%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL456+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 0.10s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL456+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
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 00:34:45 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.41 % Refutation found
% 0.10/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.41 fof(f3,axiom,(
% 0.10/0.41 ( modus_tollens<=> (! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) )) ),
% 0.10/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f24,axiom,(
% 0.10/0.41 ( r3<=> (! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) )) ),
% 0.10/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f27,axiom,(
% 0.10/0.41 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 0.10/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f28,axiom,(
% 0.10/0.41 ( op_and=> (! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) )) ),
% 0.10/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f29,axiom,(
% 0.10/0.41 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 0.10/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f30,axiom,(
% 0.10/0.41 ( op_implies_or=> (! [X,Y] : implies(X,Y) = or(not(X),Y) )) ),
% 0.10/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f32,axiom,(
% 0.10/0.41 op_or ),
% 0.10/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f33,axiom,(
% 0.10/0.41 op_implies_and ),
% 0.10/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f36,axiom,(
% 0.10/0.41 modus_tollens ),
% 0.10/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f50,axiom,(
% 0.10/0.41 op_implies_or ),
% 0.10/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f51,axiom,(
% 0.10/0.41 op_and ),
% 0.10/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f53,conjecture,(
% 0.10/0.41 r3 ),
% 0.10/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f54,negated_conjecture,(
% 0.10/0.41 ~(r3 )),
% 0.10/0.41 inference(negated_conjecture,[status(cth)],[f53])).
% 0.10/0.41 fof(f69,plain,(
% 0.10/0.41 (~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)))))),
% 0.10/0.41 inference(NNF_transformation,[status(thm)],[f3])).
% 0.10/0.41 fof(f70,plain,(
% 0.10/0.41 (~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))))),
% 0.10/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(X,sK4_skl),skolemize(Y,sK5_skl)],[f69])).
% 0.10/0.41 fof(f71,plain,(
% 0.10/0.41 ![X0,X1]: (~modus_tollens|is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f70])).
% 0.10/0.41 fof(f153,plain,(
% 0.10/0.41 (~r3|(![P,Q]: is_a_theorem(implies(or(P,Q),or(Q,P)))))&(r3|(?[P,Q]: ~is_a_theorem(implies(or(P,Q),or(Q,P)))))),
% 0.10/0.41 inference(NNF_transformation,[status(thm)],[f24])).
% 0.10/0.41 fof(f154,plain,(
% 0.10/0.41 (~r3|(![P,Q]: is_a_theorem(implies(or(P,Q),or(Q,P)))))&(r3|~is_a_theorem(implies(or(sK47_skl,sK48_skl),or(sK48_skl,sK47_skl))))),
% 0.10/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl]),skolemize(P,sK47_skl),skolemize(Q,sK48_skl)],[f153])).
% 0.10/0.41 fof(f156,plain,(
% 0.10/0.41 r3|~is_a_theorem(implies(or(sK47_skl,sK48_skl),or(sK48_skl,sK47_skl)))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f154])).
% 0.10/0.41 fof(f165,plain,(
% 0.10/0.41 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 0.10/0.41 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 0.10/0.41 fof(f166,plain,(
% 0.10/0.41 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f165])).
% 0.10/0.41 fof(f167,plain,(
% 0.10/0.41 ~op_and|(![X,Y]: and(X,Y)=not(or(not(X),not(Y))))),
% 0.10/0.41 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 0.10/0.41 fof(f168,plain,(
% 0.10/0.41 ![X0,X1]: (~op_and|and(X0,X1)=not(or(not(X0),not(X1))))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f167])).
% 0.10/0.41 fof(f169,plain,(
% 0.10/0.41 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 0.10/0.41 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 0.10/0.41 fof(f170,plain,(
% 0.10/0.41 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f169])).
% 0.10/0.41 fof(f171,plain,(
% 0.10/0.41 ~op_implies_or|(![X,Y]: implies(X,Y)=or(not(X),Y))),
% 0.10/0.41 inference(pre_NNF_transformation,[status(thm)],[f30])).
% 0.10/0.41 fof(f172,plain,(
% 0.10/0.41 ![X0,X1]: (~op_implies_or|implies(X0,X1)=or(not(X0),X1))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f171])).
% 0.10/0.41 fof(f175,plain,(
% 0.10/0.42 op_or),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f32])).
% 0.10/0.42 fof(f176,plain,(
% 0.10/0.42 op_implies_and),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f33])).
% 0.10/0.42 fof(f179,plain,(
% 0.10/0.42 modus_tollens),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f36])).
% 0.10/0.42 fof(f193,plain,(
% 0.10/0.42 op_implies_or),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f50])).
