TSTP Solution File: LCL502+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : LCL502+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n017.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 20:27:20 EDT 2024
% Result : Theorem 9.43s 1.55s
% Output : CNFRefutation 9.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : LCL502+1 : TPTP v8.1.2. Released v3.3.0.
% 0.05/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.31 % Computer : n017.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 300
% 0.09/0.31 % WCLimit : 300
% 0.09/0.31 % DateTime : Mon Apr 29 20:58:18 EDT 2024
% 0.09/0.31 % CPUTime :
% 0.15/0.32 % Drodi V3.6.0
% 9.43/1.55 % Refutation found
% 9.43/1.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 9.43/1.55 % SZS output start CNFRefutation for theBenchmark
% 9.43/1.55 fof(f1,axiom,(
% 9.43/1.55 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 9.43/1.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.43/1.55 fof(f2,axiom,(
% 9.43/1.55 ( substitution_of_equivalents<=> (! [X,Y] :( is_a_theorem(equiv(X,Y))=> X = Y ) )) ),
% 9.43/1.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.43/1.55 fof(f3,axiom,(
% 9.43/1.55 ( modus_tollens<=> (! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) )) ),
% 9.43/1.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.43/1.55 fof(f16,axiom,(
% 9.43/1.55 ( kn1<=> (! [P] : is_a_theorem(implies(P,and(P,P))) )) ),
% 9.43/1.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.43/1.55 fof(f17,axiom,(
% 9.43/1.55 ( kn2<=> (! [P,Q] : is_a_theorem(implies(and(P,Q),P)) )) ),
% 9.43/1.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.43/1.55 fof(f18,axiom,(
% 9.43/1.55 ( kn3<=> (! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) )) ),
% 9.43/1.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.43/1.55 fof(f24,axiom,(
% 9.43/1.55 ( r3<=> (! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) )) ),
% 9.43/1.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.43/1.55 fof(f27,axiom,(
% 9.43/1.55 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 9.43/1.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.43/1.55 fof(f29,axiom,(
% 9.43/1.55 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 9.43/1.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.43/1.55 fof(f31,axiom,(
% 9.43/1.55 ( op_equiv=> (! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) )) ),
% 9.43/1.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.43/1.55 fof(f32,axiom,(
% 9.43/1.55 op_or ),
% 9.43/1.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.43/1.55 fof(f33,axiom,(
% 9.43/1.55 op_implies_and ),
% 9.43/1.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.43/1.55 fof(f34,axiom,(
% 9.43/1.55 op_equiv ),
% 9.43/1.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.43/1.55 fof(f35,axiom,(
% 9.43/1.55 modus_ponens ),
% 9.43/1.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.43/1.55 fof(f36,axiom,(
% 9.43/1.55 kn1 ),
% 9.43/1.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.43/1.55 fof(f37,axiom,(
% 9.43/1.55 kn2 ),
% 9.43/1.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.43/1.55 fof(f38,axiom,(
% 9.43/1.55 kn3 ),
% 9.43/1.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.43/1.55 fof(f39,axiom,(
% 9.43/1.55 substitution_of_equivalents ),
% 9.43/1.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.43/1.55 fof(f43,conjecture,(
% 9.43/1.55 modus_tollens ),
% 9.43/1.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.43/1.55 fof(f44,negated_conjecture,(
% 9.43/1.55 ~(modus_tollens )),
% 9.43/1.55 inference(negated_conjecture,[status(cth)],[f43])).
% 9.43/1.55 fof(f45,plain,(
% 9.43/1.55 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 9.43/1.55 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 9.43/1.55 fof(f46,plain,(
% 9.43/1.55 (~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))))),
% 9.43/1.55 inference(NNF_transformation,[status(esa)],[f45])).
% 9.43/1.55 fof(f47,plain,(
% 9.43/1.55 (~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))))),
% 9.43/1.55 inference(miniscoping,[status(esa)],[f46])).
% 9.43/1.55 fof(f48,plain,(
% 9.43/1.55 (~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)))),
% 9.43/1.55 inference(skolemization,[status(esa)],[f47])).
% 9.43/1.55 fof(f49,plain,(
% 9.43/1.55 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 9.43/1.55 inference(cnf_transformation,[status(esa)],[f48])).
% 9.43/1.55 fof(f53,plain,(
% 9.43/1.55 substitution_of_equivalents<=>(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y))),
% 9.43/1.55 inference(pre_NNF_transformation,[status(esa)],[f2])).
% 9.43/1.55 fof(f54,plain,(
% 9.43/1.55 (~substitution_of_equivalents|(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y)))&(substitution_of_equivalents|(?[X,Y]: (is_a_theorem(equiv(X,Y))&~X=Y)))),
% 9.43/1.55 inference(NNF_transformation,[status(esa)],[f53])).
% 9.43/1.55 fof(f55,plain,(
% 9.43/1.55 (~substitution_of_equivalents|(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y)))&(substitution_of_equivalents|(is_a_theorem(equiv(sk0_2,sk0_3))&~sk0_2=sk0_3))),
% 9.43/1.55 inference(skolemization,[status(esa)],[f54])).
% 9.43/1.55 fof(f56,plain,(
% 9.43/1.55 ![X0,X1]: (~substitution_of_equivalents|~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 9.43/1.55 inference(cnf_transformation,[status(esa)],[f55])).
% 9.43/1.55 fof(f59,plain,(
% 9.43/1.55 (~modus_tollens|(![X,Y]: is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))))&(modus_tollens|(?[X,Y]: ~is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))))),
% 9.43/1.55 inference(NNF_transformation,[status(esa)],[f3])).
% 9.43/1.55 fof(f60,plain,(
% 9.43/1.55 (~modus_tollens|(![X,Y]: is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))))&(modus_tollens|~is_a_theorem(implies(implies(not(sk0_5),not(sk0_4)),implies(sk0_4,sk0_5))))),
% 9.43/1.55 inference(skolemization,[status(esa)],[f59])).
% 9.43/1.55 fof(f62,plain,(
% 9.43/1.55 modus_tollens|~is_a_theorem(implies(implies(not(sk0_5),not(sk0_4)),implies(sk0_4,sk0_5)))),
% 9.43/1.55 inference(cnf_transformation,[status(esa)],[f60])).
% 9.43/1.55 fof(f111,plain,(
% 9.43/1.55 (~kn1|(![P]: is_a_theorem(implies(P,and(P,P)))))&(kn1|(?[P]: ~is_a_theorem(implies(P,and(P,P)))))),
% 9.43/1.55 inference(NNF_transformation,[status(esa)],[f16])).
% 9.43/1.55 fof(f112,plain,(
% 9.43/1.55 (~kn1|(![P]: is_a_theorem(implies(P,and(P,P)))))&(kn1|~is_a_theorem(implies(sk0_32,and(sk0_32,sk0_32))))),
% 9.43/1.55 inference(skolemization,[status(esa)],[f111])).
% 9.43/1.55 fof(f113,plain,(
% 9.43/1.55 ![X0]: (~kn1|is_a_theorem(implies(X0,and(X0,X0))))),
% 9.43/1.55 inference(cnf_transformation,[status(esa)],[f112])).
