%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL520+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 : n005.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 01:10:12 PM UTC 2026
% Result : Theorem 0.15s 0.53s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL520+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 00:36:34 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.15/0.53 % Refutation found
% 0.15/0.53 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.53 % SZS output start CNFRefutation for theBenchmark
% 0.15/0.53 fof(f1,axiom,(
% 0.15/0.53 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 0.15/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.53 fof(f16,axiom,(
% 0.15/0.53 ( kn1<=> (! [P] : is_a_theorem(implies(P,and(P,P))) )) ),
% 0.15/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.53 fof(f17,axiom,(
% 0.15/0.53 ( kn2<=> (! [P,Q] : is_a_theorem(implies(and(P,Q),P)) )) ),
% 0.15/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.53 fof(f18,axiom,(
% 0.15/0.53 ( kn3<=> (! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) )) ),
% 0.15/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.53 fof(f24,axiom,(
% 0.15/0.53 ( r3<=> (! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) )) ),
% 0.15/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.53 fof(f27,axiom,(
% 0.15/0.53 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 0.15/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.53 fof(f29,axiom,(
% 0.15/0.53 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 0.15/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.53 fof(f30,axiom,(
% 0.15/0.53 ( op_implies_or=> (! [X,Y] : implies(X,Y) = or(not(X),Y) )) ),
% 0.15/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.53 fof(f32,axiom,(
% 0.15/0.53 op_or ),
% 0.15/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.53 fof(f33,axiom,(
% 0.15/0.53 op_implies_and ),
% 0.15/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.53 fof(f35,axiom,(
% 0.15/0.53 modus_ponens ),
% 0.15/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.53 fof(f36,axiom,(
% 0.15/0.53 kn1 ),
% 0.15/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.53 fof(f37,axiom,(
% 0.15/0.53 kn2 ),
% 0.15/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.53 fof(f38,axiom,(
% 0.15/0.53 kn3 ),
% 0.15/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.53 fof(f40,axiom,(
% 0.15/0.53 op_implies_or ),
% 0.15/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.53 fof(f43,conjecture,(
% 0.15/0.53 r3 ),
% 0.15/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.53 fof(f44,negated_conjecture,(
% 0.15/0.53 ~(r3 )),
% 0.15/0.53 inference(negated_conjecture,[status(cth)],[f43])).
% 0.15/0.53 fof(f45,plain,(
% 0.15/0.53 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 0.15/0.53 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.15/0.53 fof(f46,plain,(
% 0.15/0.53 (~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))))),
% 0.15/0.53 inference(NNF_transformation,[status(thm)],[f45])).
% 0.15/0.53 fof(f47,plain,(
% 0.15/0.53 (~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))))),
% 0.15/0.53 inference(miniscoping,[status(thm)],[f46])).
% 0.15/0.53 fof(f48,plain,(
% 0.15/0.53 (~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)))),
% 0.15/0.53 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f47])).
% 0.15/0.53 fof(f49,plain,(
% 0.15/0.53 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 0.15/0.53 inference(cnf_transformation,[status(thm)],[f48])).
% 0.15/0.53 fof(f111,plain,(
% 0.15/0.53 (~kn1|(![P]: is_a_theorem(implies(P,and(P,P)))))&(kn1|(?[P]: ~is_a_theorem(implies(P,and(P,P)))))),
% 0.15/0.53 inference(NNF_transformation,[status(thm)],[f16])).
% 0.15/0.53 fof(f112,plain,(
% 0.15/0.53 (~kn1|(![P]: is_a_theorem(implies(P,and(P,P)))))&(kn1|~is_a_theorem(implies(sK32_skl,and(sK32_skl,sK32_skl))))),
% 0.15/0.53 inference(skolemize,[status(esa),new_symbols(skolem,[sK32_skl]),skolemize(P,sK32_skl)],[f111])).
% 0.15/0.53 fof(f113,plain,(
% 0.15/0.53 ![X0]: (~kn1|is_a_theorem(implies(X0,and(X0,X0))))),
% 0.15/0.53 inference(cnf_transformation,[status(thm)],[f112])).
