%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL638+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 : n019.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 01:10:25 PM UTC 2026
% Result : Theorem 0.17s 0.46s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL638+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n019.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Mon Sep 21 00:42:34 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.44 % Drodi V4.1.1
% 0.17/0.46 % Refutation found
% 0.17/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.46 % SZS output start CNFRefutation for theBenchmark
% 0.17/0.46 fof(f1,conjecture,(
% 0.17/0.46 ~ (? [X] :~ ( ~ (! [Y] :( ~ r1(X,Y)| ~ ( ~ (! [X] :( ~ r1(Y,X)| ~ (! [Y] :( ~ r1(X,Y)| p1(Y) ) )))& ~ p1(Y) ) ))| ~ (! [Y] :( ~ r1(X,Y)| ~ ( ~ (! [X] :( ~ r1(Y,X)| ~ (! [Y] :( ~ r1(X,Y)| ~ p1(Y) ) )))& p1(Y) ) ))| ~ (! [Y] :( ~ r1(X,Y)| ~ ( ~ (! [X] :( ~ r1(Y,X)| (! [Y] :( ~ r1(X,Y)| ~ (! [X] :( ~ r1(Y,X)| ~ p1(X) ) )) )))& (! [X] :( ~ r1(Y,X)| ~ (! [Y] :( ~ r1(X,Y)| ~ p1(Y) ) )) )) ))| ~ (! [Y] :( ~ r1(X,Y)| ~ ( ~ (! [X] :( ~ r1(Y,X)| (! [Y] :( ~ r1(X,Y)| p1(Y) ) )))& (! [X] :( ~ r1(Y,X)| p1(X) ) )) ))| ~ (! [Y] :( ~ r1(X,Y)| ~ (! [X] :( ~ r1(Y,X)| $false ) )))| (! [Y] :( ~ r1(X,Y)| p1(Y)| ~ (! [X] :( ~ r1(Y,X)| p1(X) ) )) )) )),
% 0.17/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.46 fof(f2,negated_conjecture,(
% 0.17/0.46 ~(~ (? [X] :~ ( ~ (! [Y] :( ~ r1(X,Y)| ~ ( ~ (! [X] :( ~ r1(Y,X)| ~ (! [Y] :( ~ r1(X,Y)| p1(Y) ) )))& ~ p1(Y) ) ))| ~ (! [Y] :( ~ r1(X,Y)| ~ ( ~ (! [X] :( ~ r1(Y,X)| ~ (! [Y] :( ~ r1(X,Y)| ~ p1(Y) ) )))& p1(Y) ) ))| ~ (! [Y] :( ~ r1(X,Y)| ~ ( ~ (! [X] :( ~ r1(Y,X)| (! [Y] :( ~ r1(X,Y)| ~ (! [X] :( ~ r1(Y,X)| ~ p1(X) ) )) )))& (! [X] :( ~ r1(Y,X)| ~ (! [Y] :( ~ r1(X,Y)| ~ p1(Y) ) )) )) ))| ~ (! [Y] :( ~ r1(X,Y)| ~ ( ~ (! [X] :( ~ r1(Y,X)| (! [Y] :( ~ r1(X,Y)| p1(Y) ) )))& (! [X] :( ~ r1(Y,X)| p1(X) ) )) ))| ~ (! [Y] :( ~ r1(X,Y)| ~ (! [X] :( ~ r1(Y,X)| $false ) )))| (! [Y] :( ~ r1(X,Y)| p1(Y)| ~ (! [X] :( ~ r1(Y,X)| p1(X) ) )) )) ))),
% 0.17/0.46 inference(negated_conjecture,[status(cth)],[f1])).
