%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL463+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 : n015.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 01:10:08 PM UTC 2026
% Result : Theorem 19.78s 3.01s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL463+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 00:37:05 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 19.78/3.01 % Refutation found
% 19.78/3.01 % SZS status Theorem for theBenchmark: Theorem is valid
% 19.78/3.01 % SZS output start CNFRefutation for theBenchmark
% 19.78/3.01 fof(f1,axiom,(
% 19.78/3.01 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 19.78/3.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 19.78/3.01 fof(f4,axiom,(
% 19.78/3.01 ( implies_1<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) )) ),
% 19.78/3.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 19.78/3.01 fof(f19,axiom,(
% 19.78/3.01 ( cn1<=> (! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R)))) )) ),
% 19.78/3.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 19.78/3.01 fof(f20,axiom,(
% 19.78/3.01 ( cn2<=> (! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q))) )) ),
% 19.78/3.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 19.78/3.01 fof(f21,axiom,(
% 19.78/3.01 ( cn3<=> (! [P] : is_a_theorem(implies(implies(not(P),P),P)) )) ),
% 19.78/3.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 19.78/3.01 fof(f27,axiom,(
% 19.78/3.01 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 19.78/3.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 19.78/3.01 fof(f29,axiom,(
% 19.78/3.01 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 19.78/3.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 19.78/3.01 fof(f32,axiom,(
% 19.78/3.01 op_or ),
% 19.78/3.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 19.78/3.01 fof(f35,axiom,(
% 19.78/3.01 modus_ponens ),
% 19.78/3.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 19.78/3.01 fof(f36,axiom,(
% 19.78/3.01 cn1 ),
% 19.78/3.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 19.78/3.01 fof(f37,axiom,(
% 19.78/3.01 cn2 ),
% 19.78/3.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 19.78/3.01 fof(f38,axiom,(
% 19.78/3.01 cn3 ),
% 19.78/3.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 19.78/3.01 fof(f41,axiom,(
% 19.78/3.01 op_implies_and ),
% 19.78/3.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 19.78/3.01 fof(f43,conjecture,(
% 19.78/3.01 implies_1 ),
% 19.78/3.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 19.78/3.01 fof(f44,negated_conjecture,(
% 19.78/3.01 ~(implies_1 )),
% 19.78/3.01 inference(negated_conjecture,[status(cth)],[f43])).
% 19.78/3.01 fof(f45,plain,(
% 19.78/3.01 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 19.78/3.01 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 19.78/3.01 fof(f46,plain,(
% 19.78/3.01 (~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))))),
% 19.78/3.01 inference(NNF_transformation,[status(thm)],[f45])).
% 19.78/3.01 fof(f47,plain,(
% 19.78/3.01 (~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))))),
% 19.78/3.01 inference(miniscoping,[status(thm)],[f46])).
% 19.78/3.01 fof(f48,plain,(
% 19.78/3.01 (~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)))),
% 19.78/3.01 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f47])).
% 19.78/3.01 fof(f49,plain,(
% 19.78/3.01 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 19.78/3.01 inference(cnf_transformation,[status(thm)],[f48])).
% 19.78/3.01 fof(f63,plain,(
% 19.78/3.01 (~implies_1|(![X,Y]: is_a_theorem(implies(X,implies(Y,X)))))&(implies_1|(?[X,Y]: ~is_a_theorem(implies(X,implies(Y,X)))))),
% 19.78/3.01 inference(NNF_transformation,[status(thm)],[f4])).
% 19.78/3.01 fof(f64,plain,(
% 19.78/3.01 (~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))))),
% 19.78/3.01 inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl]),skolemize(X,sK6_skl),skolemize(Y,sK7_skl)],[f63])).
% 19.78/3.01 fof(f66,plain,(
% 19.78/3.01 implies_1|~is_a_theorem(implies(sK6_skl,implies(sK7_skl,sK6_skl)))),
% 19.78/3.01 inference(cnf_transformation,[status(thm)],[f64])).
% 19.78/3.01 fof(f123,plain,(
% 19.78/3.01 (~cn1|(![P,Q,R]: is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))))&(cn1|(?[P,Q,R]: ~is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))))),
% 19.78/3.01 inference(NNF_transformation,[status(thm)],[f19])).