% 0.15/0.53 fof(f115,plain,(
% 0.15/0.53 (~kn2|(![P,Q]: is_a_theorem(implies(and(P,Q),P))))&(kn2|(?[P,Q]: ~is_a_theorem(implies(and(P,Q),P))))),
% 0.15/0.53 inference(NNF_transformation,[status(thm)],[f17])).
% 0.15/0.53 fof(f116,plain,(
% 0.15/0.54 (~kn2|(![P,Q]: is_a_theorem(implies(and(P,Q),P))))&(kn2|~is_a_theorem(implies(and(sK33_skl,sK34_skl),sK33_skl)))),
% 0.15/0.54 inference(skolemize,[status(esa),new_symbols(skolem,[sK33_skl,sK34_skl]),skolemize(P,sK33_skl),skolemize(Q,sK34_skl)],[f115])).
% 0.15/0.54 fof(f117,plain,(
% 0.15/0.54 ![X0,X1]: (~kn2|is_a_theorem(implies(and(X0,X1),X0)))),
% 0.15/0.54 inference(cnf_transformation,[status(thm)],[f116])).
% 0.15/0.54 fof(f119,plain,(
% 0.15/0.54 (~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)))))))),
% 0.15/0.54 inference(NNF_transformation,[status(thm)],[f18])).
% 0.15/0.54 fof(f120,plain,(
% 0.15/0.54 (~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(sK35_skl,sK36_skl),implies(not(and(sK36_skl,sK37_skl)),not(and(sK37_skl,sK35_skl))))))),
% 0.15/0.54 inference(skolemize,[status(esa),new_symbols(skolem,[sK35_skl,sK36_skl,sK37_skl]),skolemize(P,sK35_skl),skolemize(Q,sK36_skl),skolemize(R,sK37_skl)],[f119])).
% 0.15/0.54 fof(f121,plain,(
% 0.15/0.54 ![X0,X1,X2]: (~kn3|is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))))),
% 0.15/0.54 inference(cnf_transformation,[status(thm)],[f120])).
% 0.15/0.54 fof(f143,plain,(
% 0.15/0.54 (~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)))))),
% 0.15/0.54 inference(NNF_transformation,[status(thm)],[f24])).
% 0.15/0.54 fof(f144,plain,(
% 0.15/0.54 (~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))))),
% 0.15/0.54 inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl]),skolemize(P,sK47_skl),skolemize(Q,sK48_skl)],[f143])).
% 0.15/0.54 fof(f146,plain,(
% 0.15/0.54 r3|~is_a_theorem(implies(or(sK47_skl,sK48_skl),or(sK48_skl,sK47_skl)))),
% 0.15/0.54 inference(cnf_transformation,[status(thm)],[f144])).
% 0.15/0.54 fof(f155,plain,(
% 0.15/0.54 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 0.15/0.54 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 0.15/0.54 fof(f156,plain,(
% 0.15/0.54 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 0.15/0.54 inference(cnf_transformation,[status(thm)],[f155])).
% 0.15/0.54 fof(f159,plain,(
% 0.15/0.54 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 0.15/0.54 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 0.15/0.54 fof(f160,plain,(
% 0.15/0.54 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 0.15/0.54 inference(cnf_transformation,[status(thm)],[f159])).
% 0.15/0.54 fof(f161,plain,(
% 0.15/0.54 ~op_implies_or|(![X,Y]: implies(X,Y)=or(not(X),Y))),
% 0.15/0.54 inference(pre_NNF_transformation,[status(thm)],[f30])).
% 0.15/0.54 fof(f162,plain,(
% 0.15/0.54 ![X0,X1]: (~op_implies_or|implies(X0,X1)=or(not(X0),X1))),
% 0.15/0.54 inference(cnf_transformation,[status(thm)],[f161])).
% 0.15/0.54 fof(f165,plain,(
% 0.15/0.54 op_or),
% 0.15/0.54 inference(cnf_transformation,[status(thm)],[f32])).
% 0.15/0.54 fof(f166,plain,(
% 0.15/0.54 op_implies_and),
% 0.15/0.54 inference(cnf_transformation,[status(thm)],[f33])).
% 0.15/0.54 fof(f168,plain,(
% 0.15/0.54 modus_ponens),
% 0.15/0.54 inference(cnf_transformation,[status(thm)],[f35])).