% 0.17/0.46 fof(f3,plain,(
% 0.17/0.46 ?[X]: ((((((![Y]: (~r1(X,Y)|((![X]: (~r1(Y,X)|(?[Y]: (r1(X,Y)&~p1(Y)))))|p1(Y))))&(![Y]: (~r1(X,Y)|((![X]: (~r1(Y,X)|(?[Y]: (r1(X,Y)&p1(Y)))))|~p1(Y)))))&(![Y]: (~r1(X,Y)|((![X]: (~r1(Y,X)|(![Y]: (~r1(X,Y)|(?[X]: (r1(Y,X)&p1(X)))))))|(?[X]: (r1(Y,X)&(![Y]: (~r1(X,Y)|~p1(Y)))))))))&(![Y]: (~r1(X,Y)|((![X]: (~r1(Y,X)|(![Y]: (~r1(X,Y)|p1(Y)))))|(?[X]: (r1(Y,X)&~p1(X)))))))&(![Y]: (~r1(X,Y)|(?[X]: (r1(Y,X)&$true)))))&(?[Y]: ((r1(X,Y)&~p1(Y))&(![X]: (~r1(Y,X)|p1(X))))))),
% 0.17/0.46 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.17/0.46 fof(f4,definition,(
% 0.17/0.46 ![Y,X]: (sP0_prd(X,Y)<=>(r1(Y,X)&p1(X)))),
% 0.17/0.46 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.17/0.46 fof(f5,plain,(
% 0.17/0.46 ?[X]: ((((((![Y]: (~r1(X,Y)|((![X]: (~r1(Y,X)|(?[Y]: (r1(X,Y)&~p1(Y)))))|p1(Y))))&(![Y]: (~r1(X,Y)|((![X]: (~r1(Y,X)|(?[Y]: (r1(X,Y)&p1(Y)))))|~p1(Y)))))&(![Y]: (~r1(X,Y)|((![X]: (~r1(Y,X)|(![Y]: (~r1(X,Y)|(?[X]: sP0_prd(X,Y))))))|(?[X]: (r1(Y,X)&(![Y]: (~r1(X,Y)|~p1(Y)))))))))&(![Y]: (~r1(X,Y)|((![X]: (~r1(Y,X)|(![Y]: (~r1(X,Y)|p1(Y)))))|(?[X]: (r1(Y,X)&~p1(X)))))))&(![Y]: (~r1(X,Y)|(?[X]: (r1(Y,X)&$true)))))&(?[Y]: ((r1(X,Y)&~p1(Y))&(![X]: (~r1(Y,X)|p1(X))))))),
% 0.17/0.46 inference(formula_renaming,[status(thm)],[f3,f4])).
% 0.17/0.46 fof(f6,plain,(
% 0.17/0.46 ?[X]: ((((((![Y]: (~r1(X,Y)|((![X]: (~r1(Y,X)|(?[Y]: (r1(X,Y)&~p1(Y)))))|p1(Y))))&(![Y]: (~r1(X,Y)|((![X]: (~r1(Y,X)|(?[Y]: (r1(X,Y)&p1(Y)))))|~p1(Y)))))&(![Y]: (~r1(X,Y)|((![X]: (~r1(Y,X)|(![Y]: (~r1(X,Y)|(?[X]: sP0_prd(X,Y))))))|(?[X]: (r1(Y,X)&(![Y]: (~r1(X,Y)|~p1(Y)))))))))&(![Y]: (~r1(X,Y)|((![X]: (~r1(Y,X)|(![Y]: (~r1(X,Y)|p1(Y)))))|(?[X]: (r1(Y,X)&~p1(X)))))))&(![Y]: (~r1(X,Y)|((?[X]: r1(Y,X))&$true))))&(?[Y]: ((r1(X,Y)&~p1(Y))&(![X]: (~r1(Y,X)|p1(X))))))),
% 0.17/0.46 inference(miniscoping,[status(thm)],[f5])).
% 0.17/0.46 fof(f7,plain,(
% 0.17/0.46 ((((((![Y]: (~r1(sK0_skl,Y)|((![X]: (~r1(Y,X)|(r1(X,sK1_skl(X,Y))&~p1(sK1_skl(X,Y)))))|p1(Y))))&(![Y]: (~r1(sK0_skl,Y)|((![X]: (~r1(Y,X)|(r1(X,sK2_skl(X,Y))&p1(sK2_skl(X,Y)))))|~p1(Y)))))&(![Y]: (~r1(sK0_skl,Y)|((![X]: (~r1(Y,X)|(![Y]: (~r1(X,Y)|sP0_prd(sK3_skl(Y,X,Y),Y)))))|(r1(Y,sK4_skl(Y))&(![Y]: (~r1(sK4_skl(Y),Y)|~p1(Y))))))))&(![Y]: (~r1(sK0_skl,Y)|((![X]: (~r1(Y,X)|(![Y]: (~r1(X,Y)|p1(Y)))))|(r1(Y,sK5_skl(Y))&~p1(sK5_skl(Y)))))))&(![Y]: (~r1(sK0_skl,Y)|(r1(Y,sK6_skl(Y))&$true))))&((r1(sK0_skl,sK7_skl)&~p1(sK7_skl))&(![X]: (~r1(sK7_skl,X)|p1(X)))))),
% 0.17/0.46 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl,sK6_skl,sK7_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl(X,Y)),skolemize(Y,sK2_skl(X,Y)),skolemize(X,sK3_skl(Y,X,Y)),skolemize(X,sK4_skl(Y)),skolemize(X,sK5_skl(Y)),skolemize(X,sK6_skl(Y)),skolemize(Y,sK7_skl)],[f6])).
