%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO268+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 : 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 12:26:18 PM UTC 2026
% Result : Theorem 0.12s 0.45s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO268+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
% 0.12/0.36 % Computer : n019.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sun Sep 20 14:57:54 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.45 % Refutation found
% 0.12/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.45 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.45 fof(f1,axiom,(
% 0.12/0.45 (! [X,Y] :( unequally_directed_opposite_lines(X,Y)<=> unequally_directed_lines(X,reverse_line(Y)) ) )),
% 0.12/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.45 fof(f5,axiom,(
% 0.12/0.45 (! [X,Y] :( equally_directed_opposite_lines(X,Y)<=> ~ unequally_directed_opposite_lines(X,Y) ) )),
% 0.12/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.45 fof(f16,axiom,(
% 0.12/0.45 (! [L,M,N] :( unequally_directed_lines(L,M)=> ( unequally_directed_lines(L,N)| unequally_directed_lines(M,N) ) ) )),
% 0.12/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.45 fof(f18,axiom,(
% 0.12/0.45 (! [L,M] :( unequally_directed_lines(L,M)| unequally_directed_lines(L,reverse_line(M)) ) )),
% 0.12/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.45 fof(f19,axiom,(
% 0.12/0.45 (! [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)) ) ) )),
% 0.12/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.45 fof(f21,axiom,(
% 0.12/0.45 (! [L,M] :~ ( left_convergent_lines(L,M)| left_convergent_lines(L,reverse_line(M)) ) )),
% 0.12/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.45 fof(f37,conjecture,(
% 0.12/0.45 (! [L,M] :( unequally_directed_lines(L,M)<=> unequally_directed_opposite_lines(L,reverse_line(M)) ) )),
% 0.12/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.45 fof(f38,negated_conjecture,(
% 0.12/0.45 ~((! [L,M] :( unequally_directed_lines(L,M)<=> unequally_directed_opposite_lines(L,reverse_line(M)) ) ))),
% 0.12/0.45 inference(negated_conjecture,[status(cth)],[f37])).
% 0.12/0.45 fof(f39,plain,(
% 0.12/0.45 ![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))))),
% 0.12/0.45 inference(NNF_transformation,[status(thm)],[f1])).
% 0.12/0.45 fof(f40,plain,(
% 0.12/0.45 (![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))))),
% 0.12/0.45 inference(miniscoping,[status(thm)],[f39])).
% 0.12/0.45 fof(f41,plain,(
% 0.12/0.45 ![X0,X1]: (~unequally_directed_opposite_lines(X0,X1)|unequally_directed_lines(X0,reverse_line(X1)))),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f40])).
% 0.12/0.45 fof(f42,plain,(
% 0.12/0.45 ![X0,X1]: (unequally_directed_opposite_lines(X0,X1)|~unequally_directed_lines(X0,reverse_line(X1)))),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f40])).
% 0.12/0.45 fof(f55,plain,(
% 0.12/0.45 ![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)))),
% 0.12/0.45 inference(NNF_transformation,[status(thm)],[f5])).
% 0.12/0.45 fof(f56,plain,(
% 0.12/0.45 (![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)))),
% 0.12/0.45 inference(miniscoping,[status(thm)],[f55])).
% 0.12/0.45 fof(f57,plain,(
% 0.12/0.45 ![X0,X1]: (~equally_directed_opposite_lines(X0,X1)|~unequally_directed_opposite_lines(X0,X1))),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f56])).
% 0.12/0.45 fof(f58,plain,(
% 0.12/0.45 ![X0,X1]: (equally_directed_opposite_lines(X0,X1)|unequally_directed_opposite_lines(X0,X1))),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f56])).
% 0.12/0.45 fof(f101,plain,(
% 0.12/0.45 ![L,M,N]: (~unequally_directed_lines(L,M)|(unequally_directed_lines(L,N)|unequally_directed_lines(M,N)))),
% 0.12/0.45 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.12/0.45 fof(f102,plain,(
% 0.12/0.45 ![L,M]: (~unequally_directed_lines(L,M)|(![N]: (unequally_directed_lines(L,N)|unequally_directed_lines(M,N))))),
% 0.12/0.45 inference(miniscoping,[status(thm)],[f101])).
