%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL541+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 : n016.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 01:10:14 PM UTC 2026
% Result : Theorem 137.38s 17.90s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL541+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
% 0.10/0.38 % Computer : n016.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 21 00:42:38 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 137.38/17.90 % Refutation found
% 137.38/17.90 % SZS status Theorem for theBenchmark: Theorem is valid
% 137.38/17.90 % SZS output start CNFRefutation for theBenchmark
% 137.38/17.90 fof(f1,axiom,(
% 137.38/17.90 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f2,axiom,(
% 137.38/17.90 ( substitution_of_equivalents<=> (! [X,Y] :( is_a_theorem(equiv(X,Y))=> X = Y ) )) ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f3,axiom,(
% 137.38/17.90 ( modus_tollens<=> (! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) )) ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f4,axiom,(
% 137.38/17.90 ( implies_1<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) )) ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f5,axiom,(
% 137.38/17.90 ( implies_2<=> (! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )) ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f8,axiom,(
% 137.38/17.90 ( and_2<=> (! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) )) ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f9,axiom,(
% 137.38/17.90 ( and_3<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) )) ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f10,axiom,(
% 137.38/17.90 ( or_1<=> (! [X,Y] : is_a_theorem(implies(X,or(X,Y))) )) ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f11,axiom,(
% 137.38/17.90 ( or_2<=> (! [X,Y] : is_a_theorem(implies(Y,or(X,Y))) )) ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f12,axiom,(
% 137.38/17.90 ( or_3<=> (! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))) )) ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f21,axiom,(
% 137.38/17.90 ( cn3<=> (! [P] : is_a_theorem(implies(implies(not(P),P),P)) )) ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f24,axiom,(
% 137.38/17.90 ( r3<=> (! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) )) ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f27,axiom,(
% 137.38/17.90 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f29,axiom,(
% 137.38/17.90 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f31,axiom,(
% 137.38/17.90 ( op_equiv=> (! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) )) ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f32,axiom,(
% 137.38/17.90 op_or ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f33,axiom,(
% 137.38/17.90 op_implies_and ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f34,axiom,(
% 137.38/17.90 op_equiv ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f35,axiom,(
% 137.38/17.90 modus_ponens ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f36,axiom,(
% 137.38/17.90 modus_tollens ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f37,axiom,(
% 137.38/17.90 implies_1 ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f38,axiom,(
% 137.38/17.90 implies_2 ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f41,axiom,(
% 137.38/17.90 and_2 ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f42,axiom,(
% 137.38/17.90 and_3 ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f43,axiom,(
% 137.38/17.90 or_1 ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f44,axiom,(
% 137.38/17.90 or_2 ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f45,axiom,(
% 137.38/17.90 or_3 ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f49,axiom,(
% 137.38/17.90 substitution_of_equivalents ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f50,axiom,(
% 137.38/17.90 ( necessitation<=> (! [X] :( is_a_theorem(X)=> is_a_theorem(necessarily(X)) ) )) ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f63,axiom,(
% 137.38/17.90 ( axiom_m1<=> (! [X,Y] : is_a_theorem(strict_implies(and(X,Y),and(Y,X))) )) ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f75,axiom,(
% 137.38/17.90 ( op_strict_implies=> (! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) )) ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f78,axiom,(
% 137.38/17.90 necessitation ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f86,axiom,(
% 137.38/17.90 op_strict_implies ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f89,conjecture,(
% 137.38/17.90 axiom_m1 ),
% 137.38/17.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 137.38/17.90 fof(f90,negated_conjecture,(
% 137.38/17.90 ~(axiom_m1 )),
% 137.38/17.90 inference(negated_conjecture,[status(cth)],[f89])).
% 137.38/17.90 fof(f91,plain,(
% 137.38/17.90 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 137.38/17.90 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 137.38/17.90 fof(f92,plain,(
% 137.38/17.90 (~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))))),
% 137.38/17.90 inference(NNF_transformation,[status(thm)],[f91])).
% 137.38/17.90 fof(f93,plain,(
% 137.38/17.90 (~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))))),
% 137.38/17.90 inference(miniscoping,[status(thm)],[f92])).
% 137.38/17.90 fof(f94,plain,(
% 137.38/17.90 (~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)))),
% 137.38/17.90 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f93])).
% 137.38/17.90 fof(f95,plain,(
% 137.38/17.90 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f94])).
% 137.38/17.90 fof(f99,plain,(
% 137.38/17.90 substitution_of_equivalents<=>(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y))),
% 137.38/17.90 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 137.38/17.90 fof(f100,plain,(
% 137.38/17.90 (~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)))),
% 137.38/17.90 inference(NNF_transformation,[status(thm)],[f99])).