% 0.15/0.54 fof(f169,plain,(
% 0.15/0.54 kn1),
% 0.15/0.54 inference(cnf_transformation,[status(thm)],[f36])).
% 0.15/0.54 fof(f170,plain,(
% 0.15/0.54 kn2),
% 0.15/0.54 inference(cnf_transformation,[status(thm)],[f37])).
% 0.15/0.54 fof(f171,plain,(
% 0.15/0.54 kn3),
% 0.15/0.54 inference(cnf_transformation,[status(thm)],[f38])).
% 0.15/0.54 fof(f173,plain,(
% 0.15/0.54 op_implies_or),
% 0.15/0.54 inference(cnf_transformation,[status(thm)],[f40])).
% 0.15/0.54 fof(f176,plain,(
% 0.15/0.54 ~r3),
% 0.15/0.54 inference(cnf_transformation,[status(thm)],[f44])).
% 0.15/0.54 fof(f177,definition,(
% 0.15/0.54 sQ0_spl <=> (modus_ponens)),
% 0.15/0.54 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.15/0.54 fof(f179,plain,(
% 0.15/0.54 ~modus_ponens|sQ0_spl),
% 0.15/0.54 inference(component_clause,[status(thm)],[f177])).
% 0.15/0.54 fof(f180,definition,(
% 0.15/0.54 ![X0,X1]: (sQ1_spl <=> (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)))),
% 0.15/0.54 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.15/0.54 fof(f181,plain,(
% 0.15/0.54 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)|~sQ1_spl)),
% 0.15/0.54 inference(component_clause,[status(thm)],[f180])).
% 0.15/0.54 fof(f183,plain,(
% 0.15/0.54 ~sQ0_spl|sQ1_spl),
% 0.15/0.54 inference(split_clause,[status(thm)],[f49,f177,f180])).
% 0.15/0.54 fof(f258,definition,(
% 0.15/0.54 ![X0,X1]: (sQ22_spl <=> (is_a_theorem(implies(and(X0,X1),X0))))),
% 0.15/0.54 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.15/0.54 fof(f259,plain,(
% 0.15/0.54 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X0))|~sQ22_spl)),
% 0.15/0.54 inference(component_clause,[status(thm)],[f258])).
% 0.15/0.54 fof(f354,definition,(
% 0.15/0.54 sQ48_spl <=> (kn1)),
% 0.15/0.54 introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition])).
% 0.15/0.54 fof(f356,plain,(
% 0.15/0.54 ~kn1|sQ48_spl),
% 0.15/0.54 inference(component_clause,[status(thm)],[f354])).
% 0.15/0.54 fof(f357,definition,(
% 0.15/0.54 ![X0]: (sQ49_spl <=> (is_a_theorem(implies(X0,and(X0,X0)))))),
% 0.15/0.54 introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition])).
% 0.15/0.54 fof(f358,plain,(
% 0.15/0.54 ![X0]: (is_a_theorem(implies(X0,and(X0,X0)))|~sQ49_spl)),
% 0.15/0.54 inference(component_clause,[status(thm)],[f357])).
% 0.15/0.54 fof(f360,plain,(
% 0.15/0.54 ~sQ48_spl|sQ49_spl),
% 0.15/0.54 inference(split_clause,[status(thm)],[f113,f354,f357])).
% 0.15/0.54 fof(f365,definition,(
% 0.15/0.54 sQ51_spl <=> (kn2)),
% 0.15/0.54 introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition])).
% 0.15/0.54 fof(f367,plain,(
% 0.15/0.54 ~kn2|sQ51_spl),
% 0.15/0.54 inference(component_clause,[status(thm)],[f365])).
% 0.15/0.54 fof(f368,plain,(
% 0.15/0.54 ~sQ51_spl|sQ22_spl),
% 0.15/0.54 inference(split_clause,[status(thm)],[f117,f365,f258])).
% 0.15/0.54 fof(f373,definition,(
% 0.15/0.54 sQ53_spl <=> (kn3)),
% 0.15/0.54 introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition])).
% 0.15/0.54 fof(f375,plain,(
% 0.15/0.54 ~kn3|sQ53_spl),
% 0.15/0.54 inference(component_clause,[status(thm)],[f373])).
