TSTP Solution File: LCL504+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : LCL504+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n022.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 32.12s 4.45s
% Output : CNFRefutation 36.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : LCL504+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue May 30 09:43:27 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % Drodi V3.5.1
% 32.12/4.45 % Refutation found
% 32.12/4.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 32.12/4.45 % SZS output start CNFRefutation for theBenchmark
% 32.12/4.45 fof(f1,axiom,(
% 32.12/4.45 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 32.12/4.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 32.12/4.45 fof(f2,axiom,(
% 32.12/4.45 ( substitution_of_equivalents<=> (! [X,Y] :( is_a_theorem(equiv(X,Y))=> X = Y ) )) ),
% 32.12/4.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 32.12/4.45 fof(f5,axiom,(
% 32.12/4.45 ( implies_2<=> (! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )) ),
% 32.12/4.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 32.12/4.45 fof(f16,axiom,(
% 32.12/4.45 ( kn1<=> (! [P] : is_a_theorem(implies(P,and(P,P))) )) ),
% 32.12/4.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 32.12/4.45 fof(f17,axiom,(
% 32.12/4.45 ( kn2<=> (! [P,Q] : is_a_theorem(implies(and(P,Q),P)) )) ),
% 32.12/4.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 32.12/4.45 fof(f18,axiom,(
% 32.12/4.45 ( kn3<=> (! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) )) ),
% 32.12/4.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 32.12/4.45 fof(f21,axiom,(
% 32.12/4.45 ( cn3<=> (! [P] : is_a_theorem(implies(implies(not(P),P),P)) )) ),
% 32.12/4.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 32.12/4.45 fof(f24,axiom,(
% 32.12/4.45 ( r3<=> (! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) )) ),
% 32.12/4.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 32.12/4.45 fof(f27,axiom,(
% 32.12/4.45 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 32.12/4.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 32.12/4.45 fof(f29,axiom,(
% 32.12/4.45 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 32.12/4.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 32.12/4.45 fof(f31,axiom,(
% 32.12/4.45 ( op_equiv=> (! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) )) ),
% 32.12/4.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 32.12/4.45 fof(f32,axiom,(
% 32.12/4.45 op_or ),
% 32.12/4.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 32.12/4.45 fof(f33,axiom,(
% 32.12/4.45 op_implies_and ),
% 32.12/4.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 32.12/4.45 fof(f34,axiom,(
% 32.12/4.45 op_equiv ),
% 32.12/4.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 32.12/4.45 fof(f35,axiom,(
% 32.12/4.45 modus_ponens ),
% 32.12/4.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 32.12/4.45 fof(f36,axiom,(
% 32.12/4.45 kn1 ),
% 32.12/4.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 32.12/4.45 fof(f37,axiom,(
% 32.12/4.45 kn2 ),
% 32.12/4.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 32.12/4.45 fof(f38,axiom,(
% 32.12/4.45 kn3 ),
% 32.12/4.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 32.12/4.45 fof(f39,axiom,(
% 32.12/4.45 substitution_of_equivalents ),
% 32.12/4.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 32.12/4.45 fof(f43,conjecture,(
% 32.12/4.45 implies_2 ),
% 32.12/4.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 32.12/4.45 fof(f44,negated_conjecture,(
% 32.12/4.45 ~(implies_2 )),
% 32.12/4.45 inference(negated_conjecture,[status(cth)],[f43])).
% 32.12/4.45 fof(f45,plain,(
% 32.12/4.45 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 32.12/4.45 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 32.12/4.45 fof(f46,plain,(
% 32.12/4.45 (~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))))),
% 32.12/4.45 inference(NNF_transformation,[status(esa)],[f45])).
% 32.12/4.45 fof(f47,plain,(
% 32.12/4.45 (~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))))),
% 32.12/4.45 inference(miniscoping,[status(esa)],[f46])).
% 32.12/4.45 fof(f48,plain,(
% 32.12/4.45 (~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)))),
% 32.12/4.45 inference(skolemization,[status(esa)],[f47])).
% 32.12/4.45 fof(f49,plain,(
% 32.12/4.45 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 32.12/4.45 inference(cnf_transformation,[status(esa)],[f48])).
% 32.12/4.45 fof(f53,plain,(
% 32.12/4.45 substitution_of_equivalents<=>(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y))),
% 32.12/4.45 inference(pre_NNF_transformation,[status(esa)],[f2])).
% 32.12/4.45 fof(f54,plain,(
% 32.12/4.45 (~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)))),
% 32.12/4.46 inference(NNF_transformation,[status(esa)],[f53])).
% 32.12/4.46 fof(f55,plain,(
% 32.12/4.46 (~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))),
% 32.12/4.46 inference(skolemization,[status(esa)],[f54])).
% 32.12/4.46 fof(f56,plain,(
% 32.12/4.46 ![X0,X1]: (~substitution_of_equivalents|~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 32.12/4.46 inference(cnf_transformation,[status(esa)],[f55])).
% 32.12/4.46 fof(f67,plain,(
% 32.12/4.46 (~implies_2|(![X,Y]: is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))))&(implies_2|(?[X,Y]: ~is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))))),
% 32.12/4.46 inference(NNF_transformation,[status(esa)],[f5])).
% 32.12/4.46 fof(f68,plain,(
% 32.12/4.46 (~implies_2|(![X,Y]: is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))))&(implies_2|~is_a_theorem(implies(implies(sk0_8,implies(sk0_8,sk0_9)),implies(sk0_8,sk0_9))))),
% 32.12/4.46 inference(skolemization,[status(esa)],[f67])).
% 32.12/4.46 fof(f70,plain,(
% 32.12/4.46 implies_2|~is_a_theorem(implies(implies(sk0_8,implies(sk0_8,sk0_9)),implies(sk0_8,sk0_9)))),
% 32.12/4.46 inference(cnf_transformation,[status(esa)],[f68])).
% 32.12/4.46 fof(f111,plain,(
% 32.12/4.46 (~kn1|(![P]: is_a_theorem(implies(P,and(P,P)))))&(kn1|(?[P]: ~is_a_theorem(implies(P,and(P,P)))))),
% 32.12/4.46 inference(NNF_transformation,[status(esa)],[f16])).