% 137.38/17.90 fof(f101,plain,(
% 137.38/17.90 (~substitution_of_equivalents|(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y)))&(substitution_of_equivalents|(is_a_theorem(equiv(sK2_skl,sK3_skl))&~sK2_skl=sK3_skl))),
% 137.38/17.90 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(X,sK2_skl),skolemize(Y,sK3_skl)],[f100])).
% 137.38/17.90 fof(f102,plain,(
% 137.38/17.90 ![X0,X1]: (~substitution_of_equivalents|~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f101])).
% 137.38/17.90 fof(f105,plain,(
% 137.38/17.90 (~modus_tollens|(![X,Y]: is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))))&(modus_tollens|(?[X,Y]: ~is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))))),
% 137.38/17.90 inference(NNF_transformation,[status(thm)],[f3])).
% 137.38/17.90 fof(f106,plain,(
% 137.38/17.90 (~modus_tollens|(![X,Y]: is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))))&(modus_tollens|~is_a_theorem(implies(implies(not(sK5_skl),not(sK4_skl)),implies(sK4_skl,sK5_skl))))),
% 137.38/17.90 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(X,sK4_skl),skolemize(Y,sK5_skl)],[f105])).
% 137.38/17.90 fof(f107,plain,(
% 137.38/17.90 ![X0,X1]: (~modus_tollens|is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))))),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f106])).
% 137.38/17.90 fof(f109,plain,(
% 137.38/17.90 (~implies_1|(![X,Y]: is_a_theorem(implies(X,implies(Y,X)))))&(implies_1|(?[X,Y]: ~is_a_theorem(implies(X,implies(Y,X)))))),
% 137.38/17.90 inference(NNF_transformation,[status(thm)],[f4])).
% 137.38/17.90 fof(f110,plain,(
% 137.38/17.90 (~implies_1|(![X,Y]: is_a_theorem(implies(X,implies(Y,X)))))&(implies_1|~is_a_theorem(implies(sK6_skl,implies(sK7_skl,sK6_skl))))),
% 137.38/17.90 inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl]),skolemize(X,sK6_skl),skolemize(Y,sK7_skl)],[f109])).
% 137.38/17.90 fof(f111,plain,(
% 137.38/17.90 ![X0,X1]: (~implies_1|is_a_theorem(implies(X0,implies(X1,X0))))),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f110])).
% 137.38/17.90 fof(f113,plain,(
% 137.38/17.90 (~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)))))),
% 137.38/17.90 inference(NNF_transformation,[status(thm)],[f5])).
% 137.38/17.90 fof(f114,plain,(
% 137.38/17.90 (~implies_2|(![X,Y]: is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))))&(implies_2|~is_a_theorem(implies(implies(sK8_skl,implies(sK8_skl,sK9_skl)),implies(sK8_skl,sK9_skl))))),
% 137.38/17.90 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(X,sK8_skl),skolemize(Y,sK9_skl)],[f113])).
% 137.38/17.90 fof(f115,plain,(
% 137.38/17.90 ![X0,X1]: (~implies_2|is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f114])).
% 137.38/17.90 fof(f125,plain,(
% 137.38/17.90 (~and_2|(![X,Y]: is_a_theorem(implies(and(X,Y),Y))))&(and_2|(?[X,Y]: ~is_a_theorem(implies(and(X,Y),Y))))),
% 137.38/17.90 inference(NNF_transformation,[status(thm)],[f8])).
% 137.38/17.90 fof(f126,plain,(
% 137.38/17.90 (~and_2|(![X,Y]: is_a_theorem(implies(and(X,Y),Y))))&(and_2|~is_a_theorem(implies(and(sK15_skl,sK16_skl),sK16_skl)))),
% 137.38/17.90 inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl,sK16_skl]),skolemize(X,sK15_skl),skolemize(Y,sK16_skl)],[f125])).
% 137.38/17.90 fof(f127,plain,(
% 137.38/17.90 ![X0,X1]: (~and_2|is_a_theorem(implies(and(X0,X1),X1)))),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f126])).
% 137.38/17.90 fof(f129,plain,(
% 137.38/17.90 (~and_3|(![X,Y]: is_a_theorem(implies(X,implies(Y,and(X,Y))))))&(and_3|(?[X,Y]: ~is_a_theorem(implies(X,implies(Y,and(X,Y))))))),
% 137.38/17.90 inference(NNF_transformation,[status(thm)],[f9])).