% 19.78/3.01 fof(f124,plain,(
% 19.78/3.01 (~cn1|(![P,Q,R]: is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))))&(cn1|~is_a_theorem(implies(implies(sK38_skl,sK39_skl),implies(implies(sK39_skl,sK40_skl),implies(sK38_skl,sK40_skl)))))),
% 19.78/3.01 inference(skolemize,[status(esa),new_symbols(skolem,[sK38_skl,sK39_skl,sK40_skl]),skolemize(P,sK38_skl),skolemize(Q,sK39_skl),skolemize(R,sK40_skl)],[f123])).
% 19.78/3.01 fof(f125,plain,(
% 19.78/3.01 ![X0,X1,X2]: (~cn1|is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))))),
% 19.78/3.01 inference(cnf_transformation,[status(thm)],[f124])).
% 19.78/3.01 fof(f127,plain,(
% 19.78/3.01 (~cn2|(![P,Q]: is_a_theorem(implies(P,implies(not(P),Q)))))&(cn2|(?[P,Q]: ~is_a_theorem(implies(P,implies(not(P),Q)))))),
% 19.78/3.01 inference(NNF_transformation,[status(thm)],[f20])).
% 19.78/3.01 fof(f128,plain,(
% 19.78/3.01 (~cn2|(![P,Q]: is_a_theorem(implies(P,implies(not(P),Q)))))&(cn2|~is_a_theorem(implies(sK41_skl,implies(not(sK41_skl),sK42_skl))))),
% 19.78/3.01 inference(skolemize,[status(esa),new_symbols(skolem,[sK41_skl,sK42_skl]),skolemize(P,sK41_skl),skolemize(Q,sK42_skl)],[f127])).
% 19.78/3.01 fof(f129,plain,(
% 19.78/3.01 ![X0,X1]: (~cn2|is_a_theorem(implies(X0,implies(not(X0),X1))))),
% 19.78/3.01 inference(cnf_transformation,[status(thm)],[f128])).
% 19.78/3.01 fof(f131,plain,(
% 19.78/3.01 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|(?[P]: ~is_a_theorem(implies(implies(not(P),P),P))))),
% 19.78/3.01 inference(NNF_transformation,[status(thm)],[f21])).
% 19.78/3.01 fof(f132,plain,(
% 19.78/3.01 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|~is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl)))),
% 19.78/3.01 inference(skolemize,[status(esa),new_symbols(skolem,[sK43_skl]),skolemize(P,sK43_skl)],[f131])).
% 19.78/3.01 fof(f133,plain,(
% 19.78/3.01 ![X0]: (~cn3|is_a_theorem(implies(implies(not(X0),X0),X0)))),
% 19.78/3.01 inference(cnf_transformation,[status(thm)],[f132])).
% 19.78/3.01 fof(f155,plain,(
% 19.78/3.01 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 19.78/3.01 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 19.78/3.01 fof(f156,plain,(
% 19.78/3.01 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 19.78/3.01 inference(cnf_transformation,[status(thm)],[f155])).
% 19.78/3.01 fof(f159,plain,(
% 19.78/3.01 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 19.78/3.01 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 19.78/3.01 fof(f160,plain,(
% 19.78/3.01 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 19.78/3.01 inference(cnf_transformation,[status(thm)],[f159])).
% 19.78/3.01 fof(f165,plain,(
% 19.78/3.01 op_or),
% 19.78/3.01 inference(cnf_transformation,[status(thm)],[f32])).
% 19.78/3.01 fof(f168,plain,(
% 19.78/3.01 modus_ponens),
% 19.78/3.01 inference(cnf_transformation,[status(thm)],[f35])).
% 19.78/3.01 fof(f169,plain,(
% 19.78/3.01 cn1),
% 19.78/3.01 inference(cnf_transformation,[status(thm)],[f36])).
% 19.78/3.01 fof(f170,plain,(
% 19.78/3.01 cn2),
% 19.78/3.01 inference(cnf_transformation,[status(thm)],[f37])).
% 19.78/3.01 fof(f171,plain,(
% 19.78/3.01 cn3),
% 19.78/3.01 inference(cnf_transformation,[status(thm)],[f38])).
