TSTP Solution File: LCL461+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : LCL461+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:27:15 EDT 2024
% Result : Theorem 19.05s 2.83s
% Output : CNFRefutation 19.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LCL461+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32 % Computer : n022.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Apr 29 20:22:28 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.33 % Drodi V3.6.0
% 19.05/2.83 % Refutation found
% 19.05/2.83 % SZS status Theorem for theBenchmark: Theorem is valid
% 19.05/2.83 % SZS output start CNFRefutation for theBenchmark
% 19.05/2.83 fof(f1,axiom,(
% 19.05/2.83 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 19.05/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.05/2.83 fof(f2,axiom,(
% 19.05/2.83 ( substitution_of_equivalents<=> (! [X,Y] :( is_a_theorem(equiv(X,Y))=> X = Y ) )) ),
% 19.05/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.05/2.83 fof(f3,axiom,(
% 19.05/2.83 ( modus_tollens<=> (! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) )) ),
% 19.05/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.05/2.83 fof(f4,axiom,(
% 19.05/2.83 ( implies_1<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) )) ),
% 19.05/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.05/2.83 fof(f5,axiom,(
% 19.05/2.83 ( implies_2<=> (! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )) ),
% 19.05/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.05/2.83 fof(f6,axiom,(
% 19.05/2.83 ( implies_3<=> (! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )) ),
% 19.62/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.62/2.83 fof(f8,axiom,(
% 19.62/2.83 ( and_2<=> (! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) )) ),
% 19.62/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.62/2.83 fof(f9,axiom,(
% 19.62/2.83 ( and_3<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) )) ),
% 19.62/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.62/2.83 fof(f10,axiom,(
% 19.62/2.83 ( or_1<=> (! [X,Y] : is_a_theorem(implies(X,or(X,Y))) )) ),
% 19.62/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.62/2.83 fof(f12,axiom,(
% 19.62/2.83 ( or_3<=> (! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))) )) ),
% 19.62/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.62/2.83 fof(f15,axiom,(
% 19.62/2.83 ( equivalence_3<=> (! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) )) ),
% 19.62/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.62/2.83 fof(f18,axiom,(
% 19.62/2.83 ( kn3<=> (! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) )) ),
% 19.62/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.62/2.83 fof(f21,axiom,(
% 19.62/2.83 ( cn3<=> (! [P] : is_a_theorem(implies(implies(not(P),P),P)) )) ),
% 19.62/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.62/2.83 fof(f27,axiom,(
% 19.62/2.83 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 19.62/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.62/2.83 fof(f29,axiom,(
% 19.62/2.83 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 19.62/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.62/2.83 fof(f32,axiom,(
% 19.62/2.83 op_or ),
% 19.62/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.62/2.83 fof(f33,axiom,(
% 19.62/2.83 op_implies_and ),
% 19.62/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.62/2.83 fof(f35,axiom,(
% 19.62/2.83 modus_ponens ),
% 19.62/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.62/2.83 fof(f36,axiom,(
% 19.62/2.83 modus_tollens ),
% 19.62/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.62/2.83 fof(f37,axiom,(
% 19.62/2.83 implies_1 ),
% 19.62/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.62/2.83 fof(f38,axiom,(
% 19.62/2.83 implies_2 ),
% 19.62/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.62/2.83 fof(f39,axiom,(
% 19.62/2.83 implies_3 ),
% 19.62/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.62/2.83 fof(f41,axiom,(
% 19.62/2.83 and_2 ),
% 19.62/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.62/2.83 fof(f42,axiom,(
% 19.62/2.83 and_3 ),
% 19.62/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.62/2.83 fof(f43,axiom,(
% 19.62/2.83 or_1 ),
% 19.62/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.62/2.83 fof(f45,axiom,(
% 19.62/2.83 or_3 ),
% 19.62/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.62/2.83 fof(f48,axiom,(
% 19.62/2.83 equivalence_3 ),
% 19.62/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.62/2.83 fof(f49,axiom,(
% 19.62/2.83 substitution_of_equivalents ),
% 19.62/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.62/2.83 fof(f53,conjecture,(
% 19.62/2.83 kn3 ),
% 19.62/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.62/2.83 fof(f54,negated_conjecture,(
% 19.62/2.83 ~(kn3 )),
% 19.62/2.83 inference(negated_conjecture,[status(cth)],[f53])).
% 19.62/2.83 fof(f55,plain,(
% 19.62/2.83 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 19.62/2.83 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 19.62/2.83 fof(f56,plain,(
% 19.62/2.83 (~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))))),
% 19.62/2.83 inference(NNF_transformation,[status(esa)],[f55])).
% 19.62/2.83 fof(f57,plain,(
% 19.62/2.83 (~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))))),
% 19.62/2.83 inference(miniscoping,[status(esa)],[f56])).
% 19.62/2.83 fof(f58,plain,(
% 19.62/2.83 (~modus_ponens|(![Y]: ((![X]: (~is_a_theorem(X)|~is_a_theorem(implies(X,Y))))|is_a_theorem(Y))))&(modus_ponens|((is_a_theorem(sk0_1)&is_a_theorem(implies(sk0_1,sk0_0)))&~is_a_theorem(sk0_0)))),
% 19.62/2.83 inference(skolemization,[status(esa)],[f57])).
% 19.62/2.83 fof(f59,plain,(
% 19.62/2.83 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f58])).
% 19.62/2.83 fof(f63,plain,(
% 19.62/2.83 substitution_of_equivalents<=>(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y))),
% 19.62/2.83 inference(pre_NNF_transformation,[status(esa)],[f2])).
% 19.62/2.83 fof(f64,plain,(
% 19.62/2.83 (~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)))),
% 19.62/2.83 inference(NNF_transformation,[status(esa)],[f63])).
% 19.62/2.83 fof(f65,plain,(
% 19.62/2.83 (~substitution_of_equivalents|(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y)))&(substitution_of_equivalents|(is_a_theorem(equiv(sk0_2,sk0_3))&~sk0_2=sk0_3))),
% 19.62/2.83 inference(skolemization,[status(esa)],[f64])).
% 19.62/2.83 fof(f66,plain,(
% 19.62/2.83 ![X0,X1]: (~substitution_of_equivalents|~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f65])).
% 19.62/2.83 fof(f69,plain,(
% 19.62/2.83 (~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)))))),
% 19.62/2.83 inference(NNF_transformation,[status(esa)],[f3])).
% 19.62/2.83 fof(f70,plain,(
% 19.62/2.83 (~modus_tollens|(![X,Y]: is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))))&(modus_tollens|~is_a_theorem(implies(implies(not(sk0_5),not(sk0_4)),implies(sk0_4,sk0_5))))),
% 19.62/2.83 inference(skolemization,[status(esa)],[f69])).
% 19.62/2.83 fof(f71,plain,(
% 19.62/2.83 ![X0,X1]: (~modus_tollens|is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))))),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f70])).
% 19.62/2.83 fof(f73,plain,(
% 19.62/2.83 (~implies_1|(![X,Y]: is_a_theorem(implies(X,implies(Y,X)))))&(implies_1|(?[X,Y]: ~is_a_theorem(implies(X,implies(Y,X)))))),
% 19.62/2.83 inference(NNF_transformation,[status(esa)],[f4])).