% 0.15/0.54 fof(f376,definition,(
% 0.15/0.54 ![X0,X1,X2]: (sQ54_spl <=> (is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))))),
% 0.15/0.54 introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition])).
% 0.15/0.54 fof(f377,plain,(
% 0.15/0.54 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))|~sQ54_spl)),
% 0.15/0.54 inference(component_clause,[status(thm)],[f376])).
% 0.15/0.54 fof(f379,plain,(
% 0.15/0.54 ~sQ53_spl|sQ54_spl),
% 0.15/0.54 inference(split_clause,[status(thm)],[f121,f373,f376])).
% 0.15/0.54 fof(f433,definition,(
% 0.15/0.54 sQ69_spl <=> (r3)),
% 0.15/0.54 introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition])).
% 0.15/0.54 fof(f434,plain,(
% 0.15/0.54 r3|~sQ69_spl),
% 0.15/0.54 inference(component_clause,[status(thm)],[f433])).
% 0.15/0.54 fof(f440,definition,(
% 0.15/0.54 sQ71_spl <=> (is_a_theorem(implies(or(sK47_skl,sK48_skl),or(sK48_skl,sK47_skl))))),
% 0.15/0.54 introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition])).
% 0.15/0.54 fof(f442,plain,(
% 0.15/0.54 ~is_a_theorem(implies(or(sK47_skl,sK48_skl),or(sK48_skl,sK47_skl)))|sQ71_spl),
% 0.15/0.54 inference(component_clause,[status(thm)],[f440])).
% 0.15/0.54 fof(f443,plain,(
% 0.15/0.54 sQ69_spl|~sQ71_spl),
% 0.15/0.54 inference(split_clause,[status(thm)],[f146,f433,f440])).
% 0.15/0.54 fof(f466,definition,(
% 0.15/0.54 sQ78_spl <=> (op_or)),
% 0.15/0.54 introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition])).
% 0.15/0.54 fof(f468,plain,(
% 0.15/0.54 ~op_or|sQ78_spl),
% 0.15/0.54 inference(component_clause,[status(thm)],[f466])).
% 0.15/0.54 fof(f469,definition,(
% 0.15/0.54 ![X0,X1]: (sQ79_spl <=> (or(X0,X1)=not(and(not(X0),not(X1)))))),
% 0.15/0.54 introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition])).
% 0.15/0.54 fof(f470,plain,(
% 0.15/0.54 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1)))|~sQ79_spl)),
% 0.15/0.54 inference(component_clause,[status(thm)],[f469])).
% 0.15/0.54 fof(f472,plain,(
% 0.15/0.54 ~sQ78_spl|sQ79_spl),
% 0.15/0.54 inference(split_clause,[status(thm)],[f156,f466,f469])).
% 0.15/0.54 fof(f480,definition,(
% 0.15/0.54 sQ82_spl <=> (op_implies_and)),
% 0.15/0.54 introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition])).
% 0.15/0.54 fof(f482,plain,(
% 0.15/0.54 ~op_implies_and|sQ82_spl),
% 0.15/0.54 inference(component_clause,[status(thm)],[f480])).
% 0.15/0.54 fof(f483,definition,(
% 0.15/0.54 ![X0,X1]: (sQ83_spl <=> (implies(X0,X1)=not(and(X0,not(X1)))))),
% 0.15/0.54 introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition])).
% 0.15/0.54 fof(f484,plain,(
% 0.15/0.54 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1)))|~sQ83_spl)),
% 0.15/0.54 inference(component_clause,[status(thm)],[f483])).
% 0.15/0.54 fof(f486,plain,(
% 0.15/0.54 ~sQ82_spl|sQ83_spl),
% 0.15/0.54 inference(split_clause,[status(thm)],[f160,f480,f483])).
% 0.15/0.54 fof(f487,definition,(
% 0.15/0.54 sQ84_spl <=> (op_implies_or)),
% 0.15/0.54 introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition])).
% 0.15/0.54 fof(f489,plain,(
% 0.15/0.54 ~op_implies_or|sQ84_spl),
% 0.15/0.54 inference(component_clause,[status(thm)],[f487])).
