TSTP Solution File: LCL520+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : LCL520+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n006.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 12:19:30 EDT 2023
% Result : Theorem 1.21s 0.60s
% Output : CNFRefutation 1.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL520+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue May 30 09:43:02 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % Drodi V3.5.1
% 1.21/0.60 % Refutation found
% 1.21/0.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.21/0.60 % SZS output start CNFRefutation for theBenchmark
% 1.21/0.60 fof(f1,axiom,(
% 1.21/0.60 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 1.21/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.60 fof(f16,axiom,(
% 1.21/0.60 ( kn1<=> (! [P] : is_a_theorem(implies(P,and(P,P))) )) ),
% 1.21/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.60 fof(f17,axiom,(
% 1.21/0.60 ( kn2<=> (! [P,Q] : is_a_theorem(implies(and(P,Q),P)) )) ),
% 1.21/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.60 fof(f18,axiom,(
% 1.21/0.60 ( kn3<=> (! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) )) ),
% 1.21/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.60 fof(f24,axiom,(
% 1.21/0.60 ( r3<=> (! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) )) ),
% 1.21/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.60 fof(f27,axiom,(
% 1.21/0.60 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 1.21/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.60 fof(f28,axiom,(
% 1.21/0.60 ( op_and=> (! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) )) ),
% 1.21/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.60 fof(f29,axiom,(
% 1.21/0.60 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 1.21/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.60 fof(f30,axiom,(
% 1.21/0.60 ( op_implies_or=> (! [X,Y] : implies(X,Y) = or(not(X),Y) )) ),
% 1.21/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.60 fof(f31,axiom,(
% 1.21/0.60 ( op_equiv=> (! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) )) ),
% 1.21/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.60 fof(f32,axiom,(
% 1.21/0.60 op_or ),
% 1.21/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.60 fof(f33,axiom,(
% 1.21/0.60 op_implies_and ),
% 1.21/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.60 fof(f34,axiom,(
% 1.21/0.60 op_equiv ),
% 1.21/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.60 fof(f35,axiom,(
% 1.21/0.60 modus_ponens ),
% 1.21/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.60 fof(f36,axiom,(
% 1.21/0.60 kn1 ),
% 1.21/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.60 fof(f37,axiom,(
% 1.21/0.60 kn2 ),
% 1.21/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.60 fof(f38,axiom,(
% 1.21/0.60 kn3 ),
% 1.21/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.60 fof(f40,axiom,(
% 1.21/0.60 op_implies_or ),
% 1.21/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.60 fof(f41,axiom,(
% 1.21/0.60 op_and ),
% 1.21/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.60 fof(f43,conjecture,(
% 1.21/0.60 r3 ),
% 1.21/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.60 fof(f44,negated_conjecture,(
% 1.21/0.60 ~(r3 )),
% 1.21/0.60 inference(negated_conjecture,[status(cth)],[f43])).
% 1.21/0.60 fof(f45,plain,(
% 1.21/0.60 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 1.21/0.60 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 1.21/0.60 fof(f46,plain,(
% 1.21/0.60 (~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))))),
% 1.21/0.60 inference(NNF_transformation,[status(esa)],[f45])).
% 1.21/0.60 fof(f47,plain,(
% 1.21/0.60 (~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))))),
% 1.21/0.60 inference(miniscoping,[status(esa)],[f46])).
% 1.21/0.60 fof(f48,plain,(
% 1.21/0.60 (~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)))),
% 1.21/0.60 inference(skolemization,[status(esa)],[f47])).
% 1.21/0.60 fof(f49,plain,(
% 1.21/0.60 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 1.21/0.60 inference(cnf_transformation,[status(esa)],[f48])).
% 1.21/0.60 fof(f111,plain,(
% 1.21/0.60 (~kn1|(![P]: is_a_theorem(implies(P,and(P,P)))))&(kn1|(?[P]: ~is_a_theorem(implies(P,and(P,P)))))),
% 1.21/0.60 inference(NNF_transformation,[status(esa)],[f16])).
% 1.21/0.60 fof(f112,plain,(
% 1.21/0.60 (~kn1|(![P]: is_a_theorem(implies(P,and(P,P)))))&(kn1|~is_a_theorem(implies(sk0_32,and(sk0_32,sk0_32))))),
% 1.21/0.60 inference(skolemization,[status(esa)],[f111])).
% 1.21/0.60 fof(f113,plain,(
% 1.21/0.60 ![X0]: (~kn1|is_a_theorem(implies(X0,and(X0,X0))))),
% 1.21/0.60 inference(cnf_transformation,[status(esa)],[f112])).
% 1.21/0.60 fof(f115,plain,(
% 1.21/0.60 (~kn2|(![P,Q]: is_a_theorem(implies(and(P,Q),P))))&(kn2|(?[P,Q]: ~is_a_theorem(implies(and(P,Q),P))))),
% 1.21/0.60 inference(NNF_transformation,[status(esa)],[f17])).
