%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL453+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 0.12s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL453+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % 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 00:35:01 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.41 % Refutation found
% 0.12/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.41 fof(f1,axiom,(
% 0.12/0.41 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f4,axiom,(
% 0.12/0.41 ( implies_1<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) )) ),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f5,axiom,(
% 0.12/0.41 ( implies_2<=> (! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )) ),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f12,axiom,(
% 0.12/0.41 ( or_3<=> (! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))) )) ),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f21,axiom,(
% 0.12/0.41 ( cn3<=> (! [P] : is_a_theorem(implies(implies(not(P),P),P)) )) ),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f27,axiom,(
% 0.12/0.41 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f29,axiom,(
% 0.12/0.41 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f32,axiom,(
% 0.12/0.41 op_or ),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f33,axiom,(
% 0.12/0.41 op_implies_and ),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f35,axiom,(
% 0.12/0.41 modus_ponens ),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f37,axiom,(
% 0.12/0.41 implies_1 ),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f38,axiom,(
% 0.12/0.41 implies_2 ),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f45,axiom,(
% 0.12/0.41 or_3 ),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f53,conjecture,(
% 0.12/0.41 cn3 ),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f54,negated_conjecture,(
% 0.12/0.41 ~(cn3 )),
% 0.12/0.41 inference(negated_conjecture,[status(cth)],[f53])).
% 0.12/0.41 fof(f55,plain,(
% 0.12/0.41 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 0.12/0.41 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.12/0.41 fof(f56,plain,(
% 0.12/0.41 (~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))))),
% 0.12/0.41 inference(NNF_transformation,[status(thm)],[f55])).
% 0.12/0.41 fof(f57,plain,(
% 0.12/0.41 (~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))))),
% 0.12/0.41 inference(miniscoping,[status(thm)],[f56])).
% 0.12/0.41 fof(f58,plain,(
% 0.12/0.41 (~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)))),
% 0.12/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f57])).
% 0.12/0.41 fof(f59,plain,(
% 0.12/0.41 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f58])).
% 0.12/0.41 fof(f73,plain,(
% 0.12/0.41 (~implies_1|(![X,Y]: is_a_theorem(implies(X,implies(Y,X)))))&(implies_1|(?[X,Y]: ~is_a_theorem(implies(X,implies(Y,X)))))),
% 0.12/0.41 inference(NNF_transformation,[status(thm)],[f4])).
% 0.12/0.41 fof(f74,plain,(
% 0.12/0.41 (~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))))),
% 0.12/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl]),skolemize(X,sK6_skl),skolemize(Y,sK7_skl)],[f73])).
% 0.12/0.41 fof(f75,plain,(
% 0.12/0.41 ![X0,X1]: (~implies_1|is_a_theorem(implies(X0,implies(X1,X0))))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f74])).
% 0.12/0.41 fof(f77,plain,(
% 0.12/0.41 (~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)))))),
% 0.12/0.41 inference(NNF_transformation,[status(thm)],[f5])).
% 0.12/0.41 fof(f78,plain,(
% 0.12/0.41 (~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))))),
% 0.12/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(X,sK8_skl),skolemize(Y,sK9_skl)],[f77])).
% 0.12/0.42 fof(f79,plain,(
% 0.12/0.42 ![X0,X1]: (~implies_2|is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f78])).
% 0.12/0.42 fof(f105,plain,(
% 0.12/0.42 (~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))))))),
% 0.12/0.42 inference(NNF_transformation,[status(thm)],[f12])).
% 0.12/0.42 fof(f106,plain,(
% 0.12/0.42 (~or_3|(![X,Y,Z]: is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))))&(or_3|~is_a_theorem(implies(implies(sK23_skl,sK25_skl),implies(implies(sK24_skl,sK25_skl),implies(or(sK23_skl,sK24_skl),sK25_skl)))))),
% 0.12/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl,sK24_skl,sK25_skl]),skolemize(X,sK23_skl),skolemize(Y,sK24_skl),skolemize(Z,sK25_skl)],[f105])).
% 0.12/0.42 fof(f107,plain,(
% 0.12/0.42 ![X0,X1,X2]: (~or_3|is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))))),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f106])).
% 0.12/0.42 fof(f141,plain,(
% 0.12/0.42 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|(?[P]: ~is_a_theorem(implies(implies(not(P),P),P))))),
% 0.12/0.42 inference(NNF_transformation,[status(thm)],[f21])).
% 0.12/0.42 fof(f142,plain,(
% 0.12/0.42 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|~is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl)))),
% 0.12/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK43_skl]),skolemize(P,sK43_skl)],[f141])).
% 0.12/0.42 fof(f144,plain,(
% 0.12/0.42 cn3|~is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl))),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f142])).
