%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL537+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 12.30s 1.96s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL537+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.02 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.30 % Computer : n012.cluster.edu
% 0.06/0.30 % Model : x86_64 x86_64
% 0.06/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.30 % Memory : 8046.5625MB
% 0.06/0.30 % OS : Linux 6.8.0-71-generic
% 0.06/0.30 % CPULimit : 300
% 0.06/0.30 % WCLimit : 300
% 0.06/0.30 % DateTime : Mon Sep 21 00:37:07 UTC 2026
% 0.06/0.30 % CPUTime :
% 0.06/0.31 % Drodi V4.1.1
% 12.30/1.96 % Refutation found
% 12.30/1.96 % SZS status Theorem for theBenchmark: Theorem is valid
% 12.30/1.96 % SZS output start CNFRefutation for theBenchmark
% 12.30/1.96 fof(f1,axiom,(
% 12.30/1.96 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f2,axiom,(
% 12.30/1.96 ( substitution_of_equivalents<=> (! [X,Y] :( is_a_theorem(equiv(X,Y))=> X = Y ) )) ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f4,axiom,(
% 12.30/1.96 ( implies_1<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) )) ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f5,axiom,(
% 12.30/1.96 ( implies_2<=> (! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )) ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f7,axiom,(
% 12.30/1.96 ( and_1<=> (! [X,Y] : is_a_theorem(implies(and(X,Y),X)) )) ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f9,axiom,(
% 12.30/1.96 ( and_3<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) )) ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f11,axiom,(
% 12.30/1.96 ( or_2<=> (! [X,Y] : is_a_theorem(implies(Y,or(X,Y))) )) ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f12,axiom,(
% 12.30/1.96 ( or_3<=> (! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))) )) ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f15,axiom,(
% 12.30/1.96 ( equivalence_3<=> (! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) )) ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f21,axiom,(
% 12.30/1.96 ( cn3<=> (! [P] : is_a_theorem(implies(implies(not(P),P),P)) )) ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f27,axiom,(
% 12.30/1.96 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f29,axiom,(
% 12.30/1.96 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f32,axiom,(
% 12.30/1.96 op_or ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f33,axiom,(
% 12.30/1.96 op_implies_and ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f35,axiom,(
% 12.30/1.96 modus_ponens ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f37,axiom,(
% 12.30/1.96 implies_1 ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f38,axiom,(
% 12.30/1.96 implies_2 ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f40,axiom,(
% 12.30/1.96 and_1 ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f42,axiom,(
% 12.30/1.96 and_3 ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f44,axiom,(
% 12.30/1.96 or_2 ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f45,axiom,(
% 12.30/1.96 or_3 ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f48,axiom,(
% 12.30/1.96 equivalence_3 ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f49,axiom,(
% 12.30/1.96 substitution_of_equivalents ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f55,axiom,(
% 12.30/1.96 ( axiom_M<=> (! [X] : is_a_theorem(implies(necessarily(X),X)) )) ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f56,axiom,(
% 12.30/1.96 ( axiom_4<=> (! [X] : is_a_theorem(implies(necessarily(X),necessarily(necessarily(X)))) )) ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f57,axiom,(
% 12.30/1.96 ( axiom_B<=> (! [X] : is_a_theorem(implies(X,necessarily(possibly(X)))) )) ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f58,axiom,(
% 12.30/1.96 ( axiom_5<=> (! [X] : is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) )) ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f73,axiom,(
% 12.30/1.96 ( op_possibly=> (! [X] : possibly(X) = not(necessarily(not(X))) )) ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f77,axiom,(
% 12.30/1.96 op_possibly ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f80,axiom,(
% 12.30/1.96 axiom_M ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f81,axiom,(
% 12.30/1.96 axiom_4 ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f82,axiom,(
% 12.30/1.96 axiom_B ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f83,conjecture,(
% 12.30/1.96 axiom_5 ),
% 12.30/1.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.30/1.96 fof(f84,negated_conjecture,(
% 12.30/1.96 ~(axiom_5 )),
% 12.30/1.96 inference(negated_conjecture,[status(cth)],[f83])).
% 12.30/1.96 fof(f85,plain,(
% 12.30/1.96 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 12.30/1.96 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 12.30/1.96 fof(f86,plain,(
% 12.30/1.96 (~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))))),
% 12.30/1.96 inference(NNF_transformation,[status(thm)],[f85])).
