|~spl0_79)),
% 6.22/1.16 inference(forward_demodulation,[status(thm)],[f623,f3584])).
% 6.22/1.16 fof(f3640,plain,(
% 6.22/1.16 ![X0,X1]: (is_a_theorem(or(not(and(X0,X1)),X0))|~spl0_81|~spl0_94|~spl0_76|~spl0_85|~spl0_13|~spl0_83|~spl0_79|~spl0_70|~spl0_1)),
% 6.22/1.16 inference(resolution,[status(thm)],[f3585,f3321])).
% 6.22/1.16 fof(f3641,plain,(
% 6.22/1.16 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X0))|~spl0_81|~spl0_94|~spl0_76|~spl0_85|~spl0_13|~spl0_83|~spl0_79|~spl0_70|~spl0_1)),
% 6.22/1.16 inference(forward_demodulation,[status(thm)],[f495,f3640])).
% 6.22/1.16 fof(f3667,plain,(
% 6.22/1.16 $false|~spl0_81|~spl0_94|~spl0_76|~spl0_85|~spl0_13|~spl0_83|~spl0_79|~spl0_70|~spl0_1|spl0_52),
% 6.22/1.16 inference(backward_subsumption_resolution,[status(thm)],[f375,f3641])).
% 6.22/1.16 fof(f3668,plain,(
% 6.22/1.16 ~spl0_81|~spl0_94|~spl0_76|~spl0_85|~spl0_13|~spl0_83|~spl0_79|~spl0_70|~spl0_1|spl0_52),
% 6.22/1.16 inference(contradiction_clause,[status(thm)],[f3667])).
% 6.22/1.16 fof(f3669,plain,(
% 6.22/1.16 $false|~spl0_51),
% 6.22/1.16 inference(forward_subsumption_resolution,[status(thm)],[f370,f180])).
% 6.22/1.16 fof(f3670,plain,(
% 6.22/1.16 ~spl0_51),
% 6.22/1.16 inference(contradiction_clause,[status(thm)],[f3669])).
% 6.22/1.16 fof(f3671,plain,(
% 6.22/1.16 $false),
% 6.22/1.16 inference(sat_refutation,[status(thm)],[f187,f376,f432,f443,f465,f476,f483,f490,f497,f508,f510,f512,f514,f516,f570,f574,f582,f587,f1291,f2130,f3668,f3670])).
% 6.22/1.16 % SZS output end CNFRefutation for theBenchmark.p
% 6.63/1.19 % Elapsed time: 0.831149 seconds
% 6.63/1.19 % CPU time: 6.377518 seconds
% 6.63/1.19 % Memory used: 205.382 MB
%------------------------------------------------------------------------------