%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL644+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 : n006.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 01:10:27 PM UTC 2026
% Result : Theorem 0.20s 0.46s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL644+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
% 0.20/0.44 % Computer : n006.cluster.edu
% 0.20/0.44 % Model : x86_64 x86_64
% 0.20/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.44 % Memory : 8046.5625MB
% 0.20/0.44 % OS : Linux 6.8.0-71-generic
% 0.20/0.44 % CPULimit : 300
% 0.20/0.44 % WCLimit : 300
% 0.20/0.44 % DateTime : Mon Sep 21 00:42:57 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.46 % Drodi V4.1.1
% 0.20/0.46 % Refutation found
% 0.20/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.46 % SZS output start CNFRefutation for theBenchmark
% 0.20/0.46 fof(f1,conjecture,(
% 0.20/0.46 ~ (? [X] :~ ( ~ ( (! [Y] :( ~ r1(X,Y)| ~ ( p2(Y)& (! [X] :( ~ r1(Y,X)| p2(X) ) ))| p1(Y) ))| (! [Y] :( ~ r1(X,Y)| p2(Y)| ~ ( p1(Y)& (! [X] :( ~ r1(Y,X)| p1(X) ))& p1(Y) ) ))| ~ ( (! [Y] :( ~ r1(X,Y)| (! [X] :( ~ r1(Y,X)| ~ ( p2(X)& (! [Y] :( ~ r1(X,Y)| p2(Y) ) ))| p1(X) ))| p2(Y)| ~ ( p1(Y)& (! [X] :( ~ r1(Y,X)| p1(X) ))& p1(Y) ) ))& (! [Y] :( ~ r1(X,Y)| ~ ( p2(Y)& (! [X] :( ~ r1(Y,X)| p2(X) ) ))| p1(Y)| (! [X] :( ~ r1(Y,X)| p2(X)| ~ ( p1(X)& (! [Y] :( ~ r1(X,Y)| p1(Y) ))& p1(X) ) ) )))& (! [Y] :( ~ r1(X,Y)| ~ ( p2(Y)& (! [X] :( ~ r1(Y,X)| p2(X) ) ))| p1(Y)| p2(Y)| ~ ( p1(Y)& (! [X] :( ~ r1(Y,X)| p1(X) ))& p1(Y) ) ) )) )| (! [Y] :( ~ r1(X,Y)| p1(Y)| ~ ( (! [X] :( ~ r1(Y,X)| p1(X) ))& p1(Y) ) ))| (! [Y] :( ~ r1(X,Y)| p1(Y)| ~ ( (! [X] :( ~ r1(Y,X)| p1(X) ))& p1(Y) ) ) )) )),
% 0.20/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.46 fof(f2,negated_conjecture,(
% 0.20/0.46 ~(~ (? [X] :~ ( ~ ( (! [Y] :( ~ r1(X,Y)| ~ ( p2(Y)& (! [X] :( ~ r1(Y,X)| p2(X) ) ))| p1(Y) ))| (! [Y] :( ~ r1(X,Y)| p2(Y)| ~ ( p1(Y)& (! [X] :( ~ r1(Y,X)| p1(X) ))& p1(Y) ) ))| ~ ( (! [Y] :( ~ r1(X,Y)| (! [X] :( ~ r1(Y,X)| ~ ( p2(X)& (! [Y] :( ~ r1(X,Y)| p2(Y) ) ))| p1(X) ))| p2(Y)| ~ ( p1(Y)& (! [X] :( ~ r1(Y,X)| p1(X) ))& p1(Y) ) ))& (! [Y] :( ~ r1(X,Y)| ~ ( p2(Y)& (! [X] :( ~ r1(Y,X)| p2(X) ) ))| p1(Y)| (! [X] :( ~ r1(Y,X)| p2(X)| ~ ( p1(X)& (! [Y] :( ~ r1(X,Y)| p1(Y) ))& p1(X) ) ) )))& (! [Y] :( ~ r1(X,Y)| ~ ( p2(Y)& (! [X] :( ~ r1(Y,X)| p2(X) ) ))| p1(Y)| p2(Y)| ~ ( p1(Y)& (! [X] :( ~ r1(Y,X)| p1(X) ))& p1(Y) ) ) )) )| (! [Y] :( ~ r1(X,Y)| p1(Y)| ~ ( (! [X] :( ~ r1(Y,X)| p1(X) ))& p1(Y) ) ))| (! [Y] :( ~ r1(X,Y)| p1(Y)| ~ ( (! [X] :( ~ r1(Y,X)| p1(X) ))& p1(Y) ) ) )) ))),
% 0.20/0.46 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.46 fof(f3,plain,(
% 0.20/0.46 ?[X]: (((((![Y]: ((~r1(X,Y)|(~p2(Y)|(?[X]: (r1(Y,X)&~p2(X)))))|p1(Y)))|(![Y]: ((~r1(X,Y)|p2(Y))|((~p1(Y)|(?[X]: (r1(Y,X)&~p1(X))))|~p1(Y)))))|(((?[Y]: (((r1(X,Y)&(?[X]: ((r1(Y,X)&(p2(X)&(![Y]: (~r1(X,Y)|p2(Y)))))&~p1(X))))&~p2(Y))&((p1(Y)&(![X]: (~r1(Y,X)|p1(X))))&p1(Y))))|(?[Y]: (((r1(X,Y)&(p2(Y)&(![X]: (~r1(Y,X)|p2(X)))))&~p1(Y))&(?[X]: ((r1(Y,X)&~p2(X))&((p1(X)&(![Y]: (~r1(X,Y)|p1(Y))))&p1(X)))))))|(?[Y]: ((((r1(X,Y)&(p2(Y)&(![X]: (~r1(Y,X)|p2(X)))))&~p1(Y))&~p2(Y))&((p1(Y)&(![X]: (~r1(Y,X)|p1(X))))&p1(Y))))))&(?[Y]: ((r1(X,Y)&~p1(Y))&((![X]: (~r1(Y,X)|p1(X)))&p1(Y)))))&(?[Y]: ((r1(X,Y)&~p1(Y))&((![X]: (~r1(Y,X)|p1(X)))&p1(Y)))))),
% 0.20/0.46 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.20/0.46 fof(f4,definition,(
% 0.20/0.46 ![Y,X]: (sP0_prd(X,Y)<=>(r1(Y,X)&~p2(X)))),
% 0.20/0.46 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.20/0.46 fof(f5,definition,(
% 0.20/0.46 ![Y,X]: (sP1_prd(X,Y)<=>(r1(Y,X)&~p1(X)))),
% 0.20/0.46 introduced(definition,[new_symbols(definition,[sP1_prd])],[])).