% 0.15/0.54 fof(f490,definition,(
% 0.15/0.54 ![X0,X1]: (sQ85_spl <=> (implies(X0,X1)=or(not(X0),X1)))),
% 0.15/0.54 introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition])).
% 0.15/0.54 fof(f491,plain,(
% 0.15/0.54 ![X0,X1]: (implies(X0,X1)=or(not(X0),X1)|~sQ85_spl)),
% 0.15/0.54 inference(component_clause,[status(thm)],[f490])).
% 0.15/0.54 fof(f493,plain,(
% 0.15/0.54 ~sQ84_spl|sQ85_spl),
% 0.15/0.54 inference(split_clause,[status(thm)],[f162,f487,f490])).
% 0.15/0.54 fof(f503,plain,(
% 0.15/0.54 $false|sQ0_spl),
% 0.15/0.54 inference(forward_subsumption_resolution,[status(thm)],[f179,f168])).
% 0.15/0.54 fof(f504,plain,(
% 0.15/0.54 sQ0_spl),
% 0.15/0.54 inference(contradiction_clause,[status(thm)],[f503])).
% 0.15/0.54 fof(f507,plain,(
% 0.15/0.54 $false|sQ84_spl),
% 0.15/0.54 inference(forward_subsumption_resolution,[status(thm)],[f489,f173])).
% 0.15/0.54 fof(f508,plain,(
% 0.15/0.54 sQ84_spl),
% 0.15/0.54 inference(contradiction_clause,[status(thm)],[f507])).
% 0.15/0.54 fof(f509,plain,(
% 0.15/0.54 $false|sQ82_spl),
% 0.15/0.54 inference(forward_subsumption_resolution,[status(thm)],[f482,f166])).
% 0.15/0.54 fof(f510,plain,(
% 0.15/0.54 sQ82_spl),
% 0.15/0.54 inference(contradiction_clause,[status(thm)],[f509])).
% 0.15/0.54 fof(f513,plain,(
% 0.15/0.54 $false|sQ78_spl),
% 0.15/0.54 inference(forward_subsumption_resolution,[status(thm)],[f468,f165])).
% 0.15/0.54 fof(f514,plain,(
% 0.15/0.54 sQ78_spl),
% 0.15/0.54 inference(contradiction_clause,[status(thm)],[f513])).
% 0.15/0.54 fof(f536,plain,(
% 0.15/0.54 $false|sQ51_spl),
% 0.15/0.54 inference(forward_subsumption_resolution,[status(thm)],[f367,f170])).
% 0.15/0.54 fof(f537,plain,(
% 0.15/0.54 sQ51_spl),
% 0.15/0.54 inference(contradiction_clause,[status(thm)],[f536])).
% 0.15/0.54 fof(f576,plain,(
% 0.15/0.54 $false|sQ48_spl),
% 0.15/0.54 inference(forward_subsumption_resolution,[status(thm)],[f356,f169])).
% 0.15/0.54 fof(f577,plain,(
% 0.15/0.54 sQ48_spl),
% 0.15/0.54 inference(contradiction_clause,[status(thm)],[f576])).
% 0.15/0.54 fof(f579,plain,(
% 0.15/0.54 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(not(and(X1,X2)),not(and(X2,X0))))|~sQ54_spl|~sQ1_spl)),
% 0.15/0.54 inference(resolution,[status(thm)],[f377,f181])).
% 0.15/0.54 fof(f581,plain,(
% 0.15/0.54 $false|sQ53_spl),
% 0.15/0.54 inference(forward_subsumption_resolution,[status(thm)],[f375,f171])).
% 0.15/0.54 fof(f582,plain,(
% 0.15/0.54 sQ53_spl),
% 0.15/0.54 inference(contradiction_clause,[status(thm)],[f581])).
% 0.15/0.54 fof(f694,plain,(
% 0.15/0.54 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1)|~sQ83_spl|~sQ79_spl)),
% 0.15/0.54 inference(forward_demodulation,[status(thm)],[f484,f470])).
% 0.15/0.54 fof(f696,plain,(
% 0.15/0.54 ![X0,X1,X2]: (or(and(X0,not(X1)),X2)=implies(implies(X0,X1),X2)|~sQ79_spl|~sQ83_spl)),
% 0.15/0.54 inference(paramodulation,[status(thm)],[f484,f694])).
