%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL494+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 : n004.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 0.10s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL494+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
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % 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 00:36:20 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.41 % Refutation found
% 0.10/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.41 fof(f1,axiom,(
% 0.10/0.41 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 0.10/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f14,axiom,(
% 0.10/0.41 ( equivalence_2<=> (! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(Y,X))) )) ),
% 0.10/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f23,axiom,(
% 0.10/0.41 ( r2<=> (! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) )) ),
% 0.10/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f24,axiom,(
% 0.10/0.41 ( r3<=> (! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) )) ),
% 0.10/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f27,axiom,(
% 0.10/0.41 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 0.10/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f28,axiom,(
% 0.10/0.41 ( op_and=> (! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) )) ),
% 0.10/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f29,axiom,(
% 0.10/0.41 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 0.10/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f30,axiom,(
% 0.10/0.41 ( op_implies_or=> (! [X,Y] : implies(X,Y) = or(not(X),Y) )) ),
% 0.10/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f31,axiom,(
% 0.10/0.41 ( op_equiv=> (! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) )) ),
% 0.10/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f32,axiom,(
% 0.10/0.41 op_implies_or ),
% 0.10/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f33,axiom,(
% 0.10/0.41 op_and ),
% 0.10/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f34,axiom,(
% 0.10/0.41 op_equiv ),
% 0.10/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f35,axiom,(
% 0.10/0.41 modus_ponens ),
% 0.10/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f37,axiom,(
% 0.10/0.41 r2 ),
% 0.10/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f38,axiom,(
% 0.10/0.41 r3 ),
% 0.10/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f42,axiom,(
% 0.10/0.41 op_or ),
% 0.10/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f43,axiom,(
% 0.10/0.41 op_implies_and ),
% 0.10/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f45,conjecture,(
% 0.10/0.41 equivalence_2 ),
% 0.10/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f46,negated_conjecture,(
% 0.10/0.41 ~(equivalence_2 )),
% 0.10/0.41 inference(negated_conjecture,[status(cth)],[f45])).
% 0.10/0.41 fof(f47,plain,(
% 0.10/0.41 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 0.10/0.41 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.10/0.41 fof(f48,plain,(
% 0.10/0.41 (~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))))),
% 0.10/0.41 inference(NNF_transformation,[status(thm)],[f47])).
% 0.10/0.41 fof(f49,plain,(
% 0.10/0.41 (~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))))),
% 0.10/0.41 inference(miniscoping,[status(thm)],[f48])).
% 0.10/0.41 fof(f50,plain,(
% 0.10/0.41 (~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)))),
% 0.10/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f49])).
% 0.10/0.41 fof(f51,plain,(
% 0.10/0.41 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f50])).
% 0.10/0.41 fof(f105,plain,(
% 0.10/0.41 (~equivalence_2|(![X,Y]: is_a_theorem(implies(equiv(X,Y),implies(Y,X)))))&(equivalence_2|(?[X,Y]: ~is_a_theorem(implies(equiv(X,Y),implies(Y,X)))))),
% 0.10/0.41 inference(NNF_transformation,[status(thm)],[f14])).
% 0.10/0.41 fof(f106,plain,(
% 0.10/0.41 (~equivalence_2|(![X,Y]: is_a_theorem(implies(equiv(X,Y),implies(Y,X)))))&(equivalence_2|~is_a_theorem(implies(equiv(sK28_skl,sK29_skl),implies(sK29_skl,sK28_skl))))),
% 0.10/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK28_skl,sK29_skl]),skolemize(X,sK28_skl),skolemize(Y,sK29_skl)],[f105])).
% 0.10/0.41 fof(f108,plain,(
% 0.10/0.41 equivalence_2|~is_a_theorem(implies(equiv(sK28_skl,sK29_skl),implies(sK29_skl,sK28_skl)))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f106])).
% 0.10/0.41 fof(f141,plain,(
% 0.10/0.41 (~r2|(![P,Q]: is_a_theorem(implies(Q,or(P,Q)))))&(r2|(?[P,Q]: ~is_a_theorem(implies(Q,or(P,Q)))))),
% 0.10/0.41 inference(NNF_transformation,[status(thm)],[f23])).
