%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL493+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:10:10 PM UTC 2026
% Result : Theorem 8.80s 1.54s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL493+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n013.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 00:35:21 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 8.80/1.54 % Refutation found
% 8.80/1.54 % SZS status Theorem for theBenchmark: Theorem is valid
% 8.80/1.54 % SZS output start CNFRefutation for theBenchmark
% 8.80/1.54 fof(f1,axiom,(
% 8.80/1.54 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 8.80/1.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.80/1.54 fof(f13,axiom,(
% 8.80/1.54 ( equivalence_1<=> (! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(X,Y))) )) ),
% 8.80/1.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.80/1.54 fof(f22,axiom,(
% 8.80/1.54 ( r1<=> (! [P] : is_a_theorem(implies(or(P,P),P)) )) ),
% 8.80/1.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.80/1.54 fof(f23,axiom,(
% 8.80/1.54 ( r2<=> (! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) )) ),
% 8.80/1.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.80/1.54 fof(f24,axiom,(
% 8.80/1.54 ( r3<=> (! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) )) ),
% 8.80/1.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.80/1.54 fof(f26,axiom,(
% 8.80/1.54 ( r5<=> (! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) )) ),
% 8.80/1.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.80/1.54 fof(f27,axiom,(
% 8.80/1.54 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 8.80/1.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.80/1.54 fof(f28,axiom,(
% 8.80/1.54 ( op_and=> (! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) )) ),
% 8.80/1.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.80/1.54 fof(f29,axiom,(
% 8.80/1.54 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 8.80/1.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.80/1.54 fof(f30,axiom,(
% 8.80/1.54 ( op_implies_or=> (! [X,Y] : implies(X,Y) = or(not(X),Y) )) ),
% 8.80/1.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.80/1.54 fof(f31,axiom,(
% 8.80/1.54 ( op_equiv=> (! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) )) ),
% 8.80/1.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.80/1.54 fof(f32,axiom,(
% 8.80/1.54 op_implies_or ),
% 8.80/1.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.80/1.54 fof(f33,axiom,(
% 8.80/1.54 op_and ),
% 8.80/1.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.80/1.54 fof(f34,axiom,(
% 8.80/1.54 op_equiv ),
% 8.80/1.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.80/1.54 fof(f35,axiom,(
% 8.80/1.54 modus_ponens ),
% 8.80/1.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.80/1.54 fof(f36,axiom,(
% 8.80/1.54 r1 ),
% 8.80/1.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.80/1.54 fof(f37,axiom,(
% 8.80/1.54 r2 ),
% 8.80/1.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.80/1.54 fof(f38,axiom,(
% 8.80/1.54 r3 ),
% 8.80/1.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.80/1.54 fof(f40,axiom,(
% 8.80/1.54 r5 ),
% 8.80/1.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.80/1.54 fof(f42,axiom,(
% 8.80/1.54 op_or ),
% 8.80/1.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.80/1.54 fof(f43,axiom,(
% 8.80/1.54 op_implies_and ),
% 8.80/1.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.80/1.54 fof(f45,conjecture,(
% 8.80/1.54 equivalence_1 ),
% 8.80/1.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.80/1.54 fof(f46,negated_conjecture,(
% 8.80/1.54 ~(equivalence_1 )),
% 8.80/1.54 inference(negated_conjecture,[status(cth)],[f45])).
% 8.80/1.54 fof(f47,plain,(
% 8.80/1.54 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 8.80/1.54 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 8.80/1.54 fof(f48,plain,(
% 8.80/1.54 (~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))))),
% 8.80/1.54 inference(NNF_transformation,[status(thm)],[f47])).
% 8.80/1.54 fof(f49,plain,(
% 8.80/1.54 (~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))))),
% 8.80/1.54 inference(miniscoping,[status(thm)],[f48])).
% 8.80/1.54 fof(f50,plain,(
% 8.80/1.54 (~modus_ponens|(![Y]: ((![X]: (~is_a_theorem(X)|~is_a_theorem(implies(X,Y))))|is_a_theorem(Y))))&(modus_ponens|((is_a_theorem(sK1_skl)&is_a_theorem(implies(sK1_skl,sK0_skl)))&~is_a_theorem(sK0_skl)))),
% 8.80/1.54 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f49])).
% 8.80/1.54 fof(f51,plain,(
% 8.80/1.54 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 8.80/1.54 inference(cnf_transformation,[status(thm)],[f50])).
% 8.80/1.54 fof(f101,plain,(
% 8.80/1.54 (~equivalence_1|(![X,Y]: is_a_theorem(implies(equiv(X,Y),implies(X,Y)))))&(equivalence_1|(?[X,Y]: ~is_a_theorem(implies(equiv(X,Y),implies(X,Y)))))),
% 8.80/1.54 inference(NNF_transformation,[status(thm)],[f13])).