% 12.30/1.96 fof(f87,plain,(
% 12.30/1.96 (~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))))),
% 12.30/1.96 inference(miniscoping,[status(thm)],[f86])).
% 12.30/1.96 fof(f88,plain,(
% 12.30/1.96 (~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)))),
% 12.30/1.96 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f87])).
% 12.30/1.96 fof(f89,plain,(
% 12.30/1.96 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f88])).
% 12.30/1.96 fof(f93,plain,(
% 12.30/1.96 substitution_of_equivalents<=>(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y))),
% 12.30/1.96 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 12.30/1.96 fof(f94,plain,(
% 12.30/1.96 (~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)))),
% 12.30/1.96 inference(NNF_transformation,[status(thm)],[f93])).
% 12.30/1.96 fof(f95,plain,(
% 12.30/1.96 (~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))),
% 12.30/1.96 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(X,sK2_skl),skolemize(Y,sK3_skl)],[f94])).
% 12.30/1.96 fof(f96,plain,(
% 12.30/1.96 ![X0,X1]: (~substitution_of_equivalents|~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f95])).
% 12.30/1.96 fof(f103,plain,(
% 12.30/1.96 (~implies_1|(![X,Y]: is_a_theorem(implies(X,implies(Y,X)))))&(implies_1|(?[X,Y]: ~is_a_theorem(implies(X,implies(Y,X)))))),
% 12.30/1.96 inference(NNF_transformation,[status(thm)],[f4])).
% 12.30/1.96 fof(f104,plain,(
% 12.30/1.96 (~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))))),
% 12.30/1.96 inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl]),skolemize(X,sK6_skl),skolemize(Y,sK7_skl)],[f103])).
% 12.30/1.96 fof(f105,plain,(
% 12.30/1.96 ![X0,X1]: (~implies_1|is_a_theorem(implies(X0,implies(X1,X0))))),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f104])).
% 12.30/1.96 fof(f107,plain,(
% 12.30/1.96 (~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)))))),
% 12.30/1.96 inference(NNF_transformation,[status(thm)],[f5])).
% 12.30/1.96 fof(f108,plain,(
% 12.30/1.96 (~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))))),
% 12.30/1.96 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(X,sK8_skl),skolemize(Y,sK9_skl)],[f107])).
% 12.30/1.96 fof(f109,plain,(
% 12.30/1.96 ![X0,X1]: (~implies_2|is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f108])).
% 12.30/1.96 fof(f115,plain,(
% 12.30/1.96 (~and_1|(![X,Y]: is_a_theorem(implies(and(X,Y),X))))&(and_1|(?[X,Y]: ~is_a_theorem(implies(and(X,Y),X))))),
% 12.30/1.96 inference(NNF_transformation,[status(thm)],[f7])).
% 12.30/1.96 fof(f116,plain,(
% 12.30/1.96 (~and_1|(![X,Y]: is_a_theorem(implies(and(X,Y),X))))&(and_1|~is_a_theorem(implies(and(sK13_skl,sK14_skl),sK13_skl)))),
% 12.30/1.96 inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(X,sK13_skl),skolemize(Y,sK14_skl)],[f115])).
% 12.30/1.96 fof(f117,plain,(
% 12.30/1.96 ![X0,X1]: (~and_1|is_a_theorem(implies(and(X0,X1),X0)))),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f116])).
% 12.30/1.96 fof(f123,plain,(
% 12.30/1.96 (~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))))))),
% 12.30/1.96 inference(NNF_transformation,[status(thm)],[f9])).
% 12.30/1.96 fof(f124,plain,(
% 12.30/1.96 (~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)))))),
% 12.30/1.96 inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl]),skolemize(X,sK17_skl),skolemize(Y,sK18_skl)],[f123])).
% 12.30/1.96 fof(f125,plain,(
% 12.30/1.96 ![X0,X1]: (~and_3|is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f124])).
% 12.30/1.96 fof(f131,plain,(
% 12.30/1.96 (~or_2|(![X,Y]: is_a_theorem(implies(Y,or(X,Y)))))&(or_2|(?[X,Y]: ~is_a_theorem(implies(Y,or(X,Y)))))),
% 12.30/1.96 inference(NNF_transformation,[status(thm)],[f11])).
