%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL529+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 : n017.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 01:10:13 PM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL529+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
% 0.10/0.37 % Computer : n017.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 00:32:27 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.40 fof(f7,axiom,(
% 0.10/0.40 ( and_1<=> (! [X,Y] : is_a_theorem(implies(and(X,Y),X)) )) ),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f40,axiom,(
% 0.10/0.40 and_1 ),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f50,axiom,(
% 0.10/0.40 ( necessitation<=> (! [X] :( is_a_theorem(X)=> is_a_theorem(necessarily(X)) ) )) ),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f64,axiom,(
% 0.10/0.40 ( axiom_m2<=> (! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X)) )) ),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f75,axiom,(
% 0.10/0.40 ( op_strict_implies=> (! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) )) ),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f78,axiom,(
% 0.10/0.40 necessitation ),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f85,axiom,(
% 0.10/0.40 op_strict_implies ),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f88,conjecture,(
% 0.10/0.40 axiom_m2 ),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f89,negated_conjecture,(
% 0.10/0.40 ~(axiom_m2 )),
% 0.10/0.40 inference(negated_conjecture,[status(cth)],[f88])).
% 0.10/0.40 fof(f120,plain,(
% 0.10/0.40 (~and_1|(![X,Y]: is_a_theorem(implies(and(X,Y),X))))&(and_1|(?[X,Y]: ~is_a_theorem(implies(and(X,Y),X))))),
% 0.10/0.40 inference(NNF_transformation,[status(thm)],[f7])).
% 0.10/0.40 fof(f121,plain,(
% 0.10/0.40 (~and_1|(![X,Y]: is_a_theorem(implies(and(X,Y),X))))&(and_1|~is_a_theorem(implies(and(sK13_skl,sK14_skl),sK13_skl)))),
% 0.10/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(X,sK13_skl),skolemize(Y,sK14_skl)],[f120])).
% 0.10/0.40 fof(f122,plain,(
% 0.10/0.40 ![X0,X1]: (~and_1|is_a_theorem(implies(and(X0,X1),X0)))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f121])).
% 0.10/0.40 fof(f218,plain,(
% 0.10/0.40 and_1),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f40])).
% 0.10/0.40 fof(f228,plain,(
% 0.10/0.40 necessitation<=>(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X))))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(thm)],[f50])).
% 0.10/0.41 fof(f229,plain,(
% 0.10/0.41 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(?[X]: (is_a_theorem(X)&~is_a_theorem(necessarily(X)))))),
% 0.10/0.41 inference(NNF_transformation,[status(thm)],[f228])).
% 0.10/0.41 fof(f230,plain,(
% 0.10/0.41 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(is_a_theorem(sK55_skl)&~is_a_theorem(necessarily(sK55_skl))))),
% 0.10/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK55_skl]),skolemize(X,sK55_skl)],[f229])).
% 0.10/0.41 fof(f231,plain,(
% 0.10/0.41 ![X0]: (~necessitation|~is_a_theorem(X0)|is_a_theorem(necessarily(X0)))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f230])).
% 0.10/0.41 fof(f295,plain,(
% 0.10/0.41 (~axiom_m2|(![X,Y]: is_a_theorem(strict_implies(and(X,Y),X))))&(axiom_m2|(?[X,Y]: ~is_a_theorem(strict_implies(and(X,Y),X))))),
% 0.10/0.41 inference(NNF_transformation,[status(thm)],[f64])).
% 0.10/0.41 fof(f296,plain,(
% 0.10/0.41 (~axiom_m2|(![X,Y]: is_a_theorem(strict_implies(and(X,Y),X))))&(axiom_m2|~is_a_theorem(strict_implies(and(sK78_skl,sK79_skl),sK78_skl)))),
% 0.10/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK78_skl,sK79_skl]),skolemize(X,sK78_skl),skolemize(Y,sK79_skl)],[f295])).
% 0.10/0.41 fof(f298,plain,(
% 0.10/0.41 axiom_m2|~is_a_theorem(strict_implies(and(sK78_skl,sK79_skl),sK78_skl))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f296])).
% 0.10/0.41 fof(f335,plain,(
% 0.10/0.41 ~op_strict_implies|(![X,Y]: strict_implies(X,Y)=necessarily(implies(X,Y)))),
% 0.10/0.41 inference(pre_NNF_transformation,[status(thm)],[f75])).
% 0.10/0.41 fof(f336,plain,(
% 0.10/0.41 ![X0,X1]: (~op_strict_implies|strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f335])).
% 0.10/0.41 fof(f340,plain,(
% 0.10/0.41 necessitation),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f78])).
% 0.10/0.41 fof(f347,plain,(
% 0.10/0.41 op_strict_implies),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f85])).
% 0.10/0.41 fof(f350,plain,(
% 0.10/0.41 ~axiom_m2),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f89])).
% 0.10/0.41 fof(f359,plain,(
% 0.10/0.41 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X0)))),
% 0.10/0.41 inference(backward_subsumption_resolution,[status(thm)],[f122,f218])).
% 0.10/0.41 fof(f370,plain,(
% 0.10/0.41 ![X0]: (~is_a_theorem(X0)|is_a_theorem(necessarily(X0)))),
% 0.10/0.42 inference(backward_subsumption_resolution,[status(thm)],[f231,f340])).
% 0.10/0.42 fof(f374,plain,(
% 0.10/0.42 ![X0,X1]: (strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 0.10/0.42 inference(backward_subsumption_resolution,[status(thm)],[f336,f347])).
% 0.10/0.42 fof(f376,plain,(
% 0.10/0.42 ~is_a_theorem(strict_implies(and(sK78_skl,sK79_skl),sK78_skl))),
% 0.10/0.42 inference(backward_subsumption_resolution,[status(thm)],[f298,f350])).
% 0.10/0.42 fof(f399,plain,(
% 0.10/0.42 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(strict_implies(X0,X1)))),
% 0.10/0.42 inference(paramodulation,[status(thm)],[f374,f370])).
% 0.10/0.42 fof(f462,plain,(
% 0.10/0.42 ![X0,X1]: (is_a_theorem(strict_implies(and(X0,X1),X0)))),
% 0.10/0.42 inference(resolution,[status(thm)],[f399,f359])).
% 0.10/0.42 fof(f472,plain,(
% 0.10/0.42 $false),
% 0.10/0.42 inference(backward_subsumption_resolution,[status(thm)],[f376,f462])).
% 0.10/0.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.43 % Elapsed time: 0.053085 seconds
% 0.10/0.43 % CPU time: 0.167430 seconds
% 0.10/0.43 % Total memory used: 68.609 MB
% 0.10/0.43 % Net memory used: 68.473 MB
%------------------------------------------------------------------------------