% 0.10/0.42 fof(f194,plain,(
% 0.10/0.42 op_and),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f51])).
% 0.10/0.42 fof(f196,plain,(
% 0.10/0.42 ~r3),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f54])).
% 0.10/0.42 fof(f197,plain,(
% 0.10/0.42 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1))))),
% 0.10/0.42 inference(backward_subsumption_resolution,[status(thm)],[f166,f175])).
% 0.10/0.42 fof(f198,plain,(
% 0.10/0.42 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1))))),
% 0.10/0.42 inference(backward_subsumption_resolution,[status(thm)],[f170,f176])).
% 0.10/0.42 fof(f201,plain,(
% 0.10/0.42 ![X0,X1]: (is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))))),
% 0.10/0.42 inference(backward_subsumption_resolution,[status(thm)],[f71,f179])).
% 0.10/0.42 fof(f215,plain,(
% 0.10/0.42 ![X0,X1]: (implies(X0,X1)=or(not(X0),X1))),
% 0.10/0.42 inference(backward_subsumption_resolution,[status(thm)],[f172,f193])).
% 0.10/0.42 fof(f216,plain,(
% 0.10/0.42 ![X0,X1]: (and(X0,X1)=not(or(not(X0),not(X1))))),
% 0.10/0.42 inference(backward_subsumption_resolution,[status(thm)],[f168,f194])).
% 0.10/0.42 fof(f217,plain,(
% 0.10/0.42 ~is_a_theorem(implies(or(sK47_skl,sK48_skl),or(sK48_skl,sK47_skl)))),
% 0.10/0.42 inference(backward_subsumption_resolution,[status(thm)],[f156,f196])).
% 0.10/0.42 fof(f218,plain,(
% 0.10/0.42 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1))),
% 0.10/0.42 inference(backward_demodulation,[status(thm)],[f198,f197])).
% 0.10/0.42 fof(f222,plain,(
% 0.10/0.42 ![X0,X1]: (and(X0,X1)=not(implies(X0,not(X1))))),
% 0.10/0.42 inference(forward_demodulation,[status(thm)],[f215,f216])).
% 0.10/0.42 fof(f227,plain,(
% 0.10/0.42 ![X0,X1]: (is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))))),
% 0.10/0.42 inference(backward_demodulation,[status(thm)],[f218,f201])).
% 0.10/0.42 fof(f244,plain,(
% 0.10/0.42 ![X0,X1,X2]: (or(and(X0,not(X1)),X2)=implies(implies(X0,X1),X2))),
% 0.10/0.42 inference(paramodulation,[status(thm)],[f198,f218])).
% 0.10/0.42 fof(f309,plain,(
% 0.10/0.42 ![X0,X1]: (and(not(X0),X1)=not(or(X0,not(X1))))),
% 0.10/0.42 inference(paramodulation,[status(thm)],[f218,f222])).
% 0.10/0.42 fof(f364,plain,(
% 0.10/0.42 ![X0,X1]: (is_a_theorem(implies(or(X0,not(not(X1))),or(X1,X0))))),
% 0.10/0.42 inference(paramodulation,[status(thm)],[f218,f227])).
% 0.10/0.42 fof(f527,plain,(
% 0.10/0.42 ![X0,X1,X2]: (implies(or(X0,not(X1)),X2)=or(and(not(X0),X1),X2))),
% 0.10/0.42 inference(paramodulation,[status(thm)],[f309,f215])).
% 0.10/0.42 fof(f535,plain,(
% 0.10/0.42 ![X0,X1]: (is_a_theorem(or(and(not(X0),not(X1)),or(X1,X0))))),
% 0.10/0.42 inference(backward_demodulation,[status(thm)],[f527,f364])).
% 0.10/0.42 fof(f541,plain,(
% 0.10/0.42 ![X0,X1]: (is_a_theorem(implies(implies(not(X0),X1),or(X1,X0))))),
% 0.10/0.42 inference(forward_demodulation,[status(thm)],[f244,f535])).
% 0.10/0.42 fof(f543,plain,(
% 0.10/0.42 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),or(X1,X0))))),
% 0.10/0.42 inference(forward_demodulation,[status(thm)],[f218,f541])).
% 0.10/0.42 fof(f544,plain,(
% 0.10/0.42 $false),
% 0.10/0.42 inference(backward_subsumption_resolution,[status(thm)],[f217,f543])).
% 0.10/0.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.44 % Elapsed time: 0.064040 seconds
% 0.10/0.44 % CPU time: 0.226424 seconds
% 0.10/0.44 % Total memory used: 85.561 MB
% 0.10/0.44 % Net memory used: 85.475 MB
%------------------------------------------------------------------------------