% 0.12/0.42 fof(f165,plain,(
% 0.12/0.42 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 0.12/0.42 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 0.12/0.42 fof(f166,plain,(
% 0.12/0.42 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f165])).
% 0.12/0.42 fof(f169,plain,(
% 0.12/0.42 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 0.12/0.42 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 0.12/0.42 fof(f170,plain,(
% 0.12/0.42 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f169])).
% 0.12/0.42 fof(f175,plain,(
% 0.12/0.42 op_or),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f32])).
% 0.12/0.42 fof(f176,plain,(
% 0.12/0.42 op_implies_and),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f33])).
% 0.12/0.42 fof(f178,plain,(
% 0.12/0.42 modus_ponens),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f35])).
% 0.12/0.42 fof(f180,plain,(
% 0.12/0.42 implies_1),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f37])).
% 0.12/0.42 fof(f181,plain,(
% 0.12/0.42 implies_2),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f38])).
% 0.12/0.42 fof(f188,plain,(
% 0.12/0.42 or_3),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f45])).
% 0.12/0.42 fof(f196,plain,(
% 0.12/0.42 ~cn3),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f54])).
% 0.12/0.42 fof(f197,plain,(
% 0.12/0.42 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1))))),
% 0.12/0.42 inference(backward_subsumption_resolution,[status(thm)],[f166,f175])).
% 0.12/0.42 fof(f198,plain,(
% 0.12/0.42 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1))))),
% 0.12/0.42 inference(backward_subsumption_resolution,[status(thm)],[f170,f176])).
% 0.12/0.42 fof(f200,plain,(
% 0.12/0.42 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 0.12/0.42 inference(backward_subsumption_resolution,[status(thm)],[f59,f178])).
% 0.12/0.42 fof(f202,plain,(
% 0.12/0.42 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0))))),
% 0.12/0.42 inference(backward_subsumption_resolution,[status(thm)],[f75,f180])).
% 0.12/0.42 fof(f203,plain,(
% 0.12/0.42 ![X0,X1]: (is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 0.12/0.42 inference(backward_subsumption_resolution,[status(thm)],[f79,f181])).
% 0.12/0.42 fof(f210,plain,(
% 0.12/0.42 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))))),
% 0.12/0.42 inference(backward_subsumption_resolution,[status(thm)],[f107,f188])).
% 0.12/0.42 fof(f215,plain,(
% 0.12/0.42 ~is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl))),
% 0.12/0.42 inference(backward_subsumption_resolution,[status(thm)],[f144,f196])).
% 0.12/0.42 fof(f216,plain,(
% 0.12/0.42 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1))),
% 0.12/0.42 inference(backward_demodulation,[status(thm)],[f198,f197])).
% 0.12/0.42 fof(f220,plain,(
% 0.12/0.42 ~is_a_theorem(implies(or(sK43_skl,sK43_skl),sK43_skl))),
% 0.12/0.42 inference(backward_demodulation,[status(thm)],[f216,f215])).
% 0.12/0.42 fof(f270,plain,(
% 0.12/0.42 ![X0,X1]: (~is_a_theorem(implies(X0,implies(X0,X1)))|is_a_theorem(implies(X0,X1)))),
% 0.12/0.42 inference(resolution,[status(thm)],[f203,f200])).
% 0.12/0.42 fof(f335,plain,(
% 0.12/0.42 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),implies(or(X0,X0),X1))))),
% 0.12/0.42 inference(resolution,[status(thm)],[f270,f210])).
% 0.12/0.42 fof(f338,plain,(
% 0.12/0.42 ![X0]: (is_a_theorem(implies(X0,X0)))),
% 0.12/0.42 inference(resolution,[status(thm)],[f270,f202])).
% 0.12/0.42 fof(f434,plain,(
% 0.12/0.42 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(or(X0,X0),X1)))),
% 0.12/0.42 inference(resolution,[status(thm)],[f335,f200])).
% 0.12/0.42 fof(f518,plain,(
% 0.12/0.42 ~is_a_theorem(implies(sK43_skl,sK43_skl))),
% 0.12/0.42 inference(resolution,[status(thm)],[f434,f220])).
% 0.12/0.42 fof(f525,plain,(
% 0.12/0.42 $false),
% 0.12/0.42 inference(forward_subsumption_resolution,[status(thm)],[f518,f338])).
% 0.12/0.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.43 % Elapsed time: 0.067421 seconds
% 0.12/0.43 % CPU time: 0.213050 seconds
% 0.12/0.43 % Total memory used: 80.208 MB
% 0.12/0.43 % Net memory used: 79.972 MB
%------------------------------------------------------------------------------