%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO223+2 : TPTP v9.3.1. Released v3.3.0.
% 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 12:26:10 PM UTC 2026
% Result : Theorem 1.27s 0.75s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO223+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n011.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 13:48:25 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 1.27/0.75 % Refutation found
% 1.27/0.75 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.27/0.75 % SZS output start CNFRefutation for theBenchmark
% 1.27/0.75 fof(f3,axiom,(
% 1.27/0.75 (! [X] : ~ convergent_lines(X,X) )),
% 1.27/0.75 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.27/0.75 fof(f6,axiom,(
% 1.27/0.75 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 1.27/0.75 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.27/0.75 fof(f13,axiom,(
% 1.27/0.75 (! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y) )),
% 1.27/0.75 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.27/0.75 fof(f14,axiom,(
% 1.27/0.75 (! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)) )),
% 1.27/0.75 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.27/0.75 fof(f16,axiom,(
% 1.27/0.75 (! [L,M] :( convergent_lines(L,M)| unorthogonal_lines(L,M) ) )),
% 1.27/0.75 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.27/0.75 fof(f17,axiom,(
% 1.27/0.75 (! [L,M,N] :( ( convergent_lines(L,M)& unorthogonal_lines(L,M) )=> ( ( convergent_lines(L,N)& unorthogonal_lines(L,N) )| ( convergent_lines(M,N)& unorthogonal_lines(M,N) ) ) ) )),
% 1.27/0.75 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.27/0.75 fof(f18,axiom,(
% 1.27/0.75 (! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L) )),
% 1.27/0.75 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.27/0.75 fof(f19,axiom,(
% 1.27/0.75 (! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)) )),
% 1.27/0.75 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.27/0.75 fof(f20,axiom,(
% 1.27/0.75 (! [A,L,M,N] :( distinct_lines(L,M)=> ( apart_point_and_line(A,L)| apart_point_and_line(A,M)| unorthogonal_lines(L,N)| unorthogonal_lines(M,N) ) ) )),
% 1.27/0.75 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.27/0.75 fof(f21,conjecture,(
% 1.27/0.75 (! [A,L] : ~ distinct_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)) )),
% 1.27/0.75 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.27/0.75 fof(f22,negated_conjecture,(
% 1.27/0.75 ~((! [A,L] : ~ distinct_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)) ))),
% 1.27/0.75 inference(negated_conjecture,[status(cth)],[f21])).
% 1.27/0.75 fof(f25,plain,(
% 1.27/0.75 ![X0]: (~convergent_lines(X0,X0))),
% 1.27/0.75 inference(cnf_transformation,[status(thm)],[f3])).
% 1.27/0.75 fof(f32,plain,(
% 1.27/0.75 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 1.27/0.75 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 1.27/0.75 fof(f33,plain,(
% 1.27/0.75 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 1.27/0.75 inference(miniscoping,[status(thm)],[f32])).
% 1.27/0.75 fof(f34,plain,(
% 1.27/0.75 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 1.27/0.75 inference(cnf_transformation,[status(thm)],[f33])).
% 1.27/0.75 fof(f53,plain,(
% 1.27/0.75 ![X0,X1]: (~convergent_lines(parallel_through_point(X0,X1),X0))),
% 1.27/0.75 inference(cnf_transformation,[status(thm)],[f13])).
% 1.27/0.75 fof(f54,plain,(
% 1.27/0.75 ![X0,X1]: (~apart_point_and_line(X0,parallel_through_point(X1,X0)))),
% 1.27/0.75 inference(cnf_transformation,[status(thm)],[f14])).
% 1.27/0.75 fof(f58,plain,(
% 1.27/0.75 ![X0,X1]: (convergent_lines(X0,X1)|unorthogonal_lines(X0,X1))),
% 1.27/0.75 inference(cnf_transformation,[status(thm)],[f16])).
% 1.27/0.75 fof(f59,plain,(
% 1.27/0.75 ![L,M,N]: ((~convergent_lines(L,M)|~unorthogonal_lines(L,M))|((convergent_lines(L,N)&unorthogonal_lines(L,N))|(convergent_lines(M,N)&unorthogonal_lines(M,N))))),
% 1.27/0.75 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 1.27/0.75 fof(f60,definition,(
% 1.27/0.75 ![L,N]: (sP0_prd(N,L)<=>(convergent_lines(L,N)&unorthogonal_lines(L,N)))),
% 1.27/0.75 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 1.27/0.75 fof(f61,plain,(
% 1.27/0.75 ![L,M,N]: ((~convergent_lines(L,M)|~unorthogonal_lines(L,M))|(sP0_prd(N,L)|(convergent_lines(M,N)&unorthogonal_lines(M,N))))),
% 1.27/0.75 inference(formula_renaming,[status(thm)],[f59,f60])).
