%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO213+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 12:24:32 PM UTC 2026
% Result : Theorem 0.12s 0.44s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 62 ( 12 unt; 5 def)
% Number of atoms : 157 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 148 ( 53 ~; 66 |; 18 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 83 ( 77 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X] : ~ distinct_lines(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(Y,Z)
| distinct_lines(X,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [L,M,N] :
( ( unorthogonal_lines(L,M)
& convergent_lines(L,M) )
=> ( ( unorthogonal_lines(M,N)
& convergent_lines(M,N) )
| ( unorthogonal_lines(L,N)
& convergent_lines(L,N) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,conjecture,
! [L,M,N] :
( unorthogonal_lines(L,M)
=> ( unorthogonal_lines(M,N)
| distinct_lines(L,N) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
~ ! [L,M,N] :
( unorthogonal_lines(L,M)
=> ( unorthogonal_lines(M,N)
| distinct_lines(L,N) ) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f24,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f25,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f29,plain,
! [X,Y,Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z)
| ~ distinct_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f30,plain,
! [X,Y] :
( ! [Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z) )
| ~ distinct_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f33,plain,
! [X,Y] :
( ! [Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z) )
| ~ convergent_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f32]) ).
fof(f34,plain,
! [X0,X1,X2] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f51,plain,
! [X,Y] :
( distinct_lines(X,Y)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f52,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f58,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f59,plain,
! [L,M,N] :
( ( unorthogonal_lines(M,N)
& convergent_lines(M,N) )
| ( unorthogonal_lines(L,N)
& convergent_lines(L,N) )
| ~ unorthogonal_lines(L,M)
| ~ convergent_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f60,definition,
! [L,N] :
( sP0_prd(N,L)
<=> ( unorthogonal_lines(L,N)
& convergent_lines(L,N) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f61,plain,
! [L,M,N] :
( ( unorthogonal_lines(M,N)
& convergent_lines(M,N) )
| sP0_prd(N,L)
| ~ unorthogonal_lines(L,M)
| ~ convergent_lines(L,M) ),
inference(formula_renaming,[status(thm)],[f59,f60]) ).
fof(f62,plain,
! [L,M] :
( ! [N] :
( ( unorthogonal_lines(M,N)
& convergent_lines(M,N) )
| sP0_prd(N,L) )
| ~ unorthogonal_lines(L,M)
| ~ convergent_lines(L,M) ),
inference(miniscoping,[status(thm)],[f61]) ).
fof(f64,plain,
! [X0,X1,X2] :
( unorthogonal_lines(X1,X2)
| sP0_prd(X2,X0)
| ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f70,plain,
? [L,M,N] :
( ~ unorthogonal_lines(M,N)
& ~ distinct_lines(L,N)
& unorthogonal_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f71,plain,
? [L,M] :
( ? [N] :
( ~ unorthogonal_lines(M,N)
& ~ distinct_lines(L,N) )
& unorthogonal_lines(L,M) ),
inference(miniscoping,[status(thm)],[f70]) ).
fof(f72,plain,
( ~ unorthogonal_lines(sK1_skl,sK2_skl)
& ~ distinct_lines(sK0_skl,sK2_skl)
& unorthogonal_lines(sK0_skl,sK1_skl) ),
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)],[f71]) ).
fof(f73,plain,
unorthogonal_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f74,plain,
~ distinct_lines(sK0_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f75,plain,
~ unorthogonal_lines(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f76,plain,
! [L,N] :
( ( ~ unorthogonal_lines(L,N)
| ~ convergent_lines(L,N)
| sP0_prd(N,L) )
& ( ( unorthogonal_lines(L,N)
& convergent_lines(L,N) )
| ~ sP0_prd(N,L) ) ),
inference(NNF_transformation,[status(thm)],[f60]) ).