% 1.21/0.60 fof(f116,plain,(
% 1.21/0.60 (~kn2|(![P,Q]: is_a_theorem(implies(and(P,Q),P))))&(kn2|~is_a_theorem(implies(and(sk0_33,sk0_34),sk0_33)))),
% 1.21/0.60 inference(skolemization,[status(esa)],[f115])).
% 1.21/0.60 fof(f117,plain,(
% 1.21/0.60 ![X0,X1]: (~kn2|is_a_theorem(implies(and(X0,X1),X0)))),
% 1.21/0.60 inference(cnf_transformation,[status(esa)],[f116])).
% 1.21/0.60 fof(f119,plain,(
% 1.21/0.60 (~kn3|(![P,Q,R]: is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))))&(kn3|(?[P,Q,R]: ~is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))))),
% 1.21/0.60 inference(NNF_transformation,[status(esa)],[f18])).
% 1.21/0.60 fof(f120,plain,(
% 1.21/0.60 (~kn3|(![P,Q,R]: is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))))&(kn3|~is_a_theorem(implies(implies(sk0_35,sk0_36),implies(not(and(sk0_36,sk0_37)),not(and(sk0_37,sk0_35))))))),
% 1.21/0.60 inference(skolemization,[status(esa)],[f119])).
% 1.21/0.60 fof(f121,plain,(
% 1.21/0.60 ![X0,X1,X2]: (~kn3|is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))))),
% 1.21/0.60 inference(cnf_transformation,[status(esa)],[f120])).
% 1.21/0.60 fof(f143,plain,(
% 1.21/0.60 (~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)))))),
% 1.21/0.60 inference(NNF_transformation,[status(esa)],[f24])).
% 1.21/0.60 fof(f144,plain,(
% 1.21/0.60 (~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))))),
% 1.21/0.60 inference(skolemization,[status(esa)],[f143])).
% 1.21/0.60 fof(f146,plain,(
% 1.21/0.60 r3|~is_a_theorem(implies(or(sk0_47,sk0_48),or(sk0_48,sk0_47)))),
% 1.21/0.60 inference(cnf_transformation,[status(esa)],[f144])).
% 1.21/0.60 fof(f155,plain,(
% 1.21/0.60 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 1.21/0.60 inference(pre_NNF_transformation,[status(esa)],[f27])).
% 1.21/0.60 fof(f156,plain,(
% 1.21/0.60 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 1.21/0.60 inference(cnf_transformation,[status(esa)],[f155])).
% 1.21/0.60 fof(f157,plain,(
% 1.21/0.60 ~op_and|(![X,Y]: and(X,Y)=not(or(not(X),not(Y))))),
% 1.21/0.60 inference(pre_NNF_transformation,[status(esa)],[f28])).
% 1.21/0.60 fof(f158,plain,(
% 1.21/0.60 ![X0,X1]: (~op_and|and(X0,X1)=not(or(not(X0),not(X1))))),
% 1.21/0.60 inference(cnf_transformation,[status(esa)],[f157])).
% 1.21/0.60 fof(f159,plain,(
% 1.21/0.60 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 1.21/0.60 inference(pre_NNF_transformation,[status(esa)],[f29])).
% 1.21/0.60 fof(f160,plain,(
% 1.21/0.60 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 1.21/0.60 inference(cnf_transformation,[status(esa)],[f159])).
% 1.21/0.60 fof(f161,plain,(
% 1.21/0.60 ~op_implies_or|(![X,Y]: implies(X,Y)=or(not(X),Y))),
% 1.21/0.60 inference(pre_NNF_transformation,[status(esa)],[f30])).
% 1.21/0.60 fof(f162,plain,(
% 1.21/0.60 ![X0,X1]: (~op_implies_or|implies(X0,X1)=or(not(X0),X1))),
% 1.21/0.60 inference(cnf_transformation,[status(esa)],[f161])).
% 1.21/0.60 fof(f163,plain,(
% 1.21/0.60 ~op_equiv|(![X,Y]: equiv(X,Y)=and(implies(X,Y),implies(Y,X)))),
% 1.21/0.60 inference(pre_NNF_transformation,[status(esa)],[f31])).
% 1.21/0.60 fof(f164,plain,(
% 1.21/0.60 ![X0,X1]: (~op_equiv|equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 1.21/0.60 inference(cnf_transformation,[status(esa)],[f163])).
% 1.21/0.60 fof(f165,plain,(
% 1.21/0.60 op_or),
% 1.21/0.60 inference(cnf_transformation,[status(esa)],[f32])).
% 1.21/0.60 fof(f166,plain,(
% 1.21/0.60 op_implies_and),
% 1.21/0.60 inference(cnf_transformation,[status(esa)],[f33])).