% 12.30/1.96 fof(f132,plain,(
% 12.30/1.96 (~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))))),
% 12.30/1.96 inference(skolemize,[status(esa),new_symbols(skolem,[sK21_skl,sK22_skl]),skolemize(X,sK21_skl),skolemize(Y,sK22_skl)],[f131])).
% 12.30/1.96 fof(f133,plain,(
% 12.30/1.96 ![X0,X1]: (~or_2|is_a_theorem(implies(X0,or(X1,X0))))),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f132])).
% 12.30/1.96 fof(f135,plain,(
% 12.30/1.96 (~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))))))),
% 12.30/1.96 inference(NNF_transformation,[status(thm)],[f12])).
% 12.30/1.96 fof(f136,plain,(
% 12.30/1.96 (~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)))))),
% 12.30/1.96 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)],[f135])).
% 12.30/1.96 fof(f137,plain,(
% 12.30/1.96 ![X0,X1,X2]: (~or_3|is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))))),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f136])).
% 12.30/1.96 fof(f147,plain,(
% 12.30/1.96 (~equivalence_3|(![X,Y]: is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))))&(equivalence_3|(?[X,Y]: ~is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))))),
% 12.30/1.96 inference(NNF_transformation,[status(thm)],[f15])).
% 12.30/1.96 fof(f148,plain,(
% 12.30/1.96 (~equivalence_3|(![X,Y]: is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))))&(equivalence_3|~is_a_theorem(implies(implies(sK30_skl,sK31_skl),implies(implies(sK31_skl,sK30_skl),equiv(sK30_skl,sK31_skl)))))),
% 12.30/1.96 inference(skolemize,[status(esa),new_symbols(skolem,[sK30_skl,sK31_skl]),skolemize(X,sK30_skl),skolemize(Y,sK31_skl)],[f147])).
% 12.30/1.96 fof(f149,plain,(
% 12.30/1.96 ![X0,X1]: (~equivalence_3|is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))))),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f148])).
% 12.30/1.96 fof(f171,plain,(
% 12.30/1.96 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|(?[P]: ~is_a_theorem(implies(implies(not(P),P),P))))),
% 12.30/1.96 inference(NNF_transformation,[status(thm)],[f21])).
% 12.30/1.96 fof(f172,plain,(
% 12.30/1.96 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|~is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl)))),
% 12.30/1.96 inference(skolemize,[status(esa),new_symbols(skolem,[sK43_skl]),skolemize(P,sK43_skl)],[f171])).
% 12.30/1.96 fof(f173,plain,(
% 12.30/1.96 ![X0]: (~cn3|is_a_theorem(implies(implies(not(X0),X0),X0)))),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f172])).
% 12.30/1.96 fof(f174,plain,(
% 12.30/1.96 cn3|~is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl))),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f172])).
% 12.30/1.96 fof(f195,plain,(
% 12.30/1.96 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 12.30/1.96 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 12.30/1.96 fof(f196,plain,(
% 12.30/1.96 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f195])).
% 12.30/1.96 fof(f199,plain,(
% 12.30/1.96 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 12.30/1.96 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 12.30/1.96 fof(f200,plain,(
% 12.30/1.96 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f199])).
% 12.30/1.96 fof(f205,plain,(
% 12.30/1.96 op_or),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f32])).
% 12.30/1.96 fof(f206,plain,(
% 12.30/1.96 op_implies_and),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f33])).
% 12.30/1.96 fof(f208,plain,(
% 12.30/1.96 modus_ponens),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f35])).
% 12.30/1.96 fof(f210,plain,(
% 12.30/1.96 implies_1),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f37])).
% 12.30/1.96 fof(f211,plain,(
% 12.30/1.96 implies_2),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f38])).
% 12.30/1.96 fof(f213,plain,(
% 12.30/1.96 and_1),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f40])).
% 12.30/1.96 fof(f215,plain,(
% 12.30/1.96 and_3),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f42])).
% 12.30/1.96 fof(f217,plain,(
% 12.30/1.96 or_2),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f44])).
% 12.30/1.96 fof(f218,plain,(
% 12.30/1.96 or_3),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f45])).
% 12.30/1.96 fof(f221,plain,(
% 12.30/1.96 equivalence_3),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f48])).
% 12.30/1.96 fof(f222,plain,(
% 12.30/1.96 substitution_of_equivalents),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f49])).
% 12.30/1.96 fof(f254,plain,(
% 12.30/1.96 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|(?[X]: ~is_a_theorem(implies(necessarily(X),X))))),
% 12.30/1.96 inference(NNF_transformation,[status(thm)],[f55])).