fof(f77,plain,
( ! [L,N] :
( ~ unorthogonal_lines(L,N)
| ~ convergent_lines(L,N)
| sP0_prd(N,L) )
& ! [L,N] :
( ( unorthogonal_lines(L,N)
& convergent_lines(L,N) )
| ~ sP0_prd(N,L) ) ),
inference(miniscoping,[status(thm)],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( convergent_lines(X1,X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f81,plain,
convergent_lines(sK1_skl,sK2_skl),
inference(resolution,[status(thm)],[f58,f75]) ).
fof(f90,plain,
! [X0] :
( convergent_lines(sK2_skl,X0)
| convergent_lines(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f34,f81]) ).
fof(f93,plain,
! [X0] :
( distinct_lines(sK2_skl,X0)
| convergent_lines(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f90,f52]) ).
fof(f94,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| convergent_lines(sK1_skl,X1)
| distinct_lines(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f93,f34]) ).
fof(f207,definition,
( sQ11_spl
<=> convergent_lines(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f209,plain,
( sQ11_spl
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f207]) ).
fof(f257,definition,
( sQ15_spl
<=> convergent_lines(sK1_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f258,plain,
( ~ sQ15_spl
| convergent_lines(sK1_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f257]) ).
fof(f367,plain,
! [X0] :
( unorthogonal_lines(sK1_skl,X0)
| sP0_prd(X0,sK0_skl)
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f64,f73]) ).
fof(f369,definition,
! [X0] :
( sQ25_spl
<=> ( unorthogonal_lines(sK1_skl,X0)
| sP0_prd(X0,sK0_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f370,plain,
! [X0] :
( ~ sQ25_spl
| unorthogonal_lines(sK1_skl,X0)
| sP0_prd(X0,sK0_skl) ),
inference(component_clause,[status(thm)],[f369]) ).
fof(f372,plain,
( sQ25_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f367,f207,f369]) ).
fof(f391,plain,
( sQ11_spl
| convergent_lines(sK1_skl,sK1_skl)
| distinct_lines(sK2_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f209,f94]) ).
fof(f395,definition,
( sQ28_spl
<=> distinct_lines(sK2_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f396,plain,
( ~ sQ28_spl
| distinct_lines(sK2_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f395]) ).
fof(f398,plain,
( sQ11_spl
| sQ15_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f391,f395,f257,f207]) ).
fof(f400,plain,
( ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f258,f25]) ).
fof(f401,plain,
~ sQ15_spl,
inference(contradiction_clause,[status(thm)],[f400]) ).
fof(f411,plain,
! [X0] :
( ~ sQ28_spl
| distinct_lines(sK0_skl,X0)
| distinct_lines(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f396,f31]) ).
fof(f436,plain,
( ~ sQ25_spl
| sP0_prd(sK2_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f370,f75]) ).
fof(f456,plain,
( ~ sQ25_spl
| convergent_lines(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f436,f78]) ).
fof(f476,plain,
( ~ sQ25_spl
| distinct_lines(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f456,f52]) ).
fof(f477,plain,
( ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f476,f74]) ).
fof(f478,plain,
~ sQ25_spl,
inference(contradiction_clause,[status(thm)],[f477]) ).
fof(f554,plain,
( ~ sQ28_spl
| distinct_lines(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f411,f24]) ).
fof(f555,plain,
( ~ sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f554,f74]) ).
fof(f556,plain,
~ sQ28_spl,
inference(contradiction_clause,[status(thm)],[f555]) ).
fof(f557,plain,
$false,
inference(sat_refutation,[status(thm)],[f372,f398,f401,f478,f556]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO213+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n026.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 20 13:36:37 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.40 % Drodi V4.1.1
% 0.12/0.44 % Refutation found
% 0.12/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.46 % Elapsed time: 0.064637 seconds
% 0.12/0.46 % CPU time: 0.226318 seconds
% 0.12/0.46 % Total memory used: 18.917 MB
% 0.12/0.46 % Net memory used: 18.480 MB
%------------------------------------------------------------------------------