%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL686+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 01:10:56 PM UTC 2026
% Result : Theorem 0.19s 0.48s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL686+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n009.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Mon Sep 21 00:57:57 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.46 % Drodi V4.1.1
% 0.19/0.48 % Refutation found
% 0.19/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.48 % SZS output start CNFRefutation for theBenchmark
% 0.19/0.48 fof(f1,axiom,(
% 0.19/0.48 (! [X] : r1(X,X) )),
% 0.19/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.48 fof(f3,conjecture,(
% 0.19/0.48 ~ (? [X] :~ ( (! [Y] :( ~ r1(X,Y)| ~ p3(Y)| (! [X] :( ~ r1(Y,X)| ~ p1(X) ) )))| (! [Y] :( ~ r1(X,Y)| ~ (! [X] :( ~ r1(Y,X)| ~ ( (! [Y] :( ~ r1(X,Y)| $false ))| ~ (! [Y] :( ~ r1(X,Y)| ~ ( ( p2(Y)& ~ p1(Y) )| ( ~ p2(Y)& p1(Y) ) ) ))| (! [Y] :( ~ r1(X,Y)| p3(Y) ))| (! [Y] :( ~ r1(X,Y)| ( ~ p1(Y)& ~ p2(Y) )| ( p2(Y)& p1(Y) ) ) )) ) )) )) )),
% 0.19/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.48 fof(f4,negated_conjecture,(
% 0.19/0.48 ~(~ (? [X] :~ ( (! [Y] :( ~ r1(X,Y)| ~ p3(Y)| (! [X] :( ~ r1(Y,X)| ~ p1(X) ) )))| (! [Y] :( ~ r1(X,Y)| ~ (! [X] :( ~ r1(Y,X)| ~ ( (! [Y] :( ~ r1(X,Y)| $false ))| ~ (! [Y] :( ~ r1(X,Y)| ~ ( ( p2(Y)& ~ p1(Y) )| ( ~ p2(Y)& p1(Y) ) ) ))| (! [Y] :( ~ r1(X,Y)| p3(Y) ))| (! [Y] :( ~ r1(X,Y)| ( ~ p1(Y)& ~ p2(Y) )| ( p2(Y)& p1(Y) ) ) )) ) )) )) ))),
% 0.19/0.48 inference(negated_conjecture,[status(cth)],[f3])).
% 0.19/0.48 fof(f5,plain,(
% 0.19/0.48 ![X0]: (r1(X0,X0))),
% 0.19/0.48 inference(cnf_transformation,[status(thm)],[f1])).
% 0.19/0.48 fof(f9,plain,(
% 0.19/0.48 ?[X]: ((?[Y]: ((r1(X,Y)&p3(Y))&(?[X]: (r1(Y,X)&p1(X)))))&(?[Y]: (r1(X,Y)&(![X]: (~r1(Y,X)|((((?[Y]: (r1(X,Y)&$true))&(![Y]: (~r1(X,Y)|((~p2(Y)|p1(Y))&(p2(Y)|~p1(Y))))))&(?[Y]: (r1(X,Y)&~p3(Y))))&(?[Y]: ((r1(X,Y)&(p1(Y)|p2(Y)))&(~p2(Y)|~p1(Y))))))))))),
% 0.19/0.48 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.19/0.48 fof(f10,plain,(
% 0.19/0.48 ?[X]: ((?[Y]: ((r1(X,Y)&p3(Y))&(?[X]: (r1(Y,X)&p1(X)))))&(?[Y]: (r1(X,Y)&(![X]: (~r1(Y,X)|(((((?[Y]: r1(X,Y))&$true)&(![Y]: (~r1(X,Y)|((~p2(Y)|p1(Y))&(p2(Y)|~p1(Y))))))&(?[Y]: (r1(X,Y)&~p3(Y))))&(?[Y]: ((r1(X,Y)&(p1(Y)|p2(Y)))&(~p2(Y)|~p1(Y))))))))))),
% 0.19/0.48 inference(miniscoping,[status(thm)],[f9])).