% 32.12/4.46 fof(f112,plain,(
% 32.12/4.46 (~kn1|(![P]: is_a_theorem(implies(P,and(P,P)))))&(kn1|~is_a_theorem(implies(sk0_32,and(sk0_32,sk0_32))))),
% 32.12/4.46 inference(skolemization,[status(esa)],[f111])).
% 32.12/4.46 fof(f113,plain,(
% 32.12/4.46 ![X0]: (~kn1|is_a_theorem(implies(X0,and(X0,X0))))),
% 32.12/4.46 inference(cnf_transformation,[status(esa)],[f112])).
% 32.12/4.46 fof(f115,plain,(
% 32.12/4.46 (~kn2|(![P,Q]: is_a_theorem(implies(and(P,Q),P))))&(kn2|(?[P,Q]: ~is_a_theorem(implies(and(P,Q),P))))),
% 32.12/4.46 inference(NNF_transformation,[status(esa)],[f17])).
% 32.12/4.46 fof(f116,plain,(
% 32.12/4.46 (~kn2|(![P,Q]: is_a_theorem(implies(and(P,Q),P))))&(kn2|~is_a_theorem(implies(and(sk0_33,sk0_34),sk0_33)))),
% 32.12/4.46 inference(skolemization,[status(esa)],[f115])).
% 32.12/4.46 fof(f117,plain,(
% 32.12/4.46 ![X0,X1]: (~kn2|is_a_theorem(implies(and(X0,X1),X0)))),
% 32.12/4.46 inference(cnf_transformation,[status(esa)],[f116])).
% 32.12/4.46 fof(f119,plain,(
% 32.12/4.46 (~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)))))))),
% 32.12/4.46 inference(NNF_transformation,[status(esa)],[f18])).
% 32.12/4.46 fof(f120,plain,(
% 32.12/4.46 (~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))))))),
% 32.12/4.46 inference(skolemization,[status(esa)],[f119])).
% 32.12/4.46 fof(f121,plain,(
% 32.12/4.46 ![X0,X1,X2]: (~kn3|is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))))),
% 32.12/4.46 inference(cnf_transformation,[status(esa)],[f120])).
% 32.12/4.46 fof(f131,plain,(
% 32.12/4.46 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|(?[P]: ~is_a_theorem(implies(implies(not(P),P),P))))),
% 32.12/4.46 inference(NNF_transformation,[status(esa)],[f21])).
% 32.12/4.46 fof(f132,plain,(
% 32.12/4.46 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|~is_a_theorem(implies(implies(not(sk0_43),sk0_43),sk0_43)))),
% 32.12/4.46 inference(skolemization,[status(esa)],[f131])).
% 32.12/4.46 fof(f133,plain,(
% 32.12/4.46 ![X0]: (~cn3|is_a_theorem(implies(implies(not(X0),X0),X0)))),
% 32.12/4.46 inference(cnf_transformation,[status(esa)],[f132])).
% 32.12/4.46 fof(f134,plain,(
% 32.12/4.46 cn3|~is_a_theorem(implies(implies(not(sk0_43),sk0_43),sk0_43))),
% 32.12/4.46 inference(cnf_transformation,[status(esa)],[f132])).
% 32.12/4.46 fof(f143,plain,(
% 32.12/4.46 (~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)))))),
% 32.12/4.46 inference(NNF_transformation,[status(esa)],[f24])).
% 32.12/4.46 fof(f144,plain,(
% 32.12/4.46 (~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))))),
% 32.12/4.46 inference(skolemization,[status(esa)],[f143])).
% 32.12/4.46 fof(f145,plain,(
% 32.12/4.46 ![X0,X1]: (~r3|is_a_theorem(implies(or(X0,X1),or(X1,X0))))),
% 32.12/4.46 inference(cnf_transformation,[status(esa)],[f144])).
% 32.12/4.46 fof(f146,plain,(
% 32.12/4.46 r3|~is_a_theorem(implies(or(sk0_47,sk0_48),or(sk0_48,sk0_47)))),
% 32.12/4.46 inference(cnf_transformation,[status(esa)],[f144])).
% 32.12/4.46 fof(f155,plain,(
% 32.12/4.46 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 32.12/4.46 inference(pre_NNF_transformation,[status(esa)],[f27])).
% 32.12/4.46 fof(f156,plain,(
% 32.12/4.46 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 32.12/4.46 inference(cnf_transformation,[status(esa)],[f155])).
% 32.12/4.46 fof(f159,plain,(
% 32.12/4.46 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 32.12/4.46 inference(pre_NNF_transformation,[status(esa)],[f29])).
% 32.12/4.46 fof(f160,plain,(
% 32.12/4.46 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 32.12/4.46 inference(cnf_transformation,[status(esa)],[f159])).
% 32.12/4.46 fof(f163,plain,(
% 32.12/4.46 ~op_equiv|(![X,Y]: equiv(X,Y)=and(implies(X,Y),implies(Y,X)))),
% 32.12/4.46 inference(pre_NNF_transformation,[status(esa)],[f31])).
% 32.12/4.46 fof(f164,plain,(
% 32.12/4.46 ![X0,X1]: (~op_equiv|equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 32.12/4.46 inference(cnf_transformation,[status(esa)],[f163])).
% 32.12/4.46 fof(f165,plain,(
% 32.12/4.46 op_or),
% 32.12/4.46 inference(cnf_transformation,[status(esa)],[f32])).
% 32.12/4.46 fof(f166,plain,(
% 32.12/4.46 op_implies_and),
% 32.12/4.46 inference(cnf_transformation,[status(esa)],[f33])).
% 32.12/4.46 fof(f167,plain,(
% 32.12/4.46 op_equiv),
% 32.12/4.46 inference(cnf_transformation,[status(esa)],[f34])).
% 32.12/4.46 fof(f168,plain,(
% 32.12/4.46 modus_ponens),
% 32.12/4.46 inference(cnf_transformation,[status(esa)],[f35])).
% 32.12/4.46 fof(f169,plain,(
% 32.12/4.46 kn1),
% 32.12/4.46 inference(cnf_transformation,[status(esa)],[f36])).
% 32.12/4.46 fof(f170,plain,(
% 32.12/4.46 kn2),
% 32.12/4.46 inference(cnf_transformation,[status(esa)],[f37])).
% 32.12/4.46 fof(f171,plain,(
% 32.12/4.46 kn3),
% 32.12/4.46 inference(cnf_transformation,[status(esa)],[f38])).