% 12.30/1.96 fof(f255,plain,(
% 12.30/1.96 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|~is_a_theorem(implies(necessarily(sK64_skl),sK64_skl)))),
% 12.30/1.96 inference(skolemize,[status(esa),new_symbols(skolem,[sK64_skl]),skolemize(X,sK64_skl)],[f254])).
% 12.30/1.96 fof(f256,plain,(
% 12.30/1.96 ![X0]: (~axiom_M|is_a_theorem(implies(necessarily(X0),X0)))),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f255])).
% 12.30/1.96 fof(f258,plain,(
% 12.30/1.96 (~axiom_4|(![X]: is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))))&(axiom_4|(?[X]: ~is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))))),
% 12.30/1.96 inference(NNF_transformation,[status(thm)],[f56])).
% 12.30/1.96 fof(f259,plain,(
% 12.30/1.96 (~axiom_4|(![X]: is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))))&(axiom_4|~is_a_theorem(implies(necessarily(sK65_skl),necessarily(necessarily(sK65_skl)))))),
% 12.30/1.96 inference(skolemize,[status(esa),new_symbols(skolem,[sK65_skl]),skolemize(X,sK65_skl)],[f258])).
% 12.30/1.96 fof(f260,plain,(
% 12.30/1.96 ![X0]: (~axiom_4|is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))))),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f259])).
% 12.30/1.96 fof(f262,plain,(
% 12.30/1.96 (~axiom_B|(![X]: is_a_theorem(implies(X,necessarily(possibly(X))))))&(axiom_B|(?[X]: ~is_a_theorem(implies(X,necessarily(possibly(X))))))),
% 12.30/1.96 inference(NNF_transformation,[status(thm)],[f57])).
% 12.30/1.96 fof(f263,plain,(
% 12.30/1.96 (~axiom_B|(![X]: is_a_theorem(implies(X,necessarily(possibly(X))))))&(axiom_B|~is_a_theorem(implies(sK66_skl,necessarily(possibly(sK66_skl)))))),
% 12.30/1.96 inference(skolemize,[status(esa),new_symbols(skolem,[sK66_skl]),skolemize(X,sK66_skl)],[f262])).
% 12.30/1.96 fof(f264,plain,(
% 12.30/1.96 ![X0]: (~axiom_B|is_a_theorem(implies(X0,necessarily(possibly(X0)))))),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f263])).
% 12.30/1.96 fof(f266,plain,(
% 12.30/1.96 (~axiom_5|(![X]: is_a_theorem(implies(possibly(X),necessarily(possibly(X))))))&(axiom_5|(?[X]: ~is_a_theorem(implies(possibly(X),necessarily(possibly(X))))))),
% 12.30/1.96 inference(NNF_transformation,[status(thm)],[f58])).
% 12.30/1.96 fof(f267,plain,(
% 12.30/1.96 (~axiom_5|(![X]: is_a_theorem(implies(possibly(X),necessarily(possibly(X))))))&(axiom_5|~is_a_theorem(implies(possibly(sK67_skl),necessarily(possibly(sK67_skl)))))),
% 12.30/1.96 inference(skolemize,[status(esa),new_symbols(skolem,[sK67_skl]),skolemize(X,sK67_skl)],[f266])).
% 12.30/1.96 fof(f269,plain,(
% 12.30/1.96 axiom_5|~is_a_theorem(implies(possibly(sK67_skl),necessarily(possibly(sK67_skl))))),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f267])).
% 12.30/1.96 fof(f326,plain,(
% 12.30/1.96 ~op_possibly|(![X]: possibly(X)=not(necessarily(not(X))))),
% 12.30/1.96 inference(pre_NNF_transformation,[status(thm)],[f73])).
% 12.30/1.96 fof(f327,plain,(
% 12.30/1.96 ![X0]: (~op_possibly|possibly(X0)=not(necessarily(not(X0))))),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f326])).
% 12.30/1.96 fof(f334,plain,(
% 12.30/1.96 op_possibly),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f77])).
% 12.30/1.96 fof(f337,plain,(
% 12.30/1.96 axiom_M),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f80])).
% 12.30/1.96 fof(f338,plain,(
% 12.30/1.96 axiom_4),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f81])).