% 0.12/0.45 fof(f103,plain,(
% 0.12/0.45 ![X0,X1,X2]: (~unequally_directed_lines(X0,X1)|unequally_directed_lines(X0,X2)|unequally_directed_lines(X1,X2))),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f102])).
% 0.12/0.45 fof(f110,plain,(
% 0.12/0.45 ![X0,X1]: (unequally_directed_lines(X0,X1)|unequally_directed_lines(X0,reverse_line(X1)))),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f18])).
% 0.12/0.45 fof(f111,plain,(
% 0.12/0.45 ![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))))),
% 0.12/0.45 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 0.12/0.45 fof(f112,plain,(
% 0.12/0.45 ![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)))),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f111])).
% 0.12/0.45 fof(f117,plain,(
% 0.12/0.45 ![L,M]: (~left_convergent_lines(L,M)&~left_convergent_lines(L,reverse_line(M)))),
% 0.12/0.45 inference(pre_NNF_transformation,[status(thm)],[f21])).
% 0.12/0.45 fof(f118,plain,(
% 0.12/0.45 (![L,M]: ~left_convergent_lines(L,M))&(![L,M]: ~left_convergent_lines(L,reverse_line(M)))),
% 0.12/0.45 inference(miniscoping,[status(thm)],[f117])).
% 0.12/0.45 fof(f119,plain,(
% 0.12/0.45 ![X0,X1]: (~left_convergent_lines(X0,X1))),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f118])).
% 0.12/0.45 fof(f152,plain,(
% 0.12/0.45 (?[L,M]: (unequally_directed_lines(L,M)<~>unequally_directed_opposite_lines(L,reverse_line(M))))),
% 0.12/0.45 inference(pre_NNF_transformation,[status(thm)],[f38])).
% 0.12/0.45 fof(f153,plain,(
% 0.12/0.45 ?[L,M]: ((unequally_directed_lines(L,M)|unequally_directed_opposite_lines(L,reverse_line(M)))&(~unequally_directed_lines(L,M)|~unequally_directed_opposite_lines(L,reverse_line(M))))),
% 0.12/0.45 inference(NNF_transformation,[status(thm)],[f152])).
% 0.12/0.45 fof(f154,plain,(
% 0.12/0.45 ((unequally_directed_lines(sK0_skl,sK1_skl)|unequally_directed_opposite_lines(sK0_skl,reverse_line(sK1_skl)))&(~unequally_directed_lines(sK0_skl,sK1_skl)|~unequally_directed_opposite_lines(sK0_skl,reverse_line(sK1_skl))))),
% 0.12/0.45 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(L,sK0_skl),skolemize(M,sK1_skl)],[f153])).
% 0.12/0.45 fof(f155,plain,(
% 0.12/0.45 unequally_directed_lines(sK0_skl,sK1_skl)|unequally_directed_opposite_lines(sK0_skl,reverse_line(sK1_skl))),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f154])).
% 0.12/0.45 fof(f156,plain,(
% 0.12/0.45 ~unequally_directed_lines(sK0_skl,sK1_skl)|~unequally_directed_opposite_lines(sK0_skl,reverse_line(sK1_skl))),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f154])).
% 0.12/0.45 fof(f162,definition,(
% 0.12/0.45 sQ0_spl <=> (unequally_directed_lines(sK0_skl,sK1_skl))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f164,plain,(
% 0.12/0.45 ~unequally_directed_lines(sK0_skl,sK1_skl)|sQ0_spl),
% 0.12/0.45 inference(component_clause,[status(thm)],[f162])).
% 0.12/0.45 fof(f165,definition,(
% 0.12/0.45 sQ1_spl <=> (unequally_directed_opposite_lines(sK0_skl,reverse_line(sK1_skl)))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f166,plain,(
% 0.12/0.45 unequally_directed_opposite_lines(sK0_skl,reverse_line(sK1_skl))|~sQ1_spl),
% 0.12/0.45 inference(component_clause,[status(thm)],[f165])).
% 0.12/0.45 fof(f167,plain,(
% 0.12/0.45 ~unequally_directed_opposite_lines(sK0_skl,reverse_line(sK1_skl))|sQ1_spl),
% 0.12/0.45 inference(component_clause,[status(thm)],[f165])).