% 8.80/1.54 fof(f102,plain,(
% 8.80/1.54 (~equivalence_1|(![X,Y]: is_a_theorem(implies(equiv(X,Y),implies(X,Y)))))&(equivalence_1|~is_a_theorem(implies(equiv(sK26_skl,sK27_skl),implies(sK26_skl,sK27_skl))))),
% 8.80/1.54 inference(skolemize,[status(esa),new_symbols(skolem,[sK26_skl,sK27_skl]),skolemize(X,sK26_skl),skolemize(Y,sK27_skl)],[f101])).
% 8.80/1.54 fof(f104,plain,(
% 8.80/1.54 equivalence_1|~is_a_theorem(implies(equiv(sK26_skl,sK27_skl),implies(sK26_skl,sK27_skl)))),
% 8.80/1.54 inference(cnf_transformation,[status(thm)],[f102])).
% 8.80/1.54 fof(f137,plain,(
% 8.80/1.54 (~r1|(![P]: is_a_theorem(implies(or(P,P),P))))&(r1|(?[P]: ~is_a_theorem(implies(or(P,P),P))))),
% 8.80/1.54 inference(NNF_transformation,[status(thm)],[f22])).
% 8.80/1.54 fof(f138,plain,(
% 8.80/1.54 (~r1|(![P]: is_a_theorem(implies(or(P,P),P))))&(r1|~is_a_theorem(implies(or(sK44_skl,sK44_skl),sK44_skl)))),
% 8.80/1.54 inference(skolemize,[status(esa),new_symbols(skolem,[sK44_skl]),skolemize(P,sK44_skl)],[f137])).
% 8.80/1.54 fof(f139,plain,(
% 8.80/1.54 ![X0]: (~r1|is_a_theorem(implies(or(X0,X0),X0)))),
% 8.80/1.54 inference(cnf_transformation,[status(thm)],[f138])).
% 8.80/1.54 fof(f141,plain,(
% 8.80/1.54 (~r2|(![P,Q]: is_a_theorem(implies(Q,or(P,Q)))))&(r2|(?[P,Q]: ~is_a_theorem(implies(Q,or(P,Q)))))),
% 8.80/1.54 inference(NNF_transformation,[status(thm)],[f23])).
% 8.80/1.54 fof(f142,plain,(
% 8.80/1.54 (~r2|(![P,Q]: is_a_theorem(implies(Q,or(P,Q)))))&(r2|~is_a_theorem(implies(sK46_skl,or(sK45_skl,sK46_skl))))),
% 8.80/1.54 inference(skolemize,[status(esa),new_symbols(skolem,[sK45_skl,sK46_skl]),skolemize(P,sK45_skl),skolemize(Q,sK46_skl)],[f141])).
% 8.80/1.54 fof(f143,plain,(
% 8.80/1.54 ![X0,X1]: (~r2|is_a_theorem(implies(X0,or(X1,X0))))),
% 8.80/1.54 inference(cnf_transformation,[status(thm)],[f142])).
% 8.80/1.54 fof(f145,plain,(
% 8.80/1.54 (~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)))))),
% 8.80/1.54 inference(NNF_transformation,[status(thm)],[f24])).
% 8.80/1.54 fof(f146,plain,(
% 8.80/1.54 (~r3|(![P,Q]: is_a_theorem(implies(or(P,Q),or(Q,P)))))&(r3|~is_a_theorem(implies(or(sK47_skl,sK48_skl),or(sK48_skl,sK47_skl))))),
% 8.80/1.54 inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl]),skolemize(P,sK47_skl),skolemize(Q,sK48_skl)],[f145])).
% 8.80/1.54 fof(f147,plain,(
% 8.80/1.54 ![X0,X1]: (~r3|is_a_theorem(implies(or(X0,X1),or(X1,X0))))),
% 8.80/1.54 inference(cnf_transformation,[status(thm)],[f146])).
% 8.80/1.54 fof(f153,plain,(
% 8.80/1.54 (~r5|(![P,Q,R]: is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))))&(r5|(?[P,Q,R]: ~is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))))),
% 8.80/1.54 inference(NNF_transformation,[status(thm)],[f26])).
% 8.80/1.54 fof(f154,plain,(
% 8.80/1.54 (~r5|(![P,Q,R]: is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))))&(r5|~is_a_theorem(implies(implies(sK53_skl,sK54_skl),implies(or(sK52_skl,sK53_skl),or(sK52_skl,sK54_skl)))))),
% 8.80/1.54 inference(skolemize,[status(esa),new_symbols(skolem,[sK52_skl,sK53_skl,sK54_skl]),skolemize(P,sK52_skl),skolemize(Q,sK53_skl),skolemize(R,sK54_skl)],[f153])).
% 8.80/1.54 fof(f155,plain,(
% 8.80/1.54 ![X0,X1,X2]: (~r5|is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))))),
% 8.80/1.54 inference(cnf_transformation,[status(thm)],[f154])).
% 8.80/1.54 fof(f157,plain,(
% 8.80/1.54 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 8.80/1.54 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 8.80/1.54 fof(f158,plain,(
% 8.80/1.54 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 8.80/1.54 inference(cnf_transformation,[status(thm)],[f157])).
