%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL457+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:10:07 PM UTC 2026
% Result : Theorem 20.13s 3.24s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL457+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n004.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 00:33:05 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.47 % Drodi V4.1.1
% 20.13/3.24 % Refutation found
% 20.13/3.24 % SZS status Theorem for theBenchmark: Theorem is valid
% 20.13/3.24 % SZS output start CNFRefutation for theBenchmark
% 20.13/3.24 fof(f1,axiom,(
% 20.13/3.24 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 20.13/3.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.13/3.24 fof(f2,axiom,(
% 20.13/3.24 ( substitution_of_equivalents<=> (! [X,Y] :( is_a_theorem(equiv(X,Y))=> X = Y ) )) ),
% 20.13/3.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.13/3.24 fof(f3,axiom,(
% 20.13/3.24 ( modus_tollens<=> (! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) )) ),
% 20.13/3.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.13/3.24 fof(f4,axiom,(
% 20.13/3.24 ( implies_1<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) )) ),
% 20.13/3.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.13/3.24 fof(f5,axiom,(
% 20.13/3.24 ( implies_2<=> (! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )) ),
% 20.13/3.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.13/3.24 fof(f6,axiom,(
% 20.13/3.24 ( implies_3<=> (! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )) ),
% 20.13/3.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.13/3.24 fof(f9,axiom,(
% 20.13/3.24 ( and_3<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) )) ),
% 20.13/3.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.13/3.24 fof(f15,axiom,(
% 20.13/3.24 ( equivalence_3<=> (! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) )) ),
% 20.13/3.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.13/3.24 fof(f25,axiom,(
% 20.13/3.24 ( r4<=> (! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) )) ),
% 20.13/3.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.13/3.24 fof(f27,axiom,(
% 20.13/3.24 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 20.13/3.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.13/3.24 fof(f28,axiom,(
% 20.13/3.24 ( op_and=> (! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) )) ),
% 20.13/3.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.13/3.24 fof(f29,axiom,(
% 20.13/3.24 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 20.13/3.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.13/3.24 fof(f30,axiom,(
% 20.13/3.24 ( op_implies_or=> (! [X,Y] : implies(X,Y) = or(not(X),Y) )) ),
% 20.13/3.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.13/3.24 fof(f31,axiom,(
% 20.13/3.24 ( op_equiv=> (! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) )) ),
% 20.13/3.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.13/3.24 fof(f32,axiom,(
% 20.13/3.24 op_or ),
% 20.13/3.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.13/3.24 fof(f33,axiom,(
% 20.13/3.24 op_implies_and ),
% 20.13/3.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.13/3.24 fof(f34,axiom,(
% 20.13/3.24 op_equiv ),
% 20.13/3.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.13/3.24 fof(f35,axiom,(
% 20.13/3.24 modus_ponens ),
% 20.13/3.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.13/3.24 fof(f36,axiom,(
% 20.13/3.24 modus_tollens ),
% 20.13/3.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.13/3.24 fof(f37,axiom,(
% 20.13/3.24 implies_1 ),
% 20.13/3.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.13/3.24 fof(f38,axiom,(
% 20.13/3.24 implies_2 ),
% 20.13/3.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.13/3.24 fof(f39,axiom,(
% 20.13/3.24 implies_3 ),
% 20.13/3.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.13/3.24 fof(f42,axiom,(
% 20.13/3.24 and_3 ),
% 20.13/3.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.13/3.24 fof(f48,axiom,(
% 20.13/3.24 equivalence_3 ),
% 20.13/3.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.13/3.24 fof(f49,axiom,(
% 20.13/3.24 substitution_of_equivalents ),
% 20.13/3.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.13/3.24 fof(f50,axiom,(
% 20.13/3.24 op_implies_or ),
% 20.13/3.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.13/3.24 fof(f51,axiom,(
% 20.13/3.24 op_and ),
% 20.13/3.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.13/3.24 fof(f53,conjecture,(
% 20.13/3.24 r4 ),
% 20.13/3.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.13/3.24 fof(f54,negated_conjecture,(
% 20.13/3.24 ~(r4 )),
% 20.13/3.24 inference(negated_conjecture,[status(cth)],[f53])).
