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Drodi-SAT---4.1.1.THM-Ass.s

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%------------------------------------------------------------------------------
% File     : Drodi-SAT---4.1.1
% Problem  : GEO219+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 : n001.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 12:26:09 PM UTC 2026

% Result   : Theorem 0.08s 0.43s
% Output   : Assurance 0s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : GEO219+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
% 0.08/0.36  % Computer : n001.cluster.edu
% 0.08/0.36  % Model    : x86_64 x86_64
% 0.08/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36  % Memory   : 8046.5625MB
% 0.08/0.36  % OS       : Linux 6.8.0-71-generic
% 0.08/0.36  % CPULimit : 300
% 0.08/0.36  % WCLimit  : 300
% 0.08/0.36  % DateTime : Sun Sep 20 13:52:27 UTC 2026
% 0.08/0.36  % CPUTime  : 
% 0.08/0.37  % Drodi V4.1.1
% 0.08/0.43  % Refutation found
% 0.08/0.43  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.43  % SZS output start CNFRefutation for theBenchmark
% 0.08/0.43  fof(f6,axiom,(
% 0.08/0.43    (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 0.08/0.43    file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.43  fof(f19,axiom,(
% 0.08/0.43    (! [L,M] :( convergent_lines(L,M)| unorthogonal_lines(L,M) ) )),
% 0.08/0.43    file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.43  fof(f25,axiom,(
% 0.08/0.43    (! [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) ) ) )),
% 0.08/0.43    file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.43  fof(f33,axiom,(
% 0.08/0.43    (! [X,Y] :( parallel_lines(X,Y)<=> ~ convergent_lines(X,Y) ) )),
% 0.08/0.43    file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.43  fof(f35,axiom,(
% 0.08/0.43    (! [X,Y] :( orthogonal_lines(X,Y)<=> ~ unorthogonal_lines(X,Y) ) )),
% 0.08/0.43    file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.43  fof(f36,conjecture,(
% 0.08/0.43    (! [L,M,N] :( ( orthogonal_lines(L,M)& parallel_lines(L,N) )=> orthogonal_lines(M,N) ) )),
% 0.08/0.43    file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.43  fof(f37,negated_conjecture,(
% 0.08/0.43    ~((! [L,M,N] :( ( orthogonal_lines(L,M)& parallel_lines(L,N) )=> orthogonal_lines(M,N) ) ))),
% 0.08/0.43    inference(negated_conjecture,[status(cth)],[f36])).
% 0.08/0.43  fof(f47,plain,(
% 0.08/0.43    ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 0.08/0.43    inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.08/0.43  fof(f48,plain,(
% 0.08/0.43    ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 0.08/0.43    inference(miniscoping,[status(thm)],[f47])).
% 0.08/0.43  fof(f49,plain,(
% 0.08/0.43    ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 0.08/0.43    inference(cnf_transformation,[status(thm)],[f48])).
% 0.08/0.43  fof(f76,plain,(
% 0.08/0.43    ![X0,X1]: (convergent_lines(X0,X1)|unorthogonal_lines(X0,X1))),
% 0.08/0.43    inference(cnf_transformation,[status(thm)],[f19])).
% 0.08/0.43  fof(f90,plain,(
% 0.08/0.43    ![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)))),
% 0.08/0.43    inference(pre_NNF_transformation,[status(thm)],[f25])).
% 0.08/0.43  fof(f91,definition,(
% 0.08/0.43    ![L,M]: (sP1_prd(M,L)<=>(convergent_lines(L,M)&unorthogonal_lines(L,M)))),
% 0.08/0.43    introduced(definition,[new_symbols(definition,[sP1_prd])],[])).
% 0.08/0.43  fof(f92,plain,(
% 0.08/0.43    ![L,M,N]: ((sP1_prd(M,L)|(convergent_lines(L,N)&unorthogonal_lines(L,N)))|(~convergent_lines(M,N)|~unorthogonal_lines(M,N)))),
% 0.08/0.43    inference(formula_renaming,[status(thm)],[f90,f91])).
% 0.08/0.43  fof(f93,plain,(
% 0.08/0.43    ![M,N]: ((![L]: (sP1_prd(M,L)|(convergent_lines(L,N)&unorthogonal_lines(L,N))))|(~convergent_lines(M,N)|~unorthogonal_lines(M,N)))),
% 0.08/0.43    inference(miniscoping,[status(thm)],[f92])).
% 0.08/0.43  fof(f94,plain,(
% 0.08/0.43    ![X0,X1,X2]: (sP1_prd(X0,X1)|convergent_lines(X1,X2)|~convergent_lines(X0,X2)|~unorthogonal_lines(X0,X2))),
% 0.08/0.43    inference(cnf_transformation,[status(thm)],[f93])).
% 0.08/0.43  fof(f115,plain,(
% 0.08/0.43    ![X,Y]: ((~parallel_lines(X,Y)|~convergent_lines(X,Y))&(parallel_lines(X,Y)|convergent_lines(X,Y)))),
% 0.08/0.43    inference(NNF_transformation,[status(thm)],[f33])).
