%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO234+3 : 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 : n010.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 12:26:12 PM UTC 2026
% Result : Theorem 0.13s 0.43s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO234+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n010.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % 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 14:10:54 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.43 % Refutation found
% 0.13/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.43 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.43 fof(f1,axiom,(
% 0.13/0.43 (! [X,Y] :( unequally_directed_opposite_lines(X,Y)<=> unequally_directed_lines(X,reverse_line(Y)) ) )),
% 0.13/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.43 fof(f4,axiom,(
% 0.13/0.43 (! [X,Y] :( equally_directed_lines(X,Y)<=> ~ unequally_directed_lines(X,Y) ) )),
% 0.13/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.43 fof(f15,axiom,(
% 0.13/0.43 (! [L] : equally_directed_lines(L,L) )),
% 0.13/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.43 fof(f16,axiom,(
% 0.13/0.43 (! [L,M,N] :( unequally_directed_lines(L,M)=> ( unequally_directed_lines(L,N)| unequally_directed_lines(M,N) ) ) )),
% 0.13/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.43 fof(f18,axiom,(
% 0.13/0.43 (! [L,M] :( unequally_directed_lines(L,M)| unequally_directed_lines(L,reverse_line(M)) ) )),
% 0.13/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.43 fof(f19,axiom,(
% 0.13/0.43 (! [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)) ) ) )),
% 0.13/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.43 fof(f21,axiom,(
% 0.13/0.43 (! [L,M] :~ ( left_convergent_lines(L,M)| left_convergent_lines(L,reverse_line(M)) ) )),
% 0.13/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.43 fof(f37,conjecture,(
% 0.13/0.43 (! [L,M,N] :( unequally_directed_opposite_lines(L,M)=> ( unequally_directed_lines(L,N)| unequally_directed_opposite_lines(M,N) ) ) )),
% 0.13/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.43 fof(f38,negated_conjecture,(
% 0.13/0.43 ~((! [L,M,N] :( unequally_directed_opposite_lines(L,M)=> ( unequally_directed_lines(L,N)| unequally_directed_opposite_lines(M,N) ) ) ))),
% 0.13/0.43 inference(negated_conjecture,[status(cth)],[f37])).
% 0.13/0.43 fof(f39,plain,(
% 0.13/0.43 ![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))))),
% 0.13/0.43 inference(NNF_transformation,[status(thm)],[f1])).
% 0.13/0.43 fof(f40,plain,(
% 0.13/0.43 (![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))))),
% 0.13/0.43 inference(miniscoping,[status(thm)],[f39])).
% 0.13/0.43 fof(f41,plain,(
% 0.13/0.43 ![X0,X1]: (~unequally_directed_opposite_lines(X0,X1)|unequally_directed_lines(X0,reverse_line(X1)))),
% 0.13/0.43 inference(cnf_transformation,[status(thm)],[f40])).
% 0.13/0.43 fof(f42,plain,(
% 0.13/0.43 ![X0,X1]: (unequally_directed_opposite_lines(X0,X1)|~unequally_directed_lines(X0,reverse_line(X1)))),
% 0.13/0.43 inference(cnf_transformation,[status(thm)],[f40])).
% 0.13/0.43 fof(f51,plain,(
% 0.13/0.43 ![X,Y]: ((~equally_directed_lines(X,Y)|~unequally_directed_lines(X,Y))&(equally_directed_lines(X,Y)|unequally_directed_lines(X,Y)))),
% 0.13/0.43 inference(NNF_transformation,[status(thm)],[f4])).
% 0.13/0.43 fof(f52,plain,(
% 0.13/0.43 (![X,Y]: (~equally_directed_lines(X,Y)|~unequally_directed_lines(X,Y)))&(![X,Y]: (equally_directed_lines(X,Y)|unequally_directed_lines(X,Y)))),
% 0.13/0.43 inference(miniscoping,[status(thm)],[f51])).