% 9.43/1.55 fof(f115,plain,(
% 9.43/1.55 (~kn2|(![P,Q]: is_a_theorem(implies(and(P,Q),P))))&(kn2|(?[P,Q]: ~is_a_theorem(implies(and(P,Q),P))))),
% 9.43/1.55 inference(NNF_transformation,[status(esa)],[f17])).
% 9.43/1.55 fof(f116,plain,(
% 9.43/1.55 (~kn2|(![P,Q]: is_a_theorem(implies(and(P,Q),P))))&(kn2|~is_a_theorem(implies(and(sk0_33,sk0_34),sk0_33)))),
% 9.43/1.55 inference(skolemization,[status(esa)],[f115])).
% 9.43/1.55 fof(f117,plain,(
% 9.43/1.55 ![X0,X1]: (~kn2|is_a_theorem(implies(and(X0,X1),X0)))),
% 9.43/1.55 inference(cnf_transformation,[status(esa)],[f116])).
% 9.43/1.55 fof(f119,plain,(
% 9.43/1.55 (~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)))))))),
% 9.43/1.55 inference(NNF_transformation,[status(esa)],[f18])).
% 9.43/1.55 fof(f120,plain,(
% 9.43/1.55 (~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))))))),
% 9.43/1.55 inference(skolemization,[status(esa)],[f119])).
% 9.43/1.55 fof(f121,plain,(
% 9.43/1.55 ![X0,X1,X2]: (~kn3|is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))))),
% 9.43/1.55 inference(cnf_transformation,[status(esa)],[f120])).
% 9.43/1.55 fof(f143,plain,(
% 9.43/1.55 (~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)))))),
% 9.43/1.55 inference(NNF_transformation,[status(esa)],[f24])).
% 9.43/1.55 fof(f144,plain,(
% 9.43/1.55 (~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))))),
% 9.43/1.55 inference(skolemization,[status(esa)],[f143])).
% 9.43/1.55 fof(f145,plain,(
% 9.43/1.55 ![X0,X1]: (~r3|is_a_theorem(implies(or(X0,X1),or(X1,X0))))),
% 9.43/1.55 inference(cnf_transformation,[status(esa)],[f144])).
% 9.43/1.55 fof(f146,plain,(
% 9.43/1.55 r3|~is_a_theorem(implies(or(sk0_47,sk0_48),or(sk0_48,sk0_47)))),
% 9.43/1.55 inference(cnf_transformation,[status(esa)],[f144])).
% 9.43/1.55 fof(f155,plain,(
% 9.43/1.55 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 9.43/1.55 inference(pre_NNF_transformation,[status(esa)],[f27])).
% 9.43/1.55 fof(f156,plain,(
% 9.43/1.55 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 9.43/1.55 inference(cnf_transformation,[status(esa)],[f155])).
% 9.43/1.55 fof(f159,plain,(
% 9.43/1.55 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 9.43/1.55 inference(pre_NNF_transformation,[status(esa)],[f29])).
% 9.43/1.55 fof(f160,plain,(
% 9.43/1.55 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 9.43/1.55 inference(cnf_transformation,[status(esa)],[f159])).
% 9.43/1.55 fof(f163,plain,(
% 9.43/1.55 ~op_equiv|(![X,Y]: equiv(X,Y)=and(implies(X,Y),implies(Y,X)))),
% 9.43/1.55 inference(pre_NNF_transformation,[status(esa)],[f31])).
% 9.43/1.55 fof(f164,plain,(
% 9.43/1.55 ![X0,X1]: (~op_equiv|equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 9.43/1.55 inference(cnf_transformation,[status(esa)],[f163])).
% 9.43/1.55 fof(f165,plain,(
% 9.43/1.55 op_or),
% 9.43/1.55 inference(cnf_transformation,[status(esa)],[f32])).
% 9.43/1.55 fof(f166,plain,(
% 9.43/1.55 op_implies_and),
% 9.43/1.55 inference(cnf_transformation,[status(esa)],[f33])).
% 9.43/1.55 fof(f167,plain,(
% 9.43/1.55 op_equiv),
% 9.43/1.55 inference(cnf_transformation,[status(esa)],[f34])).
% 9.43/1.55 fof(f168,plain,(
% 9.43/1.55 modus_ponens),
% 9.43/1.55 inference(cnf_transformation,[status(esa)],[f35])).
% 9.43/1.55 fof(f169,plain,(
% 9.43/1.55 kn1),
% 9.43/1.55 inference(cnf_transformation,[status(esa)],[f36])).
% 9.43/1.55 fof(f170,plain,(
% 9.43/1.55 kn2),
% 9.43/1.55 inference(cnf_transformation,[status(esa)],[f37])).
% 9.43/1.55 fof(f171,plain,(
% 9.43/1.55 kn3),
% 9.43/1.55 inference(cnf_transformation,[status(esa)],[f38])).
% 9.43/1.55 fof(f172,plain,(
% 9.43/1.55 substitution_of_equivalents),
% 9.43/1.55 inference(cnf_transformation,[status(esa)],[f39])).
% 9.43/1.55 fof(f176,plain,(
% 9.43/1.55 ~modus_tollens),
% 9.43/1.55 inference(cnf_transformation,[status(esa)],[f44])).
% 9.43/1.55 fof(f177,plain,(
% 9.43/1.55 spl0_0 <=> modus_ponens),
% 9.43/1.55 introduced(split_symbol_definition)).
% 9.43/1.55 fof(f179,plain,(
% 9.43/1.55 ~modus_ponens|spl0_0),
% 9.43/1.55 inference(component_clause,[status(thm)],[f177])).
% 9.43/1.55 fof(f180,plain,(
% 9.43/1.55 spl0_1 <=> ~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)),
% 9.43/1.55 introduced(split_symbol_definition)).
% 9.43/1.55 fof(f181,plain,(
% 9.43/1.55 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)|~spl0_1)),
% 9.43/1.55 inference(component_clause,[status(thm)],[f180])).
% 9.43/1.55 fof(f183,plain,(
% 9.43/1.55 ~spl0_0|spl0_1),
% 9.43/1.55 inference(split_clause,[status(thm)],[f49,f177,f180])).
% 9.43/1.55 fof(f196,plain,(
% 9.43/1.55 spl0_5 <=> substitution_of_equivalents),
% 9.43/1.55 introduced(split_symbol_definition)).
% 9.43/1.55 fof(f198,plain,(
% 9.43/1.55 ~substitution_of_equivalents|spl0_5),
% 9.43/1.55 inference(component_clause,[status(thm)],[f196])).
% 9.43/1.55 fof(f199,plain,(
% 9.43/1.55 spl0_6 <=> ~is_a_theorem(equiv(X0,X1))|X0=X1),
% 9.43/1.55 introduced(split_symbol_definition)).
% 9.43/1.55 fof(f200,plain,(
% 9.43/1.55 ![X0,X1]: (~is_a_theorem(equiv(X0,X1))|X0=X1|~spl0_6)),
% 9.43/1.55 inference(component_clause,[status(thm)],[f199])).