% 0.17/0.46 fof(f8,plain,(
% 0.17/0.46 ?[X]: ((((((![Y]: (~r1(sK0_skl,Y)|((![X]: (~r1(Y,X)|(?[Y]: (r1(X,sK1_skl(X,Y))&~p1(sK1_skl(X,Y))))))|p1(Y))))&(![Y]: (~r1(sK0_skl,Y)|((![X]: (~r1(Y,X)|(?[Y]: (r1(X,sK2_skl(X,Y))&p1(sK2_skl(X,Y))))))|~p1(Y)))))&(![Y]: (~r1(sK0_skl,Y)|((![X]: (~r1(Y,X)|(![Y]: (~r1(X,Y)|(?[X]: sP0_prd(sK3_skl(Y,X,Y),Y))))))|(?[X]: (r1(Y,sK4_skl(Y))&(![Y]: (~r1(sK4_skl(Y),Y)|~p1(Y)))))))))&(![Y]: (~r1(sK0_skl,Y)|((![X]: (~r1(Y,X)|(![Y]: (~r1(X,Y)|p1(Y)))))|(?[X]: (r1(Y,sK5_skl(Y))&~p1(sK5_skl(Y))))))))&(![Y]: (~r1(sK0_skl,Y)|(?[X]: r1(Y,sK6_skl(Y))))))&(?[Y]: ((r1(sK0_skl,sK7_skl)&~p1(sK7_skl))&(![X]: (~r1(sK7_skl,X)|p1(X))))))),
% 0.17/0.46 inference(true_and_false_simplification,[status(thm)],[f7])).
% 0.17/0.46 fof(f9,plain,(
% 0.17/0.46 ![X0,X1]: (~r1(sK0_skl,X0)|~r1(X0,X1)|r1(X1,sK1_skl(X1,X0))|p1(X0))),
% 0.17/0.46 inference(cnf_transformation,[status(thm)],[f8])).
% 0.17/0.46 fof(f10,plain,(
% 0.17/0.46 ![X0,X1]: (~r1(sK0_skl,X0)|~r1(X0,X1)|~p1(sK1_skl(X1,X0))|p1(X0))),
% 0.17/0.46 inference(cnf_transformation,[status(thm)],[f8])).
% 0.17/0.46 fof(f15,plain,(
% 0.17/0.46 ![X0,X1,X2]: (~r1(sK0_skl,X0)|~r1(X0,X1)|~r1(X1,X2)|p1(X2)|r1(X0,sK5_skl(X0)))),
% 0.17/0.46 inference(cnf_transformation,[status(thm)],[f8])).
% 0.17/0.46 fof(f16,plain,(
% 0.17/0.46 ![X0,X1,X2]: (~r1(sK0_skl,X0)|~r1(X0,X1)|~r1(X1,X2)|p1(X2)|~p1(sK5_skl(X0)))),
% 0.17/0.46 inference(cnf_transformation,[status(thm)],[f8])).
% 0.17/0.46 fof(f17,plain,(
% 0.17/0.46 ![X0]: (~r1(sK0_skl,X0)|r1(X0,sK6_skl(X0)))),
% 0.17/0.46 inference(cnf_transformation,[status(thm)],[f8])).
% 0.17/0.46 fof(f18,plain,(
% 0.17/0.46 r1(sK0_skl,sK7_skl)),
% 0.17/0.46 inference(cnf_transformation,[status(thm)],[f8])).
% 0.17/0.46 fof(f19,plain,(
% 0.17/0.46 ~p1(sK7_skl)),
% 0.17/0.46 inference(cnf_transformation,[status(thm)],[f8])).
% 0.17/0.46 fof(f20,plain,(
% 0.17/0.46 ![X0]: (~r1(sK7_skl,X0)|p1(X0))),
% 0.17/0.46 inference(cnf_transformation,[status(thm)],[f8])).
% 0.17/0.46 fof(f26,plain,(
% 0.17/0.46 r1(sK7_skl,sK6_skl(sK7_skl))),
% 0.17/0.46 inference(resolution,[status(thm)],[f17,f18])).