% 32.12/4.46 fof(f172,plain,(
% 32.12/4.46 substitution_of_equivalents),
% 32.12/4.46 inference(cnf_transformation,[status(esa)],[f39])).
% 32.12/4.46 fof(f176,plain,(
% 32.12/4.46 ~implies_2),
% 32.12/4.46 inference(cnf_transformation,[status(esa)],[f44])).
% 32.12/4.46 fof(f177,plain,(
% 32.12/4.46 spl0_0 <=> modus_ponens),
% 32.12/4.46 introduced(split_symbol_definition)).
% 32.12/4.46 fof(f179,plain,(
% 32.12/4.46 ~modus_ponens|spl0_0),
% 32.12/4.46 inference(component_clause,[status(thm)],[f177])).
% 32.12/4.46 fof(f180,plain,(
% 32.12/4.46 spl0_1 <=> ~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)),
% 32.12/4.46 introduced(split_symbol_definition)).
% 32.12/4.46 fof(f181,plain,(
% 32.12/4.46 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)|~spl0_1)),
% 32.12/4.46 inference(component_clause,[status(thm)],[f180])).
% 32.12/4.46 fof(f183,plain,(
% 32.12/4.46 ~spl0_0|spl0_1),
% 32.12/4.46 inference(split_clause,[status(thm)],[f49,f177,f180])).
% 32.12/4.46 fof(f196,plain,(
% 32.12/4.46 spl0_5 <=> substitution_of_equivalents),
% 32.12/4.46 introduced(split_symbol_definition)).
% 32.12/4.46 fof(f198,plain,(
% 32.12/4.46 ~substitution_of_equivalents|spl0_5),
% 32.12/4.46 inference(component_clause,[status(thm)],[f196])).
% 32.12/4.46 fof(f199,plain,(
% 32.12/4.46 spl0_6 <=> ~is_a_theorem(equiv(X0,X1))|X0=X1),
% 32.12/4.46 introduced(split_symbol_definition)).
% 32.12/4.46 fof(f200,plain,(
% 32.12/4.46 ![X0,X1]: (~is_a_theorem(equiv(X0,X1))|X0=X1|~spl0_6)),
% 32.12/4.46 inference(component_clause,[status(thm)],[f199])).
% 32.12/4.46 fof(f202,plain,(
% 32.12/4.46 ~spl0_5|spl0_6),
% 32.12/4.46 inference(split_clause,[status(thm)],[f56,f196,f199])).
% 32.12/4.46 fof(f233,plain,(
% 32.12/4.46 spl0_15 <=> implies_2),
% 32.12/4.46 introduced(split_symbol_definition)).
% 32.12/4.46 fof(f234,plain,(
% 32.12/4.46 implies_2|~spl0_15),
% 32.12/4.46 inference(component_clause,[status(thm)],[f233])).
% 32.12/4.46 fof(f236,plain,(
% 32.12/4.46 spl0_16 <=> is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))),
% 32.12/4.46 introduced(split_symbol_definition)).
% 32.12/4.46 fof(f237,plain,(
% 32.12/4.46 ![X0,X1]: (is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))|~spl0_16)),
% 32.12/4.46 inference(component_clause,[status(thm)],[f236])).
% 32.12/4.46 fof(f240,plain,(
% 32.12/4.46 spl0_17 <=> is_a_theorem(implies(implies(sk0_8,implies(sk0_8,sk0_9)),implies(sk0_8,sk0_9)))),
% 32.12/4.46 introduced(split_symbol_definition)).
% 32.12/4.46 fof(f242,plain,(
% 32.12/4.46 ~is_a_theorem(implies(implies(sk0_8,implies(sk0_8,sk0_9)),implies(sk0_8,sk0_9)))|spl0_17),
% 32.12/4.46 inference(component_clause,[status(thm)],[f240])).
% 32.12/4.46 fof(f243,plain,(
% 32.12/4.46 spl0_15|~spl0_17),
% 32.12/4.46 inference(split_clause,[status(thm)],[f70,f233,f240])).
% 32.12/4.46 fof(f258,plain,(
% 32.12/4.46 spl0_22 <=> is_a_theorem(implies(and(X0,X1),X0))),
% 32.12/4.46 introduced(split_symbol_definition)).
% 32.12/4.46 fof(f259,plain,(
% 32.12/4.46 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X0))|~spl0_22)),
% 32.12/4.46 inference(component_clause,[status(thm)],[f258])).
% 32.12/4.46 fof(f302,plain,(
% 32.12/4.46 spl0_34 <=> is_a_theorem(implies(X0,or(X1,X0)))),
% 32.12/4.46 introduced(split_symbol_definition)).
% 32.12/4.46 fof(f303,plain,(
% 32.12/4.46 ![X0,X1]: (is_a_theorem(implies(X0,or(X1,X0)))|~spl0_34)),
% 32.12/4.46 inference(component_clause,[status(thm)],[f302])).
% 32.12/4.46 fof(f354,plain,(
% 32.12/4.46 spl0_48 <=> kn1),
% 32.12/4.46 introduced(split_symbol_definition)).
% 32.12/4.46 fof(f356,plain,(
% 32.12/4.46 ~kn1|spl0_48),
% 32.12/4.46 inference(component_clause,[status(thm)],[f354])).
% 32.12/4.46 fof(f357,plain,(
% 32.12/4.46 spl0_49 <=> is_a_theorem(implies(X0,and(X0,X0)))),
% 32.12/4.46 introduced(split_symbol_definition)).
% 32.12/4.46 fof(f358,plain,(
% 32.12/4.46 ![X0]: (is_a_theorem(implies(X0,and(X0,X0)))|~spl0_49)),
% 32.12/4.46 inference(component_clause,[status(thm)],[f357])).
% 32.12/4.46 fof(f360,plain,(
% 32.12/4.46 ~spl0_48|spl0_49),
% 32.12/4.46 inference(split_clause,[status(thm)],[f113,f354,f357])).
% 32.12/4.46 fof(f365,plain,(
% 32.12/4.46 spl0_51 <=> kn2),
% 32.12/4.46 introduced(split_symbol_definition)).
% 32.12/4.46 fof(f367,plain,(
% 32.12/4.46 ~kn2|spl0_51),
% 32.12/4.46 inference(component_clause,[status(thm)],[f365])).