% 137.38/17.90 fof(f130,plain,(
% 137.38/17.90 (~and_3|(![X,Y]: is_a_theorem(implies(X,implies(Y,and(X,Y))))))&(and_3|~is_a_theorem(implies(sK17_skl,implies(sK18_skl,and(sK17_skl,sK18_skl)))))),
% 137.38/17.90 inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl]),skolemize(X,sK17_skl),skolemize(Y,sK18_skl)],[f129])).
% 137.38/17.90 fof(f131,plain,(
% 137.38/17.90 ![X0,X1]: (~and_3|is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f130])).
% 137.38/17.90 fof(f133,plain,(
% 137.38/17.90 (~or_1|(![X,Y]: is_a_theorem(implies(X,or(X,Y)))))&(or_1|(?[X,Y]: ~is_a_theorem(implies(X,or(X,Y)))))),
% 137.38/17.90 inference(NNF_transformation,[status(thm)],[f10])).
% 137.38/17.90 fof(f134,plain,(
% 137.38/17.90 (~or_1|(![X,Y]: is_a_theorem(implies(X,or(X,Y)))))&(or_1|~is_a_theorem(implies(sK19_skl,or(sK19_skl,sK20_skl))))),
% 137.38/17.90 inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl,sK20_skl]),skolemize(X,sK19_skl),skolemize(Y,sK20_skl)],[f133])).
% 137.38/17.90 fof(f135,plain,(
% 137.38/17.90 ![X0,X1]: (~or_1|is_a_theorem(implies(X0,or(X0,X1))))),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f134])).
% 137.38/17.90 fof(f137,plain,(
% 137.38/17.90 (~or_2|(![X,Y]: is_a_theorem(implies(Y,or(X,Y)))))&(or_2|(?[X,Y]: ~is_a_theorem(implies(Y,or(X,Y)))))),
% 137.38/17.90 inference(NNF_transformation,[status(thm)],[f11])).
% 137.38/17.90 fof(f138,plain,(
% 137.38/17.90 (~or_2|(![X,Y]: is_a_theorem(implies(Y,or(X,Y)))))&(or_2|~is_a_theorem(implies(sK22_skl,or(sK21_skl,sK22_skl))))),
% 137.38/17.90 inference(skolemize,[status(esa),new_symbols(skolem,[sK21_skl,sK22_skl]),skolemize(X,sK21_skl),skolemize(Y,sK22_skl)],[f137])).
% 137.38/17.90 fof(f139,plain,(
% 137.38/17.90 ![X0,X1]: (~or_2|is_a_theorem(implies(X0,or(X1,X0))))),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f138])).
% 137.38/17.90 fof(f141,plain,(
% 137.38/17.90 (~or_3|(![X,Y,Z]: is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))))&(or_3|(?[X,Y,Z]: ~is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))))),
% 137.38/17.90 inference(NNF_transformation,[status(thm)],[f12])).
% 137.38/17.90 fof(f142,plain,(
% 137.38/17.90 (~or_3|(![X,Y,Z]: is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))))&(or_3|~is_a_theorem(implies(implies(sK23_skl,sK25_skl),implies(implies(sK24_skl,sK25_skl),implies(or(sK23_skl,sK24_skl),sK25_skl)))))),
% 137.38/17.90 inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl,sK24_skl,sK25_skl]),skolemize(X,sK23_skl),skolemize(Y,sK24_skl),skolemize(Z,sK25_skl)],[f141])).
% 137.38/17.90 fof(f143,plain,(
% 137.38/17.90 ![X0,X1,X2]: (~or_3|is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))))),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f142])).
% 137.38/17.90 fof(f177,plain,(
% 137.38/17.90 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|(?[P]: ~is_a_theorem(implies(implies(not(P),P),P))))),
% 137.38/17.90 inference(NNF_transformation,[status(thm)],[f21])).
% 137.38/17.90 fof(f178,plain,(
% 137.38/17.90 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|~is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl)))),
% 137.38/17.90 inference(skolemize,[status(esa),new_symbols(skolem,[sK43_skl]),skolemize(P,sK43_skl)],[f177])).
% 137.38/17.90 fof(f179,plain,(
% 137.38/17.90 ![X0]: (~cn3|is_a_theorem(implies(implies(not(X0),X0),X0)))),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f178])).
% 137.38/17.90 fof(f180,plain,(
% 137.38/17.90 cn3|~is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl))),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f178])).