% 0.10/0.41 fof(f142,plain,(
% 0.10/0.41 (~r2|(![P,Q]: is_a_theorem(implies(Q,or(P,Q)))))&(r2|~is_a_theorem(implies(sK46_skl,or(sK45_skl,sK46_skl))))),
% 0.10/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK45_skl,sK46_skl]),skolemize(P,sK45_skl),skolemize(Q,sK46_skl)],[f141])).
% 0.10/0.41 fof(f143,plain,(
% 0.10/0.41 ![X0,X1]: (~r2|is_a_theorem(implies(X0,or(X1,X0))))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f142])).
% 0.10/0.41 fof(f145,plain,(
% 0.10/0.41 (~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)))))),
% 0.10/0.41 inference(NNF_transformation,[status(thm)],[f24])).
% 0.10/0.41 fof(f146,plain,(
% 0.10/0.41 (~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))))),
% 0.10/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl]),skolemize(P,sK47_skl),skolemize(Q,sK48_skl)],[f145])).
% 0.10/0.41 fof(f147,plain,(
% 0.10/0.41 ![X0,X1]: (~r3|is_a_theorem(implies(or(X0,X1),or(X1,X0))))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f146])).
% 0.10/0.41 fof(f157,plain,(
% 0.10/0.41 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 0.10/0.41 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 0.10/0.41 fof(f158,plain,(
% 0.10/0.41 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f157])).
% 0.10/0.41 fof(f159,plain,(
% 0.10/0.41 ~op_and|(![X,Y]: and(X,Y)=not(or(not(X),not(Y))))),
% 0.10/0.41 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 0.10/0.41 fof(f160,plain,(
% 0.10/0.41 ![X0,X1]: (~op_and|and(X0,X1)=not(or(not(X0),not(X1))))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f159])).
% 0.10/0.41 fof(f161,plain,(
% 0.10/0.41 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 0.10/0.41 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 0.10/0.41 fof(f162,plain,(
% 0.10/0.41 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f161])).
% 0.10/0.41 fof(f163,plain,(
% 0.10/0.41 ~op_implies_or|(![X,Y]: implies(X,Y)=or(not(X),Y))),
% 0.10/0.41 inference(pre_NNF_transformation,[status(thm)],[f30])).
% 0.10/0.41 fof(f164,plain,(
% 0.10/0.41 ![X0,X1]: (~op_implies_or|implies(X0,X1)=or(not(X0),X1))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f163])).
% 0.10/0.41 fof(f165,plain,(
% 0.10/0.41 ~op_equiv|(![X,Y]: equiv(X,Y)=and(implies(X,Y),implies(Y,X)))),
% 0.10/0.41 inference(pre_NNF_transformation,[status(thm)],[f31])).
% 0.10/0.41 fof(f166,plain,(
% 0.10/0.41 ![X0,X1]: (~op_equiv|equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f165])).
% 0.10/0.41 fof(f167,plain,(
% 0.10/0.41 op_implies_or),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f32])).
% 0.10/0.41 fof(f168,plain,(
% 0.10/0.41 op_and),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f33])).
% 0.10/0.41 fof(f169,plain,(
% 0.10/0.41 op_equiv),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f34])).
% 0.10/0.41 fof(f170,plain,(
% 0.10/0.41 modus_ponens),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f35])).
% 0.10/0.41 fof(f172,plain,(
% 0.10/0.41 r2),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f37])).
% 0.10/0.41 fof(f173,plain,(
% 0.10/0.41 r3),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f38])).
% 0.10/0.41 fof(f177,plain,(
% 0.10/0.41 op_or),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f42])).
% 0.10/0.41 fof(f178,plain,(
% 0.10/0.41 op_implies_and),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f43])).
% 0.10/0.41 fof(f180,plain,(
% 0.10/0.41 ~equivalence_2),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f46])).