% 0.17/0.46 fof(f31,definition,(
% 0.17/0.46 sQ1_spl <=> (p1(sK7_skl))),
% 0.17/0.46 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.17/0.46 fof(f32,plain,(
% 0.17/0.46 p1(sK7_skl)|~sQ1_spl),
% 0.17/0.46 inference(component_clause,[status(thm)],[f31])).
% 0.17/0.46 fof(f56,plain,(
% 0.17/0.46 ![X0,X1]: (~r1(sK7_skl,X0)|~r1(X0,X1)|p1(X1)|~p1(sK5_skl(sK7_skl)))),
% 0.17/0.46 inference(resolution,[status(thm)],[f16,f18])).
% 0.17/0.46 fof(f57,definition,(
% 0.17/0.46 ![X0,X1]: (sQ6_spl <=> (~r1(sK7_skl,X0)|~r1(X0,X1)|p1(X1)))),
% 0.17/0.46 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.17/0.46 fof(f58,plain,(
% 0.17/0.46 ![X0,X1]: (~r1(sK7_skl,X0)|~r1(X0,X1)|p1(X1)|~sQ6_spl)),
% 0.17/0.46 inference(component_clause,[status(thm)],[f57])).
% 0.17/0.46 fof(f60,definition,(
% 0.17/0.46 sQ7_spl <=> (p1(sK5_skl(sK7_skl)))),
% 0.17/0.46 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.17/0.46 fof(f62,plain,(
% 0.17/0.46 ~p1(sK5_skl(sK7_skl))|sQ7_spl),
% 0.17/0.46 inference(component_clause,[status(thm)],[f60])).
% 0.17/0.46 fof(f63,plain,(
% 0.17/0.46 sQ6_spl|~sQ7_spl),
% 0.17/0.46 inference(split_clause,[status(thm)],[f56,f57,f60])).
% 0.17/0.46 fof(f64,plain,(
% 0.17/0.46 ![X0]: (~r1(sK6_skl(sK7_skl),X0)|p1(X0)|~sQ6_spl)),
% 0.17/0.46 inference(resolution,[status(thm)],[f58,f26])).
% 0.17/0.46 fof(f65,plain,(
% 0.17/0.46 ![X0]: (~r1(sK7_skl,X0)|r1(X0,sK1_skl(X0,sK7_skl))|p1(sK7_skl))),
% 0.17/0.46 inference(resolution,[status(thm)],[f9,f18])).
% 0.17/0.46 fof(f66,definition,(
% 0.17/0.46 ![X0]: (sQ8_spl <=> (~r1(sK7_skl,X0)|r1(X0,sK1_skl(X0,sK7_skl))))),
% 0.17/0.46 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.17/0.46 fof(f67,plain,(
% 0.17/0.46 ![X0]: (~r1(sK7_skl,X0)|r1(X0,sK1_skl(X0,sK7_skl))|~sQ8_spl)),
% 0.17/0.46 inference(component_clause,[status(thm)],[f66])).
% 0.17/0.46 fof(f69,plain,(
% 0.17/0.46 sQ8_spl|sQ1_spl),
% 0.17/0.46 inference(split_clause,[status(thm)],[f65,f66,f31])).
% 0.17/0.46 fof(f70,plain,(
% 0.17/0.46 $false|~sQ1_spl),
% 0.17/0.46 inference(forward_subsumption_resolution,[status(thm)],[f32,f19])).
% 0.17/0.46 fof(f71,plain,(
% 0.17/0.46 ~sQ1_spl),
% 0.17/0.46 inference(contradiction_clause,[status(thm)],[f70])).
% 0.17/0.46 fof(f72,plain,(
% 0.17/0.46 ![X0,X1]: (~r1(sK7_skl,X0)|~r1(X0,X1)|p1(X1)|r1(sK7_skl,sK5_skl(sK7_skl)))),
% 0.17/0.46 inference(resolution,[status(thm)],[f15,f18])).
% 0.17/0.46 fof(f73,definition,(
% 0.17/0.46 sQ9_spl <=> (r1(sK7_skl,sK5_skl(sK7_skl)))),
% 0.17/0.46 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.17/0.46 fof(f74,plain,(
% 0.17/0.46 r1(sK7_skl,sK5_skl(sK7_skl))|~sQ9_spl),
% 0.17/0.46 inference(component_clause,[status(thm)],[f73])).