% 32.12/4.46 fof(f368,plain,(
% 32.12/4.46 ~spl0_51|spl0_22),
% 32.12/4.46 inference(split_clause,[status(thm)],[f117,f365,f258])).
% 32.12/4.46 fof(f373,plain,(
% 32.12/4.46 spl0_53 <=> kn3),
% 32.12/4.46 introduced(split_symbol_definition)).
% 32.12/4.46 fof(f375,plain,(
% 32.12/4.46 ~kn3|spl0_53),
% 32.12/4.46 inference(component_clause,[status(thm)],[f373])).
% 32.12/4.46 fof(f376,plain,(
% 32.12/4.46 spl0_54 <=> is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))),
% 32.12/4.46 introduced(split_symbol_definition)).
% 32.12/4.46 fof(f377,plain,(
% 32.12/4.46 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))|~spl0_54)),
% 32.12/4.46 inference(component_clause,[status(thm)],[f376])).
% 32.12/4.46 fof(f379,plain,(
% 32.12/4.46 ~spl0_53|spl0_54),
% 32.12/4.46 inference(split_clause,[status(thm)],[f121,f373,f376])).
% 32.12/4.46 fof(f395,plain,(
% 32.12/4.46 spl0_59 <=> is_a_theorem(implies(X0,implies(not(X0),X1)))),
% 32.12/4.46 introduced(split_symbol_definition)).
% 32.12/4.46 fof(f396,plain,(
% 32.12/4.46 ![X0,X1]: (is_a_theorem(implies(X0,implies(not(X0),X1)))|~spl0_59)),
% 32.12/4.46 inference(component_clause,[status(thm)],[f395])).
% 32.12/4.46 fof(f403,plain,(
% 32.12/4.46 spl0_61 <=> cn3),
% 32.12/4.46 introduced(split_symbol_definition)).
% 32.12/4.46 fof(f406,plain,(
% 32.12/4.46 spl0_62 <=> is_a_theorem(implies(implies(not(X0),X0),X0))),
% 32.12/4.46 introduced(split_symbol_definition)).
% 32.12/4.46 fof(f407,plain,(
% 32.12/4.46 ![X0]: (is_a_theorem(implies(implies(not(X0),X0),X0))|~spl0_62)),
% 32.12/4.46 inference(component_clause,[status(thm)],[f406])).
% 32.12/4.46 fof(f409,plain,(
% 32.12/4.46 ~spl0_61|spl0_62),
% 32.12/4.46 inference(split_clause,[status(thm)],[f133,f403,f406])).
% 32.12/4.46 fof(f410,plain,(
% 32.12/4.46 spl0_63 <=> is_a_theorem(implies(implies(not(sk0_43),sk0_43),sk0_43))),
% 32.12/4.46 introduced(split_symbol_definition)).
% 32.12/4.46 fof(f412,plain,(
% 32.12/4.46 ~is_a_theorem(implies(implies(not(sk0_43),sk0_43),sk0_43))|spl0_63),
% 32.12/4.46 inference(component_clause,[status(thm)],[f410])).
% 32.12/4.46 fof(f413,plain,(
% 32.12/4.46 spl0_61|~spl0_63),
% 32.12/4.46 inference(split_clause,[status(thm)],[f134,f403,f410])).
% 32.12/4.46 fof(f433,plain,(
% 32.12/4.46 spl0_69 <=> r3),
% 32.12/4.46 introduced(split_symbol_definition)).
% 32.12/4.46 fof(f436,plain,(
% 32.12/4.46 spl0_70 <=> is_a_theorem(implies(or(X0,X1),or(X1,X0)))),
% 32.12/4.46 introduced(split_symbol_definition)).
% 32.12/4.46 fof(f437,plain,(
% 32.12/4.46 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),or(X1,X0)))|~spl0_70)),
% 32.12/4.46 inference(component_clause,[status(thm)],[f436])).
% 32.12/4.46 fof(f439,plain,(
% 32.12/4.46 ~spl0_69|spl0_70),
% 32.12/4.46 inference(split_clause,[status(thm)],[f145,f433,f436])).
% 32.12/4.46 fof(f440,plain,(
% 32.12/4.46 spl0_71 <=> is_a_theorem(implies(or(sk0_47,sk0_48),or(sk0_48,sk0_47)))),
% 32.12/4.46 introduced(split_symbol_definition)).
% 32.12/4.46 fof(f442,plain,(
% 32.12/4.46 ~is_a_theorem(implies(or(sk0_47,sk0_48),or(sk0_48,sk0_47)))|spl0_71),
% 32.12/4.46 inference(component_clause,[status(thm)],[f440])).
% 32.12/4.46 fof(f443,plain,(
% 32.12/4.46 spl0_69|~spl0_71),
% 32.12/4.46 inference(split_clause,[status(thm)],[f146,f433,f440])).
% 32.12/4.46 fof(f466,plain,(
% 32.12/4.46 spl0_78 <=> op_or),
% 32.12/4.46 introduced(split_symbol_definition)).
% 32.12/4.46 fof(f468,plain,(
% 32.12/4.46 ~op_or|spl0_78),
% 32.12/4.46 inference(component_clause,[status(thm)],[f466])).
% 32.12/4.46 fof(f469,plain,(
% 32.12/4.46 spl0_79 <=> or(X0,X1)=not(and(not(X0),not(X1)))),
% 32.12/4.46 introduced(split_symbol_definition)).
% 32.12/4.46 fof(f470,plain,(
% 32.12/4.46 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1)))|~spl0_79)),
% 32.12/4.46 inference(component_clause,[status(thm)],[f469])).
% 32.12/4.46 fof(f472,plain,(
% 32.12/4.46 ~spl0_78|spl0_79),
% 32.12/4.46 inference(split_clause,[status(thm)],[f156,f466,f469])).
% 32.12/4.46 fof(f480,plain,(
% 32.12/4.46 spl0_82 <=> op_implies_and),
% 32.12/4.46 introduced(split_symbol_definition)).
% 32.12/4.46 fof(f482,plain,(
% 32.12/4.46 ~op_implies_and|spl0_82),
% 32.12/4.46 inference(component_clause,[status(thm)],[f480])).
% 32.12/4.46 fof(f483,plain,(
% 32.12/4.46 spl0_83 <=> implies(X0,X1)=not(and(X0,not(X1)))),
% 32.12/4.46 introduced(split_symbol_definition)).
