TSTP Solution File: LCL526+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : LCL526+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n019.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 20:27:22 EDT 2024
% Result : Theorem 0.17s 0.49s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL526+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32 % Computer : n019.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Mon Apr 29 20:24:44 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.10/0.33 % Drodi V3.6.0
% 0.17/0.49 % Refutation found
% 0.17/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.49 % SZS output start CNFRefutation for theBenchmark
% 0.17/0.49 fof(f1,axiom,(
% 0.17/0.49 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 0.17/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f2,axiom,(
% 0.17/0.49 ( substitution_of_equivalents<=> (! [X,Y] :( is_a_theorem(equiv(X,Y))=> X = Y ) )) ),
% 0.17/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f7,axiom,(
% 0.17/0.49 ( and_1<=> (! [X,Y] : is_a_theorem(implies(and(X,Y),X)) )) ),
% 0.17/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f8,axiom,(
% 0.17/0.49 ( and_2<=> (! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) )) ),
% 0.17/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f9,axiom,(
% 0.17/0.49 ( and_3<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) )) ),
% 0.17/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f31,axiom,(
% 0.17/0.49 ( op_equiv=> (! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) )) ),
% 0.17/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f34,axiom,(
% 0.17/0.49 op_equiv ),
% 0.17/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f35,axiom,(
% 0.17/0.49 modus_ponens ),
% 0.17/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f36,axiom,(
% 0.17/0.49 modus_tollens ),
% 0.17/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f38,axiom,(
% 0.17/0.49 implies_2 ),
% 0.17/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f40,axiom,(
% 0.17/0.49 and_1 ),
% 0.17/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f41,axiom,(
% 0.17/0.49 and_2 ),
% 0.17/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f42,axiom,(
% 0.17/0.49 and_3 ),
% 0.17/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f45,axiom,(
% 0.17/0.49 or_3 ),
% 0.17/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f46,axiom,(
% 0.17/0.49 equivalence_1 ),
% 0.17/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f47,axiom,(
% 0.17/0.49 equivalence_2 ),
% 0.17/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f48,axiom,(
% 0.17/0.49 equivalence_3 ),
% 0.17/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f49,axiom,(
% 0.17/0.49 substitution_of_equivalents ),
% 0.17/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f52,axiom,(
% 0.17/0.49 ( adjunction<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(Y) )=> is_a_theorem(and(X,Y)) ) )) ),
% 0.17/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f53,axiom,(
% 0.17/0.49 ( substitution_strict_equiv<=> (! [X,Y] :( is_a_theorem(strict_equiv(X,Y))=> X = Y ) )) ),
% 0.17/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f55,axiom,(
% 0.17/0.49 ( axiom_M<=> (! [X] : is_a_theorem(implies(necessarily(X),X)) )) ),
% 0.17/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f75,axiom,(
% 0.17/0.49 ( op_strict_implies=> (! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) )) ),
% 0.17/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f76,axiom,(
% 0.17/0.49 ( op_strict_equiv=> (! [X,Y] : strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X)) )) ),
% 0.17/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f80,axiom,(
% 0.17/0.49 axiom_M ),
% 0.17/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f85,axiom,(
% 0.17/0.49 op_strict_implies ),
% 0.17/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f87,axiom,(
% 0.17/0.49 op_strict_equiv ),
% 0.17/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f88,conjecture,(
% 0.17/0.49 substitution_strict_equiv ),
% 0.17/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.49 fof(f89,negated_conjecture,(
% 0.17/0.49 ~(substitution_strict_equiv )),
% 0.17/0.49 inference(negated_conjecture,[status(cth)],[f88])).
% 0.17/0.49 fof(f90,plain,(
% 0.17/0.49 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 0.17/0.49 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 0.17/0.49 fof(f91,plain,(
% 0.17/0.49 (~modus_ponens|(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y))))&(modus_ponens|(?[X,Y]: ((is_a_theorem(X)&is_a_theorem(implies(X,Y)))&~is_a_theorem(Y))))),
% 0.17/0.49 inference(NNF_transformation,[status(esa)],[f90])).
% 0.17/0.49 fof(f92,plain,(
% 0.17/0.49 (~modus_ponens|(![Y]: ((![X]: (~is_a_theorem(X)|~is_a_theorem(implies(X,Y))))|is_a_theorem(Y))))&(modus_ponens|(?[Y]: ((?[X]: (is_a_theorem(X)&is_a_theorem(implies(X,Y))))&~is_a_theorem(Y))))),
% 0.17/0.50 inference(miniscoping,[status(esa)],[f91])).
% 0.17/0.50 fof(f93,plain,(
% 0.17/0.50 (~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)))),
% 0.17/0.50 inference(skolemization,[status(esa)],[f92])).
% 0.17/0.50 fof(f94,plain,(
% 0.17/0.50 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f93])).
% 0.17/0.50 fof(f98,plain,(
% 0.17/0.50 substitution_of_equivalents<=>(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y))),
% 0.17/0.50 inference(pre_NNF_transformation,[status(esa)],[f2])).
% 0.17/0.50 fof(f99,plain,(
% 0.17/0.50 (~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)))),
% 0.17/0.50 inference(NNF_transformation,[status(esa)],[f98])).