% 1.21/0.60 fof(f167,plain,(
% 1.21/0.60 op_equiv),
% 1.21/0.60 inference(cnf_transformation,[status(esa)],[f34])).
% 1.21/0.60 fof(f168,plain,(
% 1.21/0.60 modus_ponens),
% 1.21/0.60 inference(cnf_transformation,[status(esa)],[f35])).
% 1.21/0.60 fof(f169,plain,(
% 1.21/0.60 kn1),
% 1.21/0.60 inference(cnf_transformation,[status(esa)],[f36])).
% 1.21/0.60 fof(f170,plain,(
% 1.21/0.60 kn2),
% 1.21/0.60 inference(cnf_transformation,[status(esa)],[f37])).
% 1.21/0.60 fof(f171,plain,(
% 1.21/0.60 kn3),
% 1.21/0.60 inference(cnf_transformation,[status(esa)],[f38])).
% 1.21/0.60 fof(f173,plain,(
% 1.21/0.60 op_implies_or),
% 1.21/0.60 inference(cnf_transformation,[status(esa)],[f40])).
% 1.21/0.60 fof(f174,plain,(
% 1.21/0.60 op_and),
% 1.21/0.60 inference(cnf_transformation,[status(esa)],[f41])).
% 1.21/0.60 fof(f176,plain,(
% 1.21/0.60 ~r3),
% 1.21/0.60 inference(cnf_transformation,[status(esa)],[f44])).
% 1.21/0.60 fof(f177,plain,(
% 1.21/0.60 spl0_0 <=> modus_ponens),
% 1.21/0.60 introduced(split_symbol_definition)).
% 1.21/0.61 fof(f179,plain,(
% 1.21/0.61 ~modus_ponens|spl0_0),
% 1.21/0.61 inference(component_clause,[status(thm)],[f177])).
% 1.21/0.61 fof(f180,plain,(
% 1.21/0.61 spl0_1 <=> ~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)),
% 1.21/0.61 introduced(split_symbol_definition)).
% 1.21/0.61 fof(f181,plain,(
% 1.21/0.61 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)|~spl0_1)),
% 1.21/0.61 inference(component_clause,[status(thm)],[f180])).
% 1.21/0.61 fof(f183,plain,(
% 1.21/0.61 ~spl0_0|spl0_1),
% 1.21/0.61 inference(split_clause,[status(thm)],[f49,f177,f180])).
% 1.21/0.61 fof(f258,plain,(
% 1.21/0.61 spl0_22 <=> is_a_theorem(implies(and(X0,X1),X0))),
% 1.21/0.61 introduced(split_symbol_definition)).
% 1.21/0.61 fof(f259,plain,(
% 1.21/0.61 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X0))|~spl0_22)),
% 1.21/0.61 inference(component_clause,[status(thm)],[f258])).
% 1.21/0.61 fof(f354,plain,(
% 1.21/0.61 spl0_48 <=> kn1),
% 1.21/0.61 introduced(split_symbol_definition)).
% 1.21/0.61 fof(f356,plain,(
% 1.21/0.61 ~kn1|spl0_48),
% 1.21/0.61 inference(component_clause,[status(thm)],[f354])).
% 1.21/0.61 fof(f357,plain,(
% 1.21/0.61 spl0_49 <=> is_a_theorem(implies(X0,and(X0,X0)))),
% 1.21/0.61 introduced(split_symbol_definition)).
% 1.21/0.61 fof(f358,plain,(
% 1.21/0.61 ![X0]: (is_a_theorem(implies(X0,and(X0,X0)))|~spl0_49)),
% 1.21/0.61 inference(component_clause,[status(thm)],[f357])).
% 1.21/0.61 fof(f360,plain,(
% 1.21/0.61 ~spl0_48|spl0_49),
% 1.21/0.61 inference(split_clause,[status(thm)],[f113,f354,f357])).
% 1.21/0.61 fof(f365,plain,(
% 1.21/0.61 spl0_51 <=> kn2),
% 1.21/0.61 introduced(split_symbol_definition)).
% 1.21/0.61 fof(f367,plain,(
% 1.21/0.61 ~kn2|spl0_51),
% 1.21/0.61 inference(component_clause,[status(thm)],[f365])).
% 1.21/0.61 fof(f368,plain,(
% 1.21/0.61 ~spl0_51|spl0_22),
% 1.21/0.61 inference(split_clause,[status(thm)],[f117,f365,f258])).
% 1.21/0.61 fof(f373,plain,(
% 1.21/0.61 spl0_53 <=> kn3),
% 1.21/0.61 introduced(split_symbol_definition)).
% 1.21/0.61 fof(f375,plain,(
% 1.21/0.61 ~kn3|spl0_53),
% 1.21/0.61 inference(component_clause,[status(thm)],[f373])).
% 1.21/0.61 fof(f376,plain,(
% 1.21/0.61 spl0_54 <=> is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))),
% 1.21/0.61 introduced(split_symbol_definition)).