% 0.15/0.54 fof(f770,plain,(
% 0.15/0.54 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0)))))|~sQ83_spl|~sQ79_spl|~sQ54_spl)),
% 0.15/0.54 inference(forward_demodulation,[status(thm)],[f694,f377])).
% 0.15/0.54 fof(f772,plain,(
% 0.15/0.54 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),or(and(X1,X2),not(and(X2,not(X0))))))|~sQ54_spl|~sQ83_spl|~sQ79_spl)),
% 0.15/0.54 inference(paramodulation,[status(thm)],[f694,f770])).
% 0.15/0.54 fof(f778,plain,(
% 0.15/0.54 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),or(and(X1,X2),implies(X2,X0))))|~sQ54_spl|~sQ83_spl|~sQ79_spl)),
% 0.15/0.54 inference(forward_demodulation,[status(thm)],[f484,f772])).
% 0.15/0.54 fof(f969,plain,(
% 0.15/0.54 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(or(and(X1,X2),not(and(X2,X0))))|~sQ83_spl|~sQ79_spl|~sQ54_spl|~sQ1_spl)),
% 0.15/0.54 inference(forward_demodulation,[status(thm)],[f694,f579])).
% 0.15/0.54 fof(f975,plain,(
% 0.15/0.54 ![X0,X1,X2]: (~is_a_theorem(implies(not(X0),X1))|is_a_theorem(or(and(X1,X2),implies(X2,X0)))|~sQ79_spl|~sQ54_spl|~sQ1_spl|~sQ83_spl)),
% 0.15/0.54 inference(paramodulation,[status(thm)],[f484,f969])).
% 0.15/0.54 fof(f978,plain,(
% 0.15/0.54 ![X0,X1,X2]: (~is_a_theorem(or(X0,X1))|is_a_theorem(or(and(X1,X2),implies(X2,X0)))|~sQ79_spl|~sQ54_spl|~sQ1_spl|~sQ83_spl)),
% 0.15/0.54 inference(forward_demodulation,[status(thm)],[f694,f975])).
% 0.15/0.54 fof(f1600,plain,(
% 0.15/0.54 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),implies(not(X2),X0))))|~sQ54_spl|~sQ79_spl|~sQ83_spl)),
% 0.15/0.54 inference(paramodulation,[status(thm)],[f696,f778])).
% 0.15/0.54 fof(f1612,plain,(
% 0.15/0.54 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),or(X2,X0))))|~sQ54_spl|~sQ79_spl|~sQ83_spl)),
% 0.15/0.54 inference(forward_demodulation,[status(thm)],[f694,f1600])).
% 0.15/0.54 fof(f1654,plain,(
% 0.15/0.54 ![X0,X1,X2]: (~is_a_theorem(or(X0,X1))|is_a_theorem(implies(implies(X1,X2),or(X2,X0)))|~sQ54_spl|~sQ79_spl|~sQ83_spl|~sQ1_spl)),
% 0.15/0.54 inference(resolution,[status(thm)],[f1612,f181])).
% 0.15/0.54 fof(f1677,plain,(
% 0.15/0.54 ![X0,X1,X2]: (~is_a_theorem(or(X0,X1))|~is_a_theorem(implies(X1,X2))|is_a_theorem(or(X2,X0))|~sQ54_spl|~sQ79_spl|~sQ83_spl|~sQ1_spl)),
% 0.15/0.54 inference(resolution,[status(thm)],[f1654,f181])).
% 0.15/0.54 fof(f1700,plain,(
% 0.15/0.54 ![X0,X1,X2,X3]: (~is_a_theorem(or(X0,X1))|~is_a_theorem(implies(X1,X2))|is_a_theorem(or(and(X0,X3),implies(X3,X2)))|~sQ79_spl|~sQ54_spl|~sQ1_spl|~sQ83_spl)),
% 0.15/0.54 inference(resolution,[status(thm)],[f1677,f978])).
% 0.15/0.54 fof(f1756,plain,(
% 0.15/0.54 ![X0,X1,X2,X3]: (~is_a_theorem(or(X0,X1))|~is_a_theorem(implies(X1,X2))|is_a_theorem(implies(implies(X0,X3),implies(not(X3),X2)))|~sQ54_spl|~sQ1_spl|~sQ79_spl|~sQ83_spl)),
% 0.15/0.54 inference(paramodulation,[status(thm)],[f696,f1700])).