% 0.17/0.50 fof(f100,plain,(
% 0.17/0.50 (~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))),
% 0.17/0.50 inference(skolemization,[status(esa)],[f99])).
% 0.17/0.50 fof(f101,plain,(
% 0.17/0.50 ![X0,X1]: (~substitution_of_equivalents|~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f100])).
% 0.17/0.50 fof(f120,plain,(
% 0.17/0.50 (~and_1|(![X,Y]: is_a_theorem(implies(and(X,Y),X))))&(and_1|(?[X,Y]: ~is_a_theorem(implies(and(X,Y),X))))),
% 0.17/0.50 inference(NNF_transformation,[status(esa)],[f7])).
% 0.17/0.50 fof(f121,plain,(
% 0.17/0.50 (~and_1|(![X,Y]: is_a_theorem(implies(and(X,Y),X))))&(and_1|~is_a_theorem(implies(and(sk0_13,sk0_14),sk0_13)))),
% 0.17/0.50 inference(skolemization,[status(esa)],[f120])).
% 0.17/0.50 fof(f122,plain,(
% 0.17/0.50 ![X0,X1]: (~and_1|is_a_theorem(implies(and(X0,X1),X0)))),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f121])).
% 0.17/0.50 fof(f124,plain,(
% 0.17/0.50 (~and_2|(![X,Y]: is_a_theorem(implies(and(X,Y),Y))))&(and_2|(?[X,Y]: ~is_a_theorem(implies(and(X,Y),Y))))),
% 0.17/0.50 inference(NNF_transformation,[status(esa)],[f8])).
% 0.17/0.50 fof(f125,plain,(
% 0.17/0.50 (~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)))),
% 0.17/0.50 inference(skolemization,[status(esa)],[f124])).
% 0.17/0.50 fof(f126,plain,(
% 0.17/0.50 ![X0,X1]: (~and_2|is_a_theorem(implies(and(X0,X1),X1)))),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f125])).
% 0.17/0.50 fof(f128,plain,(
% 0.17/0.50 (~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))))))),
% 0.17/0.50 inference(NNF_transformation,[status(esa)],[f9])).
% 0.17/0.50 fof(f129,plain,(
% 0.17/0.50 (~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)))))),
% 0.17/0.50 inference(skolemization,[status(esa)],[f128])).
% 0.17/0.50 fof(f130,plain,(
% 0.17/0.50 ![X0,X1]: (~and_3|is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f129])).
% 0.17/0.50 fof(f208,plain,(
% 0.17/0.50 ~op_equiv|(![X,Y]: equiv(X,Y)=and(implies(X,Y),implies(Y,X)))),
% 0.17/0.50 inference(pre_NNF_transformation,[status(esa)],[f31])).
% 0.17/0.50 fof(f209,plain,(
% 0.17/0.50 ![X0,X1]: (~op_equiv|equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f208])).
% 0.17/0.50 fof(f212,plain,(
% 0.17/0.50 op_equiv),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f34])).
% 0.17/0.50 fof(f213,plain,(
% 0.17/0.50 modus_ponens),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f35])).
% 0.17/0.50 fof(f214,plain,(
% 0.17/0.50 modus_tollens),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f36])).
% 0.17/0.50 fof(f216,plain,(
% 0.17/0.50 implies_2),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f38])).
% 0.17/0.50 fof(f218,plain,(
% 0.17/0.50 and_1),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f40])).
% 0.17/0.50 fof(f219,plain,(
% 0.17/0.50 and_2),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f41])).
% 0.17/0.50 fof(f220,plain,(
% 0.17/0.50 and_3),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f42])).
% 0.17/0.50 fof(f223,plain,(
% 0.17/0.50 or_3),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f45])).
% 0.17/0.50 fof(f224,plain,(
% 0.17/0.50 equivalence_1),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f46])).
% 0.17/0.50 fof(f225,plain,(
% 0.17/0.50 equivalence_2),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f47])).
% 0.17/0.50 fof(f226,plain,(
% 0.17/0.50 equivalence_3),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f48])).
% 0.17/0.50 fof(f227,plain,(
% 0.17/0.50 substitution_of_equivalents),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f49])).
% 0.17/0.50 fof(f242,plain,(
% 0.17/0.50 adjunction<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(Y))|is_a_theorem(and(X,Y))))),
% 0.17/0.50 inference(pre_NNF_transformation,[status(esa)],[f52])).
% 0.17/0.50 fof(f243,plain,(
% 0.17/0.50 (~adjunction|(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(Y))|is_a_theorem(and(X,Y)))))&(adjunction|(?[X,Y]: ((is_a_theorem(X)&is_a_theorem(Y))&~is_a_theorem(and(X,Y)))))),
% 0.17/0.50 inference(NNF_transformation,[status(esa)],[f242])).
% 0.17/0.50 fof(f244,plain,(
% 0.17/0.50 (~adjunction|(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(Y))|is_a_theorem(and(X,Y)))))&(adjunction|((is_a_theorem(sk0_58)&is_a_theorem(sk0_59))&~is_a_theorem(and(sk0_58,sk0_59))))),
% 0.17/0.50 inference(skolemization,[status(esa)],[f243])).