% 19.62/2.83 fof(f74,plain,(
% 19.62/2.83 (~implies_1|(![X,Y]: is_a_theorem(implies(X,implies(Y,X)))))&(implies_1|~is_a_theorem(implies(sk0_6,implies(sk0_7,sk0_6))))),
% 19.62/2.83 inference(skolemization,[status(esa)],[f73])).
% 19.62/2.83 fof(f75,plain,(
% 19.62/2.83 ![X0,X1]: (~implies_1|is_a_theorem(implies(X0,implies(X1,X0))))),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f74])).
% 19.62/2.83 fof(f77,plain,(
% 19.62/2.83 (~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)))))),
% 19.62/2.83 inference(NNF_transformation,[status(esa)],[f5])).
% 19.62/2.83 fof(f78,plain,(
% 19.62/2.83 (~implies_2|(![X,Y]: is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))))&(implies_2|~is_a_theorem(implies(implies(sk0_8,implies(sk0_8,sk0_9)),implies(sk0_8,sk0_9))))),
% 19.62/2.83 inference(skolemization,[status(esa)],[f77])).
% 19.62/2.83 fof(f79,plain,(
% 19.62/2.83 ![X0,X1]: (~implies_2|is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f78])).
% 19.62/2.83 fof(f81,plain,(
% 19.62/2.83 (~implies_3|(![X,Y,Z]: is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))))&(implies_3|(?[X,Y,Z]: ~is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))))),
% 19.62/2.83 inference(NNF_transformation,[status(esa)],[f6])).
% 19.62/2.83 fof(f82,plain,(
% 19.62/2.83 (~implies_3|(![X,Y,Z]: is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))))&(implies_3|~is_a_theorem(implies(implies(sk0_10,sk0_11),implies(implies(sk0_11,sk0_12),implies(sk0_10,sk0_12)))))),
% 19.62/2.83 inference(skolemization,[status(esa)],[f81])).
% 19.62/2.83 fof(f83,plain,(
% 19.62/2.83 ![X0,X1,X2]: (~implies_3|is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))))),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f82])).
% 19.62/2.83 fof(f89,plain,(
% 19.62/2.83 (~and_2|(![X,Y]: is_a_theorem(implies(and(X,Y),Y))))&(and_2|(?[X,Y]: ~is_a_theorem(implies(and(X,Y),Y))))),
% 19.62/2.83 inference(NNF_transformation,[status(esa)],[f8])).
% 19.62/2.83 fof(f90,plain,(
% 19.62/2.83 (~and_2|(![X,Y]: is_a_theorem(implies(and(X,Y),Y))))&(and_2|~is_a_theorem(implies(and(sk0_15,sk0_16),sk0_16)))),
% 19.62/2.83 inference(skolemization,[status(esa)],[f89])).
% 19.62/2.83 fof(f91,plain,(
% 19.62/2.83 ![X0,X1]: (~and_2|is_a_theorem(implies(and(X0,X1),X1)))),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f90])).
% 19.62/2.83 fof(f93,plain,(
% 19.62/2.83 (~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))))))),
% 19.62/2.83 inference(NNF_transformation,[status(esa)],[f9])).
% 19.62/2.83 fof(f94,plain,(
% 19.62/2.83 (~and_3|(![X,Y]: is_a_theorem(implies(X,implies(Y,and(X,Y))))))&(and_3|~is_a_theorem(implies(sk0_17,implies(sk0_18,and(sk0_17,sk0_18)))))),
% 19.62/2.83 inference(skolemization,[status(esa)],[f93])).
% 19.62/2.83 fof(f95,plain,(
% 19.62/2.83 ![X0,X1]: (~and_3|is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f94])).
% 19.62/2.83 fof(f97,plain,(
% 19.62/2.83 (~or_1|(![X,Y]: is_a_theorem(implies(X,or(X,Y)))))&(or_1|(?[X,Y]: ~is_a_theorem(implies(X,or(X,Y)))))),
% 19.62/2.83 inference(NNF_transformation,[status(esa)],[f10])).
% 19.62/2.83 fof(f98,plain,(
% 19.62/2.83 (~or_1|(![X,Y]: is_a_theorem(implies(X,or(X,Y)))))&(or_1|~is_a_theorem(implies(sk0_19,or(sk0_19,sk0_20))))),
% 19.62/2.83 inference(skolemization,[status(esa)],[f97])).
% 19.62/2.83 fof(f99,plain,(
% 19.62/2.83 ![X0,X1]: (~or_1|is_a_theorem(implies(X0,or(X0,X1))))),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f98])).
% 19.62/2.83 fof(f105,plain,(
% 19.62/2.83 (~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))))))),
% 19.62/2.83 inference(NNF_transformation,[status(esa)],[f12])).
% 19.62/2.83 fof(f106,plain,(
% 19.62/2.83 (~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(sk0_23,sk0_25),implies(implies(sk0_24,sk0_25),implies(or(sk0_23,sk0_24),sk0_25)))))),
% 19.62/2.83 inference(skolemization,[status(esa)],[f105])).
% 19.62/2.83 fof(f107,plain,(
% 19.62/2.83 ![X0,X1,X2]: (~or_3|is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))))),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f106])).
% 19.62/2.83 fof(f117,plain,(
% 19.62/2.83 (~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))))))),
% 19.62/2.83 inference(NNF_transformation,[status(esa)],[f15])).
% 19.62/2.83 fof(f118,plain,(
% 19.62/2.83 (~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(sk0_30,sk0_31),implies(implies(sk0_31,sk0_30),equiv(sk0_30,sk0_31)))))),
% 19.62/2.83 inference(skolemization,[status(esa)],[f117])).
% 19.62/2.83 fof(f119,plain,(
% 19.62/2.83 ![X0,X1]: (~equivalence_3|is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))))),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f118])).
% 19.62/2.83 fof(f129,plain,(
% 19.62/2.83 (~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)))))))),
% 19.62/2.83 inference(NNF_transformation,[status(esa)],[f18])).
% 19.62/2.83 fof(f130,plain,(
% 19.62/2.83 (~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(sk0_35,sk0_36),implies(not(and(sk0_36,sk0_37)),not(and(sk0_37,sk0_35))))))),
% 19.62/2.83 inference(skolemization,[status(esa)],[f129])).
% 19.62/2.83 fof(f132,plain,(
% 19.62/2.83 kn3|~is_a_theorem(implies(implies(sk0_35,sk0_36),implies(not(and(sk0_36,sk0_37)),not(and(sk0_37,sk0_35)))))),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f130])).
% 19.62/2.83 fof(f141,plain,(
% 19.62/2.83 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|(?[P]: ~is_a_theorem(implies(implies(not(P),P),P))))),
% 19.62/2.83 inference(NNF_transformation,[status(esa)],[f21])).
% 19.62/2.83 fof(f142,plain,(
% 19.62/2.83 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|~is_a_theorem(implies(implies(not(sk0_43),sk0_43),sk0_43)))),
% 19.62/2.83 inference(skolemization,[status(esa)],[f141])).
