TSTP Solution File: GEO218+3 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GEO218+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:08:22 EDT 2023
% Result : Theorem 0.12s 0.41s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 77 ( 18 unt; 0 def)
% Number of atoms : 203 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 211 ( 85 ~; 87 |; 29 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 149 (; 143 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| convergent_lines(Y,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [L,M] :
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [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) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [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) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [L,M,N] :
( ( ~ unorthogonal_lines(L,M)
& ~ unorthogonal_lines(L,N) )
=> ~ convergent_lines(M,N) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [X,Y] :
( parallel_lines(X,Y)
<=> ~ convergent_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [X,Y] :
( orthogonal_lines(X,Y)
<=> ~ unorthogonal_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,conjecture,
! [L,M,N] :
( ( parallel_lines(L,M)
& orthogonal_lines(L,N) )
=> orthogonal_lines(M,N) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [L,M,N] :
( ( parallel_lines(L,M)
& orthogonal_lines(L,N) )
=> orthogonal_lines(M,N) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f40,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f47,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f48,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
| ! [Z] :
( convergent_lines(X,Z)
| convergent_lines(Y,Z) ) ),
inference(miniscoping,[status(esa)],[f47]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| convergent_lines(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f48]) ).
fof(f76,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f77,plain,
! [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) ) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f78,plain,
! [L,N] :
( pd0_0(N,L)
=> ( convergent_lines(L,N)
& unorthogonal_lines(L,N) ) ),
introduced(predicate_definition,[f77]) ).
fof(f79,plain,
! [L,M,N] :
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| pd0_0(N,L)
| ( convergent_lines(M,N)
& unorthogonal_lines(M,N) ) ),
inference(formula_renaming,[status(thm)],[f77,f78]) ).
fof(f80,plain,
! [L,M] :
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| ! [N] :
( pd0_0(N,L)
| ( convergent_lines(M,N)
& unorthogonal_lines(M,N) ) ) ),
inference(miniscoping,[status(esa)],[f79]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1)
| pd0_0(X2,X0)
| unorthogonal_lines(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f80]) ).
fof(f83,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f90,plain,
! [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) ),
inference(pre_NNF_transformation,[status(esa)],[f25]) ).
fof(f91,plain,
! [L,M] :
( pd0_1(M,L)
=> ( convergent_lines(L,M)
& unorthogonal_lines(L,M) ) ),
introduced(predicate_definition,[f90]) ).
fof(f92,plain,
! [L,M,N] :
( pd0_1(M,L)
| ( convergent_lines(L,N)
& unorthogonal_lines(L,N) )
| ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N) ),
inference(formula_renaming,[status(thm)],[f90,f91]) ).
fof(f93,plain,
! [M,N] :
( ! [L] :
( pd0_1(M,L)
| ( convergent_lines(L,N)
& unorthogonal_lines(L,N) ) )
| ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N) ),
inference(miniscoping,[status(esa)],[f92]) ).
fof(f94,plain,
! [X0,X1,X2] :
( pd0_1(X0,X1)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X2)
| ~ unorthogonal_lines(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f93]) ).
fof(f96,plain,
! [L,M,N] :
( unorthogonal_lines(L,M)
| unorthogonal_lines(L,N)
| ~ convergent_lines(M,N) ),
inference(pre_NNF_transformation,[status(esa)],[f26]) ).
fof(f97,plain,
! [M,N] :
( ! [L] :
( unorthogonal_lines(L,M)
| unorthogonal_lines(L,N) )
| ~ convergent_lines(M,N) ),
inference(miniscoping,[status(esa)],[f96]) ).
fof(f98,plain,
! [X0,X1,X2] :
( unorthogonal_lines(X0,X1)
| unorthogonal_lines(X0,X2)
| ~ convergent_lines(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f97]) ).
fof(f115,plain,
! [X,Y] :
( ( ~ parallel_lines(X,Y)
| ~ convergent_lines(X,Y) )
& ( parallel_lines(X,Y)
| convergent_lines(X,Y) ) ),
inference(NNF_transformation,[status(esa)],[f33]) ).
fof(f116,plain,
( ! [X,Y] :
( ~ parallel_lines(X,Y)
| ~ convergent_lines(X,Y) )
& ! [X,Y] :
( parallel_lines(X,Y)
| convergent_lines(X,Y) ) ),
inference(miniscoping,[status(esa)],[f115]) ).