% 0.10/0.41 fof(f181,definition,(
% 0.10/0.41 sQ0_spl <=> (modus_ponens)),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f183,plain,(
% 0.10/0.41 ~modus_ponens|sQ0_spl),
% 0.10/0.41 inference(component_clause,[status(thm)],[f181])).
% 0.10/0.41 fof(f184,definition,(
% 0.10/0.41 ![X0,X1]: (sQ1_spl <=> (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f185,plain,(
% 0.10/0.41 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)|~sQ1_spl)),
% 0.10/0.41 inference(component_clause,[status(thm)],[f184])).
% 0.10/0.41 fof(f187,plain,(
% 0.10/0.41 ~sQ0_spl|sQ1_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f51,f181,f184])).
% 0.10/0.41 fof(f229,definition,(
% 0.10/0.41 ![X0,X1]: (sQ13_spl <=> (is_a_theorem(implies(X0,implies(X1,X0)))))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f230,plain,(
% 0.10/0.41 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0)))|~sQ13_spl)),
% 0.10/0.41 inference(component_clause,[status(thm)],[f229])).
% 0.10/0.41 fof(f306,definition,(
% 0.10/0.41 ![X0,X1]: (sQ34_spl <=> (is_a_theorem(implies(X0,or(X1,X0)))))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f307,plain,(
% 0.10/0.41 ![X0,X1]: (is_a_theorem(implies(X0,or(X1,X0)))|~sQ34_spl)),
% 0.10/0.41 inference(component_clause,[status(thm)],[f306])).
% 0.10/0.41 fof(f336,definition,(
% 0.10/0.41 sQ42_spl <=> (equivalence_2)),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f337,plain,(
% 0.10/0.41 equivalence_2|~sQ42_spl),
% 0.10/0.41 inference(component_clause,[status(thm)],[f336])).
% 0.10/0.41 fof(f339,definition,(
% 0.10/0.41 ![X0,X1]: (sQ43_spl <=> (is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f340,plain,(
% 0.10/0.41 ![X0,X1]: (is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))|~sQ43_spl)),
% 0.10/0.41 inference(component_clause,[status(thm)],[f339])).
% 0.10/0.41 fof(f343,definition,(
% 0.10/0.41 sQ44_spl <=> (is_a_theorem(implies(equiv(sK28_skl,sK29_skl),implies(sK29_skl,sK28_skl))))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f345,plain,(
% 0.10/0.41 ~is_a_theorem(implies(equiv(sK28_skl,sK29_skl),implies(sK29_skl,sK28_skl)))|sQ44_spl),
% 0.10/0.41 inference(component_clause,[status(thm)],[f343])).
% 0.10/0.41 fof(f346,plain,(
% 0.10/0.41 sQ42_spl|~sQ44_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f108,f336,f343])).
% 0.10/0.41 fof(f429,definition,(
% 0.10/0.41 sQ67_spl <=> (r2)),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f431,plain,(
% 0.10/0.41 ~r2|sQ67_spl),
% 0.10/0.41 inference(component_clause,[status(thm)],[f429])).
% 0.10/0.41 fof(f432,plain,(
% 0.10/0.41 ~sQ67_spl|sQ34_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f143,f429,f306])).
% 0.10/0.41 fof(f437,definition,(
% 0.10/0.41 sQ69_spl <=> (r3)),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f439,plain,(
% 0.10/0.41 ~r3|sQ69_spl),
% 0.10/0.41 inference(component_clause,[status(thm)],[f437])).
% 0.10/0.41 fof(f440,definition,(
% 0.10/0.41 ![X0,X1]: (sQ70_spl <=> (is_a_theorem(implies(or(X0,X1),or(X1,X0)))))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f441,plain,(
% 0.10/0.41 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),or(X1,X0)))|~sQ70_spl)),
% 0.10/0.41 inference(component_clause,[status(thm)],[f440])).
% 0.10/0.41 fof(f443,plain,(
% 0.10/0.41 ~sQ69_spl|sQ70_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f147,f437,f440])).
% 0.10/0.41 fof(f470,definition,(
% 0.10/0.41 sQ78_spl <=> (op_or)),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f472,plain,(
% 0.10/0.41 ~op_or|sQ78_spl),
% 0.10/0.41 inference(component_clause,[status(thm)],[f470])).