% 19.78/3.01 fof(f174,plain,(
% 19.78/3.01 op_implies_and),
% 19.78/3.01 inference(cnf_transformation,[status(thm)],[f41])).
% 19.78/3.01 fof(f176,plain,(
% 19.78/3.01 ~implies_1),
% 19.78/3.01 inference(cnf_transformation,[status(thm)],[f44])).
% 19.78/3.01 fof(f177,plain,(
% 19.78/3.01 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1))))),
% 19.78/3.01 inference(backward_subsumption_resolution,[status(thm)],[f156,f165])).
% 19.78/3.01 fof(f179,plain,(
% 19.78/3.01 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 19.78/3.01 inference(backward_subsumption_resolution,[status(thm)],[f49,f168])).
% 19.78/3.01 fof(f180,plain,(
% 19.78/3.01 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))))),
% 19.78/3.01 inference(backward_subsumption_resolution,[status(thm)],[f125,f169])).
% 19.78/3.01 fof(f181,plain,(
% 19.78/3.01 ![X0,X1]: (is_a_theorem(implies(X0,implies(not(X0),X1))))),
% 19.78/3.01 inference(backward_subsumption_resolution,[status(thm)],[f129,f170])).
% 19.78/3.01 fof(f182,plain,(
% 19.78/3.01 ![X0]: (is_a_theorem(implies(implies(not(X0),X0),X0)))),
% 19.78/3.01 inference(backward_subsumption_resolution,[status(thm)],[f133,f171])).
% 19.78/3.01 fof(f184,plain,(
% 19.78/3.01 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1))))),
% 19.78/3.01 inference(backward_subsumption_resolution,[status(thm)],[f160,f174])).
% 19.78/3.01 fof(f185,plain,(
% 19.78/3.01 ~is_a_theorem(implies(sK6_skl,implies(sK7_skl,sK6_skl)))),
% 19.78/3.01 inference(backward_subsumption_resolution,[status(thm)],[f66,f176])).
% 19.78/3.01 fof(f187,plain,(
% 19.78/3.01 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1))),
% 19.78/3.01 inference(backward_demodulation,[status(thm)],[f184,f177])).
% 19.78/3.01 fof(f192,plain,(
% 19.78/3.01 ![X0]: (is_a_theorem(implies(or(X0,X0),X0)))),
% 19.78/3.01 inference(backward_demodulation,[status(thm)],[f187,f182])).
% 19.78/3.01 fof(f193,plain,(
% 19.78/3.01 ![X0,X1]: (is_a_theorem(implies(X0,or(X0,X1))))),
% 19.78/3.01 inference(backward_demodulation,[status(thm)],[f187,f181])).
% 19.78/3.01 fof(f199,plain,(
% 19.78/3.01 ![X0,X1,X2]: (or(and(X0,not(X1)),X2)=implies(implies(X0,X1),X2))),
% 19.78/3.01 inference(paramodulation,[status(thm)],[f184,f187])).
% 19.78/3.01 fof(f200,plain,(
% 19.78/3.01 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(implies(X1,X2),implies(X0,X2))))),
% 19.78/3.01 inference(resolution,[status(thm)],[f180,f179])).
% 19.78/3.01 fof(f201,plain,(
% 19.78/3.01 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),implies(not(X0),X2)))))),
% 19.78/3.01 inference(paramodulation,[status(thm)],[f187,f180])).
% 19.78/3.01 fof(f204,plain,(
% 19.78/3.01 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),or(X0,X2)))))),
% 19.78/3.01 inference(forward_demodulation,[status(thm)],[f187,f201])).
% 19.78/3.01 fof(f207,plain,(
% 19.78/3.01 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),implies(or(X0,X0),X1))))),
% 19.78/3.01 inference(resolution,[status(thm)],[f200,f192])).
% 19.78/3.01 fof(f210,plain,(
% 19.78/3.01 ![X0,X1,X2]: (is_a_theorem(implies(implies(implies(or(X0,X0),X1),X2),implies(implies(X0,X1),X2))))),
% 19.78/3.01 inference(resolution,[status(thm)],[f207,f200])).
% 19.78/3.01 fof(f211,plain,(
% 19.78/3.01 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(or(X0,X0),X1)))),
% 19.78/3.01 inference(resolution,[status(thm)],[f207,f179])).
