%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO269+3 : 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 : n014.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 12:26:18 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 : GEO269+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 14:57:50 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(f1,axiom,(
% 0.10/0.40 (! [X,Y] :( unequally_directed_opposite_lines(X,Y)<=> unequally_directed_lines(X,reverse_line(Y)) ) )),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f4,axiom,(
% 0.10/0.40 (! [X,Y] :( equally_directed_lines(X,Y)<=> ~ unequally_directed_lines(X,Y) ) )),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f5,axiom,(
% 0.10/0.40 (! [X,Y] :( equally_directed_opposite_lines(X,Y)<=> ~ unequally_directed_opposite_lines(X,Y) ) )),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f7,axiom,(
% 0.10/0.40 (! [L,M] :( convergent_lines(L,M)<=> ( unequally_directed_lines(L,M)& unequally_directed_opposite_lines(L,M) ) ) )),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f15,axiom,(
% 0.10/0.40 (! [L] : equally_directed_lines(L,L) )),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f18,axiom,(
% 0.10/0.40 (! [L,M] :( unequally_directed_lines(L,M)| unequally_directed_lines(L,reverse_line(M)) ) )),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f19,axiom,(
% 0.10/0.40 (! [L,M] :( ( unequally_directed_lines(L,M)& unequally_directed_lines(L,reverse_line(M)) )=> ( left_convergent_lines(L,M)| left_convergent_lines(L,reverse_line(M)) ) ) )),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f21,axiom,(
% 0.10/0.40 (! [L,M] :~ ( left_convergent_lines(L,M)| left_convergent_lines(L,reverse_line(M)) ) )),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f37,conjecture,(
% 0.10/0.40 (! [L] : equally_directed_opposite_lines(L,reverse_line(L)) )),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f38,negated_conjecture,(
% 0.10/0.40 ~((! [L] : equally_directed_opposite_lines(L,reverse_line(L)) ))),
% 0.10/0.40 inference(negated_conjecture,[status(cth)],[f37])).
% 0.10/0.40 fof(f39,plain,(
% 0.10/0.40 ![X,Y]: ((~unequally_directed_opposite_lines(X,Y)|unequally_directed_lines(X,reverse_line(Y)))&(unequally_directed_opposite_lines(X,Y)|~unequally_directed_lines(X,reverse_line(Y))))),
% 0.10/0.40 inference(NNF_transformation,[status(thm)],[f1])).
% 0.10/0.40 fof(f40,plain,(
% 0.10/0.40 (![X,Y]: (~unequally_directed_opposite_lines(X,Y)|unequally_directed_lines(X,reverse_line(Y))))&(![X,Y]: (unequally_directed_opposite_lines(X,Y)|~unequally_directed_lines(X,reverse_line(Y))))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f39])).
% 0.10/0.40 fof(f41,plain,(
% 0.10/0.40 ![X0,X1]: (~unequally_directed_opposite_lines(X0,X1)|unequally_directed_lines(X0,reverse_line(X1)))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f40])).
% 0.10/0.40 fof(f51,plain,(
% 0.10/0.40 ![X,Y]: ((~equally_directed_lines(X,Y)|~unequally_directed_lines(X,Y))&(equally_directed_lines(X,Y)|unequally_directed_lines(X,Y)))),
% 0.10/0.40 inference(NNF_transformation,[status(thm)],[f4])).
% 0.10/0.40 fof(f52,plain,(
% 0.10/0.40 (![X,Y]: (~equally_directed_lines(X,Y)|~unequally_directed_lines(X,Y)))&(![X,Y]: (equally_directed_lines(X,Y)|unequally_directed_lines(X,Y)))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f51])).
% 0.10/0.40 fof(f53,plain,(
% 0.10/0.40 ![X0,X1]: (~equally_directed_lines(X0,X1)|~unequally_directed_lines(X0,X1))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f52])).
% 0.10/0.40 fof(f55,plain,(
% 0.10/0.40 ![X,Y]: ((~equally_directed_opposite_lines(X,Y)|~unequally_directed_opposite_lines(X,Y))&(equally_directed_opposite_lines(X,Y)|unequally_directed_opposite_lines(X,Y)))),
% 0.10/0.40 inference(NNF_transformation,[status(thm)],[f5])).