% 8.80/1.54 fof(f159,plain,(
% 8.80/1.54 ~op_and|(![X,Y]: and(X,Y)=not(or(not(X),not(Y))))),
% 8.80/1.54 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 8.80/1.54 fof(f160,plain,(
% 8.80/1.54 ![X0,X1]: (~op_and|and(X0,X1)=not(or(not(X0),not(X1))))),
% 8.80/1.54 inference(cnf_transformation,[status(thm)],[f159])).
% 8.80/1.54 fof(f161,plain,(
% 8.80/1.54 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 8.80/1.54 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 8.80/1.54 fof(f162,plain,(
% 8.80/1.54 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 8.80/1.54 inference(cnf_transformation,[status(thm)],[f161])).
% 8.80/1.54 fof(f163,plain,(
% 8.80/1.54 ~op_implies_or|(![X,Y]: implies(X,Y)=or(not(X),Y))),
% 8.80/1.54 inference(pre_NNF_transformation,[status(thm)],[f30])).
% 8.80/1.54 fof(f164,plain,(
% 8.80/1.54 ![X0,X1]: (~op_implies_or|implies(X0,X1)=or(not(X0),X1))),
% 8.80/1.54 inference(cnf_transformation,[status(thm)],[f163])).
% 8.80/1.54 fof(f165,plain,(
% 8.80/1.54 ~op_equiv|(![X,Y]: equiv(X,Y)=and(implies(X,Y),implies(Y,X)))),
% 8.80/1.54 inference(pre_NNF_transformation,[status(thm)],[f31])).
% 8.80/1.54 fof(f166,plain,(
% 8.80/1.54 ![X0,X1]: (~op_equiv|equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 8.80/1.54 inference(cnf_transformation,[status(thm)],[f165])).
% 8.80/1.54 fof(f167,plain,(
% 8.80/1.54 op_implies_or),
% 8.80/1.54 inference(cnf_transformation,[status(thm)],[f32])).
% 8.80/1.54 fof(f168,plain,(
% 8.80/1.54 op_and),
% 8.80/1.54 inference(cnf_transformation,[status(thm)],[f33])).
% 8.80/1.54 fof(f169,plain,(
% 8.80/1.54 op_equiv),
% 8.80/1.54 inference(cnf_transformation,[status(thm)],[f34])).
% 8.80/1.54 fof(f170,plain,(
% 8.80/1.54 modus_ponens),
% 8.80/1.54 inference(cnf_transformation,[status(thm)],[f35])).
% 8.80/1.54 fof(f171,plain,(
% 8.80/1.54 r1),
% 8.80/1.54 inference(cnf_transformation,[status(thm)],[f36])).
% 8.80/1.54 fof(f172,plain,(
% 8.80/1.54 r2),
% 8.80/1.54 inference(cnf_transformation,[status(thm)],[f37])).
% 8.80/1.54 fof(f173,plain,(
% 8.80/1.54 r3),
% 8.80/1.54 inference(cnf_transformation,[status(thm)],[f38])).
% 8.80/1.54 fof(f175,plain,(
% 8.80/1.54 r5),
% 8.80/1.54 inference(cnf_transformation,[status(thm)],[f40])).
% 8.80/1.54 fof(f177,plain,(
% 8.80/1.54 op_or),
% 8.80/1.54 inference(cnf_transformation,[status(thm)],[f42])).
% 8.80/1.54 fof(f178,plain,(
% 8.80/1.54 op_implies_and),
% 8.80/1.54 inference(cnf_transformation,[status(thm)],[f43])).
% 8.80/1.54 fof(f180,plain,(
% 8.80/1.54 ~equivalence_1),
% 8.80/1.54 inference(cnf_transformation,[status(thm)],[f46])).
% 8.80/1.54 fof(f181,definition,(
% 8.80/1.54 sQ0_spl <=> (modus_ponens)),
% 8.80/1.54 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 8.80/1.54 fof(f183,plain,(
% 8.80/1.54 ~modus_ponens|sQ0_spl),
% 8.80/1.54 inference(component_clause,[status(thm)],[f181])).
% 8.80/1.54 fof(f184,definition,(
% 8.80/1.54 ![X0,X1]: (sQ1_spl <=> (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)))),
% 8.80/1.54 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 8.80/1.54 fof(f185,plain,(
% 8.80/1.54 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)|~sQ1_spl)),
% 8.80/1.54 inference(component_clause,[status(thm)],[f184])).
% 8.80/1.54 fof(f187,plain,(
% 8.80/1.54 ~sQ0_spl|sQ1_spl),
% 8.80/1.54 inference(split_clause,[status(thm)],[f51,f181,f184])).