% 19.62/2.83 fof(f143,plain,(
% 19.62/2.83 ![X0]: (~cn3|is_a_theorem(implies(implies(not(X0),X0),X0)))),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f142])).
% 19.62/2.83 fof(f144,plain,(
% 19.62/2.83 cn3|~is_a_theorem(implies(implies(not(sk0_43),sk0_43),sk0_43))),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f142])).
% 19.62/2.83 fof(f165,plain,(
% 19.62/2.83 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 19.62/2.83 inference(pre_NNF_transformation,[status(esa)],[f27])).
% 19.62/2.83 fof(f166,plain,(
% 19.62/2.83 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f165])).
% 19.62/2.83 fof(f169,plain,(
% 19.62/2.83 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 19.62/2.83 inference(pre_NNF_transformation,[status(esa)],[f29])).
% 19.62/2.83 fof(f170,plain,(
% 19.62/2.83 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f169])).
% 19.62/2.83 fof(f175,plain,(
% 19.62/2.83 op_or),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f32])).
% 19.62/2.83 fof(f176,plain,(
% 19.62/2.83 op_implies_and),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f33])).
% 19.62/2.83 fof(f178,plain,(
% 19.62/2.83 modus_ponens),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f35])).
% 19.62/2.83 fof(f179,plain,(
% 19.62/2.83 modus_tollens),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f36])).
% 19.62/2.83 fof(f180,plain,(
% 19.62/2.83 implies_1),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f37])).
% 19.62/2.83 fof(f181,plain,(
% 19.62/2.83 implies_2),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f38])).
% 19.62/2.83 fof(f182,plain,(
% 19.62/2.83 implies_3),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f39])).
% 19.62/2.83 fof(f184,plain,(
% 19.62/2.83 and_2),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f41])).
% 19.62/2.83 fof(f185,plain,(
% 19.62/2.83 and_3),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f42])).
% 19.62/2.83 fof(f186,plain,(
% 19.62/2.83 or_1),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f43])).
% 19.62/2.83 fof(f188,plain,(
% 19.62/2.83 or_3),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f45])).
% 19.62/2.83 fof(f191,plain,(
% 19.62/2.83 equivalence_3),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f48])).
% 19.62/2.83 fof(f192,plain,(
% 19.62/2.83 substitution_of_equivalents),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f49])).
% 19.62/2.83 fof(f196,plain,(
% 19.62/2.83 ~kn3),
% 19.62/2.83 inference(cnf_transformation,[status(esa)],[f54])).
% 19.62/2.83 fof(f197,plain,(
% 19.62/2.83 spl0_0 <=> modus_ponens),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f199,plain,(
% 19.62/2.83 ~modus_ponens|spl0_0),
% 19.62/2.83 inference(component_clause,[status(thm)],[f197])).
% 19.62/2.83 fof(f200,plain,(
% 19.62/2.83 spl0_1 <=> ~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f201,plain,(
% 19.62/2.83 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)|~spl0_1)),
% 19.62/2.83 inference(component_clause,[status(thm)],[f200])).
% 19.62/2.83 fof(f203,plain,(
% 19.62/2.83 ~spl0_0|spl0_1),
% 19.62/2.83 inference(split_clause,[status(thm)],[f59,f197,f200])).
% 19.62/2.83 fof(f216,plain,(
% 19.62/2.83 spl0_5 <=> substitution_of_equivalents),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f218,plain,(
% 19.62/2.83 ~substitution_of_equivalents|spl0_5),
% 19.62/2.83 inference(component_clause,[status(thm)],[f216])).
% 19.62/2.83 fof(f219,plain,(
% 19.62/2.83 spl0_6 <=> ~is_a_theorem(equiv(X0,X1))|X0=X1),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f220,plain,(
% 19.62/2.83 ![X0,X1]: (~is_a_theorem(equiv(X0,X1))|X0=X1|~spl0_6)),
% 19.62/2.83 inference(component_clause,[status(thm)],[f219])).
% 19.62/2.83 fof(f222,plain,(
% 19.62/2.83 ~spl0_5|spl0_6),
% 19.62/2.83 inference(split_clause,[status(thm)],[f66,f216,f219])).
% 19.62/2.83 fof(f231,plain,(
% 19.62/2.83 spl0_9 <=> modus_tollens),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f233,plain,(
% 19.62/2.83 ~modus_tollens|spl0_9),
% 19.62/2.83 inference(component_clause,[status(thm)],[f231])).
% 19.62/2.83 fof(f234,plain,(
% 19.62/2.83 spl0_10 <=> is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0)))),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f235,plain,(
% 19.62/2.83 ![X0,X1]: (is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0)))|~spl0_10)),
% 19.62/2.83 inference(component_clause,[status(thm)],[f234])).
% 19.62/2.83 fof(f237,plain,(
% 19.62/2.83 ~spl0_9|spl0_10),
% 19.62/2.83 inference(split_clause,[status(thm)],[f71,f231,f234])).
% 19.62/2.83 fof(f242,plain,(
% 19.62/2.83 spl0_12 <=> implies_1),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f244,plain,(
% 19.62/2.83 ~implies_1|spl0_12),
% 19.62/2.83 inference(component_clause,[status(thm)],[f242])).
% 19.62/2.83 fof(f245,plain,(
% 19.62/2.83 spl0_13 <=> is_a_theorem(implies(X0,implies(X1,X0)))),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f246,plain,(
% 19.62/2.83 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0)))|~spl0_13)),
% 19.62/2.83 inference(component_clause,[status(thm)],[f245])).
% 19.62/2.83 fof(f248,plain,(
% 19.62/2.83 ~spl0_12|spl0_13),
% 19.62/2.83 inference(split_clause,[status(thm)],[f75,f242,f245])).
% 19.62/2.83 fof(f253,plain,(
% 19.62/2.83 spl0_15 <=> implies_2),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f255,plain,(
% 19.62/2.83 ~implies_2|spl0_15),
% 19.62/2.83 inference(component_clause,[status(thm)],[f253])).
% 19.62/2.83 fof(f256,plain,(
% 19.62/2.83 spl0_16 <=> is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f257,plain,(
% 19.62/2.83 ![X0,X1]: (is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))|~spl0_16)),
% 19.62/2.83 inference(component_clause,[status(thm)],[f256])).
% 19.62/2.83 fof(f259,plain,(
% 19.62/2.83 ~spl0_15|spl0_16),
% 19.62/2.83 inference(split_clause,[status(thm)],[f79,f253,f256])).
% 19.62/2.83 fof(f264,plain,(
% 19.62/2.83 spl0_18 <=> implies_3),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f266,plain,(
% 19.62/2.83 ~implies_3|spl0_18),
% 19.62/2.83 inference(component_clause,[status(thm)],[f264])).
% 19.62/2.83 fof(f267,plain,(
% 19.62/2.83 spl0_19 <=> is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f268,plain,(
% 19.62/2.83 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))|~spl0_19)),
% 19.62/2.83 inference(component_clause,[status(thm)],[f267])).
% 19.62/2.83 fof(f270,plain,(
% 19.62/2.83 ~spl0_18|spl0_19),
% 19.62/2.83 inference(split_clause,[status(thm)],[f83,f264,f267])).