% 1.21/0.61 fof(f377,plain,(
% 1.21/0.61 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))|~spl0_54)),
% 1.21/0.61 inference(component_clause,[status(thm)],[f376])).
% 1.21/0.61 fof(f379,plain,(
% 1.21/0.61 ~spl0_53|spl0_54),
% 1.21/0.61 inference(split_clause,[status(thm)],[f121,f373,f376])).
% 1.21/0.61 fof(f433,plain,(
% 1.21/0.61 spl0_69 <=> r3),
% 1.21/0.61 introduced(split_symbol_definition)).
% 1.21/0.61 fof(f434,plain,(
% 1.21/0.61 r3|~spl0_69),
% 1.21/0.61 inference(component_clause,[status(thm)],[f433])).
% 1.21/0.61 fof(f440,plain,(
% 1.21/0.61 spl0_71 <=> is_a_theorem(implies(or(sk0_47,sk0_48),or(sk0_48,sk0_47)))),
% 1.21/0.61 introduced(split_symbol_definition)).
% 1.21/0.61 fof(f442,plain,(
% 1.21/0.61 ~is_a_theorem(implies(or(sk0_47,sk0_48),or(sk0_48,sk0_47)))|spl0_71),
% 1.21/0.61 inference(component_clause,[status(thm)],[f440])).
% 1.21/0.61 fof(f443,plain,(
% 1.21/0.61 spl0_69|~spl0_71),
% 1.21/0.61 inference(split_clause,[status(thm)],[f146,f433,f440])).
% 1.21/0.61 fof(f466,plain,(
% 1.21/0.61 spl0_78 <=> op_or),
% 1.21/0.61 introduced(split_symbol_definition)).
% 1.21/0.61 fof(f468,plain,(
% 1.21/0.61 ~op_or|spl0_78),
% 1.21/0.61 inference(component_clause,[status(thm)],[f466])).
% 1.21/0.61 fof(f469,plain,(
% 1.21/0.61 spl0_79 <=> or(X0,X1)=not(and(not(X0),not(X1)))),
% 1.21/0.61 introduced(split_symbol_definition)).
% 1.21/0.61 fof(f470,plain,(
% 1.21/0.61 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1)))|~spl0_79)),
% 1.21/0.61 inference(component_clause,[status(thm)],[f469])).
% 1.21/0.61 fof(f472,plain,(
% 1.21/0.61 ~spl0_78|spl0_79),
% 1.21/0.61 inference(split_clause,[status(thm)],[f156,f466,f469])).
% 1.21/0.61 fof(f473,plain,(
% 1.21/0.61 spl0_80 <=> op_and),
% 1.21/0.61 introduced(split_symbol_definition)).
% 1.21/0.61 fof(f475,plain,(
% 1.21/0.61 ~op_and|spl0_80),
% 1.21/0.61 inference(component_clause,[status(thm)],[f473])).
% 1.21/0.61 fof(f476,plain,(
% 1.21/0.61 spl0_81 <=> and(X0,X1)=not(or(not(X0),not(X1)))),
% 1.21/0.61 introduced(split_symbol_definition)).
% 1.21/0.61 fof(f477,plain,(
% 1.21/0.61 ![X0,X1]: (and(X0,X1)=not(or(not(X0),not(X1)))|~spl0_81)),
% 1.21/0.61 inference(component_clause,[status(thm)],[f476])).
% 1.21/0.61 fof(f479,plain,(
% 1.21/0.61 ~spl0_80|spl0_81),
% 1.21/0.61 inference(split_clause,[status(thm)],[f158,f473,f476])).
% 1.21/0.61 fof(f480,plain,(
% 1.21/0.61 spl0_82 <=> op_implies_and),
% 1.21/0.61 introduced(split_symbol_definition)).
% 1.21/0.61 fof(f482,plain,(
% 1.21/0.61 ~op_implies_and|spl0_82),
% 1.21/0.61 inference(component_clause,[status(thm)],[f480])).
% 1.21/0.61 fof(f483,plain,(
% 1.21/0.61 spl0_83 <=> implies(X0,X1)=not(and(X0,not(X1)))),
% 1.21/0.61 introduced(split_symbol_definition)).
% 1.21/0.61 fof(f484,plain,(
% 1.21/0.61 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1)))|~spl0_83)),
% 1.21/0.61 inference(component_clause,[status(thm)],[f483])).
% 1.21/0.61 fof(f486,plain,(
% 1.21/0.61 ~spl0_82|spl0_83),
% 1.21/0.61 inference(split_clause,[status(thm)],[f160,f480,f483])).
% 1.21/0.61 fof(f487,plain,(
% 1.21/0.61 spl0_84 <=> op_implies_or),
% 1.21/0.61 introduced(split_symbol_definition)).