% 9.43/1.55 fof(f202,plain,(
% 9.43/1.55 ~spl0_5|spl0_6),
% 9.43/1.55 inference(split_clause,[status(thm)],[f56,f196,f199])).
% 9.43/1.55 fof(f211,plain,(
% 9.43/1.55 spl0_9 <=> modus_tollens),
% 9.43/1.55 introduced(split_symbol_definition)).
% 9.43/1.55 fof(f212,plain,(
% 9.43/1.55 modus_tollens|~spl0_9),
% 9.43/1.55 inference(component_clause,[status(thm)],[f211])).
% 9.43/1.55 fof(f218,plain,(
% 9.43/1.55 spl0_11 <=> is_a_theorem(implies(implies(not(sk0_5),not(sk0_4)),implies(sk0_4,sk0_5)))),
% 9.43/1.55 introduced(split_symbol_definition)).
% 9.43/1.55 fof(f220,plain,(
% 9.43/1.55 ~is_a_theorem(implies(implies(not(sk0_5),not(sk0_4)),implies(sk0_4,sk0_5)))|spl0_11),
% 9.43/1.55 inference(component_clause,[status(thm)],[f218])).
% 9.43/1.55 fof(f221,plain,(
% 9.43/1.55 spl0_9|~spl0_11),
% 9.43/1.55 inference(split_clause,[status(thm)],[f62,f211,f218])).
% 9.43/1.55 fof(f258,plain,(
% 9.43/1.55 spl0_22 <=> is_a_theorem(implies(and(X0,X1),X0))),
% 9.43/1.55 introduced(split_symbol_definition)).
% 9.43/1.55 fof(f259,plain,(
% 9.43/1.55 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X0))|~spl0_22)),
% 9.43/1.55 inference(component_clause,[status(thm)],[f258])).
% 9.43/1.55 fof(f354,plain,(
% 9.43/1.55 spl0_48 <=> kn1),
% 9.43/1.55 introduced(split_symbol_definition)).
% 9.43/1.55 fof(f356,plain,(
% 9.43/1.55 ~kn1|spl0_48),
% 9.43/1.55 inference(component_clause,[status(thm)],[f354])).
% 9.43/1.55 fof(f357,plain,(
% 9.43/1.55 spl0_49 <=> is_a_theorem(implies(X0,and(X0,X0)))),
% 9.43/1.55 introduced(split_symbol_definition)).
% 9.43/1.55 fof(f358,plain,(
% 9.43/1.55 ![X0]: (is_a_theorem(implies(X0,and(X0,X0)))|~spl0_49)),
% 9.43/1.55 inference(component_clause,[status(thm)],[f357])).
% 9.43/1.55 fof(f360,plain,(
% 9.43/1.55 ~spl0_48|spl0_49),
% 9.43/1.55 inference(split_clause,[status(thm)],[f113,f354,f357])).
% 9.43/1.55 fof(f365,plain,(
% 9.43/1.55 spl0_51 <=> kn2),
% 9.43/1.55 introduced(split_symbol_definition)).
% 9.43/1.55 fof(f367,plain,(
% 9.43/1.55 ~kn2|spl0_51),
% 9.43/1.55 inference(component_clause,[status(thm)],[f365])).
% 9.43/1.55 fof(f368,plain,(
% 9.43/1.55 ~spl0_51|spl0_22),
% 9.43/1.55 inference(split_clause,[status(thm)],[f117,f365,f258])).
% 9.43/1.55 fof(f373,plain,(
% 9.43/1.55 spl0_53 <=> kn3),
% 9.43/1.55 introduced(split_symbol_definition)).
% 9.43/1.55 fof(f375,plain,(
% 9.43/1.55 ~kn3|spl0_53),
% 9.43/1.55 inference(component_clause,[status(thm)],[f373])).
% 9.43/1.55 fof(f376,plain,(
% 9.43/1.55 spl0_54 <=> is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))),
% 9.43/1.55 introduced(split_symbol_definition)).
% 9.43/1.55 fof(f377,plain,(
% 9.43/1.55 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))|~spl0_54)),
% 9.43/1.55 inference(component_clause,[status(thm)],[f376])).
% 9.43/1.55 fof(f379,plain,(
% 9.43/1.55 ~spl0_53|spl0_54),
% 9.43/1.55 inference(split_clause,[status(thm)],[f121,f373,f376])).
% 9.43/1.55 fof(f395,plain,(
% 9.43/1.55 spl0_59 <=> is_a_theorem(implies(X0,implies(not(X0),X1)))),
% 9.43/1.55 introduced(split_symbol_definition)).
% 9.43/1.55 fof(f396,plain,(
% 9.43/1.55 ![X0,X1]: (is_a_theorem(implies(X0,implies(not(X0),X1)))|~spl0_59)),
% 9.43/1.55 inference(component_clause,[status(thm)],[f395])).
% 9.43/1.55 fof(f433,plain,(
% 9.43/1.55 spl0_69 <=> r3),
% 9.43/1.55 introduced(split_symbol_definition)).
% 9.43/1.55 fof(f436,plain,(
% 9.43/1.55 spl0_70 <=> is_a_theorem(implies(or(X0,X1),or(X1,X0)))),
% 9.43/1.55 introduced(split_symbol_definition)).
% 9.43/1.55 fof(f437,plain,(
% 9.43/1.55 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),or(X1,X0)))|~spl0_70)),
% 9.43/1.55 inference(component_clause,[status(thm)],[f436])).
% 9.43/1.55 fof(f439,plain,(
% 9.43/1.55 ~spl0_69|spl0_70),
% 9.43/1.55 inference(split_clause,[status(thm)],[f145,f433,f436])).
% 9.43/1.55 fof(f440,plain,(
% 9.43/1.55 spl0_71 <=> is_a_theorem(implies(or(sk0_47,sk0_48),or(sk0_48,sk0_47)))),
% 9.43/1.55 introduced(split_symbol_definition)).
% 9.43/1.55 fof(f442,plain,(
% 9.43/1.55 ~is_a_theorem(implies(or(sk0_47,sk0_48),or(sk0_48,sk0_47)))|spl0_71),
% 9.43/1.55 inference(component_clause,[status(thm)],[f440])).
% 9.43/1.55 fof(f443,plain,(
% 9.43/1.55 spl0_69|~spl0_71),
% 9.43/1.55 inference(split_clause,[status(thm)],[f146,f433,f440])).
% 9.43/1.55 fof(f466,plain,(
% 9.43/1.55 spl0_78 <=> op_or),
% 9.43/1.55 introduced(split_symbol_definition)).
% 9.43/1.55 fof(f468,plain,(
% 9.43/1.55 ~op_or|spl0_78),
% 9.43/1.55 inference(component_clause,[status(thm)],[f466])).
% 9.43/1.55 fof(f469,plain,(
% 9.43/1.55 spl0_79 <=> or(X0,X1)=not(and(not(X0),not(X1)))),
% 9.43/1.55 introduced(split_symbol_definition)).
% 9.43/1.55 fof(f470,plain,(
% 9.43/1.55 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1)))|~spl0_79)),
% 9.43/1.55 inference(component_clause,[status(thm)],[f469])).