% 20.13/3.24 fof(f55,plain,(
% 20.13/3.24 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 20.13/3.24 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 20.13/3.24 fof(f56,plain,(
% 20.13/3.24 (~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))))),
% 20.13/3.24 inference(NNF_transformation,[status(thm)],[f55])).
% 20.13/3.24 fof(f57,plain,(
% 20.13/3.24 (~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))))),
% 20.13/3.24 inference(miniscoping,[status(thm)],[f56])).
% 20.13/3.24 fof(f58,plain,(
% 20.13/3.24 (~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)))),
% 20.13/3.24 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f57])).
% 20.13/3.24 fof(f59,plain,(
% 20.13/3.24 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 20.13/3.24 inference(cnf_transformation,[status(thm)],[f58])).
% 20.13/3.24 fof(f63,plain,(
% 20.13/3.24 substitution_of_equivalents<=>(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y))),
% 20.13/3.24 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 20.13/3.24 fof(f64,plain,(
% 20.13/3.24 (~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)))),
% 20.13/3.24 inference(NNF_transformation,[status(thm)],[f63])).
% 20.13/3.24 fof(f65,plain,(
% 20.13/3.24 (~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))),
% 20.13/3.24 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(X,sK2_skl),skolemize(Y,sK3_skl)],[f64])).
% 20.13/3.24 fof(f66,plain,(
% 20.13/3.24 ![X0,X1]: (~substitution_of_equivalents|~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 20.13/3.24 inference(cnf_transformation,[status(thm)],[f65])).
% 20.13/3.24 fof(f69,plain,(
% 20.13/3.24 (~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)))))),
% 20.13/3.24 inference(NNF_transformation,[status(thm)],[f3])).
% 20.13/3.24 fof(f70,plain,(
% 20.13/3.24 (~modus_tollens|(![X,Y]: is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))))&(modus_tollens|~is_a_theorem(implies(implies(not(sK5_skl),not(sK4_skl)),implies(sK4_skl,sK5_skl))))),
% 20.13/3.24 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(X,sK4_skl),skolemize(Y,sK5_skl)],[f69])).
% 20.13/3.24 fof(f71,plain,(
% 20.13/3.24 ![X0,X1]: (~modus_tollens|is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))))),
% 20.13/3.24 inference(cnf_transformation,[status(thm)],[f70])).
% 20.13/3.24 fof(f73,plain,(
% 20.13/3.24 (~implies_1|(![X,Y]: is_a_theorem(implies(X,implies(Y,X)))))&(implies_1|(?[X,Y]: ~is_a_theorem(implies(X,implies(Y,X)))))),
% 20.13/3.24 inference(NNF_transformation,[status(thm)],[f4])).
% 20.13/3.24 fof(f74,plain,(
% 20.13/3.24 (~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))))),
% 20.13/3.24 inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl]),skolemize(X,sK6_skl),skolemize(Y,sK7_skl)],[f73])).
% 20.13/3.24 fof(f75,plain,(
% 20.13/3.24 ![X0,X1]: (~implies_1|is_a_theorem(implies(X0,implies(X1,X0))))),
% 20.13/3.24 inference(cnf_transformation,[status(thm)],[f74])).
% 20.13/3.24 fof(f77,plain,(
% 20.13/3.24 (~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)))))),
% 20.13/3.24 inference(NNF_transformation,[status(thm)],[f5])).
% 20.13/3.24 fof(f78,plain,(
% 20.13/3.24 (~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))))),
% 20.13/3.24 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(X,sK8_skl),skolemize(Y,sK9_skl)],[f77])).
% 20.13/3.24 fof(f79,plain,(
% 20.13/3.24 ![X0,X1]: (~implies_2|is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 20.13/3.24 inference(cnf_transformation,[status(thm)],[f78])).