% 137.38/17.90 fof(f189,plain,(
% 137.38/17.90 (~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)))))),
% 137.38/17.90 inference(NNF_transformation,[status(thm)],[f24])).
% 137.38/17.90 fof(f190,plain,(
% 137.38/17.90 (~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))))),
% 137.38/17.90 inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl]),skolemize(P,sK47_skl),skolemize(Q,sK48_skl)],[f189])).
% 137.38/17.90 fof(f191,plain,(
% 137.38/17.90 ![X0,X1]: (~r3|is_a_theorem(implies(or(X0,X1),or(X1,X0))))),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f190])).
% 137.38/17.90 fof(f192,plain,(
% 137.38/17.90 r3|~is_a_theorem(implies(or(sK47_skl,sK48_skl),or(sK48_skl,sK47_skl)))),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f190])).
% 137.38/17.90 fof(f201,plain,(
% 137.38/17.90 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 137.38/17.90 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 137.38/17.90 fof(f202,plain,(
% 137.38/17.90 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f201])).
% 137.38/17.90 fof(f205,plain,(
% 137.38/17.90 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 137.38/17.90 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 137.38/17.90 fof(f206,plain,(
% 137.38/17.90 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f205])).
% 137.38/17.90 fof(f209,plain,(
% 137.38/17.90 ~op_equiv|(![X,Y]: equiv(X,Y)=and(implies(X,Y),implies(Y,X)))),
% 137.38/17.90 inference(pre_NNF_transformation,[status(thm)],[f31])).
% 137.38/17.90 fof(f210,plain,(
% 137.38/17.90 ![X0,X1]: (~op_equiv|equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f209])).
% 137.38/17.90 fof(f211,plain,(
% 137.38/17.90 op_or),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f32])).
% 137.38/17.90 fof(f212,plain,(
% 137.38/17.90 op_implies_and),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f33])).
% 137.38/17.90 fof(f213,plain,(
% 137.38/17.90 op_equiv),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f34])).
% 137.38/17.90 fof(f214,plain,(
% 137.38/17.90 modus_ponens),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f35])).
% 137.38/17.90 fof(f215,plain,(
% 137.38/17.90 modus_tollens),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f36])).
% 137.38/17.90 fof(f216,plain,(
% 137.38/17.90 implies_1),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f37])).
% 137.38/17.90 fof(f217,plain,(
% 137.38/17.90 implies_2),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f38])).
% 137.38/17.90 fof(f220,plain,(
% 137.38/17.90 and_2),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f41])).
% 137.38/17.90 fof(f221,plain,(
% 137.38/17.90 and_3),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f42])).
% 137.38/17.90 fof(f222,plain,(
% 137.38/17.90 or_1),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f43])).
% 137.38/17.90 fof(f223,plain,(
% 137.38/17.90 or_2),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f44])).
% 137.38/17.90 fof(f224,plain,(
% 137.38/17.90 or_3),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f45])).
% 137.38/17.90 fof(f228,plain,(
% 137.38/17.90 substitution_of_equivalents),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f49])).
% 137.38/17.90 fof(f229,plain,(
% 137.38/17.90 necessitation<=>(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X))))),
% 137.38/17.90 inference(pre_NNF_transformation,[status(thm)],[f50])).
% 137.38/17.90 fof(f230,plain,(
% 137.38/17.90 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(?[X]: (is_a_theorem(X)&~is_a_theorem(necessarily(X)))))),
% 137.38/17.90 inference(NNF_transformation,[status(thm)],[f229])).
% 137.38/17.90 fof(f231,plain,(
% 137.38/17.90 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(is_a_theorem(sK55_skl)&~is_a_theorem(necessarily(sK55_skl))))),
% 137.38/17.90 inference(skolemize,[status(esa),new_symbols(skolem,[sK55_skl]),skolemize(X,sK55_skl)],[f230])).
% 137.38/17.90 fof(f232,plain,(
% 137.38/17.90 ![X0]: (~necessitation|~is_a_theorem(X0)|is_a_theorem(necessarily(X0)))),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f231])).
% 137.38/17.90 fof(f292,plain,(
% 137.38/17.90 (~axiom_m1|(![X,Y]: is_a_theorem(strict_implies(and(X,Y),and(Y,X)))))&(axiom_m1|(?[X,Y]: ~is_a_theorem(strict_implies(and(X,Y),and(Y,X)))))),
% 137.38/17.90 inference(NNF_transformation,[status(thm)],[f63])).