% 0.17/0.50 fof(f245,plain,(
% 0.17/0.50 ![X0,X1]: (~adjunction|~is_a_theorem(X0)|~is_a_theorem(X1)|is_a_theorem(and(X0,X1)))),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f244])).
% 0.17/0.50 fof(f246,plain,(
% 0.17/0.50 adjunction|is_a_theorem(sk0_58)),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f244])).
% 0.17/0.50 fof(f247,plain,(
% 0.17/0.50 adjunction|is_a_theorem(sk0_59)),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f244])).
% 0.17/0.50 fof(f248,plain,(
% 0.17/0.50 adjunction|~is_a_theorem(and(sk0_58,sk0_59))),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f244])).
% 0.17/0.50 fof(f249,plain,(
% 0.17/0.50 substitution_strict_equiv<=>(![X,Y]: (~is_a_theorem(strict_equiv(X,Y))|X=Y))),
% 0.17/0.50 inference(pre_NNF_transformation,[status(esa)],[f53])).
% 0.17/0.50 fof(f250,plain,(
% 0.17/0.50 (~substitution_strict_equiv|(![X,Y]: (~is_a_theorem(strict_equiv(X,Y))|X=Y)))&(substitution_strict_equiv|(?[X,Y]: (is_a_theorem(strict_equiv(X,Y))&~X=Y)))),
% 0.17/0.50 inference(NNF_transformation,[status(esa)],[f249])).
% 0.17/0.50 fof(f251,plain,(
% 0.17/0.50 (~substitution_strict_equiv|(![X,Y]: (~is_a_theorem(strict_equiv(X,Y))|X=Y)))&(substitution_strict_equiv|(is_a_theorem(strict_equiv(sk0_60,sk0_61))&~sk0_60=sk0_61))),
% 0.17/0.50 inference(skolemization,[status(esa)],[f250])).
% 0.17/0.50 fof(f253,plain,(
% 0.17/0.50 substitution_strict_equiv|is_a_theorem(strict_equiv(sk0_60,sk0_61))),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f251])).
% 0.17/0.50 fof(f254,plain,(
% 0.17/0.50 substitution_strict_equiv|~sk0_60=sk0_61),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f251])).
% 0.17/0.50 fof(f259,plain,(
% 0.17/0.50 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|(?[X]: ~is_a_theorem(implies(necessarily(X),X))))),
% 0.17/0.50 inference(NNF_transformation,[status(esa)],[f55])).
% 0.17/0.50 fof(f260,plain,(
% 0.17/0.50 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|~is_a_theorem(implies(necessarily(sk0_64),sk0_64)))),
% 0.17/0.50 inference(skolemization,[status(esa)],[f259])).
% 0.17/0.50 fof(f261,plain,(
% 0.17/0.50 ![X0]: (~axiom_M|is_a_theorem(implies(necessarily(X0),X0)))),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f260])).
% 0.17/0.50 fof(f335,plain,(
% 0.17/0.50 ~op_strict_implies|(![X,Y]: strict_implies(X,Y)=necessarily(implies(X,Y)))),
% 0.17/0.50 inference(pre_NNF_transformation,[status(esa)],[f75])).
% 0.17/0.50 fof(f336,plain,(
% 0.17/0.50 ![X0,X1]: (~op_strict_implies|strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f335])).
% 0.17/0.50 fof(f337,plain,(
% 0.17/0.50 ~op_strict_equiv|(![X,Y]: strict_equiv(X,Y)=and(strict_implies(X,Y),strict_implies(Y,X)))),
% 0.17/0.50 inference(pre_NNF_transformation,[status(esa)],[f76])).
% 0.17/0.50 fof(f338,plain,(
% 0.17/0.50 ![X0,X1]: (~op_strict_equiv|strict_equiv(X0,X1)=and(strict_implies(X0,X1),strict_implies(X1,X0)))),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f337])).
% 0.17/0.50 fof(f342,plain,(
% 0.17/0.50 axiom_M),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f80])).
% 0.17/0.50 fof(f347,plain,(
% 0.17/0.50 op_strict_implies),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f85])).
% 0.17/0.50 fof(f349,plain,(
% 0.17/0.50 op_strict_equiv),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f87])).
% 0.17/0.50 fof(f350,plain,(
% 0.17/0.50 ~substitution_strict_equiv),
% 0.17/0.50 inference(cnf_transformation,[status(esa)],[f89])).
% 0.17/0.50 fof(f351,plain,(
% 0.17/0.50 spl0_0 <=> modus_ponens),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f353,plain,(
% 0.17/0.50 ~modus_ponens|spl0_0),
% 0.17/0.50 inference(component_clause,[status(thm)],[f351])).
% 0.17/0.50 fof(f354,plain,(
% 0.17/0.50 spl0_1 <=> ~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f355,plain,(
% 0.17/0.50 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)|~spl0_1)),
% 0.17/0.50 inference(component_clause,[status(thm)],[f354])).
% 0.17/0.50 fof(f357,plain,(
% 0.17/0.50 ~spl0_0|spl0_1),
% 0.17/0.50 inference(split_clause,[status(thm)],[f94,f351,f354])).