% 8.80/1.54 fof(f262,definition,(
% 8.80/1.54 ![X0,X1]: (sQ22_spl <=> (is_a_theorem(implies(and(X0,X1),X0))))),
% 8.80/1.54 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 8.80/1.54 fof(f263,plain,(
% 8.80/1.54 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X0))|~sQ22_spl)),
% 8.80/1.54 inference(component_clause,[status(thm)],[f262])).
% 8.80/1.54 fof(f295,definition,(
% 8.80/1.54 ![X0,X1]: (sQ31_spl <=> (is_a_theorem(implies(X0,or(X0,X1)))))),
% 8.80/1.54 introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition])).
% 8.80/1.54 fof(f296,plain,(
% 8.80/1.54 ![X0,X1]: (is_a_theorem(implies(X0,or(X0,X1)))|~sQ31_spl)),
% 8.80/1.54 inference(component_clause,[status(thm)],[f295])).
% 8.80/1.54 fof(f306,definition,(
% 8.80/1.54 ![X0,X1]: (sQ34_spl <=> (is_a_theorem(implies(X0,or(X1,X0)))))),
% 8.80/1.54 introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition])).
% 8.80/1.54 fof(f307,plain,(
% 8.80/1.54 ![X0,X1]: (is_a_theorem(implies(X0,or(X1,X0)))|~sQ34_spl)),
% 8.80/1.54 inference(component_clause,[status(thm)],[f306])).
% 8.80/1.54 fof(f325,definition,(
% 8.80/1.54 sQ39_spl <=> (equivalence_1)),
% 8.80/1.54 introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition])).
% 8.80/1.54 fof(f326,plain,(
% 8.80/1.54 equivalence_1|~sQ39_spl),
% 8.80/1.54 inference(component_clause,[status(thm)],[f325])).
% 8.80/1.54 fof(f328,definition,(
% 8.80/1.54 ![X0,X1]: (sQ40_spl <=> (is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))))),
% 8.80/1.54 introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition])).
% 8.80/1.54 fof(f329,plain,(
% 8.80/1.54 ![X0,X1]: (is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))|~sQ40_spl)),
% 8.80/1.54 inference(component_clause,[status(thm)],[f328])).
% 8.80/1.54 fof(f332,definition,(
% 8.80/1.54 sQ41_spl <=> (is_a_theorem(implies(equiv(sK26_skl,sK27_skl),implies(sK26_skl,sK27_skl))))),
% 8.80/1.54 introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition])).
% 8.80/1.54 fof(f334,plain,(
% 8.80/1.54 ~is_a_theorem(implies(equiv(sK26_skl,sK27_skl),implies(sK26_skl,sK27_skl)))|sQ41_spl),
% 8.80/1.54 inference(component_clause,[status(thm)],[f332])).
% 8.80/1.54 fof(f335,plain,(
% 8.80/1.54 sQ39_spl|~sQ41_spl),
% 8.80/1.54 inference(split_clause,[status(thm)],[f104,f325,f332])).
% 8.80/1.54 fof(f418,definition,(
% 8.80/1.54 sQ64_spl <=> (r1)),
% 8.80/1.54 introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition])).
% 8.80/1.54 fof(f420,plain,(
% 8.80/1.54 ~r1|sQ64_spl),
% 8.80/1.54 inference(component_clause,[status(thm)],[f418])).
% 8.80/1.54 fof(f421,definition,(
% 8.80/1.54 ![X0]: (sQ65_spl <=> (is_a_theorem(implies(or(X0,X0),X0))))),
% 8.80/1.54 introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition])).
% 8.80/1.54 fof(f422,plain,(
% 8.80/1.54 ![X0]: (is_a_theorem(implies(or(X0,X0),X0))|~sQ65_spl)),
% 8.80/1.54 inference(component_clause,[status(thm)],[f421])).
% 8.80/1.54 fof(f424,plain,(
% 8.80/1.54 ~sQ64_spl|sQ65_spl),
% 8.80/1.54 inference(split_clause,[status(thm)],[f139,f418,f421])).
% 8.80/1.54 fof(f429,definition,(
% 8.80/1.54 sQ67_spl <=> (r2)),
% 8.80/1.54 introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition])).
% 8.80/1.54 fof(f431,plain,(
% 8.80/1.54 ~r2|sQ67_spl),
% 8.80/1.54 inference(component_clause,[status(thm)],[f429])).
% 8.80/1.54 fof(f432,plain,(
% 8.80/1.54 ~sQ67_spl|sQ34_spl),
% 8.80/1.54 inference(split_clause,[status(thm)],[f143,f429,f306])).
% 8.80/1.54 fof(f437,definition,(
% 8.80/1.54 sQ69_spl <=> (r3)),
% 8.80/1.54 introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition])).
% 8.80/1.54 fof(f439,plain,(
% 8.80/1.54 ~r3|sQ69_spl),
% 8.80/1.54 inference(component_clause,[status(thm)],[f437])).
% 8.80/1.54 fof(f440,definition,(
% 8.80/1.54 ![X0,X1]: (sQ70_spl <=> (is_a_theorem(implies(or(X0,X1),or(X1,X0)))))),
% 8.80/1.54 introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition])).