% 12.30/1.96 fof(f339,plain,(
% 12.30/1.96 axiom_B),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f82])).
% 12.30/1.96 fof(f340,plain,(
% 12.30/1.96 ~axiom_5),
% 12.30/1.96 inference(cnf_transformation,[status(thm)],[f84])).
% 12.30/1.96 fof(f341,plain,(
% 12.30/1.96 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 12.30/1.96 inference(backward_subsumption_resolution,[status(thm)],[f89,f208])).
% 12.30/1.96 fof(f344,plain,(
% 12.30/1.96 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0))))),
% 12.30/1.96 inference(backward_subsumption_resolution,[status(thm)],[f105,f210])).
% 12.30/1.96 fof(f345,plain,(
% 12.30/1.96 ![X0,X1]: (is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 12.30/1.96 inference(backward_subsumption_resolution,[status(thm)],[f109,f211])).
% 12.30/1.96 fof(f347,plain,(
% 12.30/1.96 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X0)))),
% 12.30/1.96 inference(backward_subsumption_resolution,[status(thm)],[f117,f213])).
% 12.30/1.96 fof(f349,plain,(
% 12.30/1.96 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 12.30/1.96 inference(forward_subsumption_resolution,[status(thm)],[f125,f215])).
% 12.30/1.96 fof(f351,plain,(
% 12.30/1.96 ![X0,X1]: (is_a_theorem(implies(X0,or(X1,X0))))),
% 12.30/1.96 inference(backward_subsumption_resolution,[status(thm)],[f133,f217])).
% 12.30/1.96 fof(f352,plain,(
% 12.30/1.96 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))))),
% 12.30/1.96 inference(forward_subsumption_resolution,[status(thm)],[f137,f218])).
% 12.30/1.96 fof(f355,plain,(
% 12.30/1.96 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))))),
% 12.30/1.96 inference(forward_subsumption_resolution,[status(thm)],[f149,f221])).
% 12.30/1.96 fof(f356,plain,(
% 12.30/1.96 ![X0,X1]: (~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 12.30/1.96 inference(backward_subsumption_resolution,[status(thm)],[f96,f222])).
% 12.30/1.96 fof(f358,plain,(
% 12.30/1.96 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1))))),
% 12.30/1.96 inference(forward_subsumption_resolution,[status(thm)],[f196,f205])).
% 12.30/1.96 fof(f363,plain,(
% 12.30/1.96 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1))),
% 12.30/1.96 inference(backward_demodulation,[status(thm)],[f364,f358])).
% 12.30/1.96 fof(f364,plain,(
% 12.30/1.96 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1))))),
% 12.30/1.96 inference(forward_subsumption_resolution,[status(thm)],[f200,f206])).
% 12.30/1.96 fof(f376,plain,(
% 12.30/1.96 ![X0]: (is_a_theorem(implies(necessarily(X0),X0)))),
% 12.30/1.96 inference(forward_subsumption_resolution,[status(thm)],[f256,f337])).
% 12.30/1.96 fof(f377,plain,(
% 12.30/1.96 ![X0]: (is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))))),
% 12.30/1.96 inference(forward_subsumption_resolution,[status(thm)],[f260,f338])).
% 12.30/1.96 fof(f379,plain,(
% 12.30/1.96 ![X0]: (is_a_theorem(implies(X0,necessarily(possibly(X0)))))),
% 12.30/1.96 inference(forward_subsumption_resolution,[status(thm)],[f264,f339])).
% 12.30/1.96 fof(f380,plain,(
% 12.30/1.96 ~is_a_theorem(implies(possibly(sK67_skl),necessarily(possibly(sK67_skl))))),
% 12.30/1.96 inference(forward_subsumption_resolution,[status(thm)],[f269,f340])).
% 12.30/1.96 fof(f381,plain,(
% 12.30/1.96 cn3|~is_a_theorem(implies(or(sK43_skl,sK43_skl),sK43_skl))),
% 12.30/1.96 inference(backward_demodulation,[status(thm)],[f363,f174])).
% 12.30/1.96 fof(f386,plain,(
% 12.30/1.96 ![X0]: (~cn3|is_a_theorem(implies(or(X0,X0),X0)))),
% 12.30/1.96 inference(backward_demodulation,[status(thm)],[f363,f173])).