% 20.13/3.24 fof(f81,plain,(
% 20.13/3.24 (~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))))))),
% 20.13/3.24 inference(NNF_transformation,[status(thm)],[f6])).
% 20.13/3.24 fof(f82,plain,(
% 20.13/3.24 (~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(sK10_skl,sK11_skl),implies(implies(sK11_skl,sK12_skl),implies(sK10_skl,sK12_skl)))))),
% 20.13/3.24 inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl]),skolemize(X,sK10_skl),skolemize(Y,sK11_skl),skolemize(Z,sK12_skl)],[f81])).
% 20.13/3.24 fof(f83,plain,(
% 20.13/3.24 ![X0,X1,X2]: (~implies_3|is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))))),
% 20.13/3.24 inference(cnf_transformation,[status(thm)],[f82])).
% 20.13/3.24 fof(f93,plain,(
% 20.13/3.24 (~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))))))),
% 20.13/3.24 inference(NNF_transformation,[status(thm)],[f9])).
% 20.13/3.24 fof(f94,plain,(
% 20.13/3.24 (~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)))))),
% 20.13/3.24 inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl]),skolemize(X,sK17_skl),skolemize(Y,sK18_skl)],[f93])).
% 20.13/3.24 fof(f95,plain,(
% 20.13/3.24 ![X0,X1]: (~and_3|is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 20.13/3.24 inference(cnf_transformation,[status(thm)],[f94])).
% 20.13/3.24 fof(f117,plain,(
% 20.13/3.24 (~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))))))),
% 20.13/3.24 inference(NNF_transformation,[status(thm)],[f15])).
% 20.13/3.24 fof(f118,plain,(
% 20.13/3.24 (~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)))))),
% 20.13/3.24 inference(skolemize,[status(esa),new_symbols(skolem,[sK30_skl,sK31_skl]),skolemize(X,sK30_skl),skolemize(Y,sK31_skl)],[f117])).
% 20.13/3.24 fof(f119,plain,(
% 20.13/3.24 ![X0,X1]: (~equivalence_3|is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))))),
% 20.13/3.24 inference(cnf_transformation,[status(thm)],[f118])).
% 20.13/3.24 fof(f157,plain,(
% 20.13/3.24 (~r4|(![P,Q,R]: is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))))&(r4|(?[P,Q,R]: ~is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))))),
% 20.13/3.24 inference(NNF_transformation,[status(thm)],[f25])).
% 20.13/3.24 fof(f158,plain,(
% 20.13/3.24 (~r4|(![P,Q,R]: is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))))&(r4|~is_a_theorem(implies(or(sK49_skl,or(sK50_skl,sK51_skl)),or(sK50_skl,or(sK49_skl,sK51_skl)))))),
% 20.13/3.24 inference(skolemize,[status(esa),new_symbols(skolem,[sK49_skl,sK50_skl,sK51_skl]),skolemize(P,sK49_skl),skolemize(Q,sK50_skl),skolemize(R,sK51_skl)],[f157])).
% 20.13/3.24 fof(f160,plain,(
% 20.13/3.24 r4|~is_a_theorem(implies(or(sK49_skl,or(sK50_skl,sK51_skl)),or(sK50_skl,or(sK49_skl,sK51_skl))))),
% 20.13/3.24 inference(cnf_transformation,[status(thm)],[f158])).
% 20.13/3.24 fof(f165,plain,(
% 20.13/3.24 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 20.13/3.24 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 20.13/3.24 fof(f166,plain,(
% 20.13/3.24 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 20.13/3.24 inference(cnf_transformation,[status(thm)],[f165])).
% 20.13/3.24 fof(f167,plain,(
% 20.13/3.24 ~op_and|(![X,Y]: and(X,Y)=not(or(not(X),not(Y))))),
% 20.13/3.24 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 20.13/3.24 fof(f168,plain,(
% 20.13/3.24 ![X0,X1]: (~op_and|and(X0,X1)=not(or(not(X0),not(X1))))),
% 20.13/3.24 inference(cnf_transformation,[status(thm)],[f167])).