% 0.19/0.48 fof(f11,plain,(
% 0.19/0.48 (((r1(sK0_skl,sK1_skl)&p3(sK1_skl))&(r1(sK1_skl,sK2_skl)&p1(sK2_skl)))&(r1(sK0_skl,sK3_skl)&(![X]: (~r1(sK3_skl,X)|((((r1(X,sK4_skl(X))&$true)&(![Y]: (~r1(X,Y)|((~p2(Y)|p1(Y))&(p2(Y)|~p1(Y))))))&(r1(X,sK5_skl(X))&~p3(sK5_skl(X))))&((r1(X,sK6_skl(X))&(p1(sK6_skl(X))|p2(sK6_skl(X))))&(~p2(sK6_skl(X))|~p1(sK6_skl(X)))))))))),
% 0.19/0.48 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl,sK6_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(X,sK2_skl),skolemize(Y,sK3_skl),skolemize(Y,sK4_skl(X)),skolemize(Y,sK5_skl(X)),skolemize(Y,sK6_skl(X))],[f10])).
% 0.19/0.48 fof(f12,plain,(
% 0.19/0.48 ?[X]: ((?[Y]: ((r1(sK0_skl,sK1_skl)&p3(sK1_skl))&(?[X]: (r1(sK1_skl,sK2_skl)&p1(sK2_skl)))))&(?[Y]: (r1(sK0_skl,sK3_skl)&(![X]: (~r1(sK3_skl,X)|((((?[Y]: r1(X,sK4_skl(X)))&(![Y]: (~r1(X,Y)|((~p2(Y)|p1(Y))&(p2(Y)|~p1(Y))))))&(?[Y]: (r1(X,sK5_skl(X))&~p3(sK5_skl(X)))))&(?[Y]: ((r1(X,sK6_skl(X))&(p1(sK6_skl(X))|p2(sK6_skl(X))))&(~p2(sK6_skl(X))|~p1(sK6_skl(X)))))))))))),
% 0.19/0.48 inference(true_and_false_simplification,[status(thm)],[f11])).
% 0.19/0.48 fof(f19,plain,(
% 0.19/0.48 ![X0,X1]: (~r1(sK3_skl,X0)|~r1(X0,X1)|~p2(X1)|p1(X1))),
% 0.19/0.48 inference(cnf_transformation,[status(thm)],[f12])).
% 0.19/0.48 fof(f20,plain,(
% 0.19/0.48 ![X0,X1]: (~r1(sK3_skl,X0)|~r1(X0,X1)|p2(X1)|~p1(X1))),
% 0.19/0.48 inference(cnf_transformation,[status(thm)],[f12])).
% 0.19/0.48 fof(f23,plain,(
% 0.19/0.48 ![X0]: (~r1(sK3_skl,X0)|r1(X0,sK6_skl(X0)))),
% 0.19/0.48 inference(cnf_transformation,[status(thm)],[f12])).
% 0.19/0.48 fof(f24,plain,(
% 0.19/0.48 ![X0]: (~r1(sK3_skl,X0)|p1(sK6_skl(X0))|p2(sK6_skl(X0)))),
% 0.19/0.48 inference(cnf_transformation,[status(thm)],[f12])).
% 0.19/0.48 fof(f25,plain,(
% 0.19/0.48 ![X0]: (~r1(sK3_skl,X0)|~p2(sK6_skl(X0))|~p1(sK6_skl(X0)))),
% 0.19/0.48 inference(cnf_transformation,[status(thm)],[f12])).
% 0.19/0.48 fof(f40,plain,(
% 0.19/0.48 ![X0]: (~r1(sK3_skl,X0)|~p2(X0)|p1(X0))),
% 0.19/0.48 inference(resolution,[status(thm)],[f19,f5])).
% 0.19/0.48 fof(f42,plain,(
% 0.19/0.48 ![X0]: (~r1(sK3_skl,X0)|p2(X0)|~p1(X0))),
% 0.19/0.48 inference(resolution,[status(thm)],[f20,f5])).
% 0.19/0.48 fof(f46,plain,(
% 0.19/0.48 p1(sK6_skl(sK3_skl))|p2(sK6_skl(sK3_skl))),
% 0.19/0.48 inference(resolution,[status(thm)],[f24,f5])).