% 9.43/1.55 fof(f472,plain,(
% 9.43/1.55 ~spl0_78|spl0_79),
% 9.43/1.55 inference(split_clause,[status(thm)],[f156,f466,f469])).
% 9.43/1.55 fof(f480,plain,(
% 9.43/1.55 spl0_82 <=> op_implies_and),
% 9.43/1.55 introduced(split_symbol_definition)).
% 9.43/1.55 fof(f482,plain,(
% 9.43/1.55 ~op_implies_and|spl0_82),
% 9.43/1.55 inference(component_clause,[status(thm)],[f480])).
% 9.43/1.55 fof(f483,plain,(
% 9.43/1.55 spl0_83 <=> implies(X0,X1)=not(and(X0,not(X1)))),
% 9.43/1.55 introduced(split_symbol_definition)).
% 9.43/1.55 fof(f484,plain,(
% 9.43/1.55 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1)))|~spl0_83)),
% 9.43/1.55 inference(component_clause,[status(thm)],[f483])).
% 9.43/1.55 fof(f486,plain,(
% 9.43/1.56 ~spl0_82|spl0_83),
% 9.43/1.56 inference(split_clause,[status(thm)],[f160,f480,f483])).
% 9.43/1.56 fof(f494,plain,(
% 9.43/1.56 spl0_86 <=> op_equiv),
% 9.43/1.56 introduced(split_symbol_definition)).
% 9.43/1.56 fof(f496,plain,(
% 9.43/1.56 ~op_equiv|spl0_86),
% 9.43/1.56 inference(component_clause,[status(thm)],[f494])).
% 9.43/1.56 fof(f497,plain,(
% 9.43/1.56 spl0_87 <=> equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))),
% 9.43/1.56 introduced(split_symbol_definition)).
% 9.43/1.56 fof(f498,plain,(
% 9.43/1.56 ![X0,X1]: (equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))|~spl0_87)),
% 9.43/1.56 inference(component_clause,[status(thm)],[f497])).
% 9.43/1.56 fof(f500,plain,(
% 9.43/1.56 ~spl0_86|spl0_87),
% 9.43/1.56 inference(split_clause,[status(thm)],[f164,f494,f497])).
% 9.43/1.56 fof(f501,plain,(
% 9.43/1.56 $false|spl0_86),
% 9.43/1.56 inference(forward_subsumption_resolution,[status(thm)],[f496,f167])).
% 9.43/1.56 fof(f502,plain,(
% 9.43/1.56 spl0_86),
% 9.43/1.56 inference(contradiction_clause,[status(thm)],[f501])).
% 9.43/1.56 fof(f503,plain,(
% 9.43/1.56 $false|spl0_0),
% 9.43/1.56 inference(forward_subsumption_resolution,[status(thm)],[f179,f168])).
% 9.43/1.56 fof(f504,plain,(
% 9.43/1.56 spl0_0),
% 9.43/1.56 inference(contradiction_clause,[status(thm)],[f503])).
% 9.43/1.56 fof(f505,plain,(
% 9.43/1.56 $false|spl0_5),
% 9.43/1.56 inference(forward_subsumption_resolution,[status(thm)],[f198,f172])).
% 9.43/1.56 fof(f506,plain,(
% 9.43/1.56 spl0_5),
% 9.43/1.56 inference(contradiction_clause,[status(thm)],[f505])).
% 9.43/1.56 fof(f507,plain,(
% 9.43/1.56 $false|spl0_82),
% 9.43/1.56 inference(forward_subsumption_resolution,[status(thm)],[f482,f166])).
% 9.43/1.56 fof(f508,plain,(
% 9.43/1.56 spl0_82),
% 9.43/1.56 inference(contradiction_clause,[status(thm)],[f507])).
% 9.43/1.56 fof(f509,plain,(
% 9.43/1.56 $false|spl0_78),
% 9.43/1.56 inference(forward_subsumption_resolution,[status(thm)],[f468,f165])).
% 9.43/1.56 fof(f510,plain,(
% 9.43/1.56 spl0_78),
% 9.43/1.56 inference(contradiction_clause,[status(thm)],[f509])).
% 9.43/1.56 fof(f517,plain,(
% 9.43/1.56 $false|spl0_51),
% 9.43/1.56 inference(forward_subsumption_resolution,[status(thm)],[f367,f170])).
% 9.43/1.56 fof(f518,plain,(
% 9.43/1.56 spl0_51),
% 9.43/1.56 inference(contradiction_clause,[status(thm)],[f517])).
% 9.43/1.56 fof(f521,plain,(
% 9.43/1.56 $false|spl0_48),
% 9.43/1.56 inference(forward_subsumption_resolution,[status(thm)],[f356,f169])).
% 9.43/1.56 fof(f522,plain,(
% 9.43/1.56 spl0_48),
% 9.43/1.56 inference(contradiction_clause,[status(thm)],[f521])).
% 9.43/1.56 fof(f545,plain,(
% 9.43/1.56 ![X0,X1,X2]: (implies(X0,and(X1,not(X2)))=not(and(X0,implies(X1,X2)))|~spl0_83)),
% 9.43/1.56 inference(paramodulation,[status(thm)],[f484,f484])).
% 9.43/1.56 fof(f755,plain,(
% 9.43/1.56 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1)|~spl0_83|~spl0_79)),
% 9.43/1.56 inference(forward_demodulation,[status(thm)],[f484,f470])).
% 9.43/1.56 fof(f756,plain,(
% 9.43/1.56 ![X0,X1,X2]: (or(and(X0,not(X1)),X2)=implies(implies(X0,X1),X2)|~spl0_79|~spl0_83)),
% 9.43/1.56 inference(paramodulation,[status(thm)],[f484,f755])).
% 9.43/1.56 fof(f757,plain,(
% 9.43/1.56 ![X0]: (is_a_theorem(or(X0,and(not(X0),not(X0))))|~spl0_49|~spl0_83|~spl0_79)),
% 9.43/1.56 inference(paramodulation,[status(thm)],[f755,f358])).
% 9.43/1.56 fof(f761,plain,(
% 9.43/1.56 ![X0,X1]: (equiv(X0,not(X1))=and(implies(X0,not(X1)),or(X1,X0))|~spl0_87|~spl0_83|~spl0_79)),
% 9.43/1.56 inference(paramodulation,[status(thm)],[f755,f498])).
% 9.43/1.56 fof(f763,plain,(
% 9.43/1.56 ![X0,X1]: (~is_a_theorem(not(X0))|~is_a_theorem(or(X0,X1))|is_a_theorem(X1)|~spl0_1|~spl0_83|~spl0_79)),
% 9.43/1.56 inference(paramodulation,[status(thm)],[f755,f181])).
% 9.43/1.56 fof(f810,plain,(
% 9.43/1.56 ![X0,X1,X2]: (implies(X0,and(not(X1),not(X2)))=not(and(X0,or(X1,X2)))|~spl0_83|~spl0_79)),
% 9.43/1.56 inference(paramodulation,[status(thm)],[f755,f545])).
% 9.43/1.56 fof(f905,plain,(
% 9.43/1.56 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0)))))|~spl0_83|~spl0_79|~spl0_54)),
% 9.43/1.56 inference(forward_demodulation,[status(thm)],[f755,f377])).