% 0.08/0.43  fof(f116,plain,(
% 0.08/0.43    (![X,Y]: (~parallel_lines(X,Y)|~convergent_lines(X,Y)))&(![X,Y]: (parallel_lines(X,Y)|convergent_lines(X,Y)))),
% 0.08/0.43    inference(miniscoping,[status(thm)],[f115])).
% 0.08/0.43  fof(f117,plain,(
% 0.08/0.43    ![X0,X1]: (~parallel_lines(X0,X1)|~convergent_lines(X0,X1))),
% 0.08/0.43    inference(cnf_transformation,[status(thm)],[f116])).
% 0.08/0.43  fof(f123,plain,(
% 0.08/0.43    ![X,Y]: ((~orthogonal_lines(X,Y)|~unorthogonal_lines(X,Y))&(orthogonal_lines(X,Y)|unorthogonal_lines(X,Y)))),
% 0.08/0.43    inference(NNF_transformation,[status(thm)],[f35])).
% 0.08/0.43  fof(f124,plain,(
% 0.08/0.43    (![X,Y]: (~orthogonal_lines(X,Y)|~unorthogonal_lines(X,Y)))&(![X,Y]: (orthogonal_lines(X,Y)|unorthogonal_lines(X,Y)))),
% 0.08/0.43    inference(miniscoping,[status(thm)],[f123])).
% 0.08/0.43  fof(f125,plain,(
% 0.08/0.43    ![X0,X1]: (~orthogonal_lines(X0,X1)|~unorthogonal_lines(X0,X1))),
% 0.08/0.43    inference(cnf_transformation,[status(thm)],[f124])).
% 0.08/0.43  fof(f126,plain,(
% 0.08/0.43    ![X0,X1]: (orthogonal_lines(X0,X1)|unorthogonal_lines(X0,X1))),
% 0.08/0.43    inference(cnf_transformation,[status(thm)],[f124])).
% 0.08/0.43  fof(f127,plain,(
% 0.08/0.43    (?[L,M,N]: ((orthogonal_lines(L,M)&parallel_lines(L,N))&~orthogonal_lines(M,N)))),
% 0.08/0.43    inference(pre_NNF_transformation,[status(thm)],[f37])).
% 0.08/0.43  fof(f128,plain,(
% 0.08/0.43    ?[M,N]: ((?[L]: (orthogonal_lines(L,M)&parallel_lines(L,N)))&~orthogonal_lines(M,N))),
% 0.08/0.43    inference(miniscoping,[status(thm)],[f127])).
% 0.08/0.43  fof(f129,plain,(
% 0.08/0.43    ((orthogonal_lines(sK2_skl,sK0_skl)&parallel_lines(sK2_skl,sK1_skl))&~orthogonal_lines(sK0_skl,sK1_skl))),
% 0.08/0.43    inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(M,sK0_skl),skolemize(N,sK1_skl),skolemize(L,sK2_skl)],[f128])).
% 0.08/0.43  fof(f130,plain,(
% 0.08/0.43    orthogonal_lines(sK2_skl,sK0_skl)),
% 0.08/0.43    inference(cnf_transformation,[status(thm)],[f129])).
% 0.08/0.43  fof(f131,plain,(
% 0.08/0.43    parallel_lines(sK2_skl,sK1_skl)),
% 0.08/0.43    inference(cnf_transformation,[status(thm)],[f129])).
% 0.08/0.43  fof(f132,plain,(
% 0.08/0.43    ~orthogonal_lines(sK0_skl,sK1_skl)),
% 0.08/0.43    inference(cnf_transformation,[status(thm)],[f129])).
% 0.08/0.43  fof(f138,plain,(
% 0.08/0.43    ![L,M]: ((~sP1_prd(M,L)|(convergent_lines(L,M)&unorthogonal_lines(L,M)))&(sP1_prd(M,L)|(~convergent_lines(L,M)|~unorthogonal_lines(L,M))))),
% 0.08/0.43    inference(NNF_transformation,[status(thm)],[f91])).
% 0.08/0.43  fof(f139,plain,(
% 0.08/0.43    (![L,M]: (~sP1_prd(M,L)|(convergent_lines(L,M)&unorthogonal_lines(L,M))))&(![L,M]: (sP1_prd(M,L)|(~convergent_lines(L,M)|~unorthogonal_lines(L,M))))),
% 0.08/0.43    inference(miniscoping,[status(thm)],[f138])).
% 0.08/0.43  fof(f141,plain,(
% 0.08/0.43    ![X0,X1]: (~sP1_prd(X0,X1)|unorthogonal_lines(X1,X0))),
% 0.08/0.43    inference(cnf_transformation,[status(thm)],[f139])).
% 0.08/0.43  fof(f143,plain,(
% 0.08/0.43    unorthogonal_lines(sK0_skl,sK1_skl)),
% 0.08/0.43    inference(resolution,[status(thm)],[f126,f132])).