% 19.78/3.01 fof(f230,plain,(
% 19.78/3.01 ![X0,X1]: (is_a_theorem(implies(or(X0,X0),or(X0,X1))))),
% 19.78/3.01 inference(resolution,[status(thm)],[f193,f211])).
% 19.78/3.01 fof(f231,plain,(
% 19.78/3.01 ![X0,X1,X2]: (is_a_theorem(implies(implies(or(X0,X1),X2),implies(X0,X2))))),
% 19.78/3.01 inference(resolution,[status(thm)],[f193,f200])).
% 19.78/3.01 fof(f236,plain,(
% 19.78/3.01 ![X0,X1,X2]: (~is_a_theorem(implies(or(X0,X1),X2))|is_a_theorem(implies(X0,X2)))),
% 19.78/3.01 inference(resolution,[status(thm)],[f231,f179])).
% 19.78/3.01 fof(f273,plain,(
% 19.78/3.01 ![X0,X1,X2]: (is_a_theorem(implies(implies(or(X0,X1),X2),implies(or(X0,X0),X2))))),
% 19.78/3.01 inference(resolution,[status(thm)],[f230,f200])).
% 19.78/3.01 fof(f277,plain,(
% 19.78/3.01 ![X0,X1,X2,X3]: (is_a_theorem(implies(implies(implies(or(X0,X0),X1),X2),implies(implies(or(X0,X3),X1),X2))))),
% 19.78/3.01 inference(resolution,[status(thm)],[f273,f200])).
% 19.78/3.01 fof(f286,plain,(
% 19.78/3.01 ![X0,X1,X2,X3]: (~is_a_theorem(implies(implies(or(X0,X0),X1),X2))|is_a_theorem(implies(implies(or(X0,X3),X1),X2)))),
% 19.78/3.01 inference(resolution,[status(thm)],[f277,f179])).
% 19.78/3.01 fof(f292,plain,(
% 19.78/3.01 ![X0,X1,X2,X3]: (is_a_theorem(implies(implies(or(X0,X1),X2),implies(implies(X2,X3),implies(or(X0,X0),X3)))))),
% 19.78/3.01 inference(resolution,[status(thm)],[f286,f180])).
% 19.78/3.01 fof(f297,plain,(
% 19.78/3.01 ![X0,X1,X2,X3,X4]: (is_a_theorem(implies(implies(implies(implies(X0,X1),implies(or(X2,X2),X1)),X3),implies(implies(or(X2,X4),X0),X3))))),
% 19.78/3.01 inference(resolution,[status(thm)],[f292,f200])).
% 19.78/3.01 fof(f355,plain,(
% 19.78/3.01 ![X0,X1,X2,X3,X4]: (~is_a_theorem(implies(implies(implies(X0,X1),implies(or(X2,X2),X1)),X3))|is_a_theorem(implies(implies(or(X2,X4),X0),X3)))),
% 19.78/3.01 inference(resolution,[status(thm)],[f297,f179])).
% 19.78/3.01 fof(f361,plain,(
% 19.78/3.01 ![X0,X1,X2,X3]: (is_a_theorem(implies(implies(or(X0,X1),or(X2,X2)),implies(implies(X2,X3),implies(or(X0,X0),X3)))))),
% 19.78/3.01 inference(resolution,[status(thm)],[f355,f210])).
% 19.78/3.01 fof(f669,plain,(
% 19.78/3.01 ![X0,X1,X2,X3]: (or(and(X0,implies(X1,X2)),X3)=implies(implies(X0,and(X1,not(X2))),X3))),
% 19.78/3.01 inference(paramodulation,[status(thm)],[f184,f199])).
% 19.78/3.01 fof(f768,plain,(
% 19.78/3.01 ![X0,X1]: (is_a_theorem(implies(implies(implies(X0,X1),and(X0,not(X1))),and(X0,not(X1)))))),
% 19.78/3.01 inference(paramodulation,[status(thm)],[f199,f192])).
% 19.78/3.01 fof(f909,plain,(
% 19.78/3.01 ![X0,X1]: (is_a_theorem(or(and(implies(X0,X1),implies(X0,X1)),and(X0,not(X1)))))),
% 19.78/3.01 inference(forward_demodulation,[status(thm)],[f669,f768])).