fof(f117,plain,
! [X0,X1] :
( ~ parallel_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f116]) ).
fof(f123,plain,
! [X,Y] :
( ( ~ orthogonal_lines(X,Y)
| ~ unorthogonal_lines(X,Y) )
& ( orthogonal_lines(X,Y)
| unorthogonal_lines(X,Y) ) ),
inference(NNF_transformation,[status(esa)],[f35]) ).
fof(f124,plain,
( ! [X,Y] :
( ~ orthogonal_lines(X,Y)
| ~ unorthogonal_lines(X,Y) )
& ! [X,Y] :
( orthogonal_lines(X,Y)
| unorthogonal_lines(X,Y) ) ),
inference(miniscoping,[status(esa)],[f123]) ).
fof(f125,plain,
! [X0,X1] :
( ~ orthogonal_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f124]) ).
fof(f126,plain,
! [X0,X1] :
( orthogonal_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f124]) ).
fof(f127,plain,
? [L,M,N] :
( parallel_lines(L,M)
& orthogonal_lines(L,N)
& ~ orthogonal_lines(M,N) ),
inference(pre_NNF_transformation,[status(esa)],[f37]) ).
fof(f128,plain,
? [M,N] :
( ? [L] :
( parallel_lines(L,M)
& orthogonal_lines(L,N) )
& ~ orthogonal_lines(M,N) ),
inference(miniscoping,[status(esa)],[f127]) ).
fof(f129,plain,
( parallel_lines(sk0_2,sk0_0)
& orthogonal_lines(sk0_2,sk0_1)
& ~ orthogonal_lines(sk0_0,sk0_1) ),
inference(skolemization,[status(esa)],[f128]) ).
fof(f130,plain,
parallel_lines(sk0_2,sk0_0),
inference(cnf_transformation,[status(esa)],[f129]) ).
fof(f131,plain,
orthogonal_lines(sk0_2,sk0_1),
inference(cnf_transformation,[status(esa)],[f129]) ).
fof(f132,plain,
~ orthogonal_lines(sk0_0,sk0_1),
inference(cnf_transformation,[status(esa)],[f129]) ).
fof(f133,plain,
! [L,N] :
( ~ pd0_0(N,L)
| ( convergent_lines(L,N)
& unorthogonal_lines(L,N) ) ),
inference(pre_NNF_transformation,[status(esa)],[f78]) ).
fof(f134,plain,
! [X0,X1] :
( ~ pd0_0(X0,X1)
| convergent_lines(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f133]) ).
fof(f136,plain,
! [L,M] :
( ~ pd0_1(M,L)
| ( convergent_lines(L,M)
& unorthogonal_lines(L,M) ) ),
inference(pre_NNF_transformation,[status(esa)],[f91]) ).
fof(f138,plain,
! [X0,X1] :
( ~ pd0_1(X0,X1)
| unorthogonal_lines(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f136]) ).
fof(f139,plain,
unorthogonal_lines(sk0_0,sk0_1),
inference(resolution,[status(thm)],[f126,f132]) ).
fof(f141,plain,
! [X0,X1] : convergent_lines(orthogonal_through_point(X0,X1),X0),
inference(resolution,[status(thm)],[f76,f83]) ).
fof(f142,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ orthogonal_lines(X0,X1) ),
inference(resolution,[status(thm)],[f76,f125]) ).
fof(f143,plain,
convergent_lines(sk0_2,sk0_1),
inference(resolution,[status(thm)],[f142,f131]) ).
fof(f149,plain,
! [X0,X1,X2] :
( convergent_lines(orthogonal_through_point(X0,X1),X2)
| convergent_lines(X0,X2) ),
inference(resolution,[status(thm)],[f49,f141]) ).
fof(f150,plain,
! [X0] :
( convergent_lines(sk0_2,X0)
| convergent_lines(sk0_1,X0) ),
inference(resolution,[status(thm)],[f49,f143]) ).
fof(f151,plain,
! [X0,X1] :
( convergent_lines(sk0_1,X0)
| convergent_lines(sk0_2,X1)
| convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f150,f49]) ).
fof(f155,plain,
! [X0] :
( convergent_lines(sk0_1,X0)
| convergent_lines(X0,sk0_2) ),
inference(resolution,[status(thm)],[f151,f40]) ).
fof(f165,plain,
! [X0,X1] :
( convergent_lines(X0,sk0_2)
| convergent_lines(sk0_1,X1)
| convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f155,f49]) ).