% 0.13/0.43 fof(f53,plain,(
% 0.13/0.43 ![X0,X1]: (~equally_directed_lines(X0,X1)|~unequally_directed_lines(X0,X1))),
% 0.13/0.43 inference(cnf_transformation,[status(thm)],[f52])).
% 0.13/0.43 fof(f100,plain,(
% 0.13/0.43 ![X0]: (equally_directed_lines(X0,X0))),
% 0.13/0.43 inference(cnf_transformation,[status(thm)],[f15])).
% 0.13/0.43 fof(f101,plain,(
% 0.13/0.43 ![L,M,N]: (~unequally_directed_lines(L,M)|(unequally_directed_lines(L,N)|unequally_directed_lines(M,N)))),
% 0.13/0.43 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.13/0.43 fof(f102,plain,(
% 0.13/0.43 ![L,M]: (~unequally_directed_lines(L,M)|(![N]: (unequally_directed_lines(L,N)|unequally_directed_lines(M,N))))),
% 0.13/0.43 inference(miniscoping,[status(thm)],[f101])).
% 0.13/0.43 fof(f103,plain,(
% 0.13/0.43 ![X0,X1,X2]: (~unequally_directed_lines(X0,X1)|unequally_directed_lines(X0,X2)|unequally_directed_lines(X1,X2))),
% 0.13/0.43 inference(cnf_transformation,[status(thm)],[f102])).
% 0.13/0.43 fof(f110,plain,(
% 0.13/0.43 ![X0,X1]: (unequally_directed_lines(X0,X1)|unequally_directed_lines(X0,reverse_line(X1)))),
% 0.13/0.43 inference(cnf_transformation,[status(thm)],[f18])).
% 0.13/0.43 fof(f111,plain,(
% 0.13/0.43 ![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))))),
% 0.13/0.43 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 0.13/0.43 fof(f112,plain,(
% 0.13/0.43 ![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)))),
% 0.13/0.43 inference(cnf_transformation,[status(thm)],[f111])).
% 0.13/0.43 fof(f117,plain,(
% 0.13/0.43 ![L,M]: (~left_convergent_lines(L,M)&~left_convergent_lines(L,reverse_line(M)))),
% 0.13/0.43 inference(pre_NNF_transformation,[status(thm)],[f21])).
% 0.13/0.43 fof(f118,plain,(
% 0.13/0.43 (![L,M]: ~left_convergent_lines(L,M))&(![L,M]: ~left_convergent_lines(L,reverse_line(M)))),
% 0.13/0.43 inference(miniscoping,[status(thm)],[f117])).
% 0.13/0.43 fof(f119,plain,(
% 0.13/0.43 ![X0,X1]: (~left_convergent_lines(X0,X1))),
% 0.13/0.43 inference(cnf_transformation,[status(thm)],[f118])).
% 0.13/0.43 fof(f152,plain,(
% 0.13/0.43 (?[L,M,N]: (unequally_directed_opposite_lines(L,M)&(~unequally_directed_lines(L,N)&~unequally_directed_opposite_lines(M,N))))),
% 0.13/0.43 inference(pre_NNF_transformation,[status(thm)],[f38])).
% 0.13/0.43 fof(f153,plain,(
% 0.13/0.43 ?[L,M]: (unequally_directed_opposite_lines(L,M)&(?[N]: (~unequally_directed_lines(L,N)&~unequally_directed_opposite_lines(M,N))))),
% 0.13/0.43 inference(miniscoping,[status(thm)],[f152])).
% 0.13/0.43 fof(f154,plain,(
% 0.13/0.43 (unequally_directed_opposite_lines(sK0_skl,sK1_skl)&(~unequally_directed_lines(sK0_skl,sK2_skl)&~unequally_directed_opposite_lines(sK1_skl,sK2_skl)))),
% 0.13/0.43 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(L,sK0_skl),skolemize(M,sK1_skl),skolemize(N,sK2_skl)],[f153])).