% 0.17/0.50 fof(f370,plain,(
% 0.17/0.50 spl0_5 <=> substitution_of_equivalents),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f372,plain,(
% 0.17/0.50 ~substitution_of_equivalents|spl0_5),
% 0.17/0.50 inference(component_clause,[status(thm)],[f370])).
% 0.17/0.50 fof(f373,plain,(
% 0.17/0.50 spl0_6 <=> ~is_a_theorem(equiv(X0,X1))|X0=X1),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f374,plain,(
% 0.17/0.50 ![X0,X1]: (~is_a_theorem(equiv(X0,X1))|X0=X1|~spl0_6)),
% 0.17/0.50 inference(component_clause,[status(thm)],[f373])).
% 0.17/0.50 fof(f376,plain,(
% 0.17/0.50 ~spl0_5|spl0_6),
% 0.17/0.50 inference(split_clause,[status(thm)],[f101,f370,f373])).
% 0.17/0.50 fof(f385,plain,(
% 0.17/0.50 spl0_9 <=> modus_tollens),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f387,plain,(
% 0.17/0.50 ~modus_tollens|spl0_9),
% 0.17/0.50 inference(component_clause,[status(thm)],[f385])).
% 0.17/0.50 fof(f407,plain,(
% 0.17/0.50 spl0_15 <=> implies_2),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f409,plain,(
% 0.17/0.50 ~implies_2|spl0_15),
% 0.17/0.50 inference(component_clause,[status(thm)],[f407])).
% 0.17/0.50 fof(f429,plain,(
% 0.17/0.50 spl0_21 <=> and_1),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f431,plain,(
% 0.17/0.50 ~and_1|spl0_21),
% 0.17/0.50 inference(component_clause,[status(thm)],[f429])).
% 0.17/0.50 fof(f432,plain,(
% 0.17/0.50 spl0_22 <=> is_a_theorem(implies(and(X0,X1),X0))),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f433,plain,(
% 0.17/0.50 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X0))|~spl0_22)),
% 0.17/0.50 inference(component_clause,[status(thm)],[f432])).
% 0.17/0.50 fof(f435,plain,(
% 0.17/0.50 ~spl0_21|spl0_22),
% 0.17/0.50 inference(split_clause,[status(thm)],[f122,f429,f432])).
% 0.17/0.50 fof(f440,plain,(
% 0.17/0.50 spl0_24 <=> and_2),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f442,plain,(
% 0.17/0.50 ~and_2|spl0_24),
% 0.17/0.50 inference(component_clause,[status(thm)],[f440])).
% 0.17/0.50 fof(f443,plain,(
% 0.17/0.50 spl0_25 <=> is_a_theorem(implies(and(X0,X1),X1))),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f444,plain,(
% 0.17/0.50 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X1))|~spl0_25)),
% 0.17/0.50 inference(component_clause,[status(thm)],[f443])).
% 0.17/0.50 fof(f446,plain,(
% 0.17/0.50 ~spl0_24|spl0_25),
% 0.17/0.50 inference(split_clause,[status(thm)],[f126,f440,f443])).
% 0.17/0.50 fof(f451,plain,(
% 0.17/0.50 spl0_27 <=> and_3),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f453,plain,(
% 0.17/0.50 ~and_3|spl0_27),
% 0.17/0.50 inference(component_clause,[status(thm)],[f451])).
% 0.17/0.50 fof(f454,plain,(
% 0.17/0.50 spl0_28 <=> is_a_theorem(implies(X0,implies(X1,and(X0,X1))))),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f455,plain,(
% 0.17/0.50 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,and(X0,X1))))|~spl0_28)),
% 0.17/0.50 inference(component_clause,[status(thm)],[f454])).
% 0.17/0.50 fof(f457,plain,(
% 0.17/0.50 ~spl0_27|spl0_28),
% 0.17/0.50 inference(split_clause,[status(thm)],[f130,f451,f454])).
% 0.17/0.50 fof(f484,plain,(
% 0.17/0.50 spl0_36 <=> or_3),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f486,plain,(
% 0.17/0.50 ~or_3|spl0_36),
% 0.17/0.50 inference(component_clause,[status(thm)],[f484])).
% 0.17/0.50 fof(f495,plain,(
% 0.17/0.50 spl0_39 <=> equivalence_1),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f497,plain,(
% 0.17/0.50 ~equivalence_1|spl0_39),
% 0.17/0.50 inference(component_clause,[status(thm)],[f495])).
% 0.17/0.50 fof(f506,plain,(
% 0.17/0.50 spl0_42 <=> equivalence_2),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f508,plain,(
% 0.17/0.50 ~equivalence_2|spl0_42),
% 0.17/0.50 inference(component_clause,[status(thm)],[f506])).
% 0.17/0.50 fof(f517,plain,(
% 0.17/0.50 spl0_45 <=> equivalence_3),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f519,plain,(
% 0.17/0.50 ~equivalence_3|spl0_45),
% 0.17/0.50 inference(component_clause,[status(thm)],[f517])).