% 20.13/3.24 fof(f169,plain,(
% 20.13/3.24 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 20.13/3.24 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 20.13/3.24 fof(f170,plain,(
% 20.13/3.24 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 20.13/3.24 inference(cnf_transformation,[status(thm)],[f169])).
% 20.13/3.24 fof(f171,plain,(
% 20.13/3.24 ~op_implies_or|(![X,Y]: implies(X,Y)=or(not(X),Y))),
% 20.13/3.24 inference(pre_NNF_transformation,[status(thm)],[f30])).
% 20.13/3.24 fof(f172,plain,(
% 20.13/3.24 ![X0,X1]: (~op_implies_or|implies(X0,X1)=or(not(X0),X1))),
% 20.13/3.24 inference(cnf_transformation,[status(thm)],[f171])).
% 20.13/3.24 fof(f173,plain,(
% 20.13/3.24 ~op_equiv|(![X,Y]: equiv(X,Y)=and(implies(X,Y),implies(Y,X)))),
% 20.13/3.24 inference(pre_NNF_transformation,[status(thm)],[f31])).
% 20.13/3.24 fof(f174,plain,(
% 20.13/3.24 ![X0,X1]: (~op_equiv|equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 20.13/3.24 inference(cnf_transformation,[status(thm)],[f173])).
% 20.13/3.24 fof(f175,plain,(
% 20.13/3.24 op_or),
% 20.13/3.24 inference(cnf_transformation,[status(thm)],[f32])).
% 20.13/3.24 fof(f176,plain,(
% 20.13/3.24 op_implies_and),
% 20.13/3.24 inference(cnf_transformation,[status(thm)],[f33])).
% 20.13/3.24 fof(f177,plain,(
% 20.13/3.24 op_equiv),
% 20.13/3.24 inference(cnf_transformation,[status(thm)],[f34])).
% 20.13/3.24 fof(f178,plain,(
% 20.13/3.24 modus_ponens),
% 20.13/3.24 inference(cnf_transformation,[status(thm)],[f35])).
% 20.13/3.24 fof(f179,plain,(
% 20.13/3.24 modus_tollens),
% 20.13/3.24 inference(cnf_transformation,[status(thm)],[f36])).
% 20.13/3.24 fof(f180,plain,(
% 20.13/3.24 implies_1),
% 20.13/3.24 inference(cnf_transformation,[status(thm)],[f37])).
% 20.13/3.24 fof(f181,plain,(
% 20.13/3.24 implies_2),
% 20.13/3.24 inference(cnf_transformation,[status(thm)],[f38])).
% 20.13/3.24 fof(f182,plain,(
% 20.13/3.24 implies_3),
% 20.13/3.24 inference(cnf_transformation,[status(thm)],[f39])).
% 20.13/3.24 fof(f185,plain,(
% 20.13/3.24 and_3),
% 20.13/3.24 inference(cnf_transformation,[status(thm)],[f42])).
% 20.13/3.24 fof(f191,plain,(
% 20.13/3.24 equivalence_3),
% 20.13/3.24 inference(cnf_transformation,[status(thm)],[f48])).
% 20.13/3.24 fof(f192,plain,(
% 20.13/3.24 substitution_of_equivalents),
% 20.13/3.24 inference(cnf_transformation,[status(thm)],[f49])).
% 20.13/3.24 fof(f193,plain,(
% 20.13/3.24 op_implies_or),
% 20.13/3.24 inference(cnf_transformation,[status(thm)],[f50])).
% 20.13/3.24 fof(f194,plain,(
% 20.13/3.24 op_and),
% 20.13/3.24 inference(cnf_transformation,[status(thm)],[f51])).
% 20.13/3.24 fof(f196,plain,(
% 20.13/3.24 ~r4),
% 20.13/3.24 inference(cnf_transformation,[status(thm)],[f54])).
% 20.13/3.24 fof(f197,plain,(
% 20.13/3.24 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1))))),
% 20.13/3.24 inference(backward_subsumption_resolution,[status(thm)],[f166,f175])).