% 137.38/17.90 fof(f293,plain,(
% 137.38/17.90 (~axiom_m1|(![X,Y]: is_a_theorem(strict_implies(and(X,Y),and(Y,X)))))&(axiom_m1|~is_a_theorem(strict_implies(and(sK76_skl,sK77_skl),and(sK77_skl,sK76_skl))))),
% 137.38/17.90 inference(skolemize,[status(esa),new_symbols(skolem,[sK76_skl,sK77_skl]),skolemize(X,sK76_skl),skolemize(Y,sK77_skl)],[f292])).
% 137.38/17.90 fof(f295,plain,(
% 137.38/17.90 axiom_m1|~is_a_theorem(strict_implies(and(sK76_skl,sK77_skl),and(sK77_skl,sK76_skl)))),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f293])).
% 137.38/17.90 fof(f336,plain,(
% 137.38/17.90 ~op_strict_implies|(![X,Y]: strict_implies(X,Y)=necessarily(implies(X,Y)))),
% 137.38/17.90 inference(pre_NNF_transformation,[status(thm)],[f75])).
% 137.38/17.90 fof(f337,plain,(
% 137.38/17.90 ![X0,X1]: (~op_strict_implies|strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f336])).
% 137.38/17.90 fof(f341,plain,(
% 137.38/17.90 necessitation),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f78])).
% 137.38/17.90 fof(f349,plain,(
% 137.38/17.90 op_strict_implies),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f86])).
% 137.38/17.90 fof(f352,plain,(
% 137.38/17.90 ~axiom_m1),
% 137.38/17.90 inference(cnf_transformation,[status(thm)],[f90])).
% 137.38/17.90 fof(f353,plain,(
% 137.38/17.90 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1))))),
% 137.38/17.90 inference(backward_subsumption_resolution,[status(thm)],[f202,f211])).
% 137.38/17.90 fof(f354,plain,(
% 137.38/17.90 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1))))),
% 137.38/17.90 inference(backward_subsumption_resolution,[status(thm)],[f206,f212])).
% 137.38/17.90 fof(f355,plain,(
% 137.38/17.90 ![X0,X1]: (equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 137.38/17.90 inference(backward_subsumption_resolution,[status(thm)],[f210,f213])).
% 137.38/17.90 fof(f356,plain,(
% 137.38/17.90 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 137.38/17.90 inference(backward_subsumption_resolution,[status(thm)],[f95,f214])).
% 137.38/17.90 fof(f357,plain,(
% 137.38/17.90 ![X0,X1]: (is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))))),
% 137.38/17.90 inference(backward_subsumption_resolution,[status(thm)],[f107,f215])).
% 137.38/17.90 fof(f358,plain,(
% 137.38/17.90 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0))))),
% 137.38/17.90 inference(backward_subsumption_resolution,[status(thm)],[f111,f216])).
% 137.38/17.90 fof(f359,plain,(
% 137.38/17.90 ![X0,X1]: (is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 137.38/17.90 inference(backward_subsumption_resolution,[status(thm)],[f115,f217])).
% 137.38/17.90 fof(f362,plain,(
% 137.38/17.90 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X1)))),
% 137.38/17.90 inference(backward_subsumption_resolution,[status(thm)],[f127,f220])).
% 137.38/17.90 fof(f363,plain,(
% 137.38/17.90 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 137.38/17.90 inference(backward_subsumption_resolution,[status(thm)],[f131,f221])).
% 137.38/17.90 fof(f364,plain,(
% 137.38/17.90 ![X0,X1]: (is_a_theorem(implies(X0,or(X0,X1))))),
% 137.38/17.90 inference(backward_subsumption_resolution,[status(thm)],[f135,f222])).
% 137.38/17.90 fof(f365,plain,(
% 137.38/17.90 ![X0,X1]: (is_a_theorem(implies(X0,or(X1,X0))))),
% 137.38/17.90 inference(backward_subsumption_resolution,[status(thm)],[f139,f223])).
% 137.38/17.90 fof(f366,plain,(
% 137.38/17.90 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))))),
% 137.38/17.90 inference(backward_subsumption_resolution,[status(thm)],[f143,f224])).
% 137.38/17.90 fof(f370,plain,(
% 137.38/17.90 ![X0,X1]: (~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 137.38/17.90 inference(backward_subsumption_resolution,[status(thm)],[f102,f228])).
% 137.38/17.90 fof(f372,plain,(
% 137.38/17.90 ![X0]: (~is_a_theorem(X0)|is_a_theorem(necessarily(X0)))),
% 137.38/17.90 inference(backward_subsumption_resolution,[status(thm)],[f232,f341])).