% 0.10/0.41 fof(f473,definition,(
% 0.10/0.41 ![X0,X1]: (sQ79_spl <=> (or(X0,X1)=not(and(not(X0),not(X1)))))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f474,plain,(
% 0.10/0.41 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1)))|~sQ79_spl)),
% 0.10/0.41 inference(component_clause,[status(thm)],[f473])).
% 0.10/0.41 fof(f476,plain,(
% 0.10/0.41 ~sQ78_spl|sQ79_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f158,f470,f473])).
% 0.10/0.41 fof(f477,definition,(
% 0.10/0.41 sQ80_spl <=> (op_and)),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f479,plain,(
% 0.10/0.41 ~op_and|sQ80_spl),
% 0.10/0.41 inference(component_clause,[status(thm)],[f477])).
% 0.10/0.41 fof(f480,definition,(
% 0.10/0.41 ![X0,X1]: (sQ81_spl <=> (and(X0,X1)=not(or(not(X0),not(X1)))))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f481,plain,(
% 0.10/0.41 ![X0,X1]: (and(X0,X1)=not(or(not(X0),not(X1)))|~sQ81_spl)),
% 0.10/0.41 inference(component_clause,[status(thm)],[f480])).
% 0.10/0.41 fof(f483,plain,(
% 0.10/0.41 ~sQ80_spl|sQ81_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f160,f477,f480])).
% 0.10/0.41 fof(f484,definition,(
% 0.10/0.41 sQ82_spl <=> (op_implies_and)),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f486,plain,(
% 0.10/0.41 ~op_implies_and|sQ82_spl),
% 0.10/0.41 inference(component_clause,[status(thm)],[f484])).
% 0.10/0.41 fof(f487,definition,(
% 0.10/0.41 ![X0,X1]: (sQ83_spl <=> (implies(X0,X1)=not(and(X0,not(X1)))))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f488,plain,(
% 0.10/0.41 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1)))|~sQ83_spl)),
% 0.10/0.41 inference(component_clause,[status(thm)],[f487])).
% 0.10/0.41 fof(f490,plain,(
% 0.10/0.41 ~sQ82_spl|sQ83_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f162,f484,f487])).
% 0.10/0.41 fof(f491,definition,(
% 0.10/0.41 sQ84_spl <=> (op_implies_or)),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f493,plain,(
% 0.10/0.41 ~op_implies_or|sQ84_spl),
% 0.10/0.41 inference(component_clause,[status(thm)],[f491])).
% 0.10/0.41 fof(f494,definition,(
% 0.10/0.41 ![X0,X1]: (sQ85_spl <=> (implies(X0,X1)=or(not(X0),X1)))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f495,plain,(
% 0.10/0.41 ![X0,X1]: (implies(X0,X1)=or(not(X0),X1)|~sQ85_spl)),
% 0.10/0.41 inference(component_clause,[status(thm)],[f494])).
% 0.10/0.41 fof(f497,plain,(
% 0.10/0.41 ~sQ84_spl|sQ85_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f164,f491,f494])).
% 0.10/0.41 fof(f498,definition,(
% 0.10/0.41 sQ86_spl <=> (op_equiv)),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f500,plain,(
% 0.10/0.41 ~op_equiv|sQ86_spl),
% 0.10/0.41 inference(component_clause,[status(thm)],[f498])).
% 0.10/0.41 fof(f501,definition,(
% 0.10/0.41 ![X0,X1]: (sQ87_spl <=> (equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f502,plain,(
% 0.10/0.41 ![X0,X1]: (equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))|~sQ87_spl)),
% 0.10/0.41 inference(component_clause,[status(thm)],[f501])).
% 0.10/0.41 fof(f504,plain,(
% 0.10/0.41 ~sQ86_spl|sQ87_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f166,f498,f501])).
% 0.10/0.41 fof(f505,plain,(
% 0.10/0.41 $false|sQ86_spl),
% 0.10/0.41 inference(forward_subsumption_resolution,[status(thm)],[f500,f169])).