% 32.12/4.46 fof(f484,plain,(
% 32.12/4.46 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1)))|~spl0_83)),
% 32.12/4.46 inference(component_clause,[status(thm)],[f483])).
% 32.12/4.46 fof(f486,plain,(
% 32.12/4.46 ~spl0_82|spl0_83),
% 32.12/4.46 inference(split_clause,[status(thm)],[f160,f480,f483])).
% 32.12/4.46 fof(f494,plain,(
% 32.12/4.46 spl0_86 <=> op_equiv),
% 32.12/4.46 introduced(split_symbol_definition)).
% 32.12/4.46 fof(f496,plain,(
% 32.12/4.46 ~op_equiv|spl0_86),
% 32.12/4.46 inference(component_clause,[status(thm)],[f494])).
% 32.12/4.46 fof(f497,plain,(
% 32.12/4.46 spl0_87 <=> equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))),
% 32.12/4.46 introduced(split_symbol_definition)).
% 32.12/4.46 fof(f498,plain,(
% 32.12/4.46 ![X0,X1]: (equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))|~spl0_87)),
% 32.12/4.46 inference(component_clause,[status(thm)],[f497])).
% 32.12/4.46 fof(f500,plain,(
% 32.12/4.46 ~spl0_86|spl0_87),
% 32.12/4.46 inference(split_clause,[status(thm)],[f164,f494,f497])).
% 32.12/4.46 fof(f501,plain,(
% 32.12/4.46 $false|spl0_86),
% 32.12/4.46 inference(forward_subsumption_resolution,[status(thm)],[f496,f167])).
% 32.12/4.46 fof(f502,plain,(
% 32.12/4.46 spl0_86),
% 32.12/4.46 inference(contradiction_clause,[status(thm)],[f501])).
% 32.12/4.46 fof(f503,plain,(
% 32.12/4.46 $false|spl0_0),
% 32.12/4.46 inference(forward_subsumption_resolution,[status(thm)],[f179,f168])).
% 32.12/4.46 fof(f504,plain,(
% 32.12/4.46 spl0_0),
% 32.12/4.46 inference(contradiction_clause,[status(thm)],[f503])).
% 32.12/4.46 fof(f505,plain,(
% 32.12/4.46 $false|spl0_5),
% 32.12/4.46 inference(forward_subsumption_resolution,[status(thm)],[f198,f172])).
% 32.12/4.46 fof(f506,plain,(
% 32.12/4.46 spl0_5),
% 32.12/4.46 inference(contradiction_clause,[status(thm)],[f505])).
% 32.12/4.46 fof(f507,plain,(
% 32.12/4.46 $false|spl0_82),
% 32.12/4.46 inference(forward_subsumption_resolution,[status(thm)],[f482,f166])).
% 32.12/4.46 fof(f508,plain,(
% 32.12/4.46 spl0_82),
% 32.12/4.46 inference(contradiction_clause,[status(thm)],[f507])).
% 32.12/4.46 fof(f509,plain,(
% 32.12/4.46 $false|spl0_78),
% 32.12/4.46 inference(forward_subsumption_resolution,[status(thm)],[f468,f165])).
% 32.12/4.46 fof(f510,plain,(
% 32.12/4.46 spl0_78),
% 32.12/4.46 inference(contradiction_clause,[status(thm)],[f509])).
% 32.12/4.46 fof(f517,plain,(
% 32.12/4.46 $false|spl0_51),
% 32.12/4.46 inference(forward_subsumption_resolution,[status(thm)],[f367,f170])).
% 32.12/4.46 fof(f518,plain,(
% 32.12/4.46 spl0_51),
% 32.12/4.46 inference(contradiction_clause,[status(thm)],[f517])).
% 32.12/4.46 fof(f521,plain,(
% 32.12/4.46 $false|spl0_48),
% 32.12/4.46 inference(forward_subsumption_resolution,[status(thm)],[f356,f169])).
% 32.12/4.46 fof(f522,plain,(
% 32.12/4.46 spl0_48),
% 32.12/4.46 inference(contradiction_clause,[status(thm)],[f521])).
% 32.12/4.46 fof(f545,plain,(
% 32.12/4.46 ![X0,X1,X2]: (implies(X0,and(X1,not(X2)))=not(and(X0,implies(X1,X2)))|~spl0_83)),
% 32.12/4.46 inference(paramodulation,[status(thm)],[f484,f484])).
% 32.12/4.46 fof(f570,plain,(
% 32.12/4.46 $false|~spl0_16|spl0_17),
% 32.12/4.46 inference(forward_subsumption_resolution,[status(thm)],[f242,f237])).
% 32.12/4.46 fof(f571,plain,(
% 32.12/4.46 ~spl0_16|spl0_17),
% 32.12/4.46 inference(contradiction_clause,[status(thm)],[f570])).
% 32.12/4.46 fof(f574,plain,(
% 32.12/4.46 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1)|~spl0_83|~spl0_79)),
% 32.12/4.46 inference(forward_demodulation,[status(thm)],[f484,f470])).
% 32.12/4.46 fof(f576,plain,(
% 32.12/4.46 ![X0,X1,X2]: (or(and(X0,not(X1)),X2)=implies(implies(X0,X1),X2)|~spl0_79|~spl0_83)),
% 32.12/4.46 inference(paramodulation,[status(thm)],[f484,f574])).
% 32.12/4.46 fof(f577,plain,(
% 32.12/4.46 ![X0]: (is_a_theorem(or(X0,and(not(X0),not(X0))))|~spl0_49|~spl0_83|~spl0_79)),
% 32.12/4.46 inference(paramodulation,[status(thm)],[f574,f358])).
% 32.12/4.46 fof(f583,plain,(
% 32.12/4.46 ![X0,X1]: (~is_a_theorem(not(X0))|~is_a_theorem(or(X0,X1))|is_a_theorem(X1)|~spl0_1|~spl0_83|~spl0_79)),
% 32.12/4.46 inference(paramodulation,[status(thm)],[f574,f181])).
% 32.12/4.46 fof(f588,plain,(
% 32.12/4.46 ~is_a_theorem(implies(or(sk0_43,sk0_43),sk0_43))|~spl0_83|~spl0_79|spl0_63),
% 32.12/4.46 inference(forward_demodulation,[status(thm)],[f574,f412])).
