%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL636+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 01:10:20 PM UTC 2026
% Result : Theorem 0.19s 0.47s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL636+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.43 % Computer : n011.cluster.edu
% 0.19/0.43 % Model : x86_64 x86_64
% 0.19/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.43 % Memory : 8046.5625MB
% 0.19/0.43 % OS : Linux 6.8.0-71-generic
% 0.19/0.43 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Mon Sep 21 00:41:40 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.45 % Drodi V4.1.1
% 0.19/0.47 % Refutation found
% 0.19/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.47 % SZS output start CNFRefutation for theBenchmark
% 0.19/0.47 fof(f1,conjecture,(
% 0.19/0.47 ~ (? [X] :~ ( ~ (! [Y] :( ~ r1(X,Y)| p2(Y) ))| ~ ( (! [Y] :( ~ r1(X,Y)| ( ( ( ~ (! [X] :( ~ r1(Y,X)| ~ ( ~ p2(X)& ~ p102(X)& p101(X) ) ))& ~ (! [X] :( ~ r1(Y,X)| ~ ( p2(X)& ~ p102(X)& p101(X) ) ) ))| ~ ( ~ p101(Y)& p100(Y) ) )& ( ( ( (! [X] :( ~ r1(Y,X)| ~ p2(X)| ~ p101(X) ))| p2(Y) )& ( (! [X] :( ~ r1(Y,X)| p2(X)| ~ p101(X) ))| ~ p2(Y) ) )| ~ p101(Y) )& ( ( ( (! [X] :( ~ r1(Y,X)| ~ p1(X)| ~ p100(X) ))| p1(Y) )& ( (! [X] :( ~ r1(Y,X)| p1(X)| ~ p100(X) ))| ~ p1(Y) ) )| ~ p100(Y) )& ( p101(Y)| ~ p102(Y) )& ( p100(Y)| ~ p101(Y) ) ) ))& ( ( ~ (! [Y] :( ~ r1(X,Y)| ~ ( ~ p2(Y)& ~ p102(Y)& p101(Y) ) ))& ~ (! [Y] :( ~ r1(X,Y)| ~ ( p2(Y)& ~ p102(Y)& p101(Y) ) ) ))| ~ ( ~ p101(X)& p100(X) ) )& ( ( ( (! [Y] :( ~ r1(X,Y)| ~ p2(Y)| ~ p101(Y) ))| p2(X) )& ( (! [Y] :( ~ r1(X,Y)| p2(Y)| ~ p101(Y) ))| ~ p2(X) ) )| ~ p101(X) )& ( ( ( (! [Y] :( ~ r1(X,Y)| ~ p1(Y)| ~ p100(Y) ))| p1(X) )& ( (! [Y] :( ~ r1(X,Y)| p1(Y)| ~ p100(Y) ))| ~ p1(X) ) )| ~ p100(X) )& ( p101(X)| ~ p102(X) )& ( p100(X)| ~ p101(X) )& ~ p101(X)& p100(X) ) ) )),
% 0.19/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.47 fof(f2,negated_conjecture,(
% 0.19/0.47 ~(~ (? [X] :~ ( ~ (! [Y] :( ~ r1(X,Y)| p2(Y) ))| ~ ( (! [Y] :( ~ r1(X,Y)| ( ( ( ~ (! [X] :( ~ r1(Y,X)| ~ ( ~ p2(X)& ~ p102(X)& p101(X) ) ))& ~ (! [X] :( ~ r1(Y,X)| ~ ( p2(X)& ~ p102(X)& p101(X) ) ) ))| ~ ( ~ p101(Y)& p100(Y) ) )& ( ( ( (! [X] :( ~ r1(Y,X)| ~ p2(X)| ~ p101(X) ))| p2(Y) )& ( (! [X] :( ~ r1(Y,X)| p2(X)| ~ p101(X) ))| ~ p2(Y) ) )| ~ p101(Y) )& ( ( ( (! [X] :( ~ r1(Y,X)| ~ p1(X)| ~ p100(X) ))| p1(Y) )& ( (! [X] :( ~ r1(Y,X)| p1(X)| ~ p100(X) ))| ~ p1(Y) ) )| ~ p100(Y) )& ( p101(Y)| ~ p102(Y) )& ( p100(Y)| ~ p101(Y) ) ) ))& ( ( ~ (! [Y] :( ~ r1(X,Y)| ~ ( ~ p2(Y)& ~ p102(Y)& p101(Y) ) ))& ~ (! [Y] :( ~ r1(X,Y)| ~ ( p2(Y)& ~ p102(Y)& p101(Y) ) ) ))| ~ ( ~ p101(X)& p100(X) ) )& ( ( ( (! [Y] :( ~ r1(X,Y)| ~ p2(Y)| ~ p101(Y) ))| p2(X) )& ( (! [Y] :( ~ r1(X,Y)| p2(Y)| ~ p101(Y) ))| ~ p2(X) ) )| ~ p101(X) )& ( ( ( (! [Y] :( ~ r1(X,Y)| ~ p1(Y)| ~ p100(Y) ))| p1(X) )& ( (! [Y] :( ~ r1(X,Y)| p1(Y)| ~ p100(Y) ))| ~ p1(X) ) )| ~ p100(X) )& ( p101(X)| ~ p102(X) )& ( p100(X)| ~ p101(X) )& ~ p101(X)& p100(X) ) ) ))),
% 0.19/0.47 inference(negated_conjecture,[status(cth)],[f1])).