% 0.10/0.41 fof(f506,plain,(
% 0.10/0.41 sQ86_spl),
% 0.10/0.41 inference(contradiction_clause,[status(thm)],[f505])).
% 0.10/0.41 fof(f507,plain,(
% 0.10/0.41 $false|sQ84_spl),
% 0.10/0.41 inference(forward_subsumption_resolution,[status(thm)],[f493,f167])).
% 0.10/0.41 fof(f508,plain,(
% 0.10/0.41 sQ84_spl),
% 0.10/0.41 inference(contradiction_clause,[status(thm)],[f507])).
% 0.10/0.41 fof(f509,plain,(
% 0.10/0.41 $false|sQ82_spl),
% 0.10/0.41 inference(forward_subsumption_resolution,[status(thm)],[f486,f178])).
% 0.10/0.41 fof(f510,plain,(
% 0.10/0.41 sQ82_spl),
% 0.10/0.41 inference(contradiction_clause,[status(thm)],[f509])).
% 0.10/0.41 fof(f511,plain,(
% 0.10/0.41 $false|sQ80_spl),
% 0.10/0.41 inference(forward_subsumption_resolution,[status(thm)],[f479,f168])).
% 0.10/0.41 fof(f512,plain,(
% 0.10/0.41 sQ80_spl),
% 0.10/0.41 inference(contradiction_clause,[status(thm)],[f511])).
% 0.10/0.41 fof(f513,plain,(
% 0.10/0.41 $false|sQ78_spl),
% 0.10/0.41 inference(forward_subsumption_resolution,[status(thm)],[f472,f177])).
% 0.10/0.41 fof(f514,plain,(
% 0.10/0.41 sQ78_spl),
% 0.10/0.41 inference(contradiction_clause,[status(thm)],[f513])).
% 0.10/0.41 fof(f530,plain,(
% 0.10/0.41 $false|~sQ43_spl|sQ44_spl),
% 0.10/0.41 inference(backward_subsumption_resolution,[status(thm)],[f345,f340])).
% 0.10/0.41 fof(f539,plain,(
% 0.10/0.41 $false|sQ0_spl),
% 0.10/0.41 inference(forward_subsumption_resolution,[status(thm)],[f183,f170])).
% 0.10/0.41 fof(f540,plain,(
% 0.10/0.41 sQ0_spl),
% 0.10/0.41 inference(contradiction_clause,[status(thm)],[f539])).
% 0.10/0.41 fof(f543,plain,(
% 0.10/0.41 ![X0,X1]: (and(X0,X1)=not(implies(X0,not(X1)))|~sQ85_spl|~sQ81_spl)),
% 0.10/0.41 inference(forward_demodulation,[status(thm)],[f495,f481])).
% 0.10/0.41 fof(f548,plain,(
% 0.10/0.41 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1)|~sQ83_spl|~sQ79_spl)),
% 0.10/0.41 inference(forward_demodulation,[status(thm)],[f488,f474])).
% 0.10/0.41 fof(f560,plain,(
% 0.10/0.41 ~sQ43_spl|sQ44_spl),
% 0.10/0.41 inference(contradiction_clause,[status(thm)],[f530])).
% 0.10/0.41 fof(f574,plain,(
% 0.10/0.41 $false|sQ69_spl),
% 0.10/0.41 inference(forward_subsumption_resolution,[status(thm)],[f439,f173])).
% 0.10/0.41 fof(f575,plain,(
% 0.10/0.41 sQ69_spl),
% 0.10/0.41 inference(contradiction_clause,[status(thm)],[f574])).
% 0.10/0.41 fof(f586,plain,(
% 0.10/0.41 $false|sQ67_spl),
% 0.10/0.41 inference(forward_subsumption_resolution,[status(thm)],[f431,f172])).
% 0.10/0.41 fof(f587,plain,(
% 0.10/0.41 sQ67_spl),
% 0.10/0.41 inference(contradiction_clause,[status(thm)],[f586])).
