%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO213+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 0.14s 10.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 59 ( 11 unt; 3 def)
% Number of atoms : 156 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 146 ( 49 ~; 70 |; 18 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 91 ( 85 !; 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(f14,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,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(f23,conjecture,
! [L,M,N] :
( unorthogonal_lines(L,M)
=> ( unorthogonal_lines(M,N)
| distinct_lines(L,N) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
~ ! [L,M,N] :
( unorthogonal_lines(L,M)
=> ( unorthogonal_lines(M,N)
| distinct_lines(L,N) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f26,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f27,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f31,plain,
! [X,Y,Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z)
| ~ distinct_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f32,plain,
! [X,Y] :
( ! [Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z) )
| ~ distinct_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f35,plain,
! [X,Y] :
( ! [Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z) )
| ~ convergent_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f36,plain,
! [X0,X1,X2] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f53,plain,
! [X,Y,Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f54,plain,
! [X,Y] :
( ! [Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z) )
| ~ convergent_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f53]) ).
fof(f55,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f61,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f62,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)],[f19]) ).
fof(f63,definition,
! [L,N] :
( sP0_prd(N,L)
<=> ( unorthogonal_lines(L,N)
& convergent_lines(L,N) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f64,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)],[f62,f63]) ).
fof(f65,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)],[f64]) ).
fof(f67,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)],[f65]) ).
fof(f73,plain,
? [L,M,N] :
( ~ unorthogonal_lines(M,N)
& ~ distinct_lines(L,N)
& unorthogonal_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f74,plain,
? [L,M] :
( ? [N] :
( ~ unorthogonal_lines(M,N)
& ~ distinct_lines(L,N) )
& unorthogonal_lines(L,M) ),
inference(miniscoping,[status(thm)],[f73]) ).
fof(f75,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)],[f74]) ).
fof(f76,plain,
unorthogonal_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f77,plain,
~ distinct_lines(sK0_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f78,plain,
~ unorthogonal_lines(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f79,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)],[f63]) ).
fof(f80,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)],[f79]) ).
fof(f81,plain,
! [X0,X1] :
( convergent_lines(X1,X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f84,plain,
convergent_lines(sK1_skl,sK2_skl),
inference(resolution,[status(thm)],[f61,f78]) ).
fof(f85,plain,
! [X0] :
( convergent_lines(sK1_skl,X0)
| distinct_lines(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f55,f84]) ).
fof(f106,plain,
! [X0,X1] :
( distinct_lines(sK2_skl,X1)
| convergent_lines(X1,X0)
| convergent_lines(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f36,f85]) ).
fof(f180,plain,
! [X0] :
( distinct_lines(sK2_skl,X0)
| convergent_lines(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f106,f27]) ).
fof(f221,definition,
( sQ13_spl
<=> convergent_lines(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f223,plain,
( sQ13_spl
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f221]) ).
fof(f231,plain,
! [X0] :
( unorthogonal_lines(sK1_skl,X0)
| sP0_prd(X0,sK0_skl)
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f67,f76]) ).
fof(f233,definition,
! [X0] :
( sQ15_spl
<=> ( unorthogonal_lines(sK1_skl,X0)
| sP0_prd(X0,sK0_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f234,plain,
! [X0] :
( ~ sQ15_spl
| unorthogonal_lines(sK1_skl,X0)
| sP0_prd(X0,sK0_skl) ),
inference(component_clause,[status(thm)],[f233]) ).
fof(f236,plain,
( sQ15_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f231,f221,f233]) ).
fof(f237,plain,
( sQ13_spl
| distinct_lines(sK2_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f223,f180]) ).
fof(f245,plain,
! [X0] :
( sQ13_spl
| distinct_lines(sK0_skl,X0)
| distinct_lines(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f237,f33]) ).
fof(f281,plain,
( ~ sQ15_spl
| sP0_prd(sK2_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f234,f78]) ).
fof(f289,plain,
( ~ sQ15_spl
| convergent_lines(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f281,f81]) ).
fof(f333,plain,
! [X0] :
( ~ sQ15_spl
| convergent_lines(sK0_skl,X0)
| distinct_lines(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f289,f55]) ).
fof(f400,plain,
( ~ sQ15_spl
| distinct_lines(sK2_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f333,f27]) ).
fof(f404,plain,
! [X0] :
( ~ sQ15_spl
| distinct_lines(sK0_skl,X0)
| distinct_lines(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f400,f33]) ).
fof(f459,plain,
( ~ sQ15_spl
| distinct_lines(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f404,f26]) ).
fof(f460,plain,
( ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f459,f77]) ).
fof(f461,plain,
~ sQ15_spl,
inference(contradiction_clause,[status(thm)],[f460]) ).
fof(f473,plain,
( sQ13_spl
| distinct_lines(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f245,f26]) ).
fof(f474,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f473,f77]) ).
fof(f475,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f474]) ).
fof(f476,plain,
$false,
inference(sat_refutation,[status(thm)],[f236,f461,f475]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO213+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/10.38 % Computer : n002.cluster.edu
% 0.08/10.38 % Model : x86_64 x86_64
% 0.08/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.38 % Memory : 8046.5625MB
% 0.08/10.38 % OS : Linux 6.8.0-71-generic
% 0.08/10.38 % CPULimit : 300
% 0.08/10.38 % WCLimit : 300
% 0.08/10.38 % DateTime : Sun Sep 20 13:33:14 UTC 2026
% 0.08/10.38 % CPUTime :
% 0.08/10.39 % Drodi V4.1.1
% 0.14/10.41 % Refutation found
% 0.14/10.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/10.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/10.43 % Elapsed time: 0.047301 seconds
% 0.14/10.43 % CPU time: 0.156700 seconds
% 0.14/10.43 % Total memory used: 17.376 MB
% 0.14/10.43 % Net memory used: 17.068 MB
%------------------------------------------------------------------------------