% 0.08/0.43  fof(f146,plain,(
% 0.08/0.43    ![X0,X1]: (convergent_lines(X0,X1)|~orthogonal_lines(X0,X1))),
% 0.08/0.43    inference(resolution,[status(thm)],[f76,f125])).
% 0.08/0.43  fof(f150,plain,(
% 0.08/0.43    convergent_lines(sK2_skl,sK0_skl)),
% 0.08/0.43    inference(resolution,[status(thm)],[f146,f130])).
% 0.08/0.43  fof(f152,plain,(
% 0.08/0.43    ![X0]: (convergent_lines(sK2_skl,X0)|convergent_lines(sK0_skl,X0))),
% 0.08/0.43    inference(resolution,[status(thm)],[f150,f49])).
% 0.08/0.43  fof(f157,plain,(
% 0.08/0.43    ![X0]: (convergent_lines(sK0_skl,X0)|~parallel_lines(sK2_skl,X0))),
% 0.08/0.43    inference(resolution,[status(thm)],[f152,f117])).
% 0.08/0.43  fof(f161,plain,(
% 0.08/0.43    convergent_lines(sK0_skl,sK1_skl)),
% 0.08/0.43    inference(resolution,[status(thm)],[f157,f131])).
% 0.08/0.43  fof(f382,definition,(
% 0.08/0.43    sQ13_spl <=> (convergent_lines(sK0_skl,sK1_skl))),
% 0.08/0.43    introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.08/0.43  fof(f384,plain,(
% 0.08/0.43    ~convergent_lines(sK0_skl,sK1_skl)|sQ13_spl),
% 0.08/0.43    inference(component_clause,[status(thm)],[f382])).
% 0.08/0.43  fof(f593,plain,(
% 0.08/0.43    $false|sQ13_spl),
% 0.08/0.43    inference(forward_subsumption_resolution,[status(thm)],[f384,f161])).
% 0.08/0.43  fof(f594,plain,(
% 0.08/0.43    sQ13_spl),
% 0.08/0.43    inference(contradiction_clause,[status(thm)],[f593])).
% 0.08/0.43  fof(f685,plain,(
% 0.08/0.43    ![X0]: (sP1_prd(sK0_skl,X0)|convergent_lines(X0,sK1_skl)|~convergent_lines(sK0_skl,sK1_skl))),
% 0.08/0.43    inference(resolution,[status(thm)],[f94,f143])).
% 0.08/0.43  fof(f688,definition,(
% 0.08/0.43    ![X0]: (sQ34_spl <=> (sP1_prd(sK0_skl,X0)|convergent_lines(X0,sK1_skl)))),
% 0.08/0.43    introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition])).
% 0.08/0.43  fof(f689,plain,(
% 0.08/0.43    ![X0]: (sP1_prd(sK0_skl,X0)|convergent_lines(X0,sK1_skl)|~sQ34_spl)),
% 0.08/0.43    inference(component_clause,[status(thm)],[f688])).
% 0.08/0.43  fof(f691,plain,(
% 0.08/0.43    sQ34_spl|~sQ13_spl),
% 0.08/0.43    inference(split_clause,[status(thm)],[f685,f688,f382])).
% 0.08/0.43  fof(f716,plain,(
% 0.08/0.43    ![X0]: (sP1_prd(sK0_skl,X0)|~parallel_lines(X0,sK1_skl)|~sQ34_spl)),
% 0.08/0.43    inference(resolution,[status(thm)],[f689,f117])).
% 0.08/0.43  fof(f947,plain,(
% 0.08/0.43    sP1_prd(sK0_skl,sK2_skl)|~sQ34_spl),
% 0.08/0.43    inference(resolution,[status(thm)],[f716,f131])).
% 0.08/0.43  fof(f949,plain,(
% 0.08/0.43    unorthogonal_lines(sK2_skl,sK0_skl)|~sQ34_spl),
% 0.08/0.43    inference(resolution,[status(thm)],[f947,f141])).
% 0.08/0.43  fof(f955,plain,(
% 0.08/0.43    ~orthogonal_lines(sK2_skl,sK0_skl)|~sQ34_spl),
% 0.08/0.43    inference(resolution,[status(thm)],[f949,f125])).
% 0.08/0.43  fof(f972,plain,(
% 0.08/0.43    $false|~sQ34_spl),
% 0.08/0.43    inference(forward_subsumption_resolution,[status(thm)],[f955,f130])).
% 0.08/0.43  fof(f973,plain,(
% 0.08/0.43    ~sQ34_spl),
% 0.08/0.43    inference(contradiction_clause,[status(thm)],[f972])).
% 0.08/0.43  fof(f974,plain,(
% 0.08/0.43    $false),
% 0.08/0.43    inference(sat_refutation,[status(thm)],[f594,f691,f973])).
% 0.08/0.43  % SZS output end CNFRefutation for theBenchmark.p
% 0.08/0.45  % Elapsed time: 0.082082 seconds
% 0.08/0.45  % CPU time: 0.433621 seconds
% 0.08/0.45  % Total memory used: 22.287 MB
% 0.08/0.45  % Net memory used: 21.478 MB
%------------------------------------------------------------------------------