% 9.43/1.56 fof(f906,plain,(
% 9.43/1.56 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(or(and(X1,X2),not(and(X2,X0))))|~spl0_83|~spl0_79|~spl0_54|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f905,f181])).
% 9.43/1.56 fof(f907,plain,(
% 9.43/1.56 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),or(and(X1,X2),not(and(X2,not(X0))))))|~spl0_54|~spl0_83|~spl0_79)),
% 9.43/1.56 inference(paramodulation,[status(thm)],[f755,f905])).
% 9.43/1.56 fof(f908,plain,(
% 9.43/1.56 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),or(and(X1,X2),implies(X2,X0))))|~spl0_54|~spl0_83|~spl0_79)),
% 9.43/1.56 inference(forward_demodulation,[status(thm)],[f484,f907])).
% 9.43/1.56 fof(f909,plain,(
% 9.43/1.56 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),not(and(not(X2),X0)))))|~spl0_54|~spl0_79|~spl0_83)),
% 9.43/1.56 inference(paramodulation,[status(thm)],[f756,f905])).
% 9.43/1.56 fof(f1001,plain,(
% 9.43/1.56 $false|spl0_53),
% 9.43/1.56 inference(forward_subsumption_resolution,[status(thm)],[f375,f171])).
% 9.43/1.56 fof(f1002,plain,(
% 9.43/1.56 spl0_53),
% 9.43/1.56 inference(contradiction_clause,[status(thm)],[f1001])).
% 9.43/1.56 fof(f1012,plain,(
% 9.43/1.56 ![X0,X1,X2]: (~is_a_theorem(or(X0,X1))|is_a_theorem(or(and(X1,X2),implies(X2,X0)))|~spl0_54|~spl0_83|~spl0_79|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f908,f181])).
% 9.43/1.56 fof(f1014,plain,(
% 9.43/1.56 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),implies(not(X2),X0))))|~spl0_54|~spl0_79|~spl0_83)),
% 9.43/1.56 inference(paramodulation,[status(thm)],[f756,f908])).
% 9.43/1.56 fof(f1015,plain,(
% 9.43/1.56 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),or(X2,X0))))|~spl0_54|~spl0_79|~spl0_83)),
% 9.43/1.56 inference(forward_demodulation,[status(thm)],[f755,f1014])).
% 9.43/1.56 fof(f1038,plain,(
% 9.43/1.56 ![X0,X1,X2]: (~is_a_theorem(or(X0,X1))|is_a_theorem(implies(implies(X1,X2),or(X2,X0)))|~spl0_54|~spl0_79|~spl0_83|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f1015,f181])).
% 9.43/1.56 fof(f1045,plain,(
% 9.43/1.56 ![X0,X1]: (is_a_theorem(implies(implies(and(not(X0),not(X0)),X1),or(X1,X0)))|~spl0_54|~spl0_1|~spl0_49|~spl0_83|~spl0_79)),
% 9.43/1.56 inference(resolution,[status(thm)],[f1038,f757])).
% 9.43/1.56 fof(f1067,plain,(
% 9.43/1.56 ~is_a_theorem(implies(or(sk0_5,not(sk0_4)),implies(sk0_4,sk0_5)))|~spl0_83|~spl0_79|spl0_11),
% 9.43/1.56 inference(forward_demodulation,[status(thm)],[f755,f220])).
% 9.43/1.56 fof(f1068,plain,(
% 9.43/1.56 ![X0,X1]: (~is_a_theorem(implies(and(not(X0),not(X0)),X1))|is_a_theorem(or(X1,X0))|~spl0_54|~spl0_49|~spl0_83|~spl0_79|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f1045,f181])).
% 9.43/1.56 fof(f1078,plain,(
% 9.43/1.56 ![X0]: (is_a_theorem(or(not(X0),X0))|~spl0_54|~spl0_49|~spl0_83|~spl0_79|~spl0_1|~spl0_22)),
% 9.43/1.56 inference(resolution,[status(thm)],[f1068,f259])).
% 9.43/1.56 fof(f1088,plain,(
% 9.43/1.56 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),or(X1,not(X0))))|~spl0_49|~spl0_22|~spl0_54|~spl0_79|~spl0_83|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f1078,f1038])).
% 9.43/1.56 fof(f1089,plain,(
% 9.43/1.56 ![X0,X1]: (is_a_theorem(or(and(X0,X1),implies(X1,not(X0))))|~spl0_49|~spl0_22|~spl0_54|~spl0_83|~spl0_79|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f1078,f1012])).
% 9.43/1.56 fof(f1092,plain,(
% 9.43/1.56 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(or(X1,not(X0)))|~spl0_49|~spl0_22|~spl0_54|~spl0_79|~spl0_83|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f1088,f181])).
% 9.43/1.56 fof(f1096,plain,(
% 9.43/1.56 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),or(X1,not(not(X0)))))|~spl0_49|~spl0_22|~spl0_54|~spl0_1|~spl0_83|~spl0_79)),
% 9.43/1.56 inference(paramodulation,[status(thm)],[f755,f1088])).
% 9.43/1.56 fof(f1120,plain,(
% 9.43/1.56 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(implies(not(X0),X2),or(X2,X1)))|~spl0_49|~spl0_22|~spl0_54|~spl0_79|~spl0_83|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f1092,f1038])).
% 9.43/1.56 fof(f1121,plain,(
% 9.43/1.56 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(or(X0,X2),or(X2,X1)))|~spl0_49|~spl0_22|~spl0_54|~spl0_79|~spl0_83|~spl0_1)),
% 9.43/1.56 inference(forward_demodulation,[status(thm)],[f755,f1120])).
% 9.43/1.56 fof(f1126,plain,(
% 9.43/1.56 ![X0,X1]: (~is_a_theorem(or(X0,X1))|is_a_theorem(or(X1,not(not(X0))))|~spl0_49|~spl0_22|~spl0_54|~spl0_83|~spl0_79|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f1096,f181])).
% 9.43/1.56 fof(f1151,plain,(
% 9.43/1.56 ~is_a_theorem(implies(sk0_47,sk0_47))|~spl0_49|~spl0_22|~spl0_54|~spl0_79|~spl0_83|~spl0_1|spl0_71),
% 9.43/1.56 inference(resolution,[status(thm)],[f1121,f442])).
% 9.43/1.56 fof(f1154,plain,(
% 9.43/1.56 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(or(X0,X2))|is_a_theorem(or(X2,X1))|~spl0_49|~spl0_22|~spl0_54|~spl0_79|~spl0_83|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f1121,f181])).
% 9.43/1.56 fof(f1185,plain,(
% 9.43/1.56 ![X0]: (is_a_theorem(not(and(not(X0),or(X0,X0))))|~spl0_49|~spl0_83|~spl0_79)),
% 9.43/1.56 inference(paramodulation,[status(thm)],[f810,f358])).
% 9.43/1.56 fof(f1229,plain,(
% 9.43/1.56 ![X0,X1]: (~is_a_theorem(or(and(not(X0),or(X0,X0)),X1))|is_a_theorem(X1)|~spl0_49|~spl0_1|~spl0_83|~spl0_79)),
% 9.43/1.56 inference(resolution,[status(thm)],[f1185,f763])).