% 12.30/1.96 fof(f389,plain,(
% 12.30/1.96 ![X0]: (is_a_theorem(or(X0,necessarily(possibly(not(X0))))))),
% 12.30/1.96 inference(paramodulation,[status(thm)],[f363,f379])).
% 12.30/1.96 fof(f414,plain,(
% 12.30/1.96 ![X0]: (possibly(X0)=not(necessarily(not(X0))))),
% 12.30/1.96 inference(forward_subsumption_resolution,[status(thm)],[f327,f334])).
% 12.30/1.96 fof(f415,plain,(
% 12.30/1.96 ![X0]: (possibly(necessarily(not(X0)))=not(necessarily(possibly(X0))))),
% 12.30/1.96 inference(paramodulation,[status(thm)],[f414,f414])).
% 12.30/1.96 fof(f416,plain,(
% 12.30/1.96 ![X0,X1]: (possibly(and(X0,not(X1)))=not(necessarily(implies(X0,X1))))),
% 12.30/1.96 inference(paramodulation,[status(thm)],[f364,f414])).
% 12.30/1.96 fof(f420,plain,(
% 12.30/1.96 ![X0,X1]: (or(necessarily(not(X0)),X1)=implies(possibly(X0),X1))),
% 12.30/1.96 inference(paramodulation,[status(thm)],[f414,f363])).
% 12.30/1.96 fof(f421,plain,(
% 12.30/1.96 ![X0,X1]: (implies(X0,necessarily(not(X1)))=not(and(X0,possibly(X1))))),
% 12.30/1.96 inference(paramodulation,[status(thm)],[f414,f364])).
% 12.30/1.96 fof(f428,plain,(
% 12.30/1.96 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(implies(X1,X0),equiv(X0,X1))))),
% 12.30/1.96 inference(resolution,[status(thm)],[f341,f355])).
% 12.30/1.98 fof(f439,plain,(
% 12.30/1.98 ![X0,X1]: (~is_a_theorem(implies(X0,implies(X0,X1)))|is_a_theorem(implies(X0,X1)))),
% 12.30/1.98 inference(resolution,[status(thm)],[f345,f341])).
% 12.30/1.98 fof(f990,plain,(
% 12.30/1.98 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X0))|is_a_theorem(equiv(X0,X1)))),
% 12.30/1.98 inference(resolution,[status(thm)],[f428,f341])).
% 12.30/1.98 fof(f1039,plain,(
% 12.30/1.98 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),implies(or(X0,X0),X1))))),
% 12.30/1.98 inference(resolution,[status(thm)],[f439,f352])).
% 12.30/1.98 fof(f1042,plain,(
% 12.30/1.98 ![X0]: (is_a_theorem(implies(X0,and(X0,X0))))),
% 12.30/1.98 inference(resolution,[status(thm)],[f439,f349])).
% 12.30/1.98 fof(f1043,plain,(
% 12.30/1.98 ![X0]: (is_a_theorem(implies(X0,X0)))),
% 12.30/1.98 inference(resolution,[status(thm)],[f439,f344])).
% 12.30/1.98 fof(f3650,plain,(
% 12.30/1.98 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(or(X0,X0),X1)))),
% 12.30/1.98 inference(resolution,[status(thm)],[f1039,f341])).
% 12.30/1.98 fof(f4911,plain,(
% 12.30/1.98 ~is_a_theorem(implies(sK43_skl,sK43_skl))|cn3),
% 12.30/1.98 inference(resolution,[status(thm)],[f3650,f381])).
% 12.30/1.98 fof(f4923,plain,(
% 12.30/1.98 cn3),
% 12.30/1.98 inference(forward_subsumption_resolution,[status(thm)],[f4911,f1043])).
% 12.30/1.98 fof(f5086,plain,(
% 12.30/1.98 ![X0]: (is_a_theorem(implies(or(X0,X0),X0)))),
% 12.30/1.98 inference(backward_subsumption_resolution,[status(thm)],[f386,f4923])).
% 12.30/1.98 fof(f7643,plain,(
% 12.30/1.98 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X0))|X0=X1)),
% 12.30/1.98 inference(resolution,[status(thm)],[f990,f356])).
% 12.30/1.98 fof(f7668,plain,(
% 12.30/1.98 ![X0]: (~is_a_theorem(implies(X0,or(X0,X0)))|X0=or(X0,X0))),
% 12.30/1.98 inference(resolution,[status(thm)],[f7643,f5086])).