% 0.19/0.48 fof(f54,definition,(
% 0.19/0.48 sQ2_spl <=> (p1(sK6_skl(sK3_skl)))),
% 0.19/0.48 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.19/0.48 fof(f57,definition,(
% 0.19/0.48 sQ3_spl <=> (p2(sK6_skl(sK3_skl)))),
% 0.19/0.48 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.19/0.48 fof(f60,plain,(
% 0.19/0.48 sQ2_spl|sQ3_spl),
% 0.19/0.48 inference(split_clause,[status(thm)],[f46,f54,f57])).
% 0.19/0.48 fof(f79,plain,(
% 0.19/0.48 r1(sK3_skl,sK6_skl(sK3_skl))),
% 0.19/0.48 inference(resolution,[status(thm)],[f23,f5])).
% 0.19/0.48 fof(f82,plain,(
% 0.19/0.48 ~p2(sK6_skl(sK3_skl))|~p1(sK6_skl(sK3_skl))),
% 0.19/0.48 inference(resolution,[status(thm)],[f25,f5])).
% 0.19/0.48 fof(f85,plain,(
% 0.19/0.48 ~sQ3_spl|~sQ2_spl),
% 0.19/0.48 inference(split_clause,[status(thm)],[f82,f57,f54])).
% 0.19/0.48 fof(f116,plain,(
% 0.19/0.48 p2(sK6_skl(sK3_skl))|~p1(sK6_skl(sK3_skl))),
% 0.19/0.48 inference(resolution,[status(thm)],[f79,f42])).
% 0.19/0.48 fof(f117,plain,(
% 0.19/0.48 ~p2(sK6_skl(sK3_skl))|p1(sK6_skl(sK3_skl))),
% 0.19/0.48 inference(resolution,[status(thm)],[f79,f40])).
% 0.19/0.48 fof(f118,plain,(
% 0.19/0.48 ~p2(sK6_skl(sK6_skl(sK3_skl)))|~p1(sK6_skl(sK6_skl(sK3_skl)))),
% 0.19/0.48 inference(resolution,[status(thm)],[f79,f25])).
% 0.19/0.48 fof(f120,plain,(
% 0.19/0.48 p1(sK6_skl(sK6_skl(sK3_skl)))|p2(sK6_skl(sK6_skl(sK3_skl)))),
% 0.19/0.48 inference(resolution,[status(thm)],[f79,f24])).
% 0.19/0.48 fof(f127,plain,(
% 0.19/0.48 sQ3_spl|~sQ2_spl),
% 0.19/0.48 inference(split_clause,[status(thm)],[f116,f57,f54])).
% 0.19/0.48 fof(f128,plain,(
% 0.19/0.48 ~sQ3_spl|sQ2_spl),
% 0.19/0.48 inference(split_clause,[status(thm)],[f117,f57,f54])).
% 0.19/0.48 fof(f129,definition,(
% 0.19/0.48 sQ12_spl <=> (p2(sK6_skl(sK6_skl(sK3_skl))))),
% 0.19/0.48 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.19/0.48 fof(f132,definition,(
% 0.19/0.48 sQ13_spl <=> (p1(sK6_skl(sK6_skl(sK3_skl))))),
% 0.19/0.48 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.19/0.48 fof(f135,plain,(
% 0.19/0.48 ~sQ12_spl|~sQ13_spl),
% 0.19/0.48 inference(split_clause,[status(thm)],[f118,f129,f132])).
% 0.19/0.48 fof(f136,plain,(
% 0.19/0.48 sQ13_spl|sQ12_spl),
% 0.19/0.48 inference(split_clause,[status(thm)],[f120,f132,f129])).
% 0.19/0.48 fof(f137,plain,(
% 0.19/0.48 $false),
% 0.19/0.48 inference(sat_refutation,[status(thm)],[f60,f85,f127,f128,f135,f136])).
% 0.19/0.48 % SZS output end CNFRefutation for theBenchmark.p
% 0.19/0.51 % Elapsed time: 0.055178 seconds
% 0.19/0.51 % CPU time: 0.147303 seconds
% 0.19/0.51 % Total memory used: 15.584 MB
% 0.19/0.51 % Net memory used: 15.157 MB
%------------------------------------------------------------------------------