% 8.80/1.54 fof(f441,plain,(
% 8.80/1.54 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),or(X1,X0)))|~sQ70_spl)),
% 8.80/1.54 inference(component_clause,[status(thm)],[f440])).
% 8.80/1.54 fof(f443,plain,(
% 8.80/1.54 ~sQ69_spl|sQ70_spl),
% 8.80/1.54 inference(split_clause,[status(thm)],[f147,f437,f440])).
% 8.80/1.54 fof(f459,definition,(
% 8.80/1.54 sQ75_spl <=> (r5)),
% 8.80/1.54 introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition])).
% 8.80/1.54 fof(f461,plain,(
% 8.80/1.54 ~r5|sQ75_spl),
% 8.80/1.54 inference(component_clause,[status(thm)],[f459])).
% 8.80/1.54 fof(f462,definition,(
% 8.80/1.54 ![X0,X1,X2]: (sQ76_spl <=> (is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1))))))),
% 8.80/1.54 introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition])).
% 8.80/1.54 fof(f463,plain,(
% 8.80/1.54 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1))))|~sQ76_spl)),
% 8.80/1.54 inference(component_clause,[status(thm)],[f462])).
% 8.80/1.54 fof(f465,plain,(
% 8.80/1.54 ~sQ75_spl|sQ76_spl),
% 8.80/1.54 inference(split_clause,[status(thm)],[f155,f459,f462])).
% 8.80/1.54 fof(f470,definition,(
% 8.80/1.54 sQ78_spl <=> (op_or)),
% 8.80/1.54 introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition])).
% 8.80/1.54 fof(f472,plain,(
% 8.80/1.54 ~op_or|sQ78_spl),
% 8.80/1.54 inference(component_clause,[status(thm)],[f470])).
% 8.80/1.54 fof(f473,definition,(
% 8.80/1.54 ![X0,X1]: (sQ79_spl <=> (or(X0,X1)=not(and(not(X0),not(X1)))))),
% 8.80/1.54 introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition])).
% 8.80/1.54 fof(f474,plain,(
% 8.80/1.54 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1)))|~sQ79_spl)),
% 8.80/1.54 inference(component_clause,[status(thm)],[f473])).
% 8.80/1.54 fof(f476,plain,(
% 8.80/1.54 ~sQ78_spl|sQ79_spl),
% 8.80/1.54 inference(split_clause,[status(thm)],[f158,f470,f473])).
% 8.80/1.54 fof(f477,definition,(
% 8.80/1.54 sQ80_spl <=> (op_and)),
% 8.80/1.54 introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition])).
% 8.80/1.54 fof(f479,plain,(
% 8.80/1.54 ~op_and|sQ80_spl),
% 8.80/1.54 inference(component_clause,[status(thm)],[f477])).
% 8.80/1.54 fof(f480,definition,(
% 8.80/1.54 ![X0,X1]: (sQ81_spl <=> (and(X0,X1)=not(or(not(X0),not(X1)))))),
% 8.80/1.54 introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition])).
% 8.80/1.54 fof(f481,plain,(
% 8.80/1.54 ![X0,X1]: (and(X0,X1)=not(or(not(X0),not(X1)))|~sQ81_spl)),
% 8.80/1.54 inference(component_clause,[status(thm)],[f480])).
% 8.80/1.54 fof(f483,plain,(
% 8.80/1.54 ~sQ80_spl|sQ81_spl),
% 8.80/1.54 inference(split_clause,[status(thm)],[f160,f477,f480])).
% 8.80/1.54 fof(f484,definition,(
% 8.80/1.54 sQ82_spl <=> (op_implies_and)),
% 8.80/1.54 introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition])).
% 8.80/1.54 fof(f486,plain,(
% 8.80/1.54 ~op_implies_and|sQ82_spl),
% 8.80/1.54 inference(component_clause,[status(thm)],[f484])).
% 8.80/1.54 fof(f487,definition,(
% 8.80/1.54 ![X0,X1]: (sQ83_spl <=> (implies(X0,X1)=not(and(X0,not(X1)))))),
% 8.80/1.54 introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition])).
% 8.80/1.54 fof(f488,plain,(
% 8.80/1.54 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1)))|~sQ83_spl)),
% 8.80/1.54 inference(component_clause,[status(thm)],[f487])).
% 8.80/1.54 fof(f490,plain,(
% 8.80/1.54 ~sQ82_spl|sQ83_spl),
% 8.80/1.54 inference(split_clause,[status(thm)],[f162,f484,f487])).
% 8.80/1.54 fof(f491,definition,(
% 8.80/1.54 sQ84_spl <=> (op_implies_or)),
% 8.80/1.54 introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition])).
% 8.80/1.54 fof(f493,plain,(
% 8.80/1.54 ~op_implies_or|sQ84_spl),
% 8.80/1.54 inference(component_clause,[status(thm)],[f491])).