% 12.30/1.98 fof(f7680,plain,(
% 12.30/1.98 ![X0]: (~is_a_theorem(implies(necessarily(necessarily(X0)),necessarily(X0)))|necessarily(necessarily(X0))=necessarily(X0))),
% 12.30/1.98 inference(resolution,[status(thm)],[f7643,f377])).
% 12.30/1.98 fof(f7757,plain,(
% 12.30/1.98 ![X0]: (~is_a_theorem(implies(and(X0,X0),X0))|and(X0,X0)=X0)),
% 12.30/1.98 inference(resolution,[status(thm)],[f7643,f1042])).
% 12.30/1.98 fof(f7773,plain,(
% 12.30/1.98 ![X0]: (X0=or(X0,X0))),
% 12.30/1.98 inference(forward_subsumption_resolution,[status(thm)],[f7668,f351])).
% 12.30/1.98 fof(f7782,plain,(
% 12.30/1.98 ![X0]: (necessarily(necessarily(X0))=necessarily(X0))),
% 12.30/1.98 inference(forward_subsumption_resolution,[status(thm)],[f7680,f376])).
% 12.30/1.98 fof(f7824,plain,(
% 12.30/1.98 ![X0]: (and(X0,X0)=X0)),
% 12.30/1.98 inference(forward_subsumption_resolution,[status(thm)],[f7757,f347])).
% 12.30/1.98 fof(f8178,plain,(
% 12.30/1.98 ![X0]: (possibly(not(X0))=not(necessarily(implies(not(X0),X0))))),
% 12.30/1.98 inference(paramodulation,[status(thm)],[f7824,f416])).
% 12.30/1.98 fof(f8333,plain,(
% 12.30/1.98 ![X0]: (possibly(not(X0))=not(necessarily(or(X0,X0))))),
% 12.30/1.98 inference(forward_demodulation,[status(thm)],[f363,f8178])).
% 12.30/1.98 fof(f8334,plain,(
% 12.30/1.98 ![X0]: (possibly(not(X0))=not(necessarily(X0)))),
% 12.30/1.98 inference(forward_demodulation,[status(thm)],[f7773,f8333])).
% 12.30/1.98 fof(f13596,plain,(
% 12.30/1.98 ![X0]: (is_a_theorem(or(X0,necessarily(not(necessarily(X0))))))),
% 12.30/1.98 inference(backward_demodulation,[status(thm)],[f8334,f389])).
% 12.30/1.98 fof(f13884,plain,(
% 12.30/1.98 ![X0]: (is_a_theorem(implies(possibly(X0),necessarily(not(necessarily(necessarily(not(X0))))))))),
% 12.30/1.98 inference(paramodulation,[status(thm)],[f420,f13596])).
% 12.30/1.98 fof(f13891,plain,(
% 12.30/1.98 ![X0]: (is_a_theorem(not(and(possibly(X0),possibly(necessarily(necessarily(not(X0))))))))),
% 12.30/1.98 inference(forward_demodulation,[status(thm)],[f421,f13884])).
% 12.30/1.98 fof(f13892,plain,(
% 12.30/1.98 ![X0]: (is_a_theorem(not(and(possibly(X0),possibly(necessarily(not(X0)))))))),
% 12.30/1.98 inference(forward_demodulation,[status(thm)],[f7782,f13891])).
% 12.30/1.98 fof(f13893,plain,(
% 12.30/1.98 ![X0]: (is_a_theorem(not(and(possibly(X0),not(necessarily(possibly(X0)))))))),
% 12.30/1.98 inference(forward_demodulation,[status(thm)],[f415,f13892])).
% 12.30/1.98 fof(f13894,plain,(
% 12.30/1.98 ![X0]: (is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))))),
% 12.30/1.98 inference(forward_demodulation,[status(thm)],[f364,f13893])).
% 12.30/1.98 fof(f13899,plain,(
% 12.30/1.98 $false),
% 12.30/1.98 inference(backward_subsumption_resolution,[status(thm)],[f380,f13894])).
% 12.30/1.98 % SZS output end CNFRefutation for theBenchmark.p
% 2.06/2.01 % Elapsed time: 1.690388 seconds
% 2.06/2.01 % CPU time: 13.084639 seconds
% 2.06/2.01 % Total memory used: 312.476 MB
% 2.06/2.01 % Net memory used: 298.610 MB
%------------------------------------------------------------------------------