% 20.13/3.24 fof(f198,plain,(
% 20.13/3.24 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1))))),
% 20.13/3.24 inference(backward_subsumption_resolution,[status(thm)],[f170,f176])).
% 20.13/3.24 fof(f199,plain,(
% 20.13/3.24 ![X0,X1]: (equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 20.13/3.24 inference(backward_subsumption_resolution,[status(thm)],[f174,f177])).
% 20.13/3.24 fof(f200,plain,(
% 20.13/3.24 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 20.13/3.24 inference(backward_subsumption_resolution,[status(thm)],[f59,f178])).
% 20.13/3.24 fof(f201,plain,(
% 20.13/3.24 ![X0,X1]: (is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))))),
% 20.13/3.24 inference(backward_subsumption_resolution,[status(thm)],[f71,f179])).
% 20.13/3.24 fof(f202,plain,(
% 20.13/3.24 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0))))),
% 20.13/3.24 inference(backward_subsumption_resolution,[status(thm)],[f75,f180])).
% 20.13/3.24 fof(f203,plain,(
% 20.13/3.24 ![X0,X1]: (is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 20.13/3.24 inference(backward_subsumption_resolution,[status(thm)],[f79,f181])).
% 20.13/3.24 fof(f204,plain,(
% 20.13/3.24 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))))),
% 20.13/3.24 inference(backward_subsumption_resolution,[status(thm)],[f83,f182])).
% 20.13/3.24 fof(f207,plain,(
% 20.13/3.24 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 20.13/3.24 inference(backward_subsumption_resolution,[status(thm)],[f95,f185])).
% 20.13/3.24 fof(f213,plain,(
% 20.13/3.24 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))))),
% 20.13/3.24 inference(backward_subsumption_resolution,[status(thm)],[f119,f191])).
% 20.13/3.24 fof(f214,plain,(
% 20.13/3.24 ![X0,X1]: (~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 20.13/3.24 inference(backward_subsumption_resolution,[status(thm)],[f66,f192])).
% 20.13/3.24 fof(f215,plain,(
% 20.13/3.24 ![X0,X1]: (implies(X0,X1)=or(not(X0),X1))),
% 20.13/3.24 inference(backward_subsumption_resolution,[status(thm)],[f172,f193])).
% 20.13/3.24 fof(f216,plain,(
% 20.13/3.24 ![X0,X1]: (and(X0,X1)=not(or(not(X0),not(X1))))),
% 20.13/3.24 inference(backward_subsumption_resolution,[status(thm)],[f168,f194])).
% 20.13/3.24 fof(f217,plain,(
% 20.13/3.24 ~is_a_theorem(implies(or(sK49_skl,or(sK50_skl,sK51_skl)),or(sK50_skl,or(sK49_skl,sK51_skl))))),
% 20.13/3.24 inference(backward_subsumption_resolution,[status(thm)],[f160,f196])).
% 20.13/3.24 fof(f218,plain,(
% 20.13/3.24 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1))),
% 20.13/3.24 inference(backward_demodulation,[status(thm)],[f198,f197])).
% 20.13/3.24 fof(f222,plain,(
% 20.13/3.24 ![X0,X1]: (and(X0,X1)=not(implies(X0,not(X1))))),
% 20.13/3.24 inference(forward_demodulation,[status(thm)],[f215,f216])).
% 20.13/3.24 fof(f227,plain,(
% 20.13/3.24 ![X0,X1]: (is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))))),
% 20.13/3.24 inference(backward_demodulation,[status(thm)],[f218,f201])).
% 20.13/3.24 fof(f235,plain,(
% 20.13/3.24 ![X0,X1]: (~is_a_theorem(implies(X0,implies(X0,X1)))|is_a_theorem(implies(X0,X1)))),
% 20.13/3.24 inference(resolution,[status(thm)],[f203,f200])).
% 20.13/3.24 fof(f236,plain,(
% 20.13/3.24 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(implies(X1,X2),implies(X0,X2))))),
% 20.13/3.25 inference(resolution,[status(thm)],[f204,f200])).