% 0.10/0.41 fof(f596,plain,(
% 0.10/0.41 ![X0,X1,X2]: (or(implies(X0,not(X1)),X2)=implies(and(X0,X1),X2)|~sQ83_spl|~sQ79_spl|~sQ85_spl|~sQ81_spl)),
% 0.10/0.42 inference(paramodulation,[status(thm)],[f543,f548])).
% 0.10/0.42 fof(f608,plain,(
% 0.10/0.42 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0)))|~sQ34_spl|~sQ85_spl)),
% 0.10/0.42 inference(paramodulation,[status(thm)],[f495,f307])).
% 0.10/0.42 fof(f609,plain,(
% 0.10/0.42 sQ13_spl|~sQ34_spl|~sQ85_spl),
% 0.10/0.42 inference(split_clause,[status(thm)],[f608,f229,f306,f494])).
% 0.10/0.42 fof(f630,plain,(
% 0.10/0.42 ![X0,X1]: (~is_a_theorem(or(X0,X1))|is_a_theorem(or(X1,X0))|~sQ70_spl|~sQ1_spl)),
% 0.10/0.42 inference(resolution,[status(thm)],[f441,f185])).
% 0.10/0.42 fof(f639,plain,(
% 0.10/0.42 ![X0,X1]: (is_a_theorem(or(X0,implies(X1,not(X0))))|~sQ13_spl|~sQ83_spl|~sQ79_spl)),
% 0.10/0.42 inference(paramodulation,[status(thm)],[f548,f230])).
% 0.10/0.42 fof(f736,plain,(
% 0.10/0.42 ![X0,X1]: (is_a_theorem(or(implies(X0,not(X1)),X1))|~sQ70_spl|~sQ1_spl|~sQ13_spl|~sQ83_spl|~sQ79_spl)),
% 0.10/0.42 inference(resolution,[status(thm)],[f630,f639])).
% 0.10/0.42 fof(f742,plain,(
% 0.10/0.42 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X1))|~sQ85_spl|~sQ81_spl|~sQ70_spl|~sQ1_spl|~sQ13_spl|~sQ83_spl|~sQ79_spl)),
% 0.10/0.42 inference(forward_demodulation,[status(thm)],[f596,f736])).
% 0.10/0.42 fof(f818,plain,(
% 0.10/0.42 ![X0,X1]: (is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))|~sQ85_spl|~sQ81_spl|~sQ70_spl|~sQ1_spl|~sQ13_spl|~sQ83_spl|~sQ79_spl|~sQ87_spl)),
% 0.10/0.42 inference(paramodulation,[status(thm)],[f502,f742])).
% 0.10/0.42 fof(f821,plain,(
% 0.10/0.42 sQ43_spl|~sQ85_spl|~sQ81_spl|~sQ70_spl|~sQ1_spl|~sQ13_spl|~sQ83_spl|~sQ79_spl|~sQ87_spl),
% 0.10/0.42 inference(split_clause,[status(thm)],[f818,f339,f494,f480,f440,f184,f229,f487,f473,f501])).
% 0.10/0.42 fof(f824,plain,(
% 0.10/0.42 $false|~sQ42_spl),
% 0.10/0.42 inference(forward_subsumption_resolution,[status(thm)],[f337,f180])).
% 0.10/0.42 fof(f825,plain,(
% 0.10/0.42 ~sQ42_spl),
% 0.10/0.42 inference(contradiction_clause,[status(thm)],[f824])).
% 0.10/0.42 fof(f826,plain,(
% 0.10/0.42 $false),
% 0.10/0.42 inference(sat_refutation,[status(thm)],[f187,f346,f432,f443,f476,f483,f490,f497,f504,f506,f508,f510,f512,f514,f540,f560,f575,f587,f609,f821,f825])).
% 0.10/0.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.43 % Elapsed time: 0.059671 seconds
% 0.10/0.43 % CPU time: 0.214252 seconds
% 0.10/0.43 % Total memory used: 85.552 MB
% 0.10/0.43 % Net memory used: 85.480 MB
%------------------------------------------------------------------------------