% 0.10/0.40 fof(f56,plain,(
% 0.10/0.40 (![X,Y]: (~equally_directed_opposite_lines(X,Y)|~unequally_directed_opposite_lines(X,Y)))&(![X,Y]: (equally_directed_opposite_lines(X,Y)|unequally_directed_opposite_lines(X,Y)))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f55])).
% 0.10/0.40 fof(f58,plain,(
% 0.10/0.40 ![X0,X1]: (equally_directed_opposite_lines(X0,X1)|unequally_directed_opposite_lines(X0,X1))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f56])).
% 0.10/0.40 fof(f64,plain,(
% 0.10/0.40 ![L,M]: ((~convergent_lines(L,M)|(unequally_directed_lines(L,M)&unequally_directed_opposite_lines(L,M)))&(convergent_lines(L,M)|(~unequally_directed_lines(L,M)|~unequally_directed_opposite_lines(L,M))))),
% 0.10/0.40 inference(NNF_transformation,[status(thm)],[f7])).
% 0.10/0.40 fof(f65,plain,(
% 0.10/0.40 (![L,M]: (~convergent_lines(L,M)|(unequally_directed_lines(L,M)&unequally_directed_opposite_lines(L,M))))&(![L,M]: (convergent_lines(L,M)|(~unequally_directed_lines(L,M)|~unequally_directed_opposite_lines(L,M))))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f64])).
% 0.10/0.40 fof(f66,plain,(
% 0.10/0.40 ![X0,X1]: (~convergent_lines(X0,X1)|unequally_directed_lines(X0,X1))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f65])).
% 0.10/0.40 fof(f67,plain,(
% 0.10/0.40 ![X0,X1]: (~convergent_lines(X0,X1)|unequally_directed_opposite_lines(X0,X1))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f65])).
% 0.10/0.40 fof(f68,plain,(
% 0.10/0.40 ![X0,X1]: (convergent_lines(X0,X1)|~unequally_directed_lines(X0,X1)|~unequally_directed_opposite_lines(X0,X1))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f65])).
% 0.10/0.40 fof(f100,plain,(
% 0.10/0.40 ![X0]: (equally_directed_lines(X0,X0))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f15])).
% 0.10/0.40 fof(f110,plain,(
% 0.10/0.40 ![X0,X1]: (unequally_directed_lines(X0,X1)|unequally_directed_lines(X0,reverse_line(X1)))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f18])).
% 0.10/0.40 fof(f111,plain,(
% 0.10/0.40 ![L,M]: ((~unequally_directed_lines(L,M)|~unequally_directed_lines(L,reverse_line(M)))|(left_convergent_lines(L,M)|left_convergent_lines(L,reverse_line(M))))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 0.10/0.40 fof(f112,plain,(
% 0.10/0.40 ![X0,X1]: (~unequally_directed_lines(X0,X1)|~unequally_directed_lines(X0,reverse_line(X1))|left_convergent_lines(X0,X1)|left_convergent_lines(X0,reverse_line(X1)))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f111])).
% 0.10/0.40 fof(f117,plain,(
% 0.10/0.40 ![L,M]: (~left_convergent_lines(L,M)&~left_convergent_lines(L,reverse_line(M)))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(thm)],[f21])).
% 0.10/0.40 fof(f118,plain,(
% 0.10/0.40 (![L,M]: ~left_convergent_lines(L,M))&(![L,M]: ~left_convergent_lines(L,reverse_line(M)))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f117])).
% 0.10/0.40 fof(f119,plain,(
% 0.10/0.40 ![X0,X1]: (~left_convergent_lines(X0,X1))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f118])).
% 0.10/0.40 fof(f152,plain,(
% 0.10/0.40 (?[L]: ~equally_directed_opposite_lines(L,reverse_line(L)))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(thm)],[f38])).
% 0.10/0.40 fof(f153,plain,(
% 0.10/0.40 ~equally_directed_opposite_lines(sK0_skl,reverse_line(sK0_skl))),
% 0.10/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(L,sK0_skl)],[f152])).
% 0.10/0.40 fof(f154,plain,(
% 0.10/0.40 ~equally_directed_opposite_lines(sK0_skl,reverse_line(sK0_skl))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f153])).
% 0.10/0.40 fof(f165,plain,(
% 0.10/0.40 ![X0,X1]: (~unequally_directed_lines(X0,X1)|~unequally_directed_lines(X0,reverse_line(X1))|left_convergent_lines(X0,X1))),
% 0.10/0.40 inference(backward_subsumption_resolution,[status(thm)],[f112,f119])).