% 20.13/3.25 fof(f253,plain,(
% 20.13/3.25 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(implies(X1,X0),equiv(X0,X1))))),
% 20.13/3.25 inference(resolution,[status(thm)],[f213,f200])).
% 20.13/3.25 fof(f265,plain,(
% 20.13/3.25 ![X0,X1,X2]: (implies(implies(X0,not(X1)),X2)=or(and(X0,X1),X2))),
% 20.13/3.25 inference(paramodulation,[status(thm)],[f222,f215])).
% 20.13/3.25 fof(f268,plain,(
% 20.13/3.25 ![X0,X1,X2]: (or(and(X0,not(X1)),X2)=implies(implies(X0,X1),X2))),
% 20.13/3.25 inference(paramodulation,[status(thm)],[f198,f218])).
% 20.13/3.25 fof(f269,plain,(
% 20.13/3.25 ![X0,X1]: (and(not(X0),X1)=not(or(X0,not(X1))))),
% 20.13/3.25 inference(paramodulation,[status(thm)],[f218,f222])).
% 20.13/3.25 fof(f270,plain,(
% 20.13/3.25 ![X0,X1]: (is_a_theorem(implies(X0,or(X1,and(X0,not(X1))))))),
% 20.13/3.25 inference(paramodulation,[status(thm)],[f218,f207])).
% 20.13/3.25 fof(f283,plain,(
% 20.13/3.25 ![X0,X1,X2]: (is_a_theorem(implies(implies(not(X0),X1),implies(implies(X1,X2),or(X0,X2)))))),
% 20.13/3.25 inference(paramodulation,[status(thm)],[f218,f204])).
% 20.13/3.25 fof(f290,plain,(
% 20.13/3.25 ![X0,X1]: (equiv(X0,not(X1))=and(implies(X0,not(X1)),or(X1,X0)))),
% 20.13/3.25 inference(paramodulation,[status(thm)],[f218,f199])).
% 20.13/3.25 fof(f298,plain,(
% 20.13/3.25 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),or(X0,X2)))))),
% 20.13/3.25 inference(forward_demodulation,[status(thm)],[f218,f283])).
% 20.13/3.25 fof(f316,plain,(
% 20.13/3.25 ![X0,X1]: (is_a_theorem(implies(implies(X0,not(X1)),implies(X1,not(X0)))))),
% 20.13/3.25 inference(paramodulation,[status(thm)],[f215,f227])).
% 20.13/3.25 fof(f320,plain,(
% 20.13/3.25 ![X0,X1]: (is_a_theorem(or(and(X0,X1),implies(X1,not(X0)))))),
% 20.13/3.25 inference(forward_demodulation,[status(thm)],[f265,f316])).
% 20.13/3.25 fof(f337,plain,(
% 20.13/3.25 ![X0]: (is_a_theorem(implies(X0,and(X0,X0))))),
% 20.13/3.25 inference(resolution,[status(thm)],[f235,f207])).
% 20.13/3.25 fof(f338,plain,(
% 20.13/3.25 ![X0]: (is_a_theorem(implies(X0,X0)))),
% 20.13/3.25 inference(resolution,[status(thm)],[f235,f202])).
% 20.13/3.25 fof(f355,plain,(
% 20.13/3.25 ![X0]: (~is_a_theorem(X0)|is_a_theorem(and(X0,X0)))),
% 20.13/3.25 inference(resolution,[status(thm)],[f337,f200])).
% 20.13/3.25 fof(f359,plain,(
% 20.13/3.25 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X2))|is_a_theorem(implies(X0,X2)))),
% 20.13/3.25 inference(resolution,[status(thm)],[f236,f200])).
% 20.13/3.25 fof(f361,plain,(
% 20.13/3.25 ![X0,X1,X2]: (~is_a_theorem(implies(not(X0),X1))|is_a_theorem(implies(implies(X1,X2),or(X0,X2))))),
% 20.13/3.25 inference(paramodulation,[status(thm)],[f218,f236])).