% 32.12/4.46 fof(f636,plain,(
% 32.12/4.46 ![X0,X1,X2]: (implies(X0,and(not(X1),not(X2)))=not(and(X0,or(X1,X2)))|~spl0_83|~spl0_79)),
% 32.12/4.46 inference(paramodulation,[status(thm)],[f574,f545])).
% 32.12/4.46 fof(f702,plain,(
% 32.12/4.46 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0)))))|~spl0_83|~spl0_79|~spl0_54)),
% 32.12/4.46 inference(forward_demodulation,[status(thm)],[f574,f377])).
% 32.12/4.46 fof(f703,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f702,f181])).
% 32.12/4.46 fof(f704,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(paramodulation,[status(thm)],[f574,f702])).
% 32.12/4.46 fof(f705,plain,(
% 32.12/4.46 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),or(and(X1,X2),implies(X2,X0))))|~spl0_54|~spl0_83|~spl0_79)),
% 32.12/4.46 inference(forward_demodulation,[status(thm)],[f484,f704])).
% 32.12/4.46 fof(f706,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(paramodulation,[status(thm)],[f576,f702])).
% 32.12/4.46 fof(f776,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f705,f181])).
% 32.12/4.46 fof(f778,plain,(
% 32.12/4.46 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),implies(not(X2),X0))))|~spl0_54|~spl0_79|~spl0_83)),
% 32.12/4.46 inference(paramodulation,[status(thm)],[f576,f705])).
% 32.12/4.46 fof(f779,plain,(
% 32.12/4.46 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),or(X2,X0))))|~spl0_54|~spl0_79|~spl0_83)),
% 32.12/4.46 inference(forward_demodulation,[status(thm)],[f574,f778])).
% 32.12/4.46 fof(f796,plain,(
% 32.12/4.46 $false|spl0_53),
% 32.12/4.46 inference(forward_subsumption_resolution,[status(thm)],[f375,f171])).
% 32.12/4.46 fof(f797,plain,(
% 32.12/4.46 spl0_53),
% 32.12/4.46 inference(contradiction_clause,[status(thm)],[f796])).
% 32.12/4.46 fof(f815,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f779,f181])).
% 32.12/4.46 fof(f822,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f815,f577])).
% 32.12/4.46 fof(f842,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f822,f181])).
% 32.12/4.46 fof(f852,plain,(
% 32.12/4.46 ![X0]: (is_a_theorem(or(not(X0),X0))|~spl0_54|~spl0_49|~spl0_83|~spl0_79|~spl0_1|~spl0_22)),
% 32.12/4.46 inference(resolution,[status(thm)],[f842,f259])).
% 32.12/4.46 fof(f864,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f852,f815])).
% 32.12/4.46 fof(f868,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f864,f181])).
% 32.12/4.46 fof(f872,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(paramodulation,[status(thm)],[f574,f864])).
% 32.12/4.46 fof(f896,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f868,f815])).
% 32.12/4.46 fof(f897,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(forward_demodulation,[status(thm)],[f574,f896])).
% 32.12/4.46 fof(f902,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f872,f181])).
% 32.12/4.46 fof(f927,plain,(
% 32.12/4.46 ~is_a_theorem(implies(sk0_47,sk0_47))|~spl0_49|~spl0_22|~spl0_54|~spl0_79|~spl0_83|~spl0_1|spl0_71),
% 32.12/4.46 inference(resolution,[status(thm)],[f897,f442])).
% 32.12/4.46 fof(f930,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f897,f181])).
% 32.12/4.46 fof(f976,plain,(
% 32.12/4.46 ![X0]: (is_a_theorem(not(and(not(X0),or(X0,X0))))|~spl0_49|~spl0_83|~spl0_79)),
% 32.12/4.46 inference(paramodulation,[status(thm)],[f636,f358])).
% 32.12/4.46 fof(f1022,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f976,f583])).
% 32.12/4.46 fof(f1120,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f703,f1022])).
% 32.12/4.46 fof(f1139,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(paramodulation,[status(thm)],[f484,f1120])).
% 32.12/4.46 fof(f1140,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(forward_demodulation,[status(thm)],[f574,f1139])).
% 32.12/4.46 fof(f1146,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f1140,f902])).
% 32.12/4.46 fof(f1147,plain,(
% 32.12/4.46 ![X0,X1]: (is_a_theorem(implies(or(X0,X0),X1))|~is_a_theorem(implies(X0,X1))|~spl0_49|~spl0_22|~spl0_54|~spl0_79|~spl0_83|~spl0_1)),
% 32.12/4.46 inference(resolution,[status(thm)],[f1140,f868])).
% 32.12/4.46 fof(f1153,plain,(
% 32.12/4.46 ~is_a_theorem(implies(sk0_43,sk0_43))|~spl0_49|~spl0_22|~spl0_54|~spl0_1|~spl0_83|~spl0_79|spl0_63),
% 32.12/4.46 inference(resolution,[status(thm)],[f1147,f588])).
% 32.12/4.46 fof(f1178,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f1146,f852])).
% 32.12/4.46 fof(f1191,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f1178,f181])).
% 32.12/4.46 fof(f1205,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f1191,f902])).
% 32.12/4.46 fof(f1217,plain,(
% 32.12/4.46 ![X0]: (is_a_theorem(X0)|~is_a_theorem(or(X0,X0))|~spl0_49|~spl0_22|~spl0_54|~spl0_83|~spl0_79|~spl0_1)),
% 32.12/4.46 inference(resolution,[status(thm)],[f1205,f902])).
% 32.12/4.46 fof(f1220,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f1205,f930])).
% 32.12/4.46 fof(f1228,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f1217,f930])).
% 32.12/4.46 fof(f1320,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f1220,f259])).
% 32.12/4.46 fof(f1332,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(paramodulation,[status(thm)],[f576,f1320])).
% 32.12/4.46 fof(f1333,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(forward_demodulation,[status(thm)],[f574,f1332])).
% 32.12/4.46 fof(f1336,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f1333,f897])).
% 32.12/4.46 fof(f1337,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(forward_demodulation,[status(thm)],[f574,f1336])).