% 1.21/0.61 fof(f489,plain,(
% 1.21/0.61 ~op_implies_or|spl0_84),
% 1.21/0.61 inference(component_clause,[status(thm)],[f487])).
% 1.21/0.61 fof(f490,plain,(
% 1.21/0.61 spl0_85 <=> implies(X0,X1)=or(not(X0),X1)),
% 1.21/0.61 introduced(split_symbol_definition)).
% 1.21/0.61 fof(f491,plain,(
% 1.21/0.61 ![X0,X1]: (implies(X0,X1)=or(not(X0),X1)|~spl0_85)),
% 1.21/0.61 inference(component_clause,[status(thm)],[f490])).
% 1.21/0.61 fof(f493,plain,(
% 1.21/0.61 ~spl0_84|spl0_85),
% 1.21/0.61 inference(split_clause,[status(thm)],[f162,f487,f490])).
% 1.21/0.61 fof(f494,plain,(
% 1.21/0.61 spl0_86 <=> op_equiv),
% 1.21/0.61 introduced(split_symbol_definition)).
% 1.21/0.61 fof(f496,plain,(
% 1.21/0.61 ~op_equiv|spl0_86),
% 1.21/0.61 inference(component_clause,[status(thm)],[f494])).
% 1.21/0.61 fof(f497,plain,(
% 1.21/0.61 spl0_87 <=> equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))),
% 1.21/0.61 introduced(split_symbol_definition)).
% 1.21/0.61 fof(f498,plain,(
% 1.21/0.61 ![X0,X1]: (equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))|~spl0_87)),
% 1.21/0.61 inference(component_clause,[status(thm)],[f497])).
% 1.21/0.61 fof(f500,plain,(
% 1.21/0.61 ~spl0_86|spl0_87),
% 1.21/0.61 inference(split_clause,[status(thm)],[f164,f494,f497])).
% 1.21/0.61 fof(f501,plain,(
% 1.21/0.61 $false|spl0_86),
% 1.21/0.61 inference(forward_subsumption_resolution,[status(thm)],[f496,f167])).
% 1.21/0.61 fof(f502,plain,(
% 1.21/0.61 spl0_86),
% 1.21/0.61 inference(contradiction_clause,[status(thm)],[f501])).
% 1.21/0.61 fof(f503,plain,(
% 1.21/0.61 $false|spl0_0),
% 1.21/0.61 inference(forward_subsumption_resolution,[status(thm)],[f179,f168])).
% 1.21/0.61 fof(f504,plain,(
% 1.21/0.61 spl0_0),
% 1.21/0.61 inference(contradiction_clause,[status(thm)],[f503])).
% 1.21/0.61 fof(f507,plain,(
% 1.21/0.61 $false|spl0_84),
% 1.21/0.61 inference(forward_subsumption_resolution,[status(thm)],[f489,f173])).
% 1.21/0.61 fof(f508,plain,(
% 1.21/0.61 spl0_84),
% 1.21/0.61 inference(contradiction_clause,[status(thm)],[f507])).
% 1.21/0.61 fof(f509,plain,(
% 1.21/0.61 $false|spl0_82),
% 1.21/0.61 inference(forward_subsumption_resolution,[status(thm)],[f482,f166])).
% 1.21/0.61 fof(f510,plain,(
% 1.21/0.61 spl0_82),
% 1.21/0.61 inference(contradiction_clause,[status(thm)],[f509])).
% 1.21/0.61 fof(f511,plain,(
% 1.21/0.61 $false|spl0_80),
% 1.21/0.61 inference(forward_subsumption_resolution,[status(thm)],[f475,f174])).
% 1.21/0.61 fof(f512,plain,(
% 1.21/0.61 spl0_80),
% 1.21/0.61 inference(contradiction_clause,[status(thm)],[f511])).
% 1.21/0.61 fof(f513,plain,(
% 1.21/0.61 $false|spl0_78),
% 1.21/0.61 inference(forward_subsumption_resolution,[status(thm)],[f468,f165])).
% 1.21/0.61 fof(f514,plain,(
% 1.21/0.61 spl0_78),
% 1.21/0.61 inference(contradiction_clause,[status(thm)],[f513])).
% 1.21/0.61 fof(f527,plain,(
% 1.21/0.61 $false|spl0_51),
% 1.21/0.61 inference(forward_subsumption_resolution,[status(thm)],[f367,f170])).
% 1.21/0.61 fof(f528,plain,(
% 1.21/0.61 spl0_51),
% 1.21/0.61 inference(contradiction_clause,[status(thm)],[f527])).
% 1.21/0.61 fof(f531,plain,(
% 1.21/0.61 $false|spl0_48),
% 1.21/0.61 inference(forward_subsumption_resolution,[status(thm)],[f356,f169])).
% 1.21/0.61 fof(f532,plain,(
% 1.21/0.61 spl0_48),
% 1.21/0.61 inference(contradiction_clause,[status(thm)],[f531])).