% 9.43/1.56 fof(f1345,plain,(
% 9.43/1.56 ![X0,X1]: (~is_a_theorem(implies(X0,not(X1)))|is_a_theorem(not(and(or(X1,X1),X0)))|~spl0_54|~spl0_49|~spl0_1|~spl0_83|~spl0_79)),
% 9.43/1.56 inference(resolution,[status(thm)],[f906,f1229])).
% 9.43/1.56 fof(f1364,plain,(
% 9.43/1.56 ![X0,X1]: (~is_a_theorem(implies(not(X0),not(X1)))|is_a_theorem(implies(or(X1,X1),X0))|~spl0_54|~spl0_49|~spl0_1|~spl0_79|~spl0_83)),
% 9.43/1.56 inference(paramodulation,[status(thm)],[f484,f1345])).
% 9.43/1.56 fof(f1365,plain,(
% 9.43/1.56 ![X0,X1]: (~is_a_theorem(or(X0,not(X1)))|is_a_theorem(implies(or(X1,X1),X0))|~spl0_54|~spl0_49|~spl0_1|~spl0_79|~spl0_83)),
% 9.43/1.56 inference(forward_demodulation,[status(thm)],[f755,f1364])).
% 9.43/1.56 fof(f1371,plain,(
% 9.43/1.56 ![X0,X1]: (is_a_theorem(implies(or(not(X0),not(X0)),X1))|~is_a_theorem(or(X0,X1))|~spl0_49|~spl0_22|~spl0_54|~spl0_83|~spl0_79|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f1365,f1126])).
% 9.43/1.56 fof(f1403,plain,(
% 9.43/1.56 ![X0]: (is_a_theorem(implies(or(not(not(X0)),not(not(X0))),X0))|~spl0_54|~spl0_49|~spl0_83|~spl0_79|~spl0_1|~spl0_22)),
% 9.43/1.56 inference(resolution,[status(thm)],[f1371,f1078])).
% 9.43/1.56 fof(f1431,plain,(
% 9.43/1.56 ![X0]: (~is_a_theorem(or(not(not(X0)),not(not(X0))))|is_a_theorem(X0)|~spl0_54|~spl0_49|~spl0_83|~spl0_79|~spl0_22|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f1403,f181])).
% 9.43/1.56 fof(f1445,plain,(
% 9.43/1.56 ![X0]: (is_a_theorem(X0)|~is_a_theorem(or(X0,not(not(X0))))|~spl0_49|~spl0_22|~spl0_54|~spl0_83|~spl0_79|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f1431,f1126])).
% 9.43/1.56 fof(f1457,plain,(
% 9.43/1.56 ![X0]: (is_a_theorem(X0)|~is_a_theorem(or(X0,X0))|~spl0_49|~spl0_22|~spl0_54|~spl0_83|~spl0_79|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f1445,f1126])).
% 9.43/1.56 fof(f1460,plain,(
% 9.43/1.56 ![X0,X1]: (is_a_theorem(X0)|~is_a_theorem(implies(X1,not(not(X0))))|~is_a_theorem(or(X1,X0))|~spl0_49|~spl0_22|~spl0_54|~spl0_79|~spl0_83|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f1445,f1154])).
% 9.43/1.56 fof(f1468,plain,(
% 9.43/1.56 ![X0,X1]: (is_a_theorem(X0)|~is_a_theorem(implies(X1,X0))|~is_a_theorem(or(X1,X0))|~spl0_49|~spl0_22|~spl0_54|~spl0_79|~spl0_83|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f1457,f1154])).
% 9.43/1.56 fof(f1527,plain,(
% 9.43/1.56 ![X0,X1]: (is_a_theorem(X0)|~is_a_theorem(or(and(not(not(X0)),X1),X0))|~spl0_49|~spl0_54|~spl0_79|~spl0_83|~spl0_1|~spl0_22)),
% 9.43/1.56 inference(resolution,[status(thm)],[f1460,f259])).
% 9.43/1.56 fof(f1539,plain,(
% 9.43/1.56 ![X0,X1]: (is_a_theorem(X0)|~is_a_theorem(implies(implies(not(not(X0)),X1),X0))|~spl0_49|~spl0_54|~spl0_1|~spl0_22|~spl0_79|~spl0_83)),
% 9.43/1.56 inference(paramodulation,[status(thm)],[f756,f1527])).
% 9.43/1.56 fof(f1540,plain,(
% 9.43/1.56 ![X0,X1]: (is_a_theorem(X0)|~is_a_theorem(implies(or(not(X0),X1),X0))|~spl0_49|~spl0_54|~spl0_1|~spl0_22|~spl0_79|~spl0_83)),
% 9.43/1.56 inference(forward_demodulation,[status(thm)],[f755,f1539])).
% 9.43/1.56 fof(f1543,plain,(
% 9.43/1.56 ![X0,X1]: (is_a_theorem(or(X0,X1))|~is_a_theorem(implies(not(or(X0,X1)),X1))|~spl0_49|~spl0_22|~spl0_54|~spl0_79|~spl0_83|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f1540,f1121])).
% 9.43/1.56 fof(f1544,plain,(
% 9.43/1.56 ![X0,X1]: (is_a_theorem(or(X0,X1))|~is_a_theorem(or(or(X0,X1),X1))|~spl0_49|~spl0_22|~spl0_54|~spl0_79|~spl0_83|~spl0_1)),
% 9.43/1.56 inference(forward_demodulation,[status(thm)],[f755,f1543])).
% 9.43/1.56 fof(f1744,plain,(
% 9.43/1.56 ![X0,X1]: (is_a_theorem(or(X0,not(and(X0,X1))))|~spl0_49|~spl0_54|~spl0_79|~spl0_83|~spl0_1|~spl0_22)),
% 9.43/1.56 inference(resolution,[status(thm)],[f1092,f259])).
% 9.43/1.56 fof(f1756,plain,(
% 9.43/1.56 ![X0,X1]: (is_a_theorem(or(X0,implies(X0,X1)))|~spl0_49|~spl0_54|~spl0_79|~spl0_1|~spl0_22|~spl0_83)),
% 9.43/1.56 inference(paramodulation,[status(thm)],[f484,f1744])).
% 9.43/1.56 fof(f1761,plain,(
% 9.43/1.56 ![X0,X1,X2]: (is_a_theorem(or(and(implies(X0,X1),X2),implies(X2,X0)))|~spl0_49|~spl0_22|~spl0_54|~spl0_83|~spl0_79|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f1756,f1012])).
% 9.43/1.56 fof(f1826,plain,(
% 9.43/1.56 ![X0,X1]: (is_a_theorem(X0)|~is_a_theorem(or(and(X0,X1),X0))|~spl0_49|~spl0_54|~spl0_79|~spl0_83|~spl0_1|~spl0_22)),
% 9.43/1.56 inference(resolution,[status(thm)],[f1468,f259])).