fof(f183,plain,
! [X0] :
( convergent_lines(X0,sk0_2)
| convergent_lines(X0,sk0_1) ),
inference(resolution,[status(thm)],[f165,f40]) ).
fof(f330,plain,
! [X0,X1,X2] :
( unorthogonal_lines(X0,X1)
| ~ convergent_lines(X1,X2)
| ~ orthogonal_lines(X0,X2) ),
inference(resolution,[status(thm)],[f98,f125]) ).
fof(f334,plain,
! [X0] :
( unorthogonal_lines(sk0_2,X0)
| ~ convergent_lines(X0,sk0_1) ),
inference(resolution,[status(thm)],[f330,f131]) ).
fof(f377,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1)
| unorthogonal_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(resolution,[status(thm)],[f82,f134]) ).
fof(f378,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
| ~ convergent_lines(X2,X1)
| ~ unorthogonal_lines(X2,X1)
| unorthogonal_lines(X0,X2) ),
inference(resolution,[status(thm)],[f94,f138]) ).
fof(f388,plain,
! [X0,X1,X2] :
( convergent_lines(orthogonal_through_point(X0,X1),X2)
| ~ convergent_lines(X0,X2)
| ~ unorthogonal_lines(X0,X2) ),
inference(resolution,[status(thm)],[f378,f83]) ).
fof(f389,plain,
! [X0,X1,X2] :
( convergent_lines(orthogonal_through_point(X0,X1),X2)
| ~ unorthogonal_lines(X0,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f388,f149]) ).
fof(f392,plain,
! [X0,X1] : ~ unorthogonal_lines(X0,orthogonal_through_point(X0,X1)),
inference(resolution,[status(thm)],[f389,f40]) ).
fof(f394,plain,
! [X0] : ~ convergent_lines(orthogonal_through_point(sk0_2,X0),sk0_1),
inference(resolution,[status(thm)],[f392,f334]) ).
fof(f404,plain,
~ unorthogonal_lines(sk0_2,sk0_1),
inference(resolution,[status(thm)],[f394,f389]) ).
fof(f413,plain,
! [X0] :
( convergent_lines(sk0_2,X0)
| ~ convergent_lines(sk0_1,X0)
| ~ unorthogonal_lines(sk0_1,X0) ),
inference(resolution,[status(thm)],[f404,f378]) ).
fof(f414,plain,
! [X0] :
( convergent_lines(sk0_2,X0)
| ~ unorthogonal_lines(sk0_1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f413,f150]) ).
fof(f440,plain,
~ unorthogonal_lines(sk0_1,sk0_2),
inference(resolution,[status(thm)],[f414,f40]) ).
fof(f441,plain,
! [X0] :
( ~ unorthogonal_lines(sk0_1,X0)
| ~ parallel_lines(sk0_2,X0) ),
inference(resolution,[status(thm)],[f414,f117]) ).
fof(f444,plain,
! [X0] :
( ~ convergent_lines(X0,sk0_1)
| ~ unorthogonal_lines(X0,sk0_1)
| convergent_lines(X0,sk0_2) ),
inference(resolution,[status(thm)],[f440,f377]) ).
fof(f445,plain,
! [X0] :
( ~ unorthogonal_lines(X0,sk0_1)
| convergent_lines(X0,sk0_2) ),
inference(forward_subsumption_resolution,[status(thm)],[f444,f183]) ).
fof(f449,plain,
! [X0] :
( unorthogonal_lines(sk0_1,X0)
| ~ convergent_lines(X0,sk0_2) ),
inference(resolution,[status(thm)],[f440,f98]) ).
fof(f482,plain,
~ unorthogonal_lines(sk0_1,sk0_0),
inference(resolution,[status(thm)],[f441,f130]) ).
fof(f556,plain,
~ convergent_lines(sk0_0,sk0_2),
inference(resolution,[status(thm)],[f449,f482]) ).
fof(f566,plain,
~ unorthogonal_lines(sk0_0,sk0_1),
inference(resolution,[status(thm)],[f556,f445]) ).
fof(f567,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f566,f139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO218+3 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue May 30 12:01:07 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % Drodi V3.5.1
% 0.12/0.41 % Refutation found
% 0.12/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.42 % Elapsed time: 0.082868 seconds
% 0.18/0.42 % CPU time: 0.480240 seconds
% 0.18/0.42 % Memory used: 7.724 MB
%------------------------------------------------------------------------------