% 0.19/0.47 fof(f3,plain,(
% 0.19/0.47 ?[X]: ((![Y]: (~r1(X,Y)|p2(Y)))&((((((((![Y]: (~r1(X,Y)|(((((((?[X]: (r1(Y,X)&((~p2(X)&~p102(X))&p101(X))))&(?[X]: (r1(Y,X)&((p2(X)&~p102(X))&p101(X)))))|(p101(Y)|~p100(Y)))&((((![X]: ((~r1(Y,X)|~p2(X))|~p101(X)))|p2(Y))&((![X]: ((~r1(Y,X)|p2(X))|~p101(X)))|~p2(Y)))|~p101(Y)))&((((![X]: ((~r1(Y,X)|~p1(X))|~p100(X)))|p1(Y))&((![X]: ((~r1(Y,X)|p1(X))|~p100(X)))|~p1(Y)))|~p100(Y)))&(p101(Y)|~p102(Y)))&(p100(Y)|~p101(Y)))))&(((?[Y]: (r1(X,Y)&((~p2(Y)&~p102(Y))&p101(Y))))&(?[Y]: (r1(X,Y)&((p2(Y)&~p102(Y))&p101(Y)))))|(p101(X)|~p100(X))))&((((![Y]: ((~r1(X,Y)|~p2(Y))|~p101(Y)))|p2(X))&((![Y]: ((~r1(X,Y)|p2(Y))|~p101(Y)))|~p2(X)))|~p101(X)))&((((![Y]: ((~r1(X,Y)|~p1(Y))|~p100(Y)))|p1(X))&((![Y]: ((~r1(X,Y)|p1(Y))|~p100(Y)))|~p1(X)))|~p100(X)))&(p101(X)|~p102(X)))&(p100(X)|~p101(X)))&~p101(X))&p100(X)))),
% 0.19/0.47 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.19/0.47 fof(f4,plain,(
% 0.19/0.47 ((![Y]: (~r1(sK0_skl,Y)|p2(Y)))&((((((((![Y]: (~r1(sK0_skl,Y)|(((((((r1(Y,sK1_skl(Y))&((~p2(sK1_skl(Y))&~p102(sK1_skl(Y)))&p101(sK1_skl(Y))))&(r1(Y,sK2_skl(Y))&((p2(sK2_skl(Y))&~p102(sK2_skl(Y)))&p101(sK2_skl(Y)))))|(p101(Y)|~p100(Y)))&((((![X]: ((~r1(Y,X)|~p2(X))|~p101(X)))|p2(Y))&((![X]: ((~r1(Y,X)|p2(X))|~p101(X)))|~p2(Y)))|~p101(Y)))&((((![X]: ((~r1(Y,X)|~p1(X))|~p100(X)))|p1(Y))&((![X]: ((~r1(Y,X)|p1(X))|~p100(X)))|~p1(Y)))|~p100(Y)))&(p101(Y)|~p102(Y)))&(p100(Y)|~p101(Y)))))&(((r1(sK0_skl,sK3_skl)&((~p2(sK3_skl)&~p102(sK3_skl))&p101(sK3_skl)))&(r1(sK0_skl,sK4_skl)&((p2(sK4_skl)&~p102(sK4_skl))&p101(sK4_skl))))|(p101(sK0_skl)|~p100(sK0_skl))))&((((![Y]: ((~r1(sK0_skl,Y)|~p2(Y))|~p101(Y)))|p2(sK0_skl))&((![Y]: ((~r1(sK0_skl,Y)|p2(Y))|~p101(Y)))|~p2(sK0_skl)))|~p101(sK0_skl)))&((((![Y]: ((~r1(sK0_skl,Y)|~p1(Y))|~p100(Y)))|p1(sK0_skl))&((![Y]: ((~r1(sK0_skl,Y)|p1(Y))|~p100(Y)))|~p1(sK0_skl)))|~p100(sK0_skl)))&(p101(sK0_skl)|~p102(sK0_skl)))&(p100(sK0_skl)|~p101(sK0_skl)))&~p101(sK0_skl))&p100(sK0_skl)))),
% 0.19/0.48 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl]),skolemize(X,sK0_skl),skolemize(X,sK1_skl(Y)),skolemize(X,sK2_skl(Y)),skolemize(Y,sK3_skl),skolemize(Y,sK4_skl)],[f3])).
% 0.19/0.48 fof(f5,plain,(
% 0.19/0.48 ![X0]: (~r1(sK0_skl,X0)|p2(X0))),
% 0.19/0.48 inference(cnf_transformation,[status(thm)],[f4])).