% 9.43/1.56 fof(f1865,plain,(
% 9.43/1.56 ![X0]: (is_a_theorem(implies(X0,X0))|~spl0_49|~spl0_54|~spl0_79|~spl0_83|~spl0_1|~spl0_22)),
% 9.43/1.56 inference(resolution,[status(thm)],[f1761,f1826])).
% 9.43/1.56 fof(f1867,plain,(
% 9.43/1.56 ![X0,X1,X2]: (is_a_theorem(implies(implies(implies(X0,X1),X2),implies(not(X2),X0)))|~spl0_49|~spl0_22|~spl0_54|~spl0_1|~spl0_79|~spl0_83)),
% 9.43/1.56 inference(paramodulation,[status(thm)],[f756,f1761])).
% 9.43/1.56 fof(f1868,plain,(
% 9.43/1.56 ![X0,X1,X2]: (is_a_theorem(implies(implies(implies(X0,X1),X2),or(X2,X0)))|~spl0_49|~spl0_22|~spl0_54|~spl0_1|~spl0_79|~spl0_83)),
% 9.43/1.56 inference(forward_demodulation,[status(thm)],[f755,f1867])).
% 9.43/1.56 fof(f1879,plain,(
% 9.43/1.56 $false|~spl0_49|~spl0_22|~spl0_54|~spl0_79|~spl0_83|~spl0_1|spl0_71),
% 9.43/1.56 inference(backward_subsumption_resolution,[status(thm)],[f1151,f1865])).
% 9.43/1.56 fof(f1880,plain,(
% 9.43/1.56 ~spl0_49|~spl0_22|~spl0_54|~spl0_79|~spl0_83|~spl0_1|spl0_71),
% 9.43/1.56 inference(contradiction_clause,[status(thm)],[f1879])).
% 9.43/1.56 fof(f1935,plain,(
% 9.43/1.56 ![X0,X1]: (~is_a_theorem(or(X0,X1))|is_a_theorem(or(X1,X0))|~spl0_70|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f437,f181])).
% 9.43/1.56 fof(f1938,plain,(
% 9.43/1.56 ![X0,X1]: (~is_a_theorem(or(X0,or(X1,X0)))|is_a_theorem(or(X1,X0))|~spl0_70|~spl0_49|~spl0_22|~spl0_54|~spl0_79|~spl0_83|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f1935,f1544])).
% 9.43/1.56 fof(f2004,plain,(
% 9.43/1.56 ![X0,X1,X2]: (~is_a_theorem(implies(implies(X0,X1),X2))|is_a_theorem(or(X2,X0))|~spl0_49|~spl0_22|~spl0_54|~spl0_79|~spl0_83|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f1868,f181])).
% 9.43/1.56 fof(f2043,plain,(
% 9.43/1.56 ![X0,X1]: (is_a_theorem(or(implies(X0,X1),X0))|~spl0_49|~spl0_54|~spl0_79|~spl0_83|~spl0_1|~spl0_22)),
% 9.43/1.56 inference(resolution,[status(thm)],[f2004,f1865])).
% 9.43/1.56 fof(f2055,plain,(
% 9.43/1.56 ![X0,X1,X2]: (is_a_theorem(or(and(X0,X1),implies(X1,implies(X0,X2))))|~spl0_49|~spl0_22|~spl0_54|~spl0_83|~spl0_79|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f2043,f1012])).
% 9.43/1.56 fof(f2239,plain,(
% 9.43/1.56 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(not(X1),implies(X0,X2))))|~spl0_49|~spl0_22|~spl0_54|~spl0_1|~spl0_79|~spl0_83)),
% 9.43/1.56 inference(paramodulation,[status(thm)],[f756,f2055])).
% 9.43/1.56 fof(f2240,plain,(
% 9.43/1.56 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),or(X1,implies(X0,X2))))|~spl0_49|~spl0_22|~spl0_54|~spl0_1|~spl0_79|~spl0_83)),
% 9.43/1.56 inference(forward_demodulation,[status(thm)],[f755,f2239])).
% 9.43/1.56 fof(f2494,plain,(
% 9.43/1.56 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(or(X1,implies(X0,X2)))|~spl0_49|~spl0_22|~spl0_54|~spl0_79|~spl0_83|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f2240,f181])).
% 9.43/1.56 fof(f2973,plain,(
% 9.43/1.56 ![X0,X1]: (~is_a_theorem(implies(X0,implies(X0,X1)))|is_a_theorem(implies(X0,X1))|~spl0_49|~spl0_22|~spl0_54|~spl0_83|~spl0_79|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f2494,f1457])).
% 9.43/1.56 fof(f3630,plain,(
% 9.43/1.56 ![X0]: (is_a_theorem(implies(implies(X0,X0),not(and(not(X0),X0))))|~spl0_49|~spl0_22|~spl0_54|~spl0_83|~spl0_79|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f909,f2973])).
% 9.43/1.56 fof(f4128,plain,(
% 9.43/1.56 ![X0]: (~is_a_theorem(implies(X0,X0))|is_a_theorem(not(and(not(X0),X0)))|~spl0_49|~spl0_22|~spl0_54|~spl0_83|~spl0_79|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f3630,f181])).
% 9.43/1.56 fof(f4129,plain,(
% 9.43/1.56 ![X0]: (is_a_theorem(not(and(not(X0),X0)))|~spl0_49|~spl0_22|~spl0_54|~spl0_83|~spl0_79|~spl0_1)),
% 9.43/1.56 inference(forward_subsumption_resolution,[status(thm)],[f4128,f1865])).
% 9.43/1.56 fof(f4178,plain,(
% 9.43/1.56 ![X0,X1]: (~is_a_theorem(or(and(not(X0),X0),X1))|is_a_theorem(X1)|~spl0_49|~spl0_22|~spl0_54|~spl0_1|~spl0_83|~spl0_79)),
% 9.43/1.56 inference(resolution,[status(thm)],[f4129,f763])).
% 9.43/1.56 fof(f4207,plain,(
% 9.43/1.56 ![X0,X1]: (is_a_theorem(implies(X0,implies(not(X0),X1)))|~spl0_49|~spl0_22|~spl0_54|~spl0_83|~spl0_79|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f4178,f2055])).
% 9.43/1.56 fof(f4208,plain,(
% 9.43/1.56 spl0_59|~spl0_49|~spl0_22|~spl0_54|~spl0_83|~spl0_79|~spl0_1),
% 9.43/1.56 inference(split_clause,[status(thm)],[f4207,f395,f357,f258,f376,f483,f469,f180])).
% 9.43/1.56 fof(f4210,plain,(
% 9.43/1.56 ![X0]: (is_a_theorem(implies(X0,not(not(X0))))|~spl0_49|~spl0_22|~spl0_54|~spl0_83|~spl0_79|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f4178,f1089])).
% 9.43/1.56 fof(f4232,plain,(
% 9.43/1.56 ![X0,X1]: (~is_a_theorem(implies(implies(not(not(X0)),X0),X1))|is_a_theorem(X1)|~spl0_49|~spl0_22|~spl0_54|~spl0_1|~spl0_79|~spl0_83)),
% 9.43/1.56 inference(paramodulation,[status(thm)],[f756,f4178])).