% 0.13/0.43 fof(f155,plain,(
% 0.13/0.43 unequally_directed_opposite_lines(sK0_skl,sK1_skl)),
% 0.13/0.43 inference(cnf_transformation,[status(thm)],[f154])).
% 0.13/0.43 fof(f156,plain,(
% 0.13/0.43 ~unequally_directed_lines(sK0_skl,sK2_skl)),
% 0.13/0.43 inference(cnf_transformation,[status(thm)],[f154])).
% 0.13/0.43 fof(f157,plain,(
% 0.13/0.43 ~unequally_directed_opposite_lines(sK1_skl,sK2_skl)),
% 0.13/0.43 inference(cnf_transformation,[status(thm)],[f154])).
% 0.13/0.43 fof(f168,plain,(
% 0.13/0.43 ![X0,X1]: (~unequally_directed_lines(X0,X1)|~unequally_directed_lines(X0,reverse_line(X1))|left_convergent_lines(X0,X1))),
% 0.13/0.43 inference(backward_subsumption_resolution,[status(thm)],[f112,f119])).
% 0.13/0.43 fof(f174,plain,(
% 0.13/0.43 ![X0,X1]: (~unequally_directed_lines(X0,X1)|~unequally_directed_lines(X0,reverse_line(X1)))),
% 0.13/0.43 inference(forward_subsumption_resolution,[status(thm)],[f168,f119])).
% 0.13/0.43 fof(f176,plain,(
% 0.13/0.43 ![X0,X1,X2]: (unequally_directed_lines(X0,X1)|unequally_directed_lines(reverse_line(X2),X1)|~unequally_directed_opposite_lines(X0,X2))),
% 0.13/0.43 inference(resolution,[status(thm)],[f103,f41])).
% 0.13/0.43 fof(f177,plain,(
% 0.13/0.43 ![X0]: (unequally_directed_lines(sK0_skl,X0)|unequally_directed_lines(reverse_line(sK1_skl),X0))),
% 0.13/0.43 inference(resolution,[status(thm)],[f176,f155])).
% 0.13/0.43 fof(f179,plain,(
% 0.13/0.43 ![X0,X1]: (unequally_directed_lines(sK0_skl,X0)|unequally_directed_lines(reverse_line(sK1_skl),X1)|unequally_directed_lines(X0,X1))),
% 0.13/0.43 inference(resolution,[status(thm)],[f177,f103])).
% 0.13/0.43 fof(f183,plain,(
% 0.13/0.43 ![X0]: (unequally_directed_lines(reverse_line(sK1_skl),X0)|unequally_directed_lines(sK2_skl,X0))),
% 0.13/0.43 inference(resolution,[status(thm)],[f179,f156])).
% 0.13/0.43 fof(f204,definition,(
% 0.13/0.43 ![X0]: (sQ3_spl <=> (unequally_directed_opposite_lines(reverse_line(sK1_skl),X0)))),
% 0.13/0.43 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.13/0.43 fof(f205,plain,(
% 0.13/0.43 ![X0]: (unequally_directed_opposite_lines(reverse_line(sK1_skl),X0)|~sQ3_spl)),
% 0.13/0.43 inference(component_clause,[status(thm)],[f204])).
% 0.13/0.43 fof(f228,plain,(
% 0.13/0.43 ![X0,X1]: (unequally_directed_lines(sK2_skl,X0)|unequally_directed_lines(reverse_line(sK1_skl),X1)|unequally_directed_lines(X0,X1))),
% 0.13/0.43 inference(resolution,[status(thm)],[f183,f103])).
% 0.13/0.43 fof(f254,plain,(
% 0.13/0.43 ![X0]: (~unequally_directed_lines(X0,X0))),
% 0.13/0.43 inference(resolution,[status(thm)],[f53,f100])).