% 0.19/0.48 fof(f20,plain,(
% 0.19/0.48 r1(sK0_skl,sK3_skl)|p101(sK0_skl)|~p100(sK0_skl)),
% 0.19/0.48 inference(cnf_transformation,[status(thm)],[f4])).
% 0.19/0.48 fof(f21,plain,(
% 0.19/0.48 ~p2(sK3_skl)|p101(sK0_skl)|~p100(sK0_skl)),
% 0.19/0.48 inference(cnf_transformation,[status(thm)],[f4])).
% 0.19/0.48 fof(f34,plain,(
% 0.19/0.48 ~p101(sK0_skl)),
% 0.19/0.48 inference(cnf_transformation,[status(thm)],[f4])).
% 0.19/0.48 fof(f35,plain,(
% 0.19/0.48 p100(sK0_skl)),
% 0.19/0.48 inference(cnf_transformation,[status(thm)],[f4])).
% 0.19/0.48 fof(f36,definition,(
% 0.19/0.48 sQ0_spl <=> (r1(sK0_skl,sK3_skl))),
% 0.19/0.48 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.19/0.48 fof(f37,plain,(
% 0.19/0.48 r1(sK0_skl,sK3_skl)|~sQ0_spl),
% 0.19/0.48 inference(component_clause,[status(thm)],[f36])).
% 0.19/0.48 fof(f39,definition,(
% 0.19/0.48 sQ1_spl <=> (p101(sK0_skl))),
% 0.19/0.48 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.19/0.48 fof(f40,plain,(
% 0.19/0.48 p101(sK0_skl)|~sQ1_spl),
% 0.19/0.48 inference(component_clause,[status(thm)],[f39])).
% 0.19/0.48 fof(f42,definition,(
% 0.19/0.48 sQ2_spl <=> (p100(sK0_skl))),
% 0.19/0.48 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.19/0.48 fof(f44,plain,(
% 0.19/0.48 ~p100(sK0_skl)|sQ2_spl),
% 0.19/0.48 inference(component_clause,[status(thm)],[f42])).
% 0.19/0.48 fof(f45,plain,(
% 0.19/0.48 sQ0_spl|sQ1_spl|~sQ2_spl),
% 0.19/0.48 inference(split_clause,[status(thm)],[f20,f36,f39,f42])).
% 0.19/0.48 fof(f46,definition,(
% 0.19/0.48 sQ3_spl <=> (p2(sK3_skl))),
% 0.19/0.48 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.19/0.48 fof(f48,plain,(
% 0.19/0.48 ~p2(sK3_skl)|sQ3_spl),
% 0.19/0.48 inference(component_clause,[status(thm)],[f46])).
% 0.19/0.48 fof(f49,plain,(
% 0.19/0.48 ~sQ3_spl|sQ1_spl|~sQ2_spl),
% 0.19/0.48 inference(split_clause,[status(thm)],[f21,f46,f39,f42])).
% 0.19/0.48 fof(f101,plain,(
% 0.19/0.48 $false|~sQ1_spl),
% 0.19/0.48 inference(forward_subsumption_resolution,[status(thm)],[f40,f34])).
% 0.19/0.48 fof(f102,plain,(
% 0.19/0.48 ~sQ1_spl),
% 0.19/0.48 inference(contradiction_clause,[status(thm)],[f101])).
% 0.19/0.48 fof(f103,plain,(
% 0.19/0.48 $false|sQ2_spl),
% 0.19/0.48 inference(forward_subsumption_resolution,[status(thm)],[f44,f35])).
% 0.19/0.48 fof(f104,plain,(
% 0.19/0.48 sQ2_spl),
% 0.19/0.48 inference(contradiction_clause,[status(thm)],[f103])).
% 0.19/0.48 fof(f106,plain,(
% 0.19/0.48 p2(sK3_skl)|~sQ0_spl),
% 0.19/0.48 inference(resolution,[status(thm)],[f37,f5])).
% 0.19/0.48 fof(f114,plain,(
% 0.19/0.48 $false|sQ3_spl|~sQ0_spl),
% 0.19/0.48 inference(forward_subsumption_resolution,[status(thm)],[f106,f48])).
% 0.19/0.48 fof(f115,plain,(
% 0.19/0.48 sQ3_spl|~sQ0_spl),
% 0.19/0.48 inference(contradiction_clause,[status(thm)],[f114])).
% 0.19/0.48 fof(f116,plain,(
% 0.19/0.48 $false),
% 0.19/0.48 inference(sat_refutation,[status(thm)],[f45,f49,f102,f104,f115])).
% 0.19/0.48 % SZS output end CNFRefutation for theBenchmark.p
% 0.19/0.50 % Elapsed time: 0.052620 seconds
% 0.19/0.50 % CPU time: 0.128276 seconds
% 0.19/0.50 % Total memory used: 13.069 MB
% 0.19/0.50 % Net memory used: 12.918 MB
%------------------------------------------------------------------------------