% 0.12/0.45 fof(f168,plain,(
% 0.12/0.45 sQ0_spl|sQ1_spl),
% 0.12/0.45 inference(split_clause,[status(thm)],[f155,f162,f165])).
% 0.12/0.45 fof(f169,plain,(
% 0.12/0.45 ~sQ0_spl|~sQ1_spl),
% 0.12/0.45 inference(split_clause,[status(thm)],[f156,f162,f165])).
% 0.12/0.45 fof(f175,plain,(
% 0.12/0.45 ![X0,X1]: (~unequally_directed_lines(X0,X1)|~unequally_directed_lines(X0,reverse_line(X1))|left_convergent_lines(X0,X1))),
% 0.12/0.45 inference(backward_subsumption_resolution,[status(thm)],[f112,f119])).
% 0.12/0.45 fof(f181,plain,(
% 0.12/0.45 ![X0,X1]: (~unequally_directed_lines(X0,X1)|~unequally_directed_lines(X0,reverse_line(X1)))),
% 0.12/0.45 inference(forward_subsumption_resolution,[status(thm)],[f175,f119])).
% 0.12/0.45 fof(f182,plain,(
% 0.12/0.45 unequally_directed_lines(sK0_skl,reverse_line(reverse_line(sK1_skl)))|~sQ1_spl),
% 0.12/0.45 inference(resolution,[status(thm)],[f41,f166])).
% 0.12/0.45 fof(f184,plain,(
% 0.12/0.45 ![X0]: (unequally_directed_lines(sK0_skl,X0)|unequally_directed_lines(reverse_line(reverse_line(sK1_skl)),X0)|~sQ1_spl)),
% 0.12/0.45 inference(resolution,[status(thm)],[f103,f182])).
% 0.12/0.45 fof(f185,plain,(
% 0.12/0.45 ![X0,X1]: (unequally_directed_lines(X0,X1)|unequally_directed_opposite_lines(X0,X1))),
% 0.12/0.45 inference(resolution,[status(thm)],[f110,f42])).
% 0.12/0.45 fof(f186,plain,(
% 0.12/0.45 ![X0,X1,X2]: (unequally_directed_lines(X0,X1)|unequally_directed_lines(X0,X2)|unequally_directed_lines(reverse_line(X1),X2))),
% 0.12/0.45 inference(resolution,[status(thm)],[f110,f103])).
% 0.12/0.45 fof(f188,plain,(
% 0.12/0.45 ![X0,X1]: (unequally_directed_lines(sK0_skl,X0)|unequally_directed_lines(reverse_line(reverse_line(sK1_skl)),X1)|unequally_directed_lines(X0,X1)|~sQ1_spl)),
% 0.12/0.45 inference(resolution,[status(thm)],[f184,f103])).
% 0.12/0.45 fof(f198,plain,(
% 0.12/0.45 unequally_directed_lines(sK0_skl,sK0_skl)|unequally_directed_lines(reverse_line(reverse_line(sK1_skl)),sK1_skl)|~sQ1_spl|sQ0_spl),
% 0.12/0.45 inference(resolution,[status(thm)],[f188,f164])).
% 0.12/0.45 fof(f219,definition,(
% 0.12/0.45 sQ7_spl <=> (unequally_directed_lines(sK0_skl,sK0_skl))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f220,plain,(
% 0.12/0.45 unequally_directed_lines(sK0_skl,sK0_skl)|~sQ7_spl),
% 0.12/0.45 inference(component_clause,[status(thm)],[f219])).
% 0.12/0.45 fof(f222,definition,(
% 0.12/0.45 sQ8_spl <=> (unequally_directed_lines(reverse_line(reverse_line(sK1_skl)),sK1_skl))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f223,plain,(
% 0.12/0.45 unequally_directed_lines(reverse_line(reverse_line(sK1_skl)),sK1_skl)|~sQ8_spl),
% 0.12/0.45 inference(component_clause,[status(thm)],[f222])).
% 0.12/0.45 fof(f225,plain,(
% 0.12/0.45 sQ7_spl|sQ8_spl|~sQ1_spl|sQ0_spl),
% 0.12/0.45 inference(split_clause,[status(thm)],[f198,f219,f222,f165,f162])).