% 0.17/0.50 fof(f668,plain,(
% 0.17/0.50 spl0_86 <=> op_equiv),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f670,plain,(
% 0.17/0.50 ~op_equiv|spl0_86),
% 0.17/0.50 inference(component_clause,[status(thm)],[f668])).
% 0.17/0.50 fof(f671,plain,(
% 0.17/0.50 spl0_87 <=> equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f672,plain,(
% 0.17/0.50 ![X0,X1]: (equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))|~spl0_87)),
% 0.17/0.50 inference(component_clause,[status(thm)],[f671])).
% 0.17/0.50 fof(f674,plain,(
% 0.17/0.50 ~spl0_86|spl0_87),
% 0.17/0.50 inference(split_clause,[status(thm)],[f209,f668,f671])).
% 0.17/0.50 fof(f709,plain,(
% 0.17/0.50 spl0_97 <=> adjunction),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f712,plain,(
% 0.17/0.50 spl0_98 <=> ~is_a_theorem(X0)|~is_a_theorem(X1)|is_a_theorem(and(X0,X1))),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f713,plain,(
% 0.17/0.50 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(X1)|is_a_theorem(and(X0,X1))|~spl0_98)),
% 0.17/0.50 inference(component_clause,[status(thm)],[f712])).
% 0.17/0.50 fof(f715,plain,(
% 0.17/0.50 ~spl0_97|spl0_98),
% 0.17/0.50 inference(split_clause,[status(thm)],[f245,f709,f712])).
% 0.17/0.50 fof(f716,plain,(
% 0.17/0.50 spl0_99 <=> is_a_theorem(sk0_58)),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f719,plain,(
% 0.17/0.50 spl0_97|spl0_99),
% 0.17/0.50 inference(split_clause,[status(thm)],[f246,f709,f716])).
% 0.17/0.50 fof(f720,plain,(
% 0.17/0.50 spl0_100 <=> is_a_theorem(sk0_59)),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f723,plain,(
% 0.17/0.50 spl0_97|spl0_100),
% 0.17/0.50 inference(split_clause,[status(thm)],[f247,f709,f720])).
% 0.17/0.50 fof(f724,plain,(
% 0.17/0.50 spl0_101 <=> is_a_theorem(and(sk0_58,sk0_59))),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f726,plain,(
% 0.17/0.50 ~is_a_theorem(and(sk0_58,sk0_59))|spl0_101),
% 0.17/0.50 inference(component_clause,[status(thm)],[f724])).
% 0.17/0.50 fof(f727,plain,(
% 0.17/0.50 spl0_97|~spl0_101),
% 0.17/0.50 inference(split_clause,[status(thm)],[f248,f709,f724])).
% 0.17/0.50 fof(f728,plain,(
% 0.17/0.50 spl0_102 <=> substitution_strict_equiv),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f729,plain,(
% 0.17/0.50 substitution_strict_equiv|~spl0_102),
% 0.17/0.50 inference(component_clause,[status(thm)],[f728])).
% 0.17/0.50 fof(f735,plain,(
% 0.17/0.50 spl0_104 <=> is_a_theorem(strict_equiv(sk0_60,sk0_61))),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f736,plain,(
% 0.17/0.50 is_a_theorem(strict_equiv(sk0_60,sk0_61))|~spl0_104),
% 0.17/0.50 inference(component_clause,[status(thm)],[f735])).
% 0.17/0.50 fof(f738,plain,(
% 0.17/0.50 spl0_102|spl0_104),
% 0.17/0.50 inference(split_clause,[status(thm)],[f253,f728,f735])).
% 0.17/0.50 fof(f739,plain,(
% 0.17/0.50 spl0_105 <=> sk0_60=sk0_61),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f742,plain,(
% 0.17/0.50 spl0_102|~spl0_105),
% 0.17/0.50 inference(split_clause,[status(thm)],[f254,f728,f739])).
% 0.17/0.50 fof(f754,plain,(
% 0.17/0.50 spl0_109 <=> axiom_M),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f756,plain,(
% 0.17/0.50 ~axiom_M|spl0_109),
% 0.17/0.50 inference(component_clause,[status(thm)],[f754])).
% 0.17/0.50 fof(f757,plain,(
% 0.17/0.50 spl0_110 <=> is_a_theorem(implies(necessarily(X0),X0))),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f758,plain,(
% 0.17/0.50 ![X0]: (is_a_theorem(implies(necessarily(X0),X0))|~spl0_110)),
% 0.17/0.50 inference(component_clause,[status(thm)],[f757])).
% 0.17/0.50 fof(f760,plain,(
% 0.17/0.50 ~spl0_109|spl0_110),
% 0.17/0.50 inference(split_clause,[status(thm)],[f261,f754,f757])).
% 0.17/0.50 fof(f966,plain,(
% 0.17/0.50 spl0_167 <=> op_strict_implies),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f968,plain,(
% 0.17/0.50 ~op_strict_implies|spl0_167),
% 0.17/0.50 inference(component_clause,[status(thm)],[f966])).