% 32.12/4.46 fof(f1588,plain,(
% 32.12/4.46 ![X0,X1]: (is_a_theorem(or(X0,not(and(X0,X1))))|~spl0_49|~spl0_54|~spl0_79|~spl0_83|~spl0_1|~spl0_22)),
% 32.12/4.46 inference(resolution,[status(thm)],[f868,f259])).
% 32.12/4.46 fof(f1601,plain,(
% 32.12/4.46 ![X0,X1]: (is_a_theorem(or(X0,implies(X0,X1)))|~spl0_49|~spl0_54|~spl0_79|~spl0_1|~spl0_22|~spl0_83)),
% 32.12/4.46 inference(paramodulation,[status(thm)],[f484,f1588])).
% 32.12/4.46 fof(f1606,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f1601,f776])).
% 32.12/4.46 fof(f1678,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f1228,f259])).
% 32.12/4.46 fof(f1721,plain,(
% 32.12/4.46 ![X0]: (is_a_theorem(implies(X0,X0))|~spl0_49|~spl0_54|~spl0_79|~spl0_83|~spl0_1|~spl0_22)),
% 32.12/4.46 inference(resolution,[status(thm)],[f1606,f1678])).
% 32.12/4.46 fof(f1723,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(paramodulation,[status(thm)],[f576,f1606])).
% 32.12/4.46 fof(f1724,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(forward_demodulation,[status(thm)],[f574,f1723])).
% 32.12/4.46 fof(f1737,plain,(
% 32.12/4.46 $false|~spl0_49|~spl0_22|~spl0_54|~spl0_79|~spl0_83|~spl0_1|spl0_71),
% 32.12/4.46 inference(backward_subsumption_resolution,[status(thm)],[f927,f1721])).
% 32.12/4.46 fof(f1738,plain,(
% 32.12/4.46 ~spl0_49|~spl0_22|~spl0_54|~spl0_79|~spl0_83|~spl0_1|spl0_71),
% 32.12/4.46 inference(contradiction_clause,[status(thm)],[f1737])).
% 32.12/4.46 fof(f1739,plain,(
% 32.12/4.46 $false|~spl0_49|~spl0_22|~spl0_54|~spl0_1|~spl0_83|~spl0_79|spl0_63),
% 32.12/4.46 inference(backward_subsumption_resolution,[status(thm)],[f1153,f1721])).
% 32.12/4.46 fof(f1740,plain,(
% 32.12/4.46 ~spl0_49|~spl0_22|~spl0_54|~spl0_1|~spl0_83|~spl0_79|spl0_63),
% 32.12/4.46 inference(contradiction_clause,[status(thm)],[f1739])).
% 32.12/4.46 fof(f1749,plain,(
% 32.12/4.46 ![X0]: (is_a_theorem(implies(or(X0,X0),X0))|~spl0_83|~spl0_79|~spl0_62)),
% 32.12/4.46 inference(forward_demodulation,[status(thm)],[f574,f407])).
% 32.12/4.46 fof(f1813,plain,(
% 32.12/4.46 ![X0,X1]: (~is_a_theorem(or(X0,X1))|is_a_theorem(or(X1,X0))|~spl0_70|~spl0_1)),
% 32.12/4.46 inference(resolution,[status(thm)],[f437,f181])).
% 32.12/4.46 fof(f1817,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f1813,f1337])).
% 32.12/4.46 fof(f1902,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f1724,f181])).
% 32.12/4.46 fof(f1943,plain,(
% 32.12/4.46 ![X0,X1,X2]: (is_a_theorem(or(or(X0,X1),implies(X1,X2)))|~spl0_49|~spl0_22|~spl0_54|~spl0_1|~spl0_79|~spl0_83)),
% 32.12/4.46 inference(resolution,[status(thm)],[f1902,f1724])).
% 32.12/4.46 fof(f1948,plain,(
% 32.12/4.46 ![X0,X1]: (is_a_theorem(or(implies(X0,X1),X0))|~spl0_49|~spl0_54|~spl0_79|~spl0_83|~spl0_1|~spl0_22)),
% 32.12/4.46 inference(resolution,[status(thm)],[f1902,f1721])).
% 32.12/4.46 fof(f1962,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f1948,f776])).
% 32.12/4.46 fof(f2151,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(paramodulation,[status(thm)],[f576,f1962])).
% 32.12/4.46 fof(f2152,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(forward_demodulation,[status(thm)],[f574,f2151])).
% 32.12/4.46 fof(f2580,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f2152,f181])).
% 32.12/4.46 fof(f2786,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f2580,f1217])).
% 32.12/4.46 fof(f3490,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f706,f2786])).
% 32.12/4.46 fof(f4058,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f3490,f181])).
% 32.12/4.46 fof(f4059,plain,(
% 32.12/4.46 ![X0]: (is_a_theorem(not(and(not(X0),X0)))|~spl0_49|~spl0_22|~spl0_54|~spl0_83|~spl0_79|~spl0_1)),
% 32.12/4.46 inference(forward_subsumption_resolution,[status(thm)],[f4058,f1721])).
% 32.12/4.46 fof(f4078,plain,(
% 32.12/4.46 ![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)),
% 32.12/4.46 inference(resolution,[status(thm)],[f4059,f583])).
% 32.12/4.46 fof(f4107,plain,(
% 32.12/4.46 ![X0,X1]: (is_a_theorem(implies(X0,implies(not(X0),X1)))|~spl0_49|~spl0_22|~spl0_54|~spl0_83|~spl0_79|~spl0_1)),
% 32.12/4.46 inference(resolution,[status(thm)],[f4078,f1962])).
% 32.12/4.46 fof(f4108,plain,(
% 32.12/4.46 spl0_59|~spl0_49|~spl0_22|~spl0_54|~spl0_83|~spl0_79|~spl0_1),
% 36.82/5.74 inference(split_clause,[status(thm)],[f4107,f395,f357,f258,f376,f483,f469,f180])).
% 36.82/5.74 fof(f4136,plain,(
% 36.82/5.74 ![X0,X1]: (is_a_theorem(implies(X0,or(X0,X1)))|~spl0_83|~spl0_79|~spl0_59)),
% 36.82/5.74 inference(forward_demodulation,[status(thm)],[f574,f396])).
% 36.82/5.74 fof(f4145,plain,(
% 36.82/5.74 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(or(X0,X1))|~spl0_83|~spl0_79|~spl0_59|~spl0_1)),
% 36.82/5.74 inference(resolution,[status(thm)],[f4136,f181])).