% 0.12/0.45 fof(f226,plain,(
% 0.12/0.45 ![X0]: (unequally_directed_lines(sK0_skl,X0)|unequally_directed_lines(sK0_skl,X0)|~sQ7_spl)),
% 0.12/0.45 inference(resolution,[status(thm)],[f220,f103])).
% 0.12/0.45 fof(f227,plain,(
% 0.12/0.45 $false|~sQ7_spl|sQ0_spl),
% 0.12/0.45 inference(backward_subsumption_resolution,[status(thm)],[f164,f228])).
% 0.12/0.45 fof(f228,plain,(
% 0.12/0.45 ![X0]: (unequally_directed_lines(sK0_skl,X0)|~sQ7_spl)),
% 0.12/0.45 inference(duplicate_literals_removal,[status(thm)],[f226])).
% 0.12/0.45 fof(f229,plain,(
% 0.12/0.45 ~sQ7_spl|sQ0_spl),
% 0.12/0.45 inference(contradiction_clause,[status(thm)],[f227])).
% 0.12/0.45 fof(f238,plain,(
% 0.12/0.45 ![X0,X1]: (unequally_directed_opposite_lines(X0,reverse_line(X1))|unequally_directed_opposite_lines(X0,X1))),
% 0.12/0.45 inference(resolution,[status(thm)],[f185,f42])).
% 0.12/0.45 fof(f250,plain,(
% 0.12/0.45 equally_directed_opposite_lines(sK0_skl,reverse_line(sK1_skl))|sQ1_spl),
% 0.12/0.45 inference(resolution,[status(thm)],[f58,f167])).
% 0.12/0.45 fof(f329,plain,(
% 0.12/0.45 ![X0,X1]: (unequally_directed_opposite_lines(X0,X1)|~equally_directed_opposite_lines(X0,reverse_line(X1)))),
% 0.12/0.45 inference(resolution,[status(thm)],[f238,f57])).
% 0.12/0.45 fof(f389,plain,(
% 0.12/0.45 ![X0]: (~unequally_directed_lines(reverse_line(reverse_line(X0)),X0))),
% 0.12/0.45 inference(resolution,[status(thm)],[f181,f186])).
% 0.12/0.45 fof(f399,plain,(
% 0.12/0.45 $false|~sQ8_spl),
% 0.12/0.45 inference(backward_subsumption_resolution,[status(thm)],[f223,f389])).
% 0.12/0.45 fof(f400,plain,(
% 0.12/0.45 ~sQ8_spl),
% 0.12/0.45 inference(contradiction_clause,[status(thm)],[f399])).
% 0.12/0.45 fof(f431,plain,(
% 0.12/0.45 unequally_directed_opposite_lines(sK0_skl,sK1_skl)|sQ1_spl),
% 0.12/0.45 inference(resolution,[status(thm)],[f329,f250])).
% 0.12/0.45 fof(f434,plain,(
% 0.12/0.45 unequally_directed_lines(sK0_skl,reverse_line(sK1_skl))|sQ1_spl),
% 0.12/0.45 inference(resolution,[status(thm)],[f431,f41])).
% 0.12/0.45 fof(f436,plain,(
% 0.12/0.45 ~unequally_directed_lines(sK0_skl,sK1_skl)|sQ1_spl),
% 0.12/0.45 inference(resolution,[status(thm)],[f434,f181])).
% 0.12/0.45 fof(f441,plain,(
% 0.12/0.45 ~sQ0_spl|sQ1_spl),
% 0.12/0.45 inference(split_clause,[status(thm)],[f436,f162,f165])).
% 0.12/0.45 fof(f443,plain,(
% 0.12/0.45 $false),
% 0.12/0.45 inference(sat_refutation,[status(thm)],[f168,f169,f225,f229,f400,f441])).
% 0.12/0.45 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.48 % Elapsed time: 0.104536 seconds
% 0.12/0.48 % CPU time: 0.576126 seconds
% 0.12/0.48 % Total memory used: 24.387 MB
% 0.12/0.48 % Net memory used: 22.968 MB
%------------------------------------------------------------------------------