% 19.62/2.83 fof(f286,plain,(
% 19.62/2.83 spl0_24 <=> and_2),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f288,plain,(
% 19.62/2.83 ~and_2|spl0_24),
% 19.62/2.83 inference(component_clause,[status(thm)],[f286])).
% 19.62/2.83 fof(f289,plain,(
% 19.62/2.83 spl0_25 <=> is_a_theorem(implies(and(X0,X1),X1))),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f290,plain,(
% 19.62/2.83 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X1))|~spl0_25)),
% 19.62/2.83 inference(component_clause,[status(thm)],[f289])).
% 19.62/2.83 fof(f292,plain,(
% 19.62/2.83 ~spl0_24|spl0_25),
% 19.62/2.83 inference(split_clause,[status(thm)],[f91,f286,f289])).
% 19.62/2.83 fof(f297,plain,(
% 19.62/2.83 spl0_27 <=> and_3),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f299,plain,(
% 19.62/2.83 ~and_3|spl0_27),
% 19.62/2.83 inference(component_clause,[status(thm)],[f297])).
% 19.62/2.83 fof(f300,plain,(
% 19.62/2.83 spl0_28 <=> is_a_theorem(implies(X0,implies(X1,and(X0,X1))))),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f301,plain,(
% 19.62/2.83 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,and(X0,X1))))|~spl0_28)),
% 19.62/2.83 inference(component_clause,[status(thm)],[f300])).
% 19.62/2.83 fof(f303,plain,(
% 19.62/2.83 ~spl0_27|spl0_28),
% 19.62/2.83 inference(split_clause,[status(thm)],[f95,f297,f300])).
% 19.62/2.83 fof(f308,plain,(
% 19.62/2.83 spl0_30 <=> or_1),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f310,plain,(
% 19.62/2.83 ~or_1|spl0_30),
% 19.62/2.83 inference(component_clause,[status(thm)],[f308])).
% 19.62/2.83 fof(f311,plain,(
% 19.62/2.83 spl0_31 <=> is_a_theorem(implies(X0,or(X0,X1)))),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f312,plain,(
% 19.62/2.83 ![X0,X1]: (is_a_theorem(implies(X0,or(X0,X1)))|~spl0_31)),
% 19.62/2.83 inference(component_clause,[status(thm)],[f311])).
% 19.62/2.83 fof(f314,plain,(
% 19.62/2.83 ~spl0_30|spl0_31),
% 19.62/2.83 inference(split_clause,[status(thm)],[f99,f308,f311])).
% 19.62/2.83 fof(f330,plain,(
% 19.62/2.83 spl0_36 <=> or_3),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f332,plain,(
% 19.62/2.83 ~or_3|spl0_36),
% 19.62/2.83 inference(component_clause,[status(thm)],[f330])).
% 19.62/2.83 fof(f333,plain,(
% 19.62/2.83 spl0_37 <=> is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1))))),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f334,plain,(
% 19.62/2.83 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1))))|~spl0_37)),
% 19.62/2.83 inference(component_clause,[status(thm)],[f333])).
% 19.62/2.83 fof(f336,plain,(
% 19.62/2.83 ~spl0_36|spl0_37),
% 19.62/2.83 inference(split_clause,[status(thm)],[f107,f330,f333])).
% 19.62/2.83 fof(f363,plain,(
% 19.62/2.83 spl0_45 <=> equivalence_3),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f365,plain,(
% 19.62/2.83 ~equivalence_3|spl0_45),
% 19.62/2.83 inference(component_clause,[status(thm)],[f363])).
% 19.62/2.83 fof(f366,plain,(
% 19.62/2.83 spl0_46 <=> is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f367,plain,(
% 19.62/2.83 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))|~spl0_46)),
% 19.62/2.83 inference(component_clause,[status(thm)],[f366])).
% 19.62/2.83 fof(f369,plain,(
% 19.62/2.83 ~spl0_45|spl0_46),
% 19.62/2.83 inference(split_clause,[status(thm)],[f119,f363,f366])).
% 19.62/2.83 fof(f377,plain,(
% 19.62/2.83 spl0_49 <=> is_a_theorem(implies(X0,and(X0,X0)))),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f378,plain,(
% 19.62/2.83 ![X0]: (is_a_theorem(implies(X0,and(X0,X0)))|~spl0_49)),
% 19.62/2.83 inference(component_clause,[status(thm)],[f377])).
% 19.62/2.83 fof(f393,plain,(
% 19.62/2.83 spl0_53 <=> kn3),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f394,plain,(
% 19.62/2.83 kn3|~spl0_53),
% 19.62/2.83 inference(component_clause,[status(thm)],[f393])).
% 19.62/2.83 fof(f400,plain,(
% 19.62/2.83 spl0_55 <=> is_a_theorem(implies(implies(sk0_35,sk0_36),implies(not(and(sk0_36,sk0_37)),not(and(sk0_37,sk0_35)))))),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f402,plain,(
% 19.62/2.83 ~is_a_theorem(implies(implies(sk0_35,sk0_36),implies(not(and(sk0_36,sk0_37)),not(and(sk0_37,sk0_35)))))|spl0_55),
% 19.62/2.83 inference(component_clause,[status(thm)],[f400])).
% 19.62/2.83 fof(f403,plain,(
% 19.62/2.83 spl0_53|~spl0_55),
% 19.62/2.83 inference(split_clause,[status(thm)],[f132,f393,f400])).
% 19.62/2.83 fof(f423,plain,(
% 19.62/2.83 spl0_61 <=> cn3),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f426,plain,(
% 19.62/2.83 spl0_62 <=> is_a_theorem(implies(implies(not(X0),X0),X0))),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f427,plain,(
% 19.62/2.83 ![X0]: (is_a_theorem(implies(implies(not(X0),X0),X0))|~spl0_62)),
% 19.62/2.83 inference(component_clause,[status(thm)],[f426])).
% 19.62/2.83 fof(f429,plain,(
% 19.62/2.83 ~spl0_61|spl0_62),
% 19.62/2.83 inference(split_clause,[status(thm)],[f143,f423,f426])).
% 19.62/2.83 fof(f430,plain,(
% 19.62/2.83 spl0_63 <=> is_a_theorem(implies(implies(not(sk0_43),sk0_43),sk0_43))),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f432,plain,(
% 19.62/2.83 ~is_a_theorem(implies(implies(not(sk0_43),sk0_43),sk0_43))|spl0_63),
% 19.62/2.83 inference(component_clause,[status(thm)],[f430])).
% 19.62/2.83 fof(f433,plain,(
% 19.62/2.83 spl0_61|~spl0_63),
% 19.62/2.83 inference(split_clause,[status(thm)],[f144,f423,f430])).
% 19.62/2.83 fof(f486,plain,(
% 19.62/2.83 spl0_78 <=> op_or),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f488,plain,(
% 19.62/2.83 ~op_or|spl0_78),
% 19.62/2.83 inference(component_clause,[status(thm)],[f486])).