% 36.82/5.74 fof(f4174,plain,(
% 36.82/5.74 ![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)),
% 36.82/5.74 inference(resolution,[status(thm)],[f4145,f1817])).
% 36.82/5.74 fof(f4226,plain,(
% 36.82/5.74 ![X0,X1]: (~is_a_theorem(implies(implies(or(X0,X0),X0),X1))|is_a_theorem(X1)|~spl0_83|~spl0_79|~spl0_62|~spl0_1)),
% 36.82/5.74 inference(resolution,[status(thm)],[f1749,f181])).
% 36.82/5.74 fof(f4234,plain,(
% 36.82/5.74 ![X0,X1,X2]: (~is_a_theorem(X0)|~is_a_theorem(implies(or(X1,X0),X2))|is_a_theorem(X2)|~spl0_59|~spl0_70|~spl0_49|~spl0_22|~spl0_54|~spl0_79|~spl0_83|~spl0_1)),
% 36.82/5.74 inference(resolution,[status(thm)],[f4174,f181])).
% 36.82/5.74 fof(f9225,plain,(
% 36.82/5.74 ![X0,X1,X2]: (~is_a_theorem(X0)|is_a_theorem(or(and(X0,X1),implies(X1,X2)))|~spl0_59|~spl0_70|~spl0_49|~spl0_22|~spl0_1|~spl0_54|~spl0_83|~spl0_79)),
% 36.82/5.74 inference(resolution,[status(thm)],[f4234,f705])).
% 36.82/5.74 fof(f10544,plain,(
% 36.82/5.74 ![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)),
% 36.82/5.74 inference(resolution,[status(thm)],[f776,f1678])).
% 36.82/5.74 fof(f14973,plain,(
% 36.82/5.74 $false|~spl0_15),
% 36.82/5.74 inference(forward_subsumption_resolution,[status(thm)],[f234,f176])).
% 36.82/5.74 fof(f14974,plain,(
% 36.82/5.74 ~spl0_15),
% 36.82/5.74 inference(contradiction_clause,[status(thm)],[f14973])).
% 36.82/5.74 fof(f20386,plain,(
% 36.82/5.74 ![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)),
% 36.82/5.74 inference(resolution,[status(thm)],[f10544,f9225])).
% 36.82/5.74 fof(f20483,plain,(
% 36.82/5.74 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(and(X0,implies(or(X1,X1),X1)))|~spl0_59|~spl0_70|~spl0_49|~spl0_22|~spl0_54|~spl0_83|~spl0_79|~spl0_62|~spl0_1)),
% 36.82/5.74 inference(resolution,[status(thm)],[f20386,f4226])).
% 36.82/5.74 fof(f32446,plain,(
% 36.82/5.74 ![X0,X1]: (is_a_theorem(implies(X0,or(X1,X0)))|~spl0_49|~spl0_22|~spl0_54|~spl0_1|~spl0_79|~spl0_83)),
% 36.82/5.74 inference(resolution,[status(thm)],[f10544,f1943])).
% 36.82/5.74 fof(f32447,plain,(
% 36.82/5.74 spl0_34|~spl0_49|~spl0_22|~spl0_54|~spl0_1|~spl0_79|~spl0_83),
% 36.82/5.74 inference(split_clause,[status(thm)],[f32446,f302,f357,f258,f376,f180,f469,f483])).
% 36.82/5.74 fof(f43111,plain,(
% 36.82/5.74 ![X0]: (~is_a_theorem(implies(X0,or(X0,X0)))|is_a_theorem(equiv(X0,or(X0,X0)))|~spl0_59|~spl0_70|~spl0_49|~spl0_22|~spl0_54|~spl0_83|~spl0_79|~spl0_62|~spl0_1|~spl0_87)),
% 36.82/5.74 inference(paramodulation,[status(thm)],[f498,f20483])).
% 36.82/5.74 fof(f43112,plain,(
% 36.82/5.74 ![X0]: (is_a_theorem(equiv(X0,or(X0,X0)))|~spl0_34|~spl0_59|~spl0_70|~spl0_49|~spl0_22|~spl0_54|~spl0_83|~spl0_79|~spl0_62|~spl0_1|~spl0_87)),
% 36.82/5.74 inference(forward_subsumption_resolution,[status(thm)],[f43111,f303])).
% 36.82/5.74 fof(f43131,plain,(
% 36.82/5.74 ![X0]: (X0=or(X0,X0)|~spl0_34|~spl0_59|~spl0_70|~spl0_49|~spl0_22|~spl0_54|~spl0_83|~spl0_79|~spl0_62|~spl0_1|~spl0_87|~spl0_6)),
% 36.82/5.74 inference(resolution,[status(thm)],[f43112,f200])).
% 36.82/5.74 fof(f43452,plain,(
% 36.82/5.74 ![X0,X1]: (is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))|~spl0_34|~spl0_59|~spl0_70|~spl0_49|~spl0_22|~spl0_54|~spl0_83|~spl0_79|~spl0_62|~spl0_1|~spl0_87|~spl0_6)),
% 36.82/5.74 inference(paramodulation,[status(thm)],[f43131,f2152])).
% 36.82/5.74 fof(f43453,plain,(
% 36.82/5.74 spl0_16|~spl0_34|~spl0_59|~spl0_70|~spl0_49|~spl0_22|~spl0_54|~spl0_83|~spl0_79|~spl0_62|~spl0_1|~spl0_87|~spl0_6),
% 36.82/5.74 inference(split_clause,[status(thm)],[f43452,f236,f302,f395,f436,f357,f258,f376,f483,f469,f406,f180,f497,f199])).
% 36.82/5.74 fof(f43774,plain,(
% 36.82/5.74 $false),
% 36.82/5.74 inference(sat_refutation,[status(thm)],[f183,f202,f243,f360,f368,f379,f409,f413,f439,f443,f472,f486,f500,f502,f504,f506,f508,f510,f518,f522,f571,f797,f1738,f1740,f4108,f14974,f32447,f43453])).
% 36.82/5.74 % SZS output end CNFRefutation for theBenchmark.p
% 36.82/5.74 % Elapsed time: 5.173731 seconds
% 36.82/5.74 % CPU time: 30.134179 seconds
% 36.82/5.74 % Memory used: 526.464 MB
%------------------------------------------------------------------------------