% 19.78/3.01 fof(f1130,plain,(
% 19.78/3.01 ![X0,X1,X2]: (is_a_theorem(implies(X0,implies(implies(X1,X2),or(X0,X2)))))),
% 19.78/3.01 inference(resolution,[status(thm)],[f204,f236])).
% 19.78/3.01 fof(f1174,plain,(
% 19.78/3.01 ![X0,X1,X2,X3]: (is_a_theorem(implies(implies(implies(implies(X0,X1),or(X2,X1)),X3),implies(X2,X3))))),
% 19.78/3.01 inference(resolution,[status(thm)],[f1130,f200])).
% 19.78/3.01 fof(f1208,plain,(
% 19.78/3.01 ![X0,X1,X2,X3]: (~is_a_theorem(implies(implies(implies(X0,X1),or(X2,X1)),X3))|is_a_theorem(implies(X2,X3)))),
% 19.78/3.01 inference(resolution,[status(thm)],[f1174,f179])).
% 19.78/3.01 fof(f1224,plain,(
% 19.78/3.01 ![X0,X1,X2,X3]: (is_a_theorem(implies(X0,implies(implies(or(X0,X1),X2),implies(implies(X3,X1),X2)))))),
% 18.72/3.08 inference(resolution,[status(thm)],[f1208,f180])).
% 18.72/3.08 fof(f1231,plain,(
% 18.72/3.08 ![X0,X1,X2,X3]: (~is_a_theorem(implies(implies(or(X0,X1),or(X2,X1)),X3))|is_a_theorem(implies(X2,X3)))),
% 18.72/3.08 inference(paramodulation,[status(thm)],[f187,f1208])).
% 18.72/3.08 fof(f1288,plain,(
% 18.72/3.08 ![X0,X1,X2,X3]: (~is_a_theorem(X0)|is_a_theorem(implies(implies(or(X0,X1),X2),implies(implies(X3,X1),X2))))),
% 18.72/3.08 inference(resolution,[status(thm)],[f1224,f179])).
% 18.72/3.08 fof(f1298,plain,(
% 18.72/3.08 ![X0,X1,X2]: (is_a_theorem(implies(X0,implies(implies(X0,X1),implies(or(X2,X2),X1)))))),
% 18.72/3.08 inference(resolution,[status(thm)],[f1231,f361])).
% 18.72/3.08 fof(f1355,plain,(
% 18.72/3.08 ![X0,X1,X2,X3]: (is_a_theorem(implies(implies(implies(implies(X0,X1),implies(or(X2,X2),X1)),X3),implies(X0,X3))))),
% 18.72/3.08 inference(resolution,[status(thm)],[f1298,f200])).
% 18.72/3.08 fof(f1572,plain,(
% 18.72/3.08 ![X0,X1,X2,X3]: (is_a_theorem(implies(implies(or(implies(or(X0,X0),X0),X1),X2),implies(implies(X3,X1),X2))))),
% 18.72/3.08 inference(resolution,[status(thm)],[f1288,f192])).
% 18.72/3.08 fof(f2495,plain,(
% 18.72/3.08 ![X0,X1,X2,X3]: (~is_a_theorem(implies(implies(implies(X0,X1),implies(or(X2,X2),X1)),X3))|is_a_theorem(implies(X0,X3)))),
% 18.72/3.08 inference(resolution,[status(thm)],[f1355,f179])).
% 18.72/3.08 fof(f3176,plain,(
% 18.72/3.08 ![X0,X1,X2,X3]: (~is_a_theorem(implies(or(implies(or(X0,X0),X0),X1),X2))|is_a_theorem(implies(implies(X3,X1),X2)))),
% 18.72/3.08 inference(resolution,[status(thm)],[f1572,f179])).
% 18.72/3.08 fof(f5457,plain,(
% 18.72/3.08 ![X0,X1]: (is_a_theorem(implies(implies(X0,implies(or(X1,X1),X1)),implies(or(X1,X1),X1))))),
% 18.72/3.08 inference(resolution,[status(thm)],[f3176,f192])).
% 18.72/3.08 fof(f5492,plain,(
% 18.72/3.08 ![X0,X1]: (is_a_theorem(implies(X0,implies(or(X1,X1),X1))))),
% 18.72/3.08 inference(resolution,[status(thm)],[f5457,f2495])).