% 19.62/2.83 fof(f489,plain,(
% 19.62/2.83 spl0_79 <=> or(X0,X1)=not(and(not(X0),not(X1)))),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f490,plain,(
% 19.62/2.83 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1)))|~spl0_79)),
% 19.62/2.83 inference(component_clause,[status(thm)],[f489])).
% 19.62/2.83 fof(f492,plain,(
% 19.62/2.83 ~spl0_78|spl0_79),
% 19.62/2.83 inference(split_clause,[status(thm)],[f166,f486,f489])).
% 19.62/2.83 fof(f500,plain,(
% 19.62/2.83 spl0_82 <=> op_implies_and),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f502,plain,(
% 19.62/2.83 ~op_implies_and|spl0_82),
% 19.62/2.83 inference(component_clause,[status(thm)],[f500])).
% 19.62/2.83 fof(f503,plain,(
% 19.62/2.83 spl0_83 <=> implies(X0,X1)=not(and(X0,not(X1)))),
% 19.62/2.83 introduced(split_symbol_definition)).
% 19.62/2.83 fof(f504,plain,(
% 19.62/2.83 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1)))|~spl0_83)),
% 19.62/2.83 inference(component_clause,[status(thm)],[f503])).
% 19.62/2.83 fof(f506,plain,(
% 19.62/2.83 ~spl0_82|spl0_83),
% 19.62/2.83 inference(split_clause,[status(thm)],[f170,f500,f503])).
% 19.62/2.83 fof(f523,plain,(
% 19.62/2.83 $false|spl0_82),
% 19.62/2.83 inference(forward_subsumption_resolution,[status(thm)],[f502,f176])).
% 19.62/2.83 fof(f524,plain,(
% 19.62/2.83 spl0_82),
% 19.62/2.83 inference(contradiction_clause,[status(thm)],[f523])).
% 19.62/2.83 fof(f525,plain,(
% 19.62/2.83 $false|spl0_78),
% 19.62/2.83 inference(forward_subsumption_resolution,[status(thm)],[f488,f175])).
% 19.62/2.83 fof(f526,plain,(
% 19.62/2.83 spl0_78),
% 19.62/2.83 inference(contradiction_clause,[status(thm)],[f525])).
% 19.62/2.83 fof(f527,plain,(
% 19.62/2.83 $false|spl0_0),
% 19.62/2.83 inference(forward_subsumption_resolution,[status(thm)],[f199,f178])).
% 19.62/2.83 fof(f528,plain,(
% 19.62/2.83 spl0_0),
% 19.62/2.83 inference(contradiction_clause,[status(thm)],[f527])).
% 19.62/2.83 fof(f529,plain,(
% 19.62/2.83 $false|spl0_5),
% 19.62/2.83 inference(forward_subsumption_resolution,[status(thm)],[f218,f192])).
% 19.62/2.83 fof(f530,plain,(
% 19.62/2.83 spl0_5),
% 19.62/2.83 inference(contradiction_clause,[status(thm)],[f529])).
% 19.62/2.83 fof(f579,plain,(
% 19.62/2.83 $false|spl0_45),
% 19.62/2.83 inference(forward_subsumption_resolution,[status(thm)],[f365,f191])).
% 19.62/2.83 fof(f580,plain,(
% 19.62/2.83 spl0_45),
% 19.62/2.83 inference(contradiction_clause,[status(thm)],[f579])).
% 19.62/2.83 fof(f585,plain,(
% 19.62/2.83 $false|spl0_36),
% 19.62/2.83 inference(forward_subsumption_resolution,[status(thm)],[f332,f188])).
% 19.62/2.83 fof(f586,plain,(
% 19.62/2.83 spl0_36),
% 19.62/2.83 inference(contradiction_clause,[status(thm)],[f585])).
% 19.62/2.83 fof(f587,plain,(
% 19.62/2.83 $false|spl0_30),
% 19.62/2.83 inference(forward_subsumption_resolution,[status(thm)],[f310,f186])).
% 19.62/2.83 fof(f588,plain,(
% 19.62/2.83 spl0_30),
% 19.62/2.83 inference(contradiction_clause,[status(thm)],[f587])).
% 19.62/2.85 fof(f589,plain,(
% 19.62/2.85 $false|spl0_27),
% 19.62/2.85 inference(forward_subsumption_resolution,[status(thm)],[f299,f185])).
% 19.62/2.85 fof(f590,plain,(
% 19.62/2.85 spl0_27),
% 19.62/2.85 inference(contradiction_clause,[status(thm)],[f589])).
% 19.62/2.85 fof(f591,plain,(
% 19.62/2.85 $false|spl0_24),
% 19.62/2.85 inference(forward_subsumption_resolution,[status(thm)],[f288,f184])).
% 19.62/2.85 fof(f592,plain,(
% 19.62/2.85 spl0_24),
% 19.62/2.85 inference(contradiction_clause,[status(thm)],[f591])).
% 19.62/2.85 fof(f593,plain,(
% 19.62/2.85 $false|spl0_15),
% 19.62/2.85 inference(forward_subsumption_resolution,[status(thm)],[f255,f181])).
% 19.62/2.85 fof(f594,plain,(
% 19.62/2.85 spl0_15),
% 19.62/2.85 inference(contradiction_clause,[status(thm)],[f593])).
% 19.62/2.85 fof(f595,plain,(
% 19.62/2.85 $false|spl0_12),
% 19.62/2.85 inference(forward_subsumption_resolution,[status(thm)],[f244,f180])).
% 19.62/2.85 fof(f596,plain,(
% 19.62/2.85 spl0_12),
% 19.62/2.85 inference(contradiction_clause,[status(thm)],[f595])).
% 19.62/2.85 fof(f597,plain,(
% 19.62/2.85 $false|spl0_9),
% 19.62/2.85 inference(forward_subsumption_resolution,[status(thm)],[f233,f179])).
% 19.62/2.85 fof(f598,plain,(
% 19.62/2.85 spl0_9),
% 19.62/2.85 inference(contradiction_clause,[status(thm)],[f597])).
% 19.62/2.85 fof(f601,plain,(
% 19.62/2.85 $false|spl0_18),
% 19.62/2.85 inference(forward_subsumption_resolution,[status(thm)],[f266,f182])).
% 19.62/2.85 fof(f602,plain,(
% 19.62/2.85 spl0_18),
% 19.62/2.85 inference(contradiction_clause,[status(thm)],[f601])).
% 19.62/2.85 fof(f606,plain,(
% 19.62/2.85 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1)|~spl0_79|~spl0_83)),
% 19.62/2.85 inference(paramodulation,[status(thm)],[f504,f490])).
% 19.62/2.85 fof(f607,plain,(
% 19.62/2.85 ![X0,X1,X2]: (or(and(not(X0),not(X1)),X2)=not(and(or(X0,X1),not(X2)))|~spl0_79)),
% 19.62/2.85 inference(paramodulation,[status(thm)],[f490,f490])).
% 19.62/2.85 fof(f613,plain,(
% 19.62/2.85 ~is_a_theorem(implies(implies(sk0_35,sk0_36),or(and(sk0_36,sk0_37),not(and(sk0_37,sk0_35)))))|~spl0_79|~spl0_83|spl0_55),
% 19.62/2.85 inference(backward_demodulation,[status(thm)],[f606,f402])).