% 1.27/0.75 fof(f62,plain,(
% 1.27/0.75 ![L,M]: ((~convergent_lines(L,M)|~unorthogonal_lines(L,M))|(![N]: (sP0_prd(N,L)|(convergent_lines(M,N)&unorthogonal_lines(M,N)))))),
% 1.27/0.75 inference(miniscoping,[status(thm)],[f61])).
% 1.27/0.75 fof(f64,plain,(
% 1.27/0.75 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~unorthogonal_lines(X0,X1)|sP0_prd(X2,X0)|unorthogonal_lines(X1,X2))),
% 1.27/0.75 inference(cnf_transformation,[status(thm)],[f62])).
% 1.27/0.75 fof(f65,plain,(
% 1.27/0.75 ![X0,X1]: (~unorthogonal_lines(orthogonal_through_point(X0,X1),X0))),
% 1.27/0.75 inference(cnf_transformation,[status(thm)],[f18])).
% 1.27/0.75 fof(f66,plain,(
% 1.27/0.75 ![X0,X1]: (~apart_point_and_line(X0,orthogonal_through_point(X1,X0)))),
% 1.27/0.75 inference(cnf_transformation,[status(thm)],[f19])).
% 1.27/0.75 fof(f67,plain,(
% 1.27/0.75 ![A,L,M,N]: (~distinct_lines(L,M)|(((apart_point_and_line(A,L)|apart_point_and_line(A,M))|unorthogonal_lines(L,N))|unorthogonal_lines(M,N)))),
% 1.27/0.75 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 1.27/0.75 fof(f68,plain,(
% 1.27/0.75 ![L,M]: (~distinct_lines(L,M)|(![N]: (((![A]: (apart_point_and_line(A,L)|apart_point_and_line(A,M)))|unorthogonal_lines(L,N))|unorthogonal_lines(M,N))))),
% 1.27/0.75 inference(miniscoping,[status(thm)],[f67])).
% 1.27/0.75 fof(f69,plain,(
% 1.27/0.75 ![X0,X1,X2,X3]: (~distinct_lines(X0,X1)|apart_point_and_line(X2,X0)|apart_point_and_line(X2,X1)|unorthogonal_lines(X0,X3)|unorthogonal_lines(X1,X3))),
% 1.27/0.75 inference(cnf_transformation,[status(thm)],[f68])).
% 1.27/0.75 fof(f70,plain,(
% 1.27/0.75 (?[A,L]: distinct_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)))),
% 1.27/0.75 inference(pre_NNF_transformation,[status(thm)],[f22])).
% 1.27/0.75 fof(f71,plain,(
% 1.27/0.75 distinct_lines(parallel_through_point(sK1_skl,sK0_skl),orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))),
% 1.27/0.75 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(A,sK0_skl),skolemize(L,sK1_skl)],[f70])).
% 1.27/0.75 fof(f72,plain,(
% 1.27/0.75 distinct_lines(parallel_through_point(sK1_skl,sK0_skl),orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))),
% 1.27/0.75 inference(cnf_transformation,[status(thm)],[f71])).
% 1.27/0.75 fof(f73,plain,(
% 1.27/0.75 ![L,N]: ((~sP0_prd(N,L)|(convergent_lines(L,N)&unorthogonal_lines(L,N)))&(sP0_prd(N,L)|(~convergent_lines(L,N)|~unorthogonal_lines(L,N))))),
% 1.27/0.75 inference(NNF_transformation,[status(thm)],[f60])).
% 1.27/0.75 fof(f74,plain,(
% 1.27/0.75 (![L,N]: (~sP0_prd(N,L)|(convergent_lines(L,N)&unorthogonal_lines(L,N))))&(![L,N]: (sP0_prd(N,L)|(~convergent_lines(L,N)|~unorthogonal_lines(L,N))))),
% 1.27/0.75 inference(miniscoping,[status(thm)],[f73])).