% 137.38/17.90 fof(f377,plain,(
% 137.38/17.90 ![X0,X1]: (strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 137.38/17.90 inference(backward_subsumption_resolution,[status(thm)],[f337,f349])).
% 137.38/17.90 fof(f379,plain,(
% 137.38/17.90 ~is_a_theorem(strict_implies(and(sK76_skl,sK77_skl),and(sK77_skl,sK76_skl)))),
% 137.38/17.90 inference(backward_subsumption_resolution,[status(thm)],[f295,f352])).
% 137.38/17.90 fof(f380,plain,(
% 137.38/17.90 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1))),
% 137.38/17.90 inference(backward_demodulation,[status(thm)],[f354,f353])).
% 137.38/17.90 fof(f387,plain,(
% 137.38/17.90 cn3|~is_a_theorem(implies(or(sK43_skl,sK43_skl),sK43_skl))),
% 137.38/17.90 inference(backward_demodulation,[status(thm)],[f380,f180])).
% 137.38/17.90 fof(f391,plain,(
% 137.38/17.90 ![X0,X1]: (is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))))),
% 137.38/17.90 inference(backward_demodulation,[status(thm)],[f380,f357])).
% 137.38/17.90 fof(f392,plain,(
% 137.38/17.90 ![X0]: (~cn3|is_a_theorem(implies(or(X0,X0),X0)))),
% 137.38/17.90 inference(backward_demodulation,[status(thm)],[f380,f179])).
% 137.38/17.90 fof(f402,plain,(
% 137.38/17.90 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(strict_implies(X0,X1)))),
% 137.38/17.90 inference(paramodulation,[status(thm)],[f377,f372])).
% 137.38/17.90 fof(f408,plain,(
% 137.38/17.90 ![X0,X1]: (strict_implies(not(X0),X1)=necessarily(or(X0,X1)))),
% 137.38/17.90 inference(paramodulation,[status(thm)],[f380,f377])).
% 137.38/17.90 fof(f417,plain,(
% 137.38/17.90 ![X0,X1,X2]: (implies(X0,and(X1,not(X2)))=not(and(X0,implies(X1,X2))))),
% 137.38/17.90 inference(paramodulation,[status(thm)],[f354,f354])).
% 137.38/17.90 fof(f422,plain,(
% 137.38/17.90 ![X0,X1,X2]: (or(and(X0,not(X1)),X2)=implies(implies(X0,X1),X2))),
% 137.38/17.90 inference(paramodulation,[status(thm)],[f354,f380])).
% 137.38/17.90 fof(f452,plain,(
% 137.38/17.90 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(implies(X1,and(X0,X1))))),
% 137.38/17.90 inference(resolution,[status(thm)],[f363,f356])).
% 137.38/17.90 fof(f514,plain,(
% 137.38/17.90 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(X1)|is_a_theorem(and(X0,X1)))),
% 137.38/17.90 inference(resolution,[status(thm)],[f452,f356])).
% 137.38/17.90 fof(f564,plain,(
% 137.38/17.90 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X0))|is_a_theorem(equiv(X0,X1)))),
% 137.38/17.90 inference(paramodulation,[status(thm)],[f355,f514])).
% 137.38/17.90 fof(f591,plain,(
% 137.38/17.90 ![X0,X1]: (~is_a_theorem(implies(X0,implies(X0,X1)))|is_a_theorem(implies(X0,X1)))),
% 137.38/17.90 inference(resolution,[status(thm)],[f359,f356])).
% 137.38/17.90 fof(f621,plain,(
% 137.38/17.90 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(implies(X2,X1),implies(or(X0,X2),X1))))),
% 137.38/17.90 inference(resolution,[status(thm)],[f366,f356])).
% 137.38/17.90 fof(f628,plain,(
% 137.38/17.90 ![X0,X1]: (is_a_theorem(strict_implies(or(X0,not(X1)),implies(X1,X0))))),
% 137.38/17.90 inference(resolution,[status(thm)],[f391,f402])).
% 137.38/17.90 fof(f1076,plain,(
% 137.38/17.90 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),implies(or(X0,X0),X1))))),
% 137.38/17.90 inference(resolution,[status(thm)],[f591,f366])).
% 137.38/17.90 fof(f1078,plain,(
% 137.38/17.90 ![X0]: (is_a_theorem(implies(X0,and(X0,X0))))),
% 137.38/17.90 inference(resolution,[status(thm)],[f591,f363])).