% 19.62/2.85 fof(f617,plain,(
% 19.62/2.85 ~is_a_theorem(implies(or(sk0_43,sk0_43),sk0_43))|~spl0_79|~spl0_83|spl0_63),
% 19.62/2.85 inference(backward_demodulation,[status(thm)],[f606,f432])).
% 19.62/2.85 fof(f618,plain,(
% 19.62/2.85 ![X0,X1]: (is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0)))|~spl0_79|~spl0_83|~spl0_10)),
% 19.62/2.85 inference(backward_demodulation,[status(thm)],[f606,f235])).
% 19.62/2.85 fof(f635,plain,(
% 19.62/2.85 ![X0,X1,X2]: (or(and(X0,not(X1)),X2)=implies(implies(X0,X1),X2)|~spl0_79|~spl0_83)),
% 19.62/2.85 inference(paramodulation,[status(thm)],[f504,f606])).
% 19.62/2.85 fof(f669,plain,(
% 19.62/2.85 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(implies(X1,X0),equiv(X0,X1)))|~spl0_46|~spl0_1)),
% 19.62/2.85 inference(resolution,[status(thm)],[f367,f201])).
% 19.62/2.85 fof(f680,plain,(
% 19.62/2.85 ![X0,X1]: (~is_a_theorem(implies(X0,implies(X0,X1)))|is_a_theorem(implies(X0,X1))|~spl0_16|~spl0_1)),
% 19.62/2.85 inference(resolution,[status(thm)],[f257,f201])).
% 19.62/2.85 fof(f701,plain,(
% 19.62/2.85 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,or(X1,X2)),implies(and(not(X1),not(X2)),X0)))|~spl0_83|~spl0_10|~spl0_79)),
% 19.62/2.85 inference(paramodulation,[status(thm)],[f490,f618])).
% 19.62/2.85 fof(f751,plain,(
% 19.62/2.85 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),implies(or(X0,X0),X1)))|~spl0_16|~spl0_1|~spl0_37)),
% 19.62/2.85 inference(resolution,[status(thm)],[f680,f334])).
% 19.62/2.85 fof(f754,plain,(
% 19.62/2.85 ![X0]: (is_a_theorem(implies(X0,and(X0,X0)))|~spl0_16|~spl0_1|~spl0_28)),
% 19.62/2.85 inference(resolution,[status(thm)],[f680,f301])).
% 19.62/2.85 fof(f755,plain,(
% 19.62/2.85 spl0_49|~spl0_16|~spl0_1|~spl0_28),
% 19.62/2.85 inference(split_clause,[status(thm)],[f754,f377,f256,f200,f300])).
% 19.62/2.85 fof(f756,plain,(
% 19.62/2.85 ![X0]: (is_a_theorem(implies(X0,X0))|~spl0_16|~spl0_1|~spl0_13)),
% 19.62/2.85 inference(resolution,[status(thm)],[f680,f246])).
% 19.62/2.85 fof(f1023,plain,(
% 19.62/2.85 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(or(X0,X0),X1))|~spl0_16|~spl0_37|~spl0_1)),
% 19.62/2.85 inference(resolution,[status(thm)],[f751,f201])).
% 19.62/2.85 fof(f1095,plain,(
% 19.62/2.85 ~is_a_theorem(implies(sk0_43,sk0_43))|~spl0_16|~spl0_37|~spl0_1|~spl0_79|~spl0_83|spl0_63),
% 19.62/2.85 inference(resolution,[status(thm)],[f1023,f617])).
% 19.62/2.85 fof(f1096,plain,(
% 19.62/2.85 $false|~spl0_13|~spl0_16|~spl0_37|~spl0_1|~spl0_79|~spl0_83|spl0_63),
% 19.62/2.85 inference(forward_subsumption_resolution,[status(thm)],[f1095,f756])).
% 19.62/2.85 fof(f1097,plain,(
% 19.62/2.85 ~spl0_13|~spl0_16|~spl0_37|~spl0_1|~spl0_79|~spl0_83|spl0_63),
% 19.62/2.85 inference(contradiction_clause,[status(thm)],[f1096])).
% 19.62/2.85 fof(f1112,plain,(
% 19.62/2.85 ![X0]: (is_a_theorem(implies(or(X0,X0),X0))|~spl0_79|~spl0_83|~spl0_62)),
% 19.62/2.85 inference(forward_demodulation,[status(thm)],[f606,f427])).
% 19.62/2.85 fof(f1561,plain,(
% 19.62/2.85 ![X0,X1,X2]: (~is_a_theorem(implies(implies(or(X0,not(X1)),implies(X1,X0)),X2))|is_a_theorem(X2)|~spl0_79|~spl0_83|~spl0_10|~spl0_1)),
% 19.62/2.85 inference(resolution,[status(thm)],[f618,f201])).
% 19.62/2.85 fof(f1590,plain,(
% 19.62/2.85 ![X0,X1]: (~is_a_theorem(implies(implies(or(X0,X0),X0),X1))|is_a_theorem(X1)|~spl0_79|~spl0_83|~spl0_62|~spl0_1)),
% 19.62/2.85 inference(resolution,[status(thm)],[f1112,f201])).
% 19.62/2.85 fof(f1622,plain,(
% 19.62/2.85 ![X0,X1]: (~is_a_theorem(implies(implies(X0,and(X0,X0)),X1))|is_a_theorem(X1)|~spl0_49|~spl0_1)),
% 19.62/2.85 inference(resolution,[status(thm)],[f378,f201])).
% 19.62/2.85 fof(f2541,plain,(
% 19.62/2.85 ![X0,X1]: (is_a_theorem(equiv(implies(X0,X1),or(X1,not(X0))))|~is_a_theorem(implies(implies(X0,X1),or(X1,not(X0))))|~spl0_79|~spl0_83|~spl0_10|~spl0_46|~spl0_1)),
% 19.62/2.85 inference(resolution,[status(thm)],[f1561,f669])).
% 19.62/2.85 fof(f2639,plain,(
% 19.62/2.85 ![X0]: (is_a_theorem(equiv(X0,or(X0,X0)))|~is_a_theorem(implies(X0,or(X0,X0)))|~spl0_79|~spl0_83|~spl0_62|~spl0_46|~spl0_1)),
% 19.62/2.85 inference(resolution,[status(thm)],[f1590,f669])).
% 19.62/2.85 fof(f2640,plain,(
% 19.62/2.85 ![X0]: (is_a_theorem(equiv(X0,or(X0,X0)))|~spl0_31|~spl0_79|~spl0_83|~spl0_62|~spl0_46|~spl0_1)),
% 19.62/2.85 inference(forward_subsumption_resolution,[status(thm)],[f2639,f312])).
% 19.62/2.85 fof(f2691,plain,(
% 19.62/2.85 ![X0]: (X0=or(X0,X0)|~spl0_31|~spl0_79|~spl0_83|~spl0_62|~spl0_46|~spl0_1|~spl0_6)),
% 19.62/2.85 inference(resolution,[status(thm)],[f2640,f220])).