% 1.21/0.61 fof(f549,plain,(
% 1.21/0.61 ![X0,X1]: (~is_a_theorem(and(X0,X1))|is_a_theorem(X0)|~spl0_1|~spl0_22)),
% 1.21/0.61 inference(resolution,[status(thm)],[f181,f259])).
% 1.21/0.61 fof(f551,plain,(
% 1.21/0.61 ![X0]: (~is_a_theorem(X0)|is_a_theorem(and(X0,X0))|~spl0_1|~spl0_49)),
% 1.21/0.61 inference(resolution,[status(thm)],[f181,f358])).
% 1.21/0.61 fof(f554,plain,(
% 1.21/0.61 ![X0,X1]: (is_a_theorem(and(implies(and(X0,X1),X0),implies(and(X0,X1),X0)))|~spl0_1|~spl0_49|~spl0_22)),
% 1.21/0.61 inference(resolution,[status(thm)],[f551,f259])).
% 1.21/0.61 fof(f556,plain,(
% 1.21/0.61 ![X0]: (is_a_theorem(and(implies(X0,and(X0,X0)),implies(X0,and(X0,X0))))|~spl0_1|~spl0_49)),
% 1.21/0.61 inference(resolution,[status(thm)],[f551,f358])).
% 1.21/0.61 fof(f565,plain,(
% 1.21/0.61 ![X0]: (is_a_theorem(implies(implies(X0,X0),equiv(X0,X0)))|~spl0_49|~spl0_87)),
% 1.21/0.61 inference(paramodulation,[status(thm)],[f498,f358])).
% 1.21/0.61 fof(f566,plain,(
% 1.21/0.61 ![X0]: (~is_a_theorem(implies(X0,X0))|is_a_theorem(equiv(X0,X0))|~spl0_49|~spl0_87|~spl0_1)),
% 1.21/0.61 inference(resolution,[status(thm)],[f565,f181])).
% 1.21/0.61 fof(f569,plain,(
% 1.21/0.61 ![X0,X1]: (and(X0,X1)=not(implies(X0,not(X1)))|~spl0_85|~spl0_81)),
% 1.21/0.61 inference(forward_demodulation,[status(thm)],[f491,f477])).
% 1.21/0.61 fof(f573,plain,(
% 1.21/0.61 ![X0,X1,X2]: (implies(implies(X0,not(X1)),X2)=or(and(X0,X1),X2)|~spl0_85|~spl0_81)),
% 1.21/0.61 inference(paramodulation,[status(thm)],[f569,f491])).
% 1.21/0.61 fof(f574,plain,(
% 1.21/0.61 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1)|~spl0_83|~spl0_79)),
% 1.21/0.61 inference(forward_demodulation,[status(thm)],[f484,f470])).
% 1.21/0.61 fof(f577,plain,(
% 1.21/0.61 ![X0,X1,X2]: (or(and(X0,not(X1)),X2)=implies(implies(X0,X1),X2)|~spl0_79|~spl0_83)),
% 1.21/0.61 inference(paramodulation,[status(thm)],[f484,f574])).
% 1.21/0.61 fof(f578,plain,(
% 1.21/0.61 ![X0,X1]: (and(not(X0),X1)=not(or(X0,not(X1)))|~spl0_85|~spl0_81|~spl0_83|~spl0_79)),
% 1.21/0.61 inference(paramodulation,[status(thm)],[f574,f569])).
% 1.21/0.61 fof(f586,plain,(
% 1.21/0.61 ![X0,X1]: (~is_a_theorem(not(X0))|~is_a_theorem(or(X0,X1))|is_a_theorem(X1)|~spl0_1|~spl0_83|~spl0_79)),
% 1.21/0.61 inference(paramodulation,[status(thm)],[f574,f181])).
% 1.21/0.61 fof(f602,plain,(
% 1.21/0.61 ![X0,X1]: (and(not(not(X0)),X1)=not(implies(X0,not(X1)))|~spl0_81|~spl0_83|~spl0_79|~spl0_85)),
% 1.21/0.61 inference(paramodulation,[status(thm)],[f491,f578])).
% 1.21/0.61 fof(f603,plain,(
% 1.21/0.61 ![X0,X1]: (and(not(not(X0)),X1)=and(X0,X1)|~spl0_81|~spl0_83|~spl0_79|~spl0_85)),
% 1.21/0.61 inference(forward_demodulation,[status(thm)],[f569,f602])).
% 1.21/0.61 fof(f623,plain,(
% 1.21/0.61 ![X0,X1]: (~is_a_theorem(and(X0,X1))|is_a_theorem(not(not(X0)))|~spl0_1|~spl0_22|~spl0_81|~spl0_83|~spl0_79|~spl0_85)),
% 1.21/0.61 inference(paramodulation,[status(thm)],[f603,f549])).