% 20.13/3.25 fof(f362,plain,(
% 20.13/3.25 ![X0,X1,X2]: (~is_a_theorem(or(X0,X1))|is_a_theorem(implies(implies(X1,X2),or(X0,X2))))),
% 20.13/3.25 inference(forward_demodulation,[status(thm)],[f218,f361])).
% 20.13/3.25 fof(f372,plain,(
% 20.13/3.25 ![X0]: (~is_a_theorem(implies(X0,X0))|is_a_theorem(equiv(X0,X0)))),
% 20.13/3.25 inference(paramodulation,[status(thm)],[f199,f355])).
% 20.13/3.25 fof(f373,plain,(
% 20.13/3.25 ![X0]: (is_a_theorem(equiv(X0,X0)))),
% 20.13/3.25 inference(forward_subsumption_resolution,[status(thm)],[f372,f338])).
% 20.13/3.25 fof(f385,plain,(
% 20.13/3.25 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X0))|is_a_theorem(equiv(X0,X1)))),
% 20.13/3.25 inference(resolution,[status(thm)],[f253,f200])).
% 20.13/3.25 fof(f559,plain,(
% 20.13/3.25 ![X0,X1,X2]: (and(implies(X0,not(X1)),X2)=not(or(and(X0,X1),not(X2))))),
% 20.13/3.25 inference(paramodulation,[status(thm)],[f265,f222])).
% 20.13/3.25 fof(f609,plain,(
% 20.13/3.25 ![X0,X1,X2]: (and(implies(X0,not(X1)),X2)=and(not(and(X0,X1)),X2))),
% 20.13/3.25 inference(forward_demodulation,[status(thm)],[f269,f559])).
% 20.13/3.25 fof(f743,plain,(
% 20.13/3.25 ![X0,X1,X2]: (and(not(and(X0,not(X1))),X2)=not(implies(implies(X0,X1),not(X2))))),
% 20.13/3.25 inference(paramodulation,[status(thm)],[f268,f269])).
% 20.13/3.25 fof(f771,plain,(
% 20.13/3.25 ![X0,X1,X2]: (and(implies(X0,not(not(X1))),X2)=not(implies(implies(X0,X1),not(X2))))),
% 20.13/3.25 inference(forward_demodulation,[status(thm)],[f609,f743])).
% 20.13/3.25 fof(f772,plain,(
% 20.13/3.25 ![X0,X1,X2]: (and(implies(X0,not(not(X1))),X2)=and(implies(X0,X1),X2))),
% 20.13/3.25 inference(forward_demodulation,[status(thm)],[f222,f771])).
% 20.13/3.25 fof(f789,plain,(
% 20.13/3.25 ![X0,X1]: (is_a_theorem(or(X0,or(X1,and(not(X0),not(X1))))))),
% 20.13/3.25 inference(paramodulation,[status(thm)],[f218,f270])).
% 20.13/3.25 fof(f1295,plain,(
% 20.13/3.25 ![X0,X1]: (equiv(X0,not(not(X1)))=and(implies(X0,not(not(X1))),implies(X1,X0)))),
% 20.13/3.25 inference(paramodulation,[status(thm)],[f215,f290])).
% 20.13/3.25 fof(f1325,plain,(
% 20.13/3.25 ![X0,X1]: (equiv(X0,not(not(X1)))=and(implies(X0,X1),implies(X1,X0)))),
% 20.13/3.25 inference(forward_demodulation,[status(thm)],[f772,f1295])).
% 20.13/3.31 fof(f1329,plain,(
% 20.13/3.31 ![X0,X1]: (equiv(X0,not(not(X1)))=equiv(X0,X1))),
% 20.13/3.31 inference(forward_demodulation,[status(thm)],[f199,f1325])).
% 20.13/3.31 fof(f1350,plain,(
% 20.13/3.31 ![X0]: (is_a_theorem(equiv(not(not(X0)),X0)))),
% 20.13/3.31 inference(paramodulation,[status(thm)],[f1329,f373])).