% 0.17/0.50 fof(f969,plain,(
% 0.17/0.50 spl0_168 <=> strict_implies(X0,X1)=necessarily(implies(X0,X1))),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f970,plain,(
% 0.17/0.50 ![X0,X1]: (strict_implies(X0,X1)=necessarily(implies(X0,X1))|~spl0_168)),
% 0.17/0.50 inference(component_clause,[status(thm)],[f969])).
% 0.17/0.50 fof(f972,plain,(
% 0.17/0.50 ~spl0_167|spl0_168),
% 0.17/0.50 inference(split_clause,[status(thm)],[f336,f966,f969])).
% 0.17/0.50 fof(f973,plain,(
% 0.17/0.50 spl0_169 <=> op_strict_equiv),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f975,plain,(
% 0.17/0.50 ~op_strict_equiv|spl0_169),
% 0.17/0.50 inference(component_clause,[status(thm)],[f973])).
% 0.17/0.50 fof(f976,plain,(
% 0.17/0.50 spl0_170 <=> strict_equiv(X0,X1)=and(strict_implies(X0,X1),strict_implies(X1,X0))),
% 0.17/0.50 introduced(split_symbol_definition)).
% 0.17/0.50 fof(f977,plain,(
% 0.17/0.50 ![X0,X1]: (strict_equiv(X0,X1)=and(strict_implies(X0,X1),strict_implies(X1,X0))|~spl0_170)),
% 0.17/0.50 inference(component_clause,[status(thm)],[f976])).
% 0.17/0.50 fof(f979,plain,(
% 0.17/0.50 ~spl0_169|spl0_170),
% 0.17/0.50 inference(split_clause,[status(thm)],[f338,f973,f976])).
% 0.17/0.50 fof(f980,plain,(
% 0.17/0.50 $false|spl0_169),
% 0.17/0.50 inference(forward_subsumption_resolution,[status(thm)],[f975,f349])).
% 0.17/0.50 fof(f981,plain,(
% 0.17/0.50 spl0_169),
% 0.17/0.50 inference(contradiction_clause,[status(thm)],[f980])).
% 0.17/0.50 fof(f982,plain,(
% 0.17/0.50 $false|spl0_0),
% 0.17/0.50 inference(forward_subsumption_resolution,[status(thm)],[f353,f213])).
% 0.17/0.50 fof(f983,plain,(
% 0.17/0.50 spl0_0),
% 0.17/0.50 inference(contradiction_clause,[status(thm)],[f982])).
% 0.17/0.50 fof(f986,plain,(
% 0.17/0.50 $false|spl0_5),
% 0.17/0.50 inference(forward_subsumption_resolution,[status(thm)],[f372,f227])).
% 0.17/0.50 fof(f987,plain,(
% 0.17/0.50 spl0_5),
% 0.17/0.50 inference(contradiction_clause,[status(thm)],[f986])).
% 0.17/0.50 fof(f988,plain,(
% 0.17/0.50 $false|spl0_167),
% 0.17/0.50 inference(forward_subsumption_resolution,[status(thm)],[f968,f347])).
% 0.17/0.50 fof(f989,plain,(
% 0.17/0.50 spl0_167),
% 0.17/0.50 inference(contradiction_clause,[status(thm)],[f988])).
% 0.17/0.50 fof(f992,plain,(
% 0.17/0.50 $false|spl0_86),
% 0.17/0.50 inference(forward_subsumption_resolution,[status(thm)],[f670,f212])).
% 0.17/0.50 fof(f993,plain,(
% 0.17/0.50 spl0_86),
% 0.17/0.50 inference(contradiction_clause,[status(thm)],[f992])).
% 0.17/0.50 fof(f1002,plain,(
% 0.17/0.50 $false|spl0_109),
% 0.17/0.50 inference(forward_subsumption_resolution,[status(thm)],[f756,f342])).
% 0.17/0.50 fof(f1003,plain,(
% 0.17/0.50 spl0_109),
% 0.17/0.50 inference(contradiction_clause,[status(thm)],[f1002])).
% 0.17/0.50 fof(f1025,plain,(
% 0.17/0.50 $false|spl0_21),
% 0.17/0.50 inference(forward_subsumption_resolution,[status(thm)],[f431,f218])).
% 0.17/0.50 fof(f1026,plain,(
% 0.17/0.50 spl0_21),
% 0.17/0.50 inference(contradiction_clause,[status(thm)],[f1025])).
% 0.17/0.50 fof(f1035,plain,(
% 0.17/0.50 $false|spl0_24),
% 0.17/0.50 inference(forward_subsumption_resolution,[status(thm)],[f442,f219])).
% 0.17/0.50 fof(f1036,plain,(
% 0.17/0.50 spl0_24),
% 0.17/0.50 inference(contradiction_clause,[status(thm)],[f1035])).
% 0.17/0.50 fof(f1064,plain,(
% 0.17/0.50 ![X0]: (~is_a_theorem(necessarily(X0))|is_a_theorem(X0)|~spl0_1|~spl0_110)),
% 0.17/0.50 inference(resolution,[status(thm)],[f355,f758])).
% 0.17/0.50 fof(f1065,plain,(
% 0.17/0.50 ![X0,X1]: (~is_a_theorem(and(X0,X1))|is_a_theorem(X1)|~spl0_1|~spl0_25)),
% 0.17/0.50 inference(resolution,[status(thm)],[f355,f444])).