% 8.80/1.54 fof(f494,definition,(
% 8.80/1.54 ![X0,X1]: (sQ85_spl <=> (implies(X0,X1)=or(not(X0),X1)))),
% 8.80/1.54 introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition])).
% 8.80/1.54 fof(f495,plain,(
% 8.80/1.54 ![X0,X1]: (implies(X0,X1)=or(not(X0),X1)|~sQ85_spl)),
% 8.80/1.54 inference(component_clause,[status(thm)],[f494])).
% 8.80/1.54 fof(f497,plain,(
% 8.80/1.54 ~sQ84_spl|sQ85_spl),
% 8.80/1.54 inference(split_clause,[status(thm)],[f164,f491,f494])).
% 8.80/1.54 fof(f498,definition,(
% 8.80/1.54 sQ86_spl <=> (op_equiv)),
% 8.80/1.54 introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition])).
% 8.80/1.54 fof(f500,plain,(
% 8.80/1.54 ~op_equiv|sQ86_spl),
% 8.80/1.54 inference(component_clause,[status(thm)],[f498])).
% 8.80/1.54 fof(f501,definition,(
% 8.80/1.54 ![X0,X1]: (sQ87_spl <=> (equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))))),
% 8.80/1.54 introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition])).
% 8.80/1.54 fof(f502,plain,(
% 8.80/1.54 ![X0,X1]: (equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))|~sQ87_spl)),
% 8.80/1.54 inference(component_clause,[status(thm)],[f501])).
% 8.80/1.54 fof(f504,plain,(
% 8.80/1.54 ~sQ86_spl|sQ87_spl),
% 8.80/1.54 inference(split_clause,[status(thm)],[f166,f498,f501])).
% 8.80/1.54 fof(f505,plain,(
% 8.80/1.54 $false|sQ86_spl),
% 8.80/1.54 inference(forward_subsumption_resolution,[status(thm)],[f500,f169])).
% 8.80/1.54 fof(f506,plain,(
% 8.80/1.54 sQ86_spl),
% 8.80/1.54 inference(contradiction_clause,[status(thm)],[f505])).
% 8.80/1.54 fof(f507,plain,(
% 8.80/1.54 $false|sQ0_spl),
% 8.80/1.54 inference(forward_subsumption_resolution,[status(thm)],[f183,f170])).
% 8.80/1.54 fof(f508,plain,(
% 8.80/1.54 sQ0_spl),
% 8.80/1.54 inference(contradiction_clause,[status(thm)],[f507])).
% 8.80/1.54 fof(f511,plain,(
% 8.80/1.54 $false|sQ84_spl),
% 8.80/1.54 inference(forward_subsumption_resolution,[status(thm)],[f493,f167])).
% 8.80/1.54 fof(f512,plain,(
% 8.80/1.54 sQ84_spl),
% 8.80/1.54 inference(contradiction_clause,[status(thm)],[f511])).
% 8.80/1.54 fof(f513,plain,(
% 8.80/1.54 $false|sQ82_spl),
% 8.80/1.54 inference(forward_subsumption_resolution,[status(thm)],[f486,f178])).
% 8.80/1.54 fof(f514,plain,(
% 8.80/1.54 sQ82_spl),
% 8.80/1.54 inference(contradiction_clause,[status(thm)],[f513])).
% 8.80/1.54 fof(f515,plain,(
% 8.80/1.54 $false|sQ80_spl),
% 8.80/1.54 inference(forward_subsumption_resolution,[status(thm)],[f479,f168])).
% 8.80/1.54 fof(f516,plain,(
% 8.80/1.54 sQ80_spl),
% 8.80/1.54 inference(contradiction_clause,[status(thm)],[f515])).
% 8.80/1.54 fof(f517,plain,(
% 8.80/1.54 $false|sQ78_spl),
% 8.80/1.54 inference(forward_subsumption_resolution,[status(thm)],[f472,f177])).
% 8.80/1.54 fof(f518,plain,(
% 8.80/1.54 sQ78_spl),
% 8.80/1.54 inference(contradiction_clause,[status(thm)],[f517])).
% 8.80/1.54 fof(f521,plain,(
% 8.80/1.54 $false|sQ75_spl),
% 8.80/1.54 inference(forward_subsumption_resolution,[status(thm)],[f461,f175])).
% 8.80/1.54 fof(f522,plain,(
% 8.80/1.54 sQ75_spl),
% 8.80/1.54 inference(contradiction_clause,[status(thm)],[f521])).
% 8.80/1.54 fof(f525,plain,(
% 8.80/1.54 $false|sQ64_spl),
% 8.80/1.54 inference(forward_subsumption_resolution,[status(thm)],[f420,f171])).
% 8.80/1.54 fof(f526,plain,(
% 8.80/1.54 sQ64_spl),
% 8.80/1.54 inference(contradiction_clause,[status(thm)],[f525])).