% 137.38/17.90 fof(f1079,plain,(
% 137.38/17.90 ![X0]: (is_a_theorem(implies(X0,X0)))),
% 137.38/17.90 inference(resolution,[status(thm)],[f591,f358])).
% 137.38/17.90 fof(f1385,plain,(
% 137.38/17.90 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(or(X0,X0),X1)))),
% 137.38/17.90 inference(resolution,[status(thm)],[f1076,f356])).
% 137.38/17.90 fof(f1419,plain,(
% 137.38/17.90 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X2,X1))|is_a_theorem(implies(or(X0,X2),X1)))),
% 137.38/17.90 inference(resolution,[status(thm)],[f621,f356])).
% 137.38/17.90 fof(f1594,plain,(
% 137.38/17.90 ~is_a_theorem(implies(sK43_skl,sK43_skl))|cn3),
% 137.38/17.90 inference(resolution,[status(thm)],[f1385,f387])).
% 137.38/17.90 fof(f1603,plain,(
% 137.38/17.90 ![X0]: (is_a_theorem(implies(or(X0,X0),X0)))),
% 137.38/17.90 inference(backward_subsumption_resolution,[status(thm)],[f392,f1604])).
% 137.38/17.90 fof(f1604,plain,(
% 137.38/17.90 cn3),
% 137.38/17.90 inference(forward_subsumption_resolution,[status(thm)],[f1594,f1079])).
% 137.38/17.90 fof(f10995,plain,(
% 137.38/17.90 ~is_a_theorem(implies(sK47_skl,or(sK48_skl,sK47_skl)))|~is_a_theorem(implies(sK48_skl,or(sK48_skl,sK47_skl)))|r3),
% 137.38/17.90 inference(resolution,[status(thm)],[f1419,f192])).
% 137.38/17.90 fof(f11011,plain,(
% 137.38/17.90 ~is_a_theorem(implies(sK48_skl,or(sK48_skl,sK47_skl)))|r3),
% 137.38/17.90 inference(forward_subsumption_resolution,[status(thm)],[f10995,f365])).
% 137.38/17.90 fof(f11023,plain,(
% 137.38/17.90 r3),
% 137.38/17.90 inference(resolution,[status(thm)],[f11011,f364])).
% 137.38/17.90 fof(f11027,plain,(
% 137.38/17.90 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),or(X1,X0))))),
% 137.38/17.90 inference(backward_subsumption_resolution,[status(thm)],[f191,f11023])).
% 137.38/17.90 fof(f17865,plain,(
% 137.38/17.90 ![X0,X1]: (~is_a_theorem(implies(or(X0,X1),or(X1,X0)))|is_a_theorem(equiv(or(X0,X1),or(X1,X0))))),
% 137.38/17.90 inference(resolution,[status(thm)],[f564,f11027])).
% 137.38/17.90 fof(f17874,plain,(
% 137.38/17.90 ![X0]: (~is_a_theorem(implies(X0,or(X0,X0)))|is_a_theorem(equiv(X0,or(X0,X0))))),
% 137.38/17.90 inference(resolution,[status(thm)],[f564,f1603])).
% 137.38/17.90 fof(f18011,plain,(
% 137.38/17.90 ![X0]: (~is_a_theorem(implies(and(X0,X0),X0))|is_a_theorem(equiv(and(X0,X0),X0)))),
% 137.38/17.90 inference(resolution,[status(thm)],[f564,f1078])).
% 137.38/17.90 fof(f18048,plain,(
% 137.38/17.90 ![X0,X1]: (is_a_theorem(equiv(or(X0,X1),or(X1,X0))))),
% 137.38/17.90 inference(forward_subsumption_resolution,[status(thm)],[f17865,f11027])).
% 137.38/17.90 fof(f18050,plain,(
% 137.38/17.90 ![X0]: (is_a_theorem(equiv(X0,or(X0,X0))))),
% 137.38/17.90 inference(forward_subsumption_resolution,[status(thm)],[f17874,f365])).
% 137.38/17.90 fof(f18129,plain,(
% 137.38/17.90 ![X0]: (is_a_theorem(equiv(and(X0,X0),X0)))),
% 137.38/17.90 inference(forward_subsumption_resolution,[status(thm)],[f18011,f362])).
% 137.38/17.90 fof(f18147,plain,(
% 137.38/17.90 ![X0]: (X0=or(X0,X0))),
% 137.38/17.90 inference(resolution,[status(thm)],[f18050,f370])).