% 0.17/0.50 fof(f1066,plain,(
% 0.17/0.50 ![X0,X1]: (~is_a_theorem(and(X0,X1))|is_a_theorem(X0)|~spl0_1|~spl0_22)),
% 0.17/0.50 inference(resolution,[status(thm)],[f355,f433])).
% 0.17/0.50 fof(f1068,plain,(
% 0.17/0.50 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(implies(X1,and(X0,X1)))|~spl0_1|~spl0_28)),
% 0.17/0.50 inference(resolution,[status(thm)],[f355,f455])).
% 0.17/0.50 fof(f1103,plain,(
% 0.17/0.50 ![X0,X1]: (~is_a_theorem(strict_implies(X0,X1))|is_a_theorem(implies(X0,X1))|~spl0_1|~spl0_110|~spl0_168)),
% 0.17/0.50 inference(paramodulation,[status(thm)],[f970,f1064])).
% 0.17/0.50 fof(f1164,plain,(
% 0.17/0.50 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(and(X1,X0))|~is_a_theorem(X1)|~spl0_1|~spl0_28)),
% 0.17/0.50 inference(resolution,[status(thm)],[f355,f1068])).
% 0.17/0.50 fof(f1226,plain,(
% 0.17/0.50 ~is_a_theorem(sk0_59)|~is_a_theorem(sk0_58)|~spl0_1|~spl0_28|spl0_101),
% 0.17/0.50 inference(resolution,[status(thm)],[f1164,f726])).
% 0.17/0.50 fof(f1227,plain,(
% 0.17/0.50 ~spl0_100|~spl0_99|~spl0_1|~spl0_28|spl0_101),
% 0.17/0.50 inference(split_clause,[status(thm)],[f1226,f720,f716,f354,f454,f724])).
% 0.17/0.50 fof(f1239,plain,(
% 0.17/0.50 $false|spl0_27),
% 0.17/0.50 inference(forward_subsumption_resolution,[status(thm)],[f453,f220])).
% 0.17/0.50 fof(f1240,plain,(
% 0.17/0.50 spl0_27),
% 0.17/0.50 inference(contradiction_clause,[status(thm)],[f1239])).
% 0.17/0.50 fof(f1248,plain,(
% 0.17/0.50 ![X0,X1]: (~is_a_theorem(strict_equiv(X0,X1))|is_a_theorem(strict_implies(X0,X1))|~spl0_1|~spl0_22|~spl0_170)),
% 0.17/0.50 inference(paramodulation,[status(thm)],[f977,f1066])).
% 0.17/0.50 fof(f1249,plain,(
% 0.17/0.50 ![X0,X1]: (~is_a_theorem(strict_equiv(X0,X1))|is_a_theorem(strict_implies(X1,X0))|~spl0_1|~spl0_25|~spl0_170)),
% 0.17/0.50 inference(paramodulation,[status(thm)],[f977,f1065])).
% 0.17/0.50 fof(f1301,plain,(
% 0.17/0.50 $false|~spl0_102),
% 0.17/0.50 inference(forward_subsumption_resolution,[status(thm)],[f729,f350])).
% 0.17/0.50 fof(f1302,plain,(
% 0.17/0.50 ~spl0_102),
% 0.17/0.50 inference(contradiction_clause,[status(thm)],[f1301])).
% 0.17/0.50 fof(f1434,plain,(
% 0.17/0.50 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X0))|is_a_theorem(equiv(X0,X1))|~spl0_98|~spl0_87)),
% 0.17/0.50 inference(paramodulation,[status(thm)],[f672,f713])).
% 0.17/0.50 fof(f1459,plain,(
% 0.17/0.50 is_a_theorem(strict_implies(sk0_60,sk0_61))|~spl0_1|~spl0_22|~spl0_170|~spl0_104),
% 0.17/0.50 inference(resolution,[status(thm)],[f1248,f736])).
% 0.17/0.50 fof(f1468,plain,(
% 0.17/0.50 is_a_theorem(implies(sk0_60,sk0_61))|~spl0_22|~spl0_170|~spl0_104|~spl0_1|~spl0_110|~spl0_168),
% 0.17/0.50 inference(resolution,[status(thm)],[f1459,f1103])).
% 0.17/0.50 fof(f1479,plain,(
% 0.17/0.50 is_a_theorem(strict_implies(sk0_61,sk0_60))|~spl0_1|~spl0_25|~spl0_170|~spl0_104),
% 0.17/0.50 inference(resolution,[status(thm)],[f1249,f736])).
% 0.17/0.50 fof(f1482,plain,(
% 0.17/0.50 is_a_theorem(implies(sk0_61,sk0_60))|~spl0_25|~spl0_170|~spl0_104|~spl0_1|~spl0_110|~spl0_168),
% 0.17/0.50 inference(resolution,[status(thm)],[f1479,f1103])).
% 0.17/0.50 fof(f1517,plain,(
% 0.17/0.50 $false|spl0_39),
% 0.17/0.50 inference(forward_subsumption_resolution,[status(thm)],[f497,f224])).