% 19.62/2.85 fof(f2726,plain,(
% 19.62/2.85 ![X0,X1]: (and(not(X0),not(X1))=not(and(or(X0,X1),not(and(not(X0),not(X1)))))|~spl0_31|~spl0_83|~spl0_62|~spl0_46|~spl0_1|~spl0_6|~spl0_79)),
% 19.62/2.85 inference(paramodulation,[status(thm)],[f607,f2691])).
% 19.62/2.85 fof(f2727,plain,(
% 19.62/2.85 ![X0,X1]: (and(not(X0),not(X1))=not(and(or(X0,X1),or(X0,X1)))|~spl0_31|~spl0_83|~spl0_62|~spl0_46|~spl0_1|~spl0_6|~spl0_79)),
% 19.62/2.85 inference(forward_demodulation,[status(thm)],[f490,f2726])).
% 19.62/2.85 fof(f2775,plain,(
% 19.62/2.85 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),implies(and(not(X1),not(X1)),X0)))|~spl0_10|~spl0_31|~spl0_79|~spl0_83|~spl0_62|~spl0_46|~spl0_1|~spl0_6)),
% 19.62/2.85 inference(paramodulation,[status(thm)],[f2691,f701])).
% 19.62/2.85 fof(f3131,plain,(
% 19.62/2.85 ![X0]: (is_a_theorem(equiv(and(X0,X0),X0))|~is_a_theorem(implies(and(X0,X0),X0))|~spl0_49|~spl0_46|~spl0_1)),
% 19.62/2.85 inference(resolution,[status(thm)],[f1622,f669])).
% 19.62/2.85 fof(f3132,plain,(
% 19.62/2.85 ![X0]: (is_a_theorem(equiv(and(X0,X0),X0))|~spl0_25|~spl0_49|~spl0_46|~spl0_1)),
% 19.62/2.85 inference(forward_subsumption_resolution,[status(thm)],[f3131,f290])).
% 19.62/2.85 fof(f3245,plain,(
% 19.62/2.85 ![X0]: (and(X0,X0)=X0|~spl0_25|~spl0_49|~spl0_46|~spl0_1|~spl0_6)),
% 19.62/2.85 inference(resolution,[status(thm)],[f3132,f220])).
% 19.62/2.85 fof(f3265,plain,(
% 19.62/2.85 ![X0,X1]: (and(not(X0),not(X1))=not(or(X0,X1))|~spl0_25|~spl0_49|~spl0_31|~spl0_83|~spl0_62|~spl0_46|~spl0_1|~spl0_6|~spl0_79)),
% 19.62/2.85 inference(backward_demodulation,[status(thm)],[f3245,f2727])).
% 19.62/2.85 fof(f3270,plain,(
% 19.62/2.85 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),implies(not(X1),X0)))|~spl0_25|~spl0_49|~spl0_10|~spl0_31|~spl0_79|~spl0_83|~spl0_62|~spl0_46|~spl0_1|~spl0_6)),
% 19.62/2.85 inference(backward_demodulation,[status(thm)],[f3245,f2775])).
% 19.62/2.85 fof(f3271,plain,(
% 19.62/2.85 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),or(X1,X0)))|~spl0_25|~spl0_49|~spl0_10|~spl0_31|~spl0_79|~spl0_83|~spl0_62|~spl0_46|~spl0_1|~spl0_6)),
% 19.62/2.85 inference(forward_demodulation,[status(thm)],[f606,f3270])).
% 19.62/2.85 fof(f3300,plain,(
% 19.62/2.85 ![X0,X1]: (or(X0,X1)=not(not(or(X0,X1)))|~spl0_25|~spl0_49|~spl0_31|~spl0_83|~spl0_62|~spl0_46|~spl0_1|~spl0_6|~spl0_79)),
% 19.62/2.85 inference(backward_demodulation,[status(thm)],[f3265,f490])).
% 19.62/2.85 fof(f3573,plain,(
% 19.62/2.85 ![X0,X1]: (or(not(X0),X1)=implies(implies(not(X0),X0),X1)|~spl0_79|~spl0_83|~spl0_25|~spl0_49|~spl0_46|~spl0_1|~spl0_6)),
% 19.62/2.85 inference(paramodulation,[status(thm)],[f3245,f635])).
% 19.62/2.85 fof(f3574,plain,(
% 19.62/2.85 ![X0,X1]: (or(not(X0),X1)=implies(or(X0,X0),X1)|~spl0_79|~spl0_83|~spl0_25|~spl0_49|~spl0_46|~spl0_1|~spl0_6)),
% 19.62/2.85 inference(forward_demodulation,[status(thm)],[f606,f3573])).
% 19.62/2.85 fof(f3575,plain,(
% 19.62/2.85 ![X0,X1]: (or(not(X0),X1)=implies(X0,X1)|~spl0_31|~spl0_62|~spl0_79|~spl0_83|~spl0_25|~spl0_49|~spl0_46|~spl0_1|~spl0_6)),
% 19.62/2.85 inference(forward_demodulation,[status(thm)],[f2691,f3574])).
% 19.62/2.85 fof(f3694,plain,(
% 19.62/2.85 ![X0]: (or(X0,X0)=not(not(X0))|~spl0_25|~spl0_49|~spl0_31|~spl0_79|~spl0_83|~spl0_62|~spl0_46|~spl0_1|~spl0_6)),
% 19.62/2.85 inference(paramodulation,[status(thm)],[f2691,f3300])).
% 19.62/2.85 fof(f3728,plain,(
% 19.62/2.85 ![X0]: (X0=not(not(X0))|~spl0_25|~spl0_49|~spl0_31|~spl0_79|~spl0_83|~spl0_62|~spl0_46|~spl0_1|~spl0_6)),
% 19.62/2.85 inference(paramodulation,[status(thm)],[f2691,f3694])).
% 19.62/2.85 fof(f3834,plain,(
% 19.62/2.85 ![X0,X1]: (and(X0,not(X1))=not(implies(X0,X1))|~spl0_25|~spl0_49|~spl0_31|~spl0_79|~spl0_62|~spl0_46|~spl0_1|~spl0_6|~spl0_83)),
% 19.62/2.85 inference(paramodulation,[status(thm)],[f504,f3728])).
% 19.62/2.85 fof(f3868,plain,(
% 19.62/2.85 ![X0,X1]: (implies(X0,not(X1))=not(and(X0,X1))|~spl0_25|~spl0_49|~spl0_31|~spl0_79|~spl0_83|~spl0_62|~spl0_46|~spl0_1|~spl0_6)),
% 19.62/2.85 inference(paramodulation,[status(thm)],[f3728,f504])).
% 19.62/2.85 fof(f4069,plain,(
% 19.62/2.85 ~is_a_theorem(implies(implies(sk0_35,sk0_36),or(and(sk0_36,sk0_37),implies(sk0_37,not(sk0_35)))))|~spl0_25|~spl0_49|~spl0_31|~spl0_62|~spl0_46|~spl0_1|~spl0_6|~spl0_79|~spl0_83|spl0_55),
% 19.62/2.85 inference(backward_demodulation,[status(thm)],[f3868,f613])).