% 20.13/3.31 fof(f1437,plain,(
% 20.13/3.31 ![X0]: (not(not(X0))=X0)),
% 20.13/3.31 inference(resolution,[status(thm)],[f1350,f214])).
% 20.13/3.31 fof(f1585,plain,(
% 20.13/3.31 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),implies(not(X1),not(X0)))))),
% 20.13/3.31 inference(paramodulation,[status(thm)],[f268,f320])).
% 20.13/3.31 fof(f1599,plain,(
% 20.13/3.31 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),or(X1,not(X0)))))),
% 20.13/3.31 inference(forward_demodulation,[status(thm)],[f218,f1585])).
% 20.13/3.31 fof(f1630,plain,(
% 20.13/3.31 ![X0,X1]: (and(not(X0),not(X1))=not(or(X0,X1)))),
% 20.13/3.31 inference(paramodulation,[status(thm)],[f1437,f269])).
% 20.13/3.31 fof(f1727,plain,(
% 20.13/3.31 ![X0,X1]: (is_a_theorem(or(X0,or(X1,not(or(X0,X1))))))),
% 20.13/3.31 inference(backward_demodulation,[status(thm)],[f1630,f789])).
% 20.13/3.31 fof(f2431,plain,(
% 20.13/3.31 ![X0]: (~is_a_theorem(implies(or(sK49_skl,or(sK50_skl,sK51_skl)),X0))|~is_a_theorem(implies(X0,or(sK50_skl,or(sK49_skl,sK51_skl)))))),
% 20.13/3.31 inference(resolution,[status(thm)],[f359,f217])).
% 20.13/3.31 fof(f2446,plain,(
% 20.13/3.31 ![X0]: (~is_a_theorem(implies(implies(implies(or(sK50_skl,sK51_skl),X0),or(sK49_skl,X0)),or(sK50_skl,or(sK49_skl,sK51_skl)))))),
% 20.13/3.31 inference(resolution,[status(thm)],[f2431,f298])).
% 20.13/3.31 fof(f2564,plain,(
% 20.13/3.31 ~is_a_theorem(or(sK50_skl,implies(or(sK50_skl,sK51_skl),sK51_skl)))),
% 20.13/3.31 inference(resolution,[status(thm)],[f362,f2446])).
% 20.13/3.31 fof(f2811,plain,(
% 20.13/3.31 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X0))|X0=X1)),
% 20.13/3.31 inference(resolution,[status(thm)],[f385,f214])).
% 20.13/3.31 fof(f6975,plain,(
% 20.13/3.31 ![X0,X1]: (~is_a_theorem(implies(implies(X0,X1),or(X1,not(X0))))|implies(X0,X1)=or(X1,not(X0)))),
% 20.13/3.31 inference(resolution,[status(thm)],[f2811,f227])).
% 20.13/3.31 fof(f7129,plain,(
% 20.13/3.31 ![X0,X1]: (is_a_theorem(or(X0,implies(or(X0,X1),X1))))),
% 20.13/3.31 inference(backward_demodulation,[status(thm)],[f7300,f1727])).
% 20.13/3.31 fof(f7300,plain,(
% 20.13/3.31 ![X0,X1]: (implies(X0,X1)=or(X1,not(X0)))),
% 20.13/3.31 inference(forward_subsumption_resolution,[status(thm)],[f6975,f1599])).
% 20.13/3.31 fof(f7596,plain,(
% 20.13/3.31 $false),
% 20.13/3.31 inference(backward_subsumption_resolution,[status(thm)],[f2564,f7129])).
% 20.13/3.31 % SZS output end CNFRefutation for theBenchmark.p
% 20.13/3.36 % Elapsed time: 2.888828 seconds
% 20.13/3.36 % CPU time: 22.354273 seconds
% 20.13/3.36 % Total memory used: 319.580 MB
% 20.13/3.36 % Net memory used: 307.907 MB
%------------------------------------------------------------------------------