% 1.27/0.75 fof(f75,plain,(
% 1.27/0.75 ![X0,X1]: (~sP0_prd(X0,X1)|convergent_lines(X1,X0))),
% 1.27/0.75 inference(cnf_transformation,[status(thm)],[f74])).
% 1.27/0.75 fof(f85,definition,(
% 1.27/0.75 ![X0]: (sQ0_spl <=> (apart_point_and_line(X0,parallel_through_point(sK1_skl,sK0_skl))|apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))))),
% 1.27/0.75 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 1.27/0.75 fof(f86,plain,(
% 1.27/0.75 ![X0]: (apart_point_and_line(X0,parallel_through_point(sK1_skl,sK0_skl))|apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))|~sQ0_spl)),
% 1.27/0.75 inference(component_clause,[status(thm)],[f85])).
% 1.27/0.75 fof(f92,plain,(
% 1.27/0.75 ![X0,X1]: (convergent_lines(orthogonal_through_point(X0,X1),X0))),
% 1.27/0.75 inference(resolution,[status(thm)],[f58,f65])).
% 1.27/0.75 fof(f94,plain,(
% 1.27/0.75 ![X0,X1,X2]: (convergent_lines(orthogonal_through_point(X0,X1),X2)|convergent_lines(X0,X2))),
% 1.27/0.75 inference(resolution,[status(thm)],[f92,f34])).
% 1.27/0.75 fof(f100,plain,(
% 1.27/0.75 apart_point_and_line(sK0_skl,parallel_through_point(sK1_skl,sK0_skl))|~sQ0_spl),
% 1.27/0.75 inference(resolution,[status(thm)],[f86,f66])).
% 1.27/0.75 fof(f102,plain,(
% 1.27/0.75 $false|~sQ0_spl),
% 1.27/0.75 inference(forward_subsumption_resolution,[status(thm)],[f100,f54])).
% 1.27/0.75 fof(f103,plain,(
% 1.27/0.75 ~sQ0_spl),
% 1.27/0.75 inference(contradiction_clause,[status(thm)],[f102])).
% 1.27/0.75 fof(f111,plain,(
% 1.27/0.75 ![X0,X1,X2,X3]: (convergent_lines(X0,X1)|convergent_lines(orthogonal_through_point(X0,X2),X3)|convergent_lines(X1,X3))),
% 1.27/0.75 inference(resolution,[status(thm)],[f94,f34])).
% 1.27/0.75 fof(f133,plain,(
% 1.27/0.75 ![X0,X1,X2]: (~convergent_lines(X0,orthogonal_through_point(X1,X2))|~unorthogonal_lines(X0,orthogonal_through_point(X1,X2))|sP0_prd(X1,X0))),
% 1.27/0.75 inference(resolution,[status(thm)],[f64,f65])).
% 1.27/0.75 fof(f230,plain,(
% 1.27/0.75 ![X0,X1]: (apart_point_and_line(X0,parallel_through_point(sK1_skl,sK0_skl))|apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))|unorthogonal_lines(parallel_through_point(sK1_skl,sK0_skl),X1)|unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X1))),
% 1.27/0.75 inference(resolution,[status(thm)],[f69,f72])).
% 1.16/0.76 fof(f241,definition,(
% 1.16/0.76 ![X1]: (sQ13_spl <=> (unorthogonal_lines(parallel_through_point(sK1_skl,sK0_skl),X1)|unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X1)))),
% 1.16/0.76 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 1.16/0.76 fof(f242,plain,(
% 1.16/0.76 ![X0]: (unorthogonal_lines(parallel_through_point(sK1_skl,sK0_skl),X0)|unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X0)|~sQ13_spl)),
% 1.16/0.76 inference(component_clause,[status(thm)],[f241])).
% 1.16/0.76 fof(f244,plain,(
% 1.16/0.76 sQ0_spl|sQ13_spl),
% 1.16/0.76 inference(split_clause,[status(thm)],[f230,f85,f241])).
% 1.16/0.76 fof(f286,plain,(
% 1.16/0.76 unorthogonal_lines(parallel_through_point(sK1_skl,sK0_skl),orthogonal_through_point(sK1_skl,sK0_skl))|~sQ13_spl),
% 1.16/0.76 inference(resolution,[status(thm)],[f242,f65])).