% 19.62/2.85 fof(f4429,plain,(
% 19.62/2.85 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),or(X1,not(X0))))|~spl0_10|~spl0_31|~spl0_62|~spl0_79|~spl0_83|~spl0_25|~spl0_49|~spl0_46|~spl0_1|~spl0_6)),
% 19.62/2.85 inference(paramodulation,[status(thm)],[f3575,f3271])).
% 19.62/2.85 fof(f4444,plain,(
% 19.62/2.85 ![X0,X1]: (is_a_theorem(equiv(implies(X0,X1),or(X1,not(X0))))|~spl0_31|~spl0_62|~spl0_25|~spl0_49|~spl0_6|~spl0_79|~spl0_83|~spl0_10|~spl0_46|~spl0_1)),
% 19.62/2.85 inference(backward_subsumption_resolution,[status(thm)],[f2541,f4429])).
% 19.62/2.85 fof(f4881,plain,(
% 19.62/2.85 ![X0,X1]: (and(X0,X1)=not(implies(X0,not(X1)))|~spl0_25|~spl0_49|~spl0_31|~spl0_79|~spl0_83|~spl0_62|~spl0_46|~spl0_1|~spl0_6)),
% 19.62/2.85 inference(paramodulation,[status(thm)],[f3728,f3834])).
% 19.62/2.85 fof(f5091,plain,(
% 19.62/2.85 ![X0,X1,X2]: (or(implies(X0,not(X1)),X2)=implies(and(X0,X1),X2)|~spl0_25|~spl0_49|~spl0_31|~spl0_79|~spl0_83|~spl0_62|~spl0_46|~spl0_1|~spl0_6)),
% 19.62/2.85 inference(paramodulation,[status(thm)],[f3868,f3575])).
% 19.62/2.85 fof(f5861,plain,(
% 19.62/2.85 $false|~spl0_53),
% 19.62/2.85 inference(forward_subsumption_resolution,[status(thm)],[f394,f196])).
% 19.62/2.85 fof(f5862,plain,(
% 19.62/2.85 ~spl0_53),
% 19.62/2.85 inference(contradiction_clause,[status(thm)],[f5861])).
% 19.62/2.85 fof(f10346,plain,(
% 19.62/2.85 ![X0,X1]: (implies(X0,X1)=or(X1,not(X0))|~spl0_31|~spl0_62|~spl0_25|~spl0_49|~spl0_79|~spl0_83|~spl0_10|~spl0_46|~spl0_1|~spl0_6)),
% 19.62/2.85 inference(resolution,[status(thm)],[f4444,f220])).
% 19.62/2.85 fof(f11027,plain,(
% 19.62/2.85 ![X0,X1]: (implies(X0,not(X1))=implies(X1,not(X0))|~spl0_10|~spl0_31|~spl0_62|~spl0_79|~spl0_83|~spl0_25|~spl0_49|~spl0_46|~spl0_1|~spl0_6)),
% 19.62/2.85 inference(paramodulation,[status(thm)],[f3575,f10346])).
% 19.62/2.85 fof(f11034,plain,(
% 19.62/2.85 ![X0,X1,X2]: (implies(implies(X0,not(X1)),X2)=or(X2,and(X0,X1))|~spl0_10|~spl0_25|~spl0_49|~spl0_31|~spl0_79|~spl0_83|~spl0_62|~spl0_46|~spl0_1|~spl0_6)),
% 19.62/2.85 inference(paramodulation,[status(thm)],[f4881,f10346])).
% 19.62/2.85 fof(f11036,plain,(
% 19.62/2.85 ![X0,X1,X2]: (implies(and(X0,X1),X2)=or(X2,implies(X0,not(X1)))|~spl0_10|~spl0_25|~spl0_49|~spl0_31|~spl0_79|~spl0_83|~spl0_62|~spl0_46|~spl0_1|~spl0_6)),
% 19.62/2.85 inference(paramodulation,[status(thm)],[f3868,f10346])).
% 19.62/2.85 fof(f11130,plain,(
% 19.62/2.85 ~is_a_theorem(implies(implies(sk0_35,sk0_36),implies(and(sk0_37,sk0_35),and(sk0_36,sk0_37))))|~spl0_10|~spl0_25|~spl0_49|~spl0_31|~spl0_62|~spl0_46|~spl0_1|~spl0_6|~spl0_79|~spl0_83|spl0_55),
% 19.62/2.85 inference(backward_demodulation,[status(thm)],[f11036,f4069])).
% 19.62/2.85 fof(f12813,plain,(
% 19.62/2.85 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,not(X2)),implies(X2,not(X0)))))|~spl0_19|~spl0_10|~spl0_31|~spl0_62|~spl0_79|~spl0_83|~spl0_25|~spl0_49|~spl0_46|~spl0_1|~spl0_6)),
% 19.62/2.85 inference(paramodulation,[status(thm)],[f11027,f268])).
% 19.62/2.85 fof(f12814,plain,(
% 19.62/2.85 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),or(implies(X2,not(X0)),and(X1,X2))))|~spl0_19|~spl0_10|~spl0_31|~spl0_62|~spl0_79|~spl0_83|~spl0_25|~spl0_49|~spl0_46|~spl0_1|~spl0_6)),
% 19.62/2.85 inference(forward_demodulation,[status(thm)],[f11034,f12813])).
% 19.62/2.85 fof(f12815,plain,(
% 19.62/2.85 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(and(X2,X0),and(X1,X2))))|~spl0_19|~spl0_10|~spl0_31|~spl0_62|~spl0_79|~spl0_83|~spl0_25|~spl0_49|~spl0_46|~spl0_1|~spl0_6)),
% 19.62/2.85 inference(forward_demodulation,[status(thm)],[f5091,f12814])).
% 19.62/2.85 fof(f13326,plain,(
% 19.99/2.88 $false|~spl0_19|~spl0_10|~spl0_25|~spl0_49|~spl0_31|~spl0_62|~spl0_46|~spl0_1|~spl0_6|~spl0_79|~spl0_83|spl0_55),
% 19.99/2.88 inference(backward_subsumption_resolution,[status(thm)],[f11130,f12815])).
% 19.99/2.88 fof(f13327,plain,(
% 19.99/2.88 ~spl0_19|~spl0_10|~spl0_25|~spl0_49|~spl0_31|~spl0_62|~spl0_46|~spl0_1|~spl0_6|~spl0_79|~spl0_83|spl0_55),
% 19.99/2.88 inference(contradiction_clause,[status(thm)],[f13326])).
% 19.99/2.88 fof(f13328,plain,(
% 19.99/2.88 $false),
% 19.99/2.88 inference(sat_refutation,[status(thm)],[f203,f222,f237,f248,f259,f270,f292,f303,f314,f336,f369,f403,f429,f433,f492,f506,f524,f526,f528,f530,f580,f586,f588,f590,f592,f594,f596,f598,f602,f755,f1097,f5862,f13327])).
% 19.99/2.88 % SZS output end CNFRefutation for theBenchmark.p
% 20.43/2.91 % Elapsed time: 2.571881 seconds
% 20.43/2.91 % CPU time: 20.080371 seconds
% 20.43/2.91 % Total memory used: 320.111 MB
% 20.43/2.91 % Net memory used: 308.958 MB
%------------------------------------------------------------------------------