% 18.72/3.08 fof(f5574,plain,(
% 18.72/3.08 ![X0,X1,X2]: (is_a_theorem(implies(implies(implies(or(X0,X0),X0),X1),implies(X2,X1))))),
% 18.72/3.08 inference(resolution,[status(thm)],[f5492,f200])).
% 18.72/3.08 fof(f5599,plain,(
% 18.72/3.08 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X0),implies(X1,implies(or(X2,X2),X0)))))),
% 18.72/3.08 inference(resolution,[status(thm)],[f5574,f2495])).
% 18.72/3.08 fof(f5607,plain,(
% 18.72/3.08 ![X0,X1,X2]: (~is_a_theorem(implies(implies(or(X0,X0),X0),X1))|is_a_theorem(implies(X2,X1)))),
% 18.72/3.08 inference(resolution,[status(thm)],[f5574,f179])).
% 18.72/3.08 fof(f5704,plain,(
% 18.72/3.08 ![X0,X1,X2]: (is_a_theorem(implies(X0,implies(X1,implies(or(X2,X2),X0)))))),
% 18.72/3.08 inference(resolution,[status(thm)],[f5599,f236])).
% 18.72/3.08 fof(f5754,plain,(
% 18.72/3.08 ![X0,X1,X2,X3]: (is_a_theorem(implies(implies(implies(X0,implies(or(X1,X1),X2)),X3),implies(X2,X3))))),
% 18.72/3.08 inference(resolution,[status(thm)],[f5704,f200])).
% 18.72/3.08 fof(f7027,plain,(
% 18.72/3.08 ![X0,X1,X2,X3]: (is_a_theorem(implies(implies(or(X0,implies(or(X1,X1),X2)),X3),implies(X2,X3))))),
% 18.72/3.08 inference(paramodulation,[status(thm)],[f187,f5754])).
% 18.72/3.08 fof(f7822,plain,(
% 18.72/3.08 ![X0,X1,X2]: (is_a_theorem(implies(X0,implies(X1,implies(or(X2,X2),X1)))))),
% 18.72/3.08 inference(resolution,[status(thm)],[f7027,f5607])).
% 18.72/3.08 fof(f8013,plain,(
% 18.72/3.08 ![X0,X1,X2]: (~is_a_theorem(X0)|is_a_theorem(implies(X1,implies(or(X2,X2),X1))))),
% 18.72/3.08 inference(resolution,[status(thm)],[f7822,f179])).
% 18.72/3.08 fof(f8034,plain,(
% 18.72/3.08 ![X0,X1]: (is_a_theorem(implies(X0,implies(or(X1,X1),X0))))),
% 18.72/3.08 inference(resolution,[status(thm)],[f8013,f909])).
% 18.72/3.08 fof(f8196,plain,(
% 18.72/3.08 ![X0,X1,X2]: (is_a_theorem(implies(implies(implies(or(X0,X0),X1),X2),implies(X1,X2))))),
% 18.72/3.08 inference(resolution,[status(thm)],[f8034,f200])).
% 18.72/3.08 fof(f8470,plain,(
% 18.72/3.08 ![X0,X1,X2]: (~is_a_theorem(implies(implies(or(X0,X0),X1),X2))|is_a_theorem(implies(X1,X2)))),
% 18.72/3.08 inference(resolution,[status(thm)],[f8196,f179])).
% 18.72/3.08 fof(f8636,plain,(
% 18.72/3.08 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0))))),
% 18.72/3.08 inference(resolution,[status(thm)],[f8470,f7027])).
% 18.72/3.08 fof(f8703,plain,(
% 18.72/3.08 $false),
% 18.72/3.08 inference(backward_subsumption_resolution,[status(thm)],[f185,f8636])).
% 18.72/3.08 % SZS output end CNFRefutation for theBenchmark.p
% 18.72/3.09 % Elapsed time: 2.718629 seconds
% 18.72/3.09 % CPU time: 21.127725 seconds
% 18.72/3.09 % Total memory used: 351.630 MB
% 18.72/3.09 % Net memory used: 339.683 MB
%------------------------------------------------------------------------------