% 9.43/1.56 fof(f4233,plain,(
% 9.43/1.56 ![X0,X1]: (~is_a_theorem(implies(or(not(X0),X0),X1))|is_a_theorem(X1)|~spl0_49|~spl0_22|~spl0_54|~spl0_1|~spl0_79|~spl0_83)),
% 9.43/1.56 inference(forward_demodulation,[status(thm)],[f755,f4232])).
% 9.43/1.56 fof(f4236,plain,(
% 9.43/1.56 ![X0,X1]: (is_a_theorem(implies(X0,or(X0,X1)))|~spl0_83|~spl0_79|~spl0_59)),
% 9.43/1.56 inference(forward_demodulation,[status(thm)],[f755,f396])).
% 9.43/1.56 fof(f4245,plain,(
% 9.43/1.56 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(or(X0,X1))|~spl0_83|~spl0_79|~spl0_59|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f4236,f181])).
% 9.43/1.56 fof(f4270,plain,(
% 9.43/1.56 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(or(X1,X0))|~spl0_59|~spl0_70|~spl0_49|~spl0_22|~spl0_54|~spl0_79|~spl0_83|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f4245,f1938])).
% 9.43/1.56 fof(f4339,plain,(
% 9.43/1.56 ![X0,X1,X2]: (~is_a_theorem(implies(or(X0,X1),X2))|is_a_theorem(X2)|~is_a_theorem(X1)|~spl0_59|~spl0_70|~spl0_49|~spl0_22|~spl0_54|~spl0_79|~spl0_83|~spl0_1)),
% 9.43/1.56 inference(resolution,[status(thm)],[f181,f4270])).
% 9.43/1.56 fof(f5599,plain,(
% 9.43/1.56 $false|~spl0_9),
% 9.43/1.56 inference(forward_subsumption_resolution,[status(thm)],[f212,f176])).
% 9.43/1.56 fof(f5600,plain,(
% 9.43/1.56 ~spl0_9),
% 9.43/1.56 inference(contradiction_clause,[status(thm)],[f5599])).
% 9.43/1.56 fof(f8636,plain,(
% 9.43/1.56 ![X0,X1,X2]: (is_a_theorem(or(and(X0,X1),implies(X1,X2)))|~is_a_theorem(X0)|~spl0_59|~spl0_70|~spl0_49|~spl0_22|~spl0_1|~spl0_54|~spl0_83|~spl0_79)),
% 9.43/1.56 inference(resolution,[status(thm)],[f4339,f908])).
% 9.43/1.56 fof(f10934,plain,(
% 9.43/1.56 ![X0,X1]: (~is_a_theorem(or(X0,implies(X1,X0)))|is_a_theorem(implies(X1,X0))|~spl0_49|~spl0_54|~spl0_79|~spl0_83|~spl0_1|~spl0_22)),
% 9.43/1.56 inference(resolution,[status(thm)],[f1012,f1826])).
% 9.43/1.56 fof(f13508,plain,(
% 9.43/1.56 ![X0,X1]: (is_a_theorem(implies(X0,and(X1,X0)))|~is_a_theorem(X1)|~spl0_59|~spl0_70|~spl0_49|~spl0_22|~spl0_1|~spl0_54|~spl0_83|~spl0_79)),
% 9.43/1.56 inference(resolution,[status(thm)],[f10934,f8636])).
% 9.43/1.56 fof(f13679,plain,(
% 9.43/1.56 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(and(X0,or(not(X1),X1)))|~spl0_59|~spl0_70|~spl0_49|~spl0_22|~spl0_54|~spl0_1|~spl0_79|~spl0_83)),
% 9.43/1.56 inference(resolution,[status(thm)],[f13508,f4233])).
% 9.43/1.56 fof(f14270,plain,(
% 9.43/1.56 ![X0]: (~is_a_theorem(implies(X0,not(not(X0))))|is_a_theorem(equiv(X0,not(not(X0))))|~spl0_59|~spl0_70|~spl0_49|~spl0_22|~spl0_54|~spl0_1|~spl0_87|~spl0_83|~spl0_79)),
% 9.43/1.56 inference(paramodulation,[status(thm)],[f761,f13679])).
% 9.43/1.56 fof(f14271,plain,(
% 9.43/1.56 ![X0]: (is_a_theorem(equiv(X0,not(not(X0))))|~spl0_59|~spl0_70|~spl0_49|~spl0_22|~spl0_54|~spl0_1|~spl0_87|~spl0_83|~spl0_79)),
% 9.76/1.59 inference(forward_subsumption_resolution,[status(thm)],[f14270,f4210])).
% 9.76/1.59 fof(f14278,plain,(
% 9.76/1.59 ![X0]: (X0=not(not(X0))|~spl0_59|~spl0_70|~spl0_49|~spl0_22|~spl0_54|~spl0_1|~spl0_87|~spl0_83|~spl0_79|~spl0_6)),
% 9.76/1.59 inference(resolution,[status(thm)],[f14271,f200])).
% 9.76/1.59 fof(f14573,plain,(
% 9.76/1.59 ![X0,X1]: (or(not(X0),X1)=implies(X0,X1)|~spl0_59|~spl0_70|~spl0_49|~spl0_22|~spl0_54|~spl0_1|~spl0_87|~spl0_83|~spl0_79|~spl0_6)),
% 9.76/1.59 inference(paramodulation,[status(thm)],[f14278,f755])).
% 9.76/1.59 fof(f14976,plain,(
% 9.76/1.59 ![X0,X1]: (is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0)))|~spl0_59|~spl0_70|~spl0_49|~spl0_22|~spl0_54|~spl0_1|~spl0_87|~spl0_83|~spl0_79|~spl0_6)),
% 9.76/1.59 inference(paramodulation,[status(thm)],[f14573,f437])).
% 9.76/1.59 fof(f17354,plain,(
% 9.76/1.59 $false|~spl0_59|~spl0_70|~spl0_49|~spl0_22|~spl0_54|~spl0_1|~spl0_87|~spl0_6|~spl0_83|~spl0_79|spl0_11),
% 9.76/1.59 inference(backward_subsumption_resolution,[status(thm)],[f1067,f14976])).
% 9.76/1.59 fof(f17355,plain,(
% 9.76/1.59 ~spl0_59|~spl0_70|~spl0_49|~spl0_22|~spl0_54|~spl0_1|~spl0_87|~spl0_6|~spl0_83|~spl0_79|spl0_11),
% 9.76/1.59 inference(contradiction_clause,[status(thm)],[f17354])).
% 9.76/1.59 fof(f17356,plain,(
% 9.76/1.59 $false),
% 9.76/1.59 inference(sat_refutation,[status(thm)],[f183,f202,f221,f360,f368,f379,f439,f443,f472,f486,f500,f502,f504,f506,f508,f510,f518,f522,f1002,f1880,f4208,f5600,f17355])).
% 9.76/1.59 % SZS output end CNFRefutation for theBenchmark.p
% 9.76/1.62 % Elapsed time: 1.295913 seconds
% 9.76/1.62 % CPU time: 10.049440 seconds
% 9.76/1.62 % Total memory used: 273.941 MB
% 9.76/1.62 % Net memory used: 266.081 MB
%------------------------------------------------------------------------------