% 0.10/0.40 fof(f171,plain,(
% 0.10/0.40 ![X0,X1]: (~unequally_directed_lines(X0,X1)|~unequally_directed_lines(X0,reverse_line(X1)))),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f165,f119])).
% 0.10/0.40 fof(f179,plain,(
% 0.10/0.40 ![X0,X1]: (convergent_lines(X0,X1)|~unequally_directed_lines(X0,X1)|equally_directed_opposite_lines(X0,X1))),
% 0.10/0.40 inference(resolution,[status(thm)],[f68,f58])).
% 0.10/0.40 fof(f185,plain,(
% 0.10/0.40 ![X0,X1]: (convergent_lines(X0,reverse_line(X1))|equally_directed_opposite_lines(X0,reverse_line(X1))|unequally_directed_lines(X0,X1))),
% 0.10/0.40 inference(resolution,[status(thm)],[f179,f110])).
% 0.10/0.40 fof(f198,definition,(
% 0.10/0.40 sQ0_spl <=> (convergent_lines(sK0_skl,reverse_line(sK0_skl)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f199,plain,(
% 0.10/0.40 convergent_lines(sK0_skl,reverse_line(sK0_skl))|~sQ0_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f198])).
% 0.10/0.40 fof(f206,plain,(
% 0.10/0.40 convergent_lines(sK0_skl,reverse_line(sK0_skl))|unequally_directed_lines(sK0_skl,sK0_skl)),
% 0.10/0.40 inference(resolution,[status(thm)],[f185,f154])).
% 0.10/0.40 fof(f208,definition,(
% 0.10/0.40 sQ2_spl <=> (unequally_directed_lines(sK0_skl,sK0_skl))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f209,plain,(
% 0.10/0.40 unequally_directed_lines(sK0_skl,sK0_skl)|~sQ2_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f208])).
% 0.10/0.40 fof(f211,plain,(
% 0.10/0.40 sQ0_spl|sQ2_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f206,f198,f208])).
% 0.10/0.40 fof(f212,plain,(
% 0.10/0.40 unequally_directed_opposite_lines(sK0_skl,reverse_line(sK0_skl))|~sQ0_spl),
% 0.10/0.40 inference(resolution,[status(thm)],[f199,f67])).
% 0.10/0.40 fof(f213,plain,(
% 0.10/0.40 unequally_directed_lines(sK0_skl,reverse_line(sK0_skl))|~sQ0_spl),
% 0.10/0.40 inference(resolution,[status(thm)],[f199,f66])).
% 0.10/0.40 fof(f246,plain,(
% 0.10/0.40 ~equally_directed_lines(sK0_skl,sK0_skl)|~sQ2_spl),
% 0.10/0.40 inference(resolution,[status(thm)],[f209,f53])).
% 0.10/0.40 fof(f248,plain,(
% 0.10/0.40 $false|~sQ2_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f246,f100])).
% 0.10/0.40 fof(f249,plain,(
% 0.10/0.40 ~sQ2_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f248])).
% 0.10/0.40 fof(f272,plain,(
% 0.10/0.40 ![X0,X1]: (~unequally_directed_lines(X0,X1)|~unequally_directed_opposite_lines(X0,X1))),
% 0.10/0.40 inference(resolution,[status(thm)],[f171,f41])).
% 0.10/0.40 fof(f278,plain,(
% 0.10/0.40 ~unequally_directed_lines(sK0_skl,reverse_line(sK0_skl))|~sQ0_spl),
% 0.10/0.40 inference(resolution,[status(thm)],[f272,f212])).
% 0.10/0.40 fof(f283,plain,(
% 0.10/0.40 $false|~sQ0_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f278,f213])).
% 0.10/0.40 fof(f284,plain,(
% 0.10/0.40 ~sQ0_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f283])).
% 0.10/0.40 fof(f285,plain,(
% 0.10/0.40 $false),
% 0.10/0.40 inference(sat_refutation,[status(thm)],[f211,f249,f284])).
% 0.10/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.42 % Elapsed time: 0.045733 seconds
% 0.10/0.42 % CPU time: 0.136970 seconds
% 0.10/0.42 % Total memory used: 19.534 MB
% 0.10/0.42 % Net memory used: 19.368 MB
%------------------------------------------------------------------------------