% 0.15/0.54 fof(f1767,plain,(
% 0.15/0.54 ![X0,X1,X2,X3]: (~is_a_theorem(or(X0,X1))|~is_a_theorem(implies(X1,X2))|is_a_theorem(implies(implies(X0,X3),or(X3,X2)))|~sQ54_spl|~sQ1_spl|~sQ79_spl|~sQ83_spl)),
% 0.15/0.54 inference(forward_demodulation,[status(thm)],[f694,f1756])).
% 0.15/0.54 fof(f1791,plain,(
% 0.15/0.54 ![X0,X1,X2,X3]: (~is_a_theorem(or(not(X0),X1))|~is_a_theorem(implies(X1,X2))|is_a_theorem(implies(or(X0,X3),or(X3,X2)))|~sQ54_spl|~sQ1_spl|~sQ83_spl|~sQ79_spl)),
% 0.15/0.54 inference(paramodulation,[status(thm)],[f694,f1767])).
% 0.15/0.54 fof(f1800,plain,(
% 0.15/0.54 ![X0,X1,X2,X3]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X2))|is_a_theorem(implies(or(X0,X3),or(X3,X2)))|~sQ85_spl|~sQ54_spl|~sQ1_spl|~sQ83_spl|~sQ79_spl)),
% 0.15/0.54 inference(forward_demodulation,[status(thm)],[f491,f1791])).
% 0.15/0.54 fof(f1819,plain,(
% 0.15/0.54 ![X0]: (~is_a_theorem(implies(sK47_skl,X0))|~is_a_theorem(implies(X0,sK47_skl))|~sQ85_spl|~sQ54_spl|~sQ1_spl|~sQ83_spl|~sQ79_spl|sQ71_spl)),
% 0.15/0.54 inference(resolution,[status(thm)],[f1800,f442])).
% 0.15/0.54 fof(f1831,plain,(
% 0.15/0.54 ~is_a_theorem(implies(and(sK47_skl,sK47_skl),sK47_skl))|~sQ85_spl|~sQ54_spl|~sQ1_spl|~sQ83_spl|~sQ79_spl|sQ71_spl|~sQ49_spl),
% 0.15/0.54 inference(resolution,[status(thm)],[f1819,f358])).
% 0.15/0.54 fof(f1834,plain,(
% 0.15/0.54 $false|~sQ22_spl|~sQ85_spl|~sQ54_spl|~sQ1_spl|~sQ83_spl|~sQ79_spl|sQ71_spl|~sQ49_spl),
% 0.15/0.54 inference(forward_subsumption_resolution,[status(thm)],[f1831,f259])).
% 0.15/0.54 fof(f1835,plain,(
% 0.15/0.54 ~sQ22_spl|~sQ85_spl|~sQ54_spl|~sQ1_spl|~sQ83_spl|~sQ79_spl|sQ71_spl|~sQ49_spl),
% 0.15/0.54 inference(contradiction_clause,[status(thm)],[f1834])).
% 0.15/0.54 fof(f1836,plain,(
% 0.15/0.54 $false|~sQ69_spl),
% 0.15/0.54 inference(forward_subsumption_resolution,[status(thm)],[f434,f176])).
% 0.15/0.54 fof(f1837,plain,(
% 0.15/0.54 ~sQ69_spl),
% 0.15/0.54 inference(contradiction_clause,[status(thm)],[f1836])).
% 0.15/0.54 fof(f1838,plain,(
% 0.15/0.54 $false),
% 0.15/0.54 inference(sat_refutation,[status(thm)],[f183,f360,f368,f379,f443,f472,f486,f493,f504,f508,f510,f514,f537,f577,f582,f1835,f1837])).
% 0.15/0.54 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/0.57 % Elapsed time: 0.194389 seconds
% 0.15/0.57 % CPU time: 1.193506 seconds
% 0.15/0.57 % Total memory used: 110.431 MB
% 0.15/0.57 % Net memory used: 109.826 MB
%------------------------------------------------------------------------------