% 0.20/0.46 fof(f6,definition,(
% 0.20/0.46 ![X]: (sP2_prd(X)<=>((?[Y]: (((r1(X,Y)&(?[X]: ((r1(Y,X)&(p2(X)&(![Y]: (~r1(X,Y)|p2(Y)))))&~p1(X))))&~p2(Y))&((p1(Y)&(![X]: (~r1(Y,X)|p1(X))))&p1(Y))))|(?[Y]: (((r1(X,Y)&(p2(Y)&(![X]: (~r1(Y,X)|p2(X)))))&~p1(Y))&(?[X]: ((r1(Y,X)&~p2(X))&((p1(X)&(![Y]: (~r1(X,Y)|p1(Y))))&p1(X))))))))),
% 0.20/0.46 introduced(definition,[new_symbols(definition,[sP2_prd])],[])).
% 0.20/0.46 fof(f7,plain,(
% 0.20/0.46 ?[X]: (((((![Y]: ((~r1(X,Y)|(~p2(Y)|(?[X]: sP0_prd(X,Y))))|p1(Y)))|(![Y]: ((~r1(X,Y)|p2(Y))|((~p1(Y)|(?[X]: sP1_prd(X,Y)))|~p1(Y)))))|(sP2_prd(X)|(?[Y]: ((((r1(X,Y)&(p2(Y)&(![X]: (~r1(Y,X)|p2(X)))))&~p1(Y))&~p2(Y))&((p1(Y)&(![X]: (~r1(Y,X)|p1(X))))&p1(Y))))))&(?[Y]: ((r1(X,Y)&~p1(Y))&((![X]: (~r1(Y,X)|p1(X)))&p1(Y)))))&(?[Y]: ((r1(X,Y)&~p1(Y))&((![X]: (~r1(Y,X)|p1(X)))&p1(Y)))))),
% 0.20/0.46 inference(formula_renaming,[status(thm)],[f3,f6,f5,f4])).
% 0.20/0.46 fof(f8,plain,(
% 0.20/0.46 (((((![Y]: ((~r1(sK0_skl,Y)|(~p2(Y)|sP0_prd(sK1_skl(Y),Y)))|p1(Y)))|(![Y]: ((~r1(sK0_skl,Y)|p2(Y))|((~p1(Y)|sP1_prd(sK2_skl(Y),Y))|~p1(Y)))))|(sP2_prd(sK0_skl)|((((r1(sK0_skl,sK3_skl)&(p2(sK3_skl)&(![X]: (~r1(sK3_skl,X)|p2(X)))))&~p1(sK3_skl))&~p2(sK3_skl))&((p1(sK3_skl)&(![X]: (~r1(sK3_skl,X)|p1(X))))&p1(sK3_skl)))))&((r1(sK0_skl,sK4_skl)&~p1(sK4_skl))&((![X]: (~r1(sK4_skl,X)|p1(X)))&p1(sK4_skl))))&((r1(sK0_skl,sK5_skl)&~p1(sK5_skl))&((![X]: (~r1(sK5_skl,X)|p1(X)))&p1(sK5_skl))))),
% 0.20/0.48 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(X,sK0_skl),skolemize(X,sK1_skl(Y)),skolemize(X,sK2_skl(Y)),skolemize(Y,sK3_skl),skolemize(Y,sK4_skl),skolemize(Y,sK5_skl)],[f7])).
% 0.20/0.48 fof(f18,plain,(
% 0.20/0.48 ~p1(sK4_skl)),
% 0.20/0.48 inference(cnf_transformation,[status(thm)],[f8])).
% 0.20/0.48 fof(f20,plain,(
% 0.20/0.48 p1(sK4_skl)),
% 0.20/0.48 inference(cnf_transformation,[status(thm)],[f8])).
% 0.20/0.48 fof(f110,plain,(
% 0.20/0.48 $false),
% 0.20/0.48 inference(forward_subsumption_resolution,[status(thm)],[f20,f18])).
% 0.20/0.48 % SZS output end CNFRefutation for theBenchmark.p
% 0.24/0.55 % Elapsed time: 0.099631 seconds
% 0.24/0.55 % CPU time: 0.057785 seconds
% 0.24/0.55 % Total memory used: 578.992 KB
% 0.24/0.55 % Net memory used: 575.984 KB
%------------------------------------------------------------------------------