% 1.21/0.61 fof(f642,plain,(
% 1.21/0.61 ![X0,X1]: (~is_a_theorem(equiv(X0,X1))|is_a_theorem(not(not(implies(X0,X1))))|~spl0_1|~spl0_22|~spl0_81|~spl0_83|~spl0_79|~spl0_85|~spl0_87)),
% 1.21/0.61 inference(paramodulation,[status(thm)],[f498,f623])).
% 1.21/0.61 fof(f687,plain,(
% 1.21/0.61 ![X0,X1]: (~is_a_theorem(not(not(X0)))|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)|~spl0_1|~spl0_83|~spl0_79|~spl0_85)),
% 1.21/0.61 inference(paramodulation,[status(thm)],[f491,f586])).
% 1.21/0.61 fof(f1096,plain,(
% 1.21/0.61 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0)))))|~spl0_83|~spl0_79|~spl0_54)),
% 1.21/0.61 inference(forward_demodulation,[status(thm)],[f574,f377])).
% 1.21/0.61 fof(f1123,plain,(
% 1.21/0.61 $false|spl0_53),
% 1.21/0.61 inference(forward_subsumption_resolution,[status(thm)],[f375,f171])).
% 1.21/0.61 fof(f1124,plain,(
% 1.21/0.61 spl0_53),
% 1.21/0.61 inference(contradiction_clause,[status(thm)],[f1123])).
% 1.21/0.61 fof(f1127,plain,(
% 1.21/0.61 ![X0,X1]: (is_a_theorem(not(not(implies(and(X0,X1),X0))))|~spl0_49|~spl0_1|~spl0_22|~spl0_81|~spl0_83|~spl0_79|~spl0_85)),
% 1.21/0.61 inference(resolution,[status(thm)],[f554,f623])).
% 1.21/0.61 fof(f1144,plain,(
% 1.21/0.61 ![X0,X1,X2]: (~is_a_theorem(implies(implies(and(X0,X1),X0),X2))|is_a_theorem(X2)|~spl0_49|~spl0_22|~spl0_81|~spl0_1|~spl0_83|~spl0_79|~spl0_85)),
% 1.21/0.61 inference(resolution,[status(thm)],[f1127,f687])).
% 1.21/0.61 fof(f1196,plain,(
% 1.21/0.61 ![X0,X1,X2]: (~is_a_theorem(or(and(and(not(X0),X1),X0),X2))|is_a_theorem(X2)|~spl0_49|~spl0_22|~spl0_1|~spl0_83|~spl0_79|~spl0_85|~spl0_81)),
% 1.21/0.61 inference(paramodulation,[status(thm)],[f573,f1144])).
% 1.21/0.61 fof(f1324,plain,(
% 1.21/0.61 ![X0]: (is_a_theorem(not(not(implies(X0,and(X0,X0)))))|~spl0_49|~spl0_1|~spl0_22|~spl0_81|~spl0_83|~spl0_79|~spl0_85)),
% 1.21/0.61 inference(resolution,[status(thm)],[f556,f623])).
% 1.21/0.61 fof(f1357,plain,(
% 1.21/0.61 ![X0,X1]: (~is_a_theorem(implies(implies(X0,and(X0,X0)),X1))|is_a_theorem(X1)|~spl0_49|~spl0_22|~spl0_81|~spl0_1|~spl0_83|~spl0_79|~spl0_85)),
% 1.21/0.61 inference(resolution,[status(thm)],[f1324,f687])).
% 1.21/0.61 fof(f1465,plain,(
% 1.21/0.61 ![X0,X1]: (is_a_theorem(or(and(and(X0,X0),X1),not(and(X1,X0))))|~spl0_54|~spl0_49|~spl0_22|~spl0_81|~spl0_1|~spl0_83|~spl0_79|~spl0_85)),
% 1.21/0.61 inference(resolution,[status(thm)],[f1096,f1357])).
% 1.21/0.61 fof(f1533,plain,(
% 1.21/0.61 ![X0]: (is_a_theorem(not(and(X0,not(X0))))|~spl0_54|~spl0_49|~spl0_22|~spl0_1|~spl0_83|~spl0_79|~spl0_85|~spl0_81)),
% 1.21/0.61 inference(resolution,[status(thm)],[f1465,f1196])).
% 1.21/0.61 fof(f1534,plain,(
% 1.21/0.61 ![X0]: (is_a_theorem(implies(X0,X0))|~spl0_54|~spl0_49|~spl0_22|~spl0_1|~spl0_83|~spl0_79|~spl0_85|~spl0_81)),
% 1.21/0.61 inference(forward_demodulation,[status(thm)],[f484,f1533])).
% 1.21/0.61 fof(f1550,plain,(
% 1.21/0.61 ![X0]: (is_a_theorem(equiv(X0,X0))|~spl0_54|~spl0_22|~spl0_83|~spl0_79|~spl0_85|~spl0_81|~spl0_49|~spl0_87|~spl0_1)),
% 1.21/0.61 inference(backward_subsumption_resolution,[status(thm)],[f566,f1534])).