% 0.17/0.46 fof(f76,plain,(
% 0.17/0.46 sQ6_spl|sQ9_spl),
% 0.17/0.46 inference(split_clause,[status(thm)],[f72,f57,f73])).
% 0.17/0.46 fof(f85,plain,(
% 0.17/0.46 r1(sK6_skl(sK7_skl),sK1_skl(sK6_skl(sK7_skl),sK7_skl))|~sQ8_spl),
% 0.17/0.46 inference(resolution,[status(thm)],[f67,f26])).
% 0.17/0.46 fof(f86,plain,(
% 0.17/0.46 p1(sK1_skl(sK6_skl(sK7_skl),sK7_skl))|~sQ8_spl|~sQ6_spl),
% 0.17/0.46 inference(resolution,[status(thm)],[f85,f64])).
% 0.17/0.46 fof(f95,plain,(
% 0.17/0.46 ~r1(sK0_skl,sK7_skl)|~r1(sK7_skl,sK6_skl(sK7_skl))|p1(sK7_skl)|~sQ8_spl|~sQ6_spl),
% 0.17/0.46 inference(resolution,[status(thm)],[f86,f10])).
% 0.17/0.46 fof(f96,definition,(
% 0.17/0.46 sQ14_spl <=> (r1(sK0_skl,sK7_skl))),
% 0.17/0.46 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 0.17/0.46 fof(f98,plain,(
% 0.17/0.46 ~r1(sK0_skl,sK7_skl)|sQ14_spl),
% 0.17/0.46 inference(component_clause,[status(thm)],[f96])).
% 0.17/0.46 fof(f99,definition,(
% 0.17/0.46 sQ15_spl <=> (r1(sK7_skl,sK6_skl(sK7_skl)))),
% 0.17/0.46 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.17/0.46 fof(f101,plain,(
% 0.17/0.46 ~r1(sK7_skl,sK6_skl(sK7_skl))|sQ15_spl),
% 0.17/0.46 inference(component_clause,[status(thm)],[f99])).
% 0.17/0.46 fof(f102,plain,(
% 0.17/0.46 ~sQ14_spl|~sQ15_spl|sQ1_spl|~sQ8_spl|~sQ6_spl),
% 0.17/0.46 inference(split_clause,[status(thm)],[f95,f96,f99,f31,f66,f57])).
% 0.17/0.46 fof(f103,plain,(
% 0.17/0.46 $false|sQ14_spl),
% 0.17/0.46 inference(forward_subsumption_resolution,[status(thm)],[f98,f18])).
% 0.17/0.46 fof(f104,plain,(
% 0.17/0.46 sQ14_spl),
% 0.17/0.46 inference(contradiction_clause,[status(thm)],[f103])).
% 0.17/0.46 fof(f105,plain,(
% 0.17/0.46 $false|sQ15_spl),
% 0.17/0.46 inference(forward_subsumption_resolution,[status(thm)],[f101,f26])).
% 0.17/0.46 fof(f106,plain,(
% 0.17/0.46 sQ15_spl),
% 0.17/0.46 inference(contradiction_clause,[status(thm)],[f105])).
% 0.17/0.46 fof(f108,plain,(
% 0.17/0.46 p1(sK5_skl(sK7_skl))|~sQ9_spl),
% 0.17/0.46 inference(resolution,[status(thm)],[f74,f20])).
% 0.17/0.46 fof(f110,plain,(
% 0.17/0.46 $false|sQ7_spl|~sQ9_spl),
% 0.17/0.46 inference(forward_subsumption_resolution,[status(thm)],[f108,f62])).
% 0.17/0.46 fof(f111,plain,(
% 0.17/0.46 sQ7_spl|~sQ9_spl),
% 0.17/0.46 inference(contradiction_clause,[status(thm)],[f110])).
% 0.17/0.46 fof(f112,plain,(
% 0.17/0.46 $false),
% 0.17/0.46 inference(sat_refutation,[status(thm)],[f63,f69,f71,f76,f102,f104,f106,f111])).
% 0.17/0.46 % SZS output end CNFRefutation for theBenchmark.p
% 0.17/0.48 % Elapsed time: 0.049255 seconds
% 0.17/0.48 % CPU time: 0.121201 seconds
% 0.17/0.48 % Total memory used: 10.883 MB
% 0.17/0.48 % Net memory used: 10.623 MB
%------------------------------------------------------------------------------