% 8.80/1.54 fof(f537,plain,(
% 8.80/1.54 $false|sQ69_spl),
% 8.80/1.54 inference(forward_subsumption_resolution,[status(thm)],[f439,f173])).
% 8.80/1.54 fof(f538,plain,(
% 8.80/1.54 sQ69_spl),
% 8.80/1.54 inference(contradiction_clause,[status(thm)],[f537])).
% 8.80/1.54 fof(f554,plain,(
% 8.80/1.54 $false|sQ67_spl),
% 8.80/1.54 inference(forward_subsumption_resolution,[status(thm)],[f431,f172])).
% 8.80/1.54 fof(f555,plain,(
% 8.80/1.54 sQ67_spl),
% 8.80/1.54 inference(contradiction_clause,[status(thm)],[f554])).
% 8.80/1.54 fof(f580,plain,(
% 8.80/1.54 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(or(X2,X0),or(X2,X1)))|~sQ76_spl|~sQ1_spl)),
% 8.80/1.54 inference(resolution,[status(thm)],[f463,f185])).
% 8.80/1.54 fof(f768,plain,(
% 8.80/1.54 $false|~sQ40_spl|sQ41_spl),
% 8.80/1.54 inference(forward_subsumption_resolution,[status(thm)],[f334,f329])).
% 8.80/1.54 fof(f769,plain,(
% 8.80/1.54 ~sQ40_spl|sQ41_spl),
% 8.80/1.54 inference(contradiction_clause,[status(thm)],[f768])).
% 8.80/1.54 fof(f854,plain,(
% 8.80/1.54 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(or(not(X2),X0),implies(X2,X1)))|~sQ76_spl|~sQ1_spl|~sQ85_spl)),
% 8.80/1.54 inference(paramodulation,[status(thm)],[f495,f580])).
% 8.80/1.54 fof(f862,plain,(
% 8.80/1.54 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(implies(X2,X0),implies(X2,X1)))|~sQ76_spl|~sQ1_spl|~sQ85_spl)),
% 8.80/1.54 inference(forward_demodulation,[status(thm)],[f495,f854])).
% 8.80/1.56 fof(f869,plain,(
% 8.80/1.56 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X2,X0))|is_a_theorem(implies(X2,X1))|~sQ76_spl|~sQ85_spl|~sQ1_spl)),
% 8.80/1.56 inference(resolution,[status(thm)],[f862,f185])).
% 8.80/1.56 fof(f913,plain,(
% 8.80/1.56 ![X0,X1]: (and(X0,X1)=not(implies(X0,not(X1)))|~sQ85_spl|~sQ81_spl)),
% 8.80/1.56 inference(forward_demodulation,[status(thm)],[f495,f481])).
% 8.80/1.56 fof(f938,plain,(
% 8.80/1.56 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1)|~sQ83_spl|~sQ79_spl)),
% 8.80/1.56 inference(forward_demodulation,[status(thm)],[f488,f474])).
% 8.80/1.56 fof(f939,plain,(
% 8.80/1.56 ![X0,X1,X2]: (or(implies(X0,not(X1)),X2)=implies(and(X0,X1),X2)|~sQ83_spl|~sQ79_spl|~sQ85_spl|~sQ81_spl)),
% 8.80/1.56 inference(paramodulation,[status(thm)],[f913,f938])).
% 8.80/1.56 fof(f1144,plain,(
% 8.80/1.56 ![X0,X1,X2]: (~is_a_theorem(implies(or(X0,X1),X2))|is_a_theorem(implies(or(X1,X0),X2))|~sQ76_spl|~sQ85_spl|~sQ1_spl|~sQ70_spl)),
% 8.80/1.56 inference(resolution,[status(thm)],[f869,f441])).
% 8.80/1.56 fof(f1146,plain,(
% 8.80/1.56 ![X0,X1,X2]: (~is_a_theorem(implies(or(X0,X1),X2))|is_a_theorem(implies(X1,X2))|~sQ76_spl|~sQ85_spl|~sQ1_spl|~sQ34_spl)),
% 8.80/1.56 inference(resolution,[status(thm)],[f869,f307])).
% 8.80/1.56 fof(f1162,plain,(
% 8.80/1.56 ![X0,X1]: (is_a_theorem(implies(X0,or(X0,X1)))|~sQ76_spl|~sQ85_spl|~sQ1_spl|~sQ34_spl|~sQ70_spl)),
% 8.80/1.56 inference(resolution,[status(thm)],[f1146,f441])).
% 8.80/1.56 fof(f1164,plain,(
% 8.80/1.56 ![X0]: (is_a_theorem(implies(X0,X0))|~sQ76_spl|~sQ85_spl|~sQ1_spl|~sQ34_spl|~sQ65_spl)),
% 8.80/1.56 inference(resolution,[status(thm)],[f1146,f422])).