% 1.16/0.76 fof(f300,definition,(
% 1.16/0.76 sQ16_spl <=> (convergent_lines(parallel_through_point(sK1_skl,sK0_skl),orthogonal_through_point(sK1_skl,sK0_skl)))),
% 1.16/0.76 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 1.16/0.76 fof(f302,plain,(
% 1.16/0.76 ~convergent_lines(parallel_through_point(sK1_skl,sK0_skl),orthogonal_through_point(sK1_skl,sK0_skl))|sQ16_spl),
% 1.16/0.76 inference(component_clause,[status(thm)],[f300])).
% 1.16/0.76 fof(f329,plain,(
% 1.16/0.76 ~convergent_lines(parallel_through_point(sK1_skl,sK0_skl),orthogonal_through_point(sK1_skl,sK0_skl))|sP0_prd(sK1_skl,parallel_through_point(sK1_skl,sK0_skl))|~sQ13_spl),
% 1.16/0.76 inference(resolution,[status(thm)],[f133,f286])).
% 1.16/0.76 fof(f334,definition,(
% 1.16/0.76 sQ23_spl <=> (sP0_prd(sK1_skl,parallel_through_point(sK1_skl,sK0_skl)))),
% 1.16/0.76 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 1.16/0.76 fof(f335,plain,(
% 1.16/0.76 sP0_prd(sK1_skl,parallel_through_point(sK1_skl,sK0_skl))|~sQ23_spl),
% 1.16/0.76 inference(component_clause,[status(thm)],[f334])).
% 1.16/0.76 fof(f337,plain,(
% 1.16/0.76 ~sQ16_spl|sQ23_spl|~sQ13_spl),
% 1.16/0.76 inference(split_clause,[status(thm)],[f329,f300,f334,f241])).
% 1.16/0.76 fof(f413,plain,(
% 1.16/0.76 ![X0,X1,X2]: (convergent_lines(X0,X1)|convergent_lines(X1,orthogonal_through_point(X0,X2)))),
% 1.16/0.76 inference(resolution,[status(thm)],[f111,f25])).
% 1.16/0.76 fof(f423,plain,(
% 1.16/0.76 convergent_lines(sK1_skl,parallel_through_point(sK1_skl,sK0_skl))|sQ16_spl),
% 1.16/0.76 inference(resolution,[status(thm)],[f413,f302])).
% 1.16/0.76 fof(f433,plain,(
% 1.16/0.76 ![X0]: (convergent_lines(sK1_skl,X0)|convergent_lines(parallel_through_point(sK1_skl,sK0_skl),X0)|sQ16_spl)),
% 1.16/0.76 inference(resolution,[status(thm)],[f423,f34])).
% 1.16/0.76 fof(f716,plain,(
% 1.16/0.76 convergent_lines(sK1_skl,sK1_skl)|sQ16_spl),
% 1.16/0.76 inference(resolution,[status(thm)],[f433,f53])).
% 1.16/0.76 fof(f722,plain,(
% 1.16/0.76 $false|sQ16_spl),
% 1.16/0.76 inference(forward_subsumption_resolution,[status(thm)],[f716,f25])).
% 1.16/0.76 fof(f723,plain,(
% 1.16/0.76 sQ16_spl),
% 1.16/0.76 inference(contradiction_clause,[status(thm)],[f722])).
% 1.16/0.76 fof(f879,plain,(
% 1.16/0.76 convergent_lines(parallel_through_point(sK1_skl,sK0_skl),sK1_skl)|~sQ23_spl),
% 1.16/0.76 inference(resolution,[status(thm)],[f335,f75])).
% 1.16/0.76 fof(f880,plain,(
% 1.16/0.76 $false|~sQ23_spl),
% 1.16/0.76 inference(forward_subsumption_resolution,[status(thm)],[f879,f53])).
% 1.16/0.76 fof(f881,plain,(
% 1.16/0.76 ~sQ23_spl),
% 1.16/0.76 inference(contradiction_clause,[status(thm)],[f880])).
% 1.16/0.76 fof(f882,plain,(
% 1.16/0.76 $false),
% 1.16/0.76 inference(sat_refutation,[status(thm)],[f103,f244,f337,f723,f881])).
% 1.16/0.76 % SZS output end CNFRefutation for theBenchmark.p
% 1.16/0.77 % Elapsed time: 0.397513 seconds
% 1.16/0.77 % CPU time: 2.836499 seconds
% 1.16/0.77 % Total memory used: 46.094 MB
% 1.16/0.77 % Net memory used: 40.272 MB
%------------------------------------------------------------------------------