% 1.21/0.61 fof(f1568,plain,(
% 1.21/0.61 ![X0]: (is_a_theorem(not(not(implies(X0,X0))))|~spl0_54|~spl0_49|~spl0_1|~spl0_22|~spl0_81|~spl0_83|~spl0_79|~spl0_85|~spl0_87)),
% 1.21/0.61 inference(resolution,[status(thm)],[f1550,f642])).
% 1.21/0.61 fof(f1624,plain,(
% 1.21/0.61 ![X0,X1]: (~is_a_theorem(implies(implies(X0,X0),X1))|is_a_theorem(X1)|~spl0_54|~spl0_49|~spl0_22|~spl0_81|~spl0_87|~spl0_1|~spl0_83|~spl0_79|~spl0_85)),
% 1.21/0.61 inference(resolution,[status(thm)],[f1568,f687])).
% 1.21/0.61 fof(f2158,plain,(
% 1.21/0.61 ![X0,X1]: (is_a_theorem(or(and(X0,X1),not(and(X1,X0))))|~spl0_49|~spl0_22|~spl0_81|~spl0_87|~spl0_1|~spl0_85|~spl0_83|~spl0_79|~spl0_54)),
% 1.21/0.61 inference(resolution,[status(thm)],[f1624,f1096])).
% 1.21/0.61 fof(f2419,plain,(
% 1.21/0.61 ![X0,X1]: (is_a_theorem(or(and(not(X0),X1),implies(X1,X0)))|~spl0_49|~spl0_22|~spl0_81|~spl0_87|~spl0_1|~spl0_85|~spl0_79|~spl0_54|~spl0_83)),
% 1.21/0.61 inference(paramodulation,[status(thm)],[f484,f2158])).
% 1.21/0.61 fof(f4203,plain,(
% 1.21/0.61 ![X0,X1]: (is_a_theorem(implies(implies(not(X0),X1),implies(not(X1),X0)))|~spl0_49|~spl0_22|~spl0_81|~spl0_87|~spl0_1|~spl0_85|~spl0_54|~spl0_79|~spl0_83)),
% 1.21/0.61 inference(paramodulation,[status(thm)],[f577,f2419])).
% 1.21/0.61 fof(f4204,plain,(
% 1.21/0.61 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),implies(not(X1),X0)))|~spl0_49|~spl0_22|~spl0_81|~spl0_87|~spl0_1|~spl0_85|~spl0_54|~spl0_79|~spl0_83)),
% 1.21/0.61 inference(forward_demodulation,[status(thm)],[f574,f4203])).
% 1.21/0.61 fof(f4205,plain,(
% 1.21/0.61 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),or(X1,X0)))|~spl0_49|~spl0_22|~spl0_81|~spl0_87|~spl0_1|~spl0_85|~spl0_54|~spl0_79|~spl0_83)),
% 1.21/0.61 inference(forward_demodulation,[status(thm)],[f574,f4204])).
% 1.21/0.61 fof(f4231,plain,(
% 1.21/0.61 $false|~spl0_49|~spl0_22|~spl0_81|~spl0_87|~spl0_1|~spl0_85|~spl0_54|~spl0_79|~spl0_83|spl0_71),
% 1.21/0.61 inference(backward_subsumption_resolution,[status(thm)],[f442,f4205])).
% 1.21/0.61 fof(f4232,plain,(
% 1.21/0.61 ~spl0_49|~spl0_22|~spl0_81|~spl0_87|~spl0_1|~spl0_85|~spl0_54|~spl0_79|~spl0_83|spl0_71),
% 1.21/0.61 inference(contradiction_clause,[status(thm)],[f4231])).
% 1.21/0.61 fof(f4249,plain,(
% 1.21/0.61 $false|~spl0_69),
% 1.21/0.61 inference(forward_subsumption_resolution,[status(thm)],[f434,f176])).
% 1.21/0.61 fof(f4250,plain,(
% 1.21/0.61 ~spl0_69),
% 1.21/0.61 inference(contradiction_clause,[status(thm)],[f4249])).
% 1.21/0.61 fof(f4251,plain,(
% 1.21/0.61 $false),
% 1.21/0.61 inference(sat_refutation,[status(thm)],[f183,f360,f368,f379,f443,f472,f479,f486,f493,f500,f502,f504,f508,f510,f512,f514,f528,f532,f1124,f4232,f4250])).
% 1.21/0.61 % SZS output end CNFRefutation for theBenchmark.p
% 1.65/0.66 % Elapsed time: 0.304826 seconds
% 1.65/0.66 % CPU time: 1.657968 seconds
% 1.65/0.66 % Memory used: 80.697 MB
%------------------------------------------------------------------------------