% 8.80/1.56 fof(f1170,plain,(
% 8.80/1.56 sQ31_spl|~sQ76_spl|~sQ85_spl|~sQ1_spl|~sQ34_spl|~sQ70_spl),
% 8.80/1.56 inference(split_clause,[status(thm)],[f1162,f295,f462,f494,f184,f306,f440])).
% 8.80/1.56 fof(f1193,plain,(
% 8.80/1.56 ![X0,X1,X2]: (~is_a_theorem(implies(implies(X0,or(X0,X1)),X2))|is_a_theorem(X2)|~sQ31_spl|~sQ1_spl)),
% 8.80/1.56 inference(resolution,[status(thm)],[f296,f185])).
% 8.80/1.56 fof(f1291,plain,(
% 8.80/1.56 ![X0,X1,X2]: (~is_a_theorem(implies(or(X0,or(not(X0),X1)),X2))|is_a_theorem(X2)|~sQ31_spl|~sQ1_spl|~sQ83_spl|~sQ79_spl)),
% 8.80/1.56 inference(paramodulation,[status(thm)],[f938,f1193])).
% 8.80/1.56 fof(f1293,plain,(
% 8.80/1.56 ![X0,X1,X2]: (~is_a_theorem(implies(or(X0,implies(X0,X1)),X2))|is_a_theorem(X2)|~sQ85_spl|~sQ31_spl|~sQ1_spl|~sQ83_spl|~sQ79_spl)),
% 8.80/1.56 inference(forward_demodulation,[status(thm)],[f495,f1291])).
% 8.80/1.56 fof(f1720,plain,(
% 8.80/1.56 ![X0,X1,X2]: (~is_a_theorem(implies(or(implies(X0,X1),X0),X2))|is_a_theorem(X2)|~sQ76_spl|~sQ70_spl|~sQ85_spl|~sQ31_spl|~sQ1_spl|~sQ83_spl|~sQ79_spl)),
% 8.80/1.56 inference(resolution,[status(thm)],[f1144,f1293])).
% 8.80/1.56 fof(f3707,plain,(
% 8.80/1.56 ![X0,X1,X2]: (~is_a_theorem(implies(implies(and(X0,X1),X0),X2))|is_a_theorem(X2)|~sQ76_spl|~sQ70_spl|~sQ31_spl|~sQ1_spl|~sQ83_spl|~sQ79_spl|~sQ85_spl|~sQ81_spl)),
% 8.80/1.56 inference(paramodulation,[status(thm)],[f939,f1720])).
% 8.80/1.56 fof(f3934,plain,(
% 8.80/1.56 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X0))|~sQ70_spl|~sQ31_spl|~sQ83_spl|~sQ79_spl|~sQ81_spl|~sQ76_spl|~sQ85_spl|~sQ1_spl|~sQ34_spl|~sQ65_spl)),
% 8.80/1.56 inference(resolution,[status(thm)],[f3707,f1164])).
% 8.80/1.56 fof(f3942,plain,(
% 8.80/1.56 sQ22_spl|~sQ70_spl|~sQ31_spl|~sQ83_spl|~sQ79_spl|~sQ81_spl|~sQ76_spl|~sQ85_spl|~sQ1_spl|~sQ34_spl|~sQ65_spl),
% 8.80/1.56 inference(split_clause,[status(thm)],[f3934,f262,f440,f295,f487,f473,f480,f462,f494,f184,f306,f421])).
% 8.80/1.56 fof(f3955,plain,(
% 8.80/1.56 ![X0,X1]: (is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))|~sQ22_spl|~sQ87_spl)),
% 8.80/1.56 inference(paramodulation,[status(thm)],[f502,f263])).
% 8.80/1.56 fof(f3956,plain,(
% 8.80/1.56 sQ40_spl|~sQ22_spl|~sQ87_spl),
% 8.80/1.56 inference(split_clause,[status(thm)],[f3955,f328,f262,f501])).
% 8.80/1.56 fof(f3957,plain,(
% 8.80/1.56 $false|~sQ39_spl),
% 8.80/1.56 inference(forward_subsumption_resolution,[status(thm)],[f326,f180])).
% 8.80/1.56 fof(f3958,plain,(
% 8.80/1.56 ~sQ39_spl),
% 8.80/1.56 inference(contradiction_clause,[status(thm)],[f3957])).
% 8.80/1.56 fof(f3959,plain,(
% 8.80/1.56 $false),
% 8.80/1.56 inference(sat_refutation,[status(thm)],[f187,f335,f424,f432,f443,f465,f476,f483,f490,f497,f504,f506,f508,f512,f514,f516,f518,f522,f526,f538,f555,f769,f1170,f3942,f3956,f3958])).
% 8.80/1.56 % SZS output end CNFRefutation for theBenchmark.p
% 8.80/1.59 % Elapsed time: 1.227835 seconds
% 8.80/1.59 % CPU time: 9.388010 seconds
% 8.80/1.59 % Total memory used: 278.189 MB
% 8.80/1.59 % Net memory used: 268.069 MB
%------------------------------------------------------------------------------