% 80.01/18.08 fof(f18495,plain,(
% 80.01/18.08 ![X0]: (and(X0,X0)=X0)),
% 80.01/18.08 inference(resolution,[status(thm)],[f18129,f370])).
% 80.01/18.08 fof(f19743,plain,(
% 80.01/18.08 ![X0,X1]: (or(not(X0),X1)=implies(implies(not(X0),X0),X1))),
% 80.01/18.08 inference(paramodulation,[status(thm)],[f18495,f422])).
% 80.01/18.08 fof(f19746,plain,(
% 80.01/18.08 ![X0,X1]: (implies(X0,not(X1))=not(and(X0,implies(not(X1),X1))))),
% 80.01/18.08 inference(paramodulation,[status(thm)],[f18495,f417])).
% 80.01/18.08 fof(f20732,plain,(
% 80.01/18.08 ![X0,X1]: (or(not(X0),X1)=implies(or(X0,X0),X1))),
% 80.01/18.08 inference(forward_demodulation,[status(thm)],[f380,f19743])).
% 80.01/18.08 fof(f20833,plain,(
% 80.01/18.08 ![X0,X1]: (or(not(X0),X1)=implies(X0,X1))),
% 80.01/18.08 inference(forward_demodulation,[status(thm)],[f18147,f20732])).
% 80.01/18.08 fof(f20834,plain,(
% 80.01/18.08 ![X0,X1]: (implies(X0,not(X1))=not(and(X0,or(X1,X1))))),
% 80.01/18.08 inference(forward_demodulation,[status(thm)],[f380,f19746])).
% 80.01/18.08 fof(f21146,plain,(
% 80.01/18.08 ![X0,X1]: (implies(X0,not(X1))=not(and(X0,X1)))),
% 80.01/18.08 inference(forward_demodulation,[status(thm)],[f18147,f20834])).
% 80.01/18.08 fof(f23668,plain,(
% 80.01/18.08 ![X0,X1]: (is_a_theorem(strict_implies(implies(X0,not(X1)),implies(X1,not(X0)))))),
% 80.01/18.08 inference(paramodulation,[status(thm)],[f20833,f628])).
% 80.01/18.08 fof(f24065,plain,(
% 80.01/18.08 ![X0,X1]: (is_a_theorem(strict_implies(not(and(X0,X1)),implies(X1,not(X0)))))),
% 80.01/18.08 inference(forward_demodulation,[status(thm)],[f21146,f23668])).
% 80.01/18.08 fof(f24066,plain,(
% 80.01/18.08 ![X0,X1]: (is_a_theorem(strict_implies(not(and(X0,X1)),not(and(X1,X0)))))),
% 80.01/18.08 inference(forward_demodulation,[status(thm)],[f21146,f24065])).
% 80.01/18.08 fof(f25305,plain,(
% 80.01/18.08 ![X0,X1]: (or(X0,X1)=or(X1,X0))),
% 80.01/18.08 inference(resolution,[status(thm)],[f18048,f370])).
% 80.01/18.08 fof(f25459,plain,(
% 80.01/18.08 ![X0,X1]: (implies(X0,X1)=or(X1,not(X0)))),
% 80.01/18.08 inference(paramodulation,[status(thm)],[f20833,f25305])).
% 80.01/18.08 fof(f27295,plain,(
% 80.01/18.08 ![X0,X1]: (strict_implies(not(X0),not(X1))=necessarily(implies(X1,X0)))),
% 80.01/18.08 inference(paramodulation,[status(thm)],[f25459,f408])).
% 80.01/18.08 fof(f27413,plain,(
% 80.01/18.08 ![X0,X1]: (is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))))),
% 80.01/18.08 inference(backward_demodulation,[status(thm)],[f27422,f24066])).
% 80.01/18.08 fof(f27422,plain,(
% 80.01/18.08 ![X0,X1]: (strict_implies(not(X0),not(X1))=strict_implies(X1,X0))),
% 80.01/18.08 inference(forward_demodulation,[status(thm)],[f377,f27295])).
% 80.01/18.08 fof(f27445,plain,(
% 80.01/18.08 $false),
% 80.01/18.08 inference(backward_subsumption_resolution,[status(thm)],[f379,f27413])).
% 80.01/18.08 % SZS output end CNFRefutation for theBenchmark.p
% 11.29/18.17 % Elapsed time: 17.772624 seconds
% 11.29/18.17 % CPU time: 140.322456 seconds
% 11.29/18.17 % Total memory used: 1.328 GB
% 11.29/18.17 % Net memory used: 1.248 GB
%------------------------------------------------------------------------------