% 0.17/0.50 fof(f1518,plain,(
% 0.17/0.50 spl0_39),
% 0.17/0.50 inference(contradiction_clause,[status(thm)],[f1517])).
% 0.17/0.50 fof(f1527,plain,(
% 0.17/0.50 $false|spl0_42),
% 0.17/0.50 inference(forward_subsumption_resolution,[status(thm)],[f508,f225])).
% 0.17/0.50 fof(f1528,plain,(
% 0.17/0.50 spl0_42),
% 0.17/0.50 inference(contradiction_clause,[status(thm)],[f1527])).
% 0.17/0.50 fof(f1626,plain,(
% 0.17/0.51 $false|spl0_15),
% 0.17/0.51 inference(forward_subsumption_resolution,[status(thm)],[f409,f216])).
% 0.17/0.51 fof(f1627,plain,(
% 0.17/0.51 spl0_15),
% 0.17/0.51 inference(contradiction_clause,[status(thm)],[f1626])).
% 0.17/0.51 fof(f1630,plain,(
% 0.17/0.51 $false|spl0_9),
% 0.17/0.51 inference(forward_subsumption_resolution,[status(thm)],[f387,f214])).
% 0.17/0.51 fof(f1631,plain,(
% 0.17/0.51 spl0_9),
% 0.17/0.51 inference(contradiction_clause,[status(thm)],[f1630])).
% 0.17/0.51 fof(f1665,plain,(
% 0.17/0.51 $false|spl0_36),
% 0.17/0.51 inference(forward_subsumption_resolution,[status(thm)],[f486,f223])).
% 0.17/0.51 fof(f1666,plain,(
% 0.17/0.51 spl0_36),
% 0.17/0.51 inference(contradiction_clause,[status(thm)],[f1665])).
% 0.17/0.51 fof(f1759,plain,(
% 0.17/0.51 $false|spl0_45),
% 0.17/0.51 inference(forward_subsumption_resolution,[status(thm)],[f519,f226])).
% 0.17/0.51 fof(f1760,plain,(
% 0.17/0.51 spl0_45),
% 0.17/0.51 inference(contradiction_clause,[status(thm)],[f1759])).
% 0.17/0.51 fof(f3006,plain,(
% 0.17/0.51 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X0))|X0=X1|~spl0_98|~spl0_87|~spl0_6)),
% 0.17/0.51 inference(resolution,[status(thm)],[f1434,f374])).
% 0.17/0.51 fof(f3033,plain,(
% 0.17/0.51 spl0_197 <=> is_a_theorem(implies(sk0_60,sk0_61))),
% 0.17/0.51 introduced(split_symbol_definition)).
% 0.17/0.51 fof(f3035,plain,(
% 0.17/0.51 ~is_a_theorem(implies(sk0_60,sk0_61))|spl0_197),
% 0.17/0.51 inference(component_clause,[status(thm)],[f3033])).
% 0.17/0.51 fof(f3036,plain,(
% 0.17/0.51 ~is_a_theorem(implies(sk0_60,sk0_61))|sk0_60=sk0_61|~spl0_98|~spl0_87|~spl0_6|~spl0_25|~spl0_170|~spl0_104|~spl0_1|~spl0_110|~spl0_168),
% 0.17/0.51 inference(resolution,[status(thm)],[f3006,f1482])).
% 0.17/0.51 fof(f3037,plain,(
% 0.17/0.51 ~spl0_197|spl0_105|~spl0_98|~spl0_87|~spl0_6|~spl0_25|~spl0_170|~spl0_104|~spl0_1|~spl0_110|~spl0_168),
% 0.17/0.51 inference(split_clause,[status(thm)],[f3036,f3033,f739,f712,f671,f373,f443,f976,f735,f354,f757,f969])).
% 0.17/0.51 fof(f3088,plain,(
% 0.17/0.51 $false|~spl0_22|~spl0_170|~spl0_104|~spl0_1|~spl0_110|~spl0_168|spl0_197),
% 0.17/0.51 inference(forward_subsumption_resolution,[status(thm)],[f3035,f1468])).
% 0.17/0.51 fof(f3089,plain,(
% 0.17/0.51 ~spl0_22|~spl0_170|~spl0_104|~spl0_1|~spl0_110|~spl0_168|spl0_197),
% 0.17/0.51 inference(contradiction_clause,[status(thm)],[f3088])).
% 0.17/0.51 fof(f3090,plain,(
% 0.17/0.51 $false),
% 0.17/0.51 inference(sat_refutation,[status(thm)],[f357,f376,f435,f446,f457,f674,f715,f719,f723,f727,f738,f742,f760,f972,f979,f981,f983,f987,f989,f993,f1003,f1026,f1036,f1227,f1240,f1302,f1518,f1528,f1627,f1631,f1666,f1760,f3037,f3089])).
% 0.17/0.51 % SZS output end CNFRefutation for theBenchmark.p
% 0.17/0.52 % Elapsed time: 0.180870 seconds
% 0.17/0.52 % CPU time: 1.293007 seconds
% 0.17/0.52 % Total memory used: 84.085 MB
% 0.17/0.52 % Net memory used: 82.917 MB
%------------------------------------------------------------------------------