% 0.13/0.43 fof(f264,plain,(
% 0.13/0.43 ![X0]: (unequally_directed_lines(sK2_skl,reverse_line(sK1_skl))|unequally_directed_opposite_lines(reverse_line(sK1_skl),X0))),
% 0.13/0.43 inference(resolution,[status(thm)],[f228,f42])).
% 0.13/0.43 fof(f275,definition,(
% 0.13/0.43 sQ8_spl <=> (unequally_directed_lines(sK2_skl,reverse_line(sK1_skl)))),
% 0.13/0.45 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.13/0.45 fof(f276,plain,(
% 0.13/0.45 unequally_directed_lines(sK2_skl,reverse_line(sK1_skl))|~sQ8_spl),
% 0.13/0.45 inference(component_clause,[status(thm)],[f275])).
% 0.13/0.45 fof(f278,plain,(
% 0.13/0.45 sQ8_spl|sQ3_spl),
% 0.13/0.45 inference(split_clause,[status(thm)],[f264,f275,f204])).
% 0.13/0.45 fof(f406,plain,(
% 0.13/0.45 ![X0]: (~unequally_directed_opposite_lines(reverse_line(X0),X0))),
% 0.13/0.45 inference(resolution,[status(thm)],[f254,f41])).
% 0.13/0.45 fof(f411,plain,(
% 0.13/0.45 $false|~sQ3_spl),
% 0.13/0.45 inference(resolution,[status(thm)],[f205,f406])).
% 0.13/0.45 fof(f413,plain,(
% 0.13/0.45 ~sQ3_spl),
% 0.13/0.45 inference(contradiction_clause,[status(thm)],[f411])).
% 0.13/0.45 fof(f415,plain,(
% 0.13/0.45 ![X0,X1]: (unequally_directed_lines(X0,X1)|unequally_directed_opposite_lines(X0,X1))),
% 0.13/0.45 inference(resolution,[status(thm)],[f110,f42])).
% 0.13/0.45 fof(f424,plain,(
% 0.13/0.45 ![X0,X1,X2]: (unequally_directed_opposite_lines(X0,X1)|unequally_directed_lines(X0,X2)|unequally_directed_lines(X1,X2))),
% 0.13/0.45 inference(resolution,[status(thm)],[f415,f103])).
% 0.13/0.45 fof(f435,plain,(
% 0.13/0.45 ~unequally_directed_lines(sK2_skl,sK1_skl)|~sQ8_spl),
% 0.13/0.45 inference(resolution,[status(thm)],[f174,f276])).
% 0.13/0.45 fof(f543,plain,(
% 0.13/0.45 ![X0,X1]: (unequally_directed_opposite_lines(X0,X1)|unequally_directed_lines(X1,X0))),
% 0.13/0.45 inference(resolution,[status(thm)],[f424,f254])).
% 0.13/0.45 fof(f554,plain,(
% 0.13/0.45 unequally_directed_opposite_lines(sK1_skl,sK2_skl)|~sQ8_spl),
% 0.13/0.45 inference(resolution,[status(thm)],[f543,f435])).
% 0.13/0.45 fof(f562,plain,(
% 0.13/0.45 $false|~sQ8_spl),
% 0.13/0.45 inference(forward_subsumption_resolution,[status(thm)],[f554,f157])).
% 0.13/0.45 fof(f563,plain,(
% 0.13/0.45 ~sQ8_spl),
% 0.13/0.45 inference(contradiction_clause,[status(thm)],[f562])).
% 0.13/0.45 fof(f564,plain,(
% 0.13/0.45 $false),
% 0.13/0.45 inference(sat_refutation,[status(thm)],[f278,f413,f563])).
% 0.13/0.45 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.46 % Elapsed time: 0.091573 seconds
% 0.13/0.46 % CPU time: 0.435179 seconds
% 0.13/0.46 % Total memory used: 23.552 MB
% 0.13/0.46 % Net memory used: 22.487 MB
%------------------------------------------------------------------------------