%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO218+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 12:24:34 PM UTC 2026
% Result : Theorem 0.12s 0.44s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 57 ( 12 unt; 3 def)
% Number of atoms : 148 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 150 ( 59 ~; 60 |; 22 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 86 ( 80 !; 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(Y,Z)
| convergent_lines(X,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [L,M,N] :
( ( ( ~ unorthogonal_lines(L,N)
| ~ convergent_lines(L,N) )
& ( ~ unorthogonal_lines(L,M)
| ~ convergent_lines(L,M) ) )
=> ( ~ unorthogonal_lines(M,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] :
( ( orthogonal_lines(L,N)
& parallel_lines(L,M) )
=> orthogonal_lines(M,N) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [L,M,N] :
( ( orthogonal_lines(L,N)
& parallel_lines(L,M) )
=> orthogonal_lines(M,N) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f40,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f47,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f48,plain,
! [X,Y] :
( ! [Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z) )
| ~ convergent_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f47]) ).
fof(f49,plain,
! [X0,X1,X2] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f76,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f90,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)],[f25]) ).
fof(f91,definition,
! [L,M] :
( sP1_prd(M,L)
<=> ( unorthogonal_lines(L,M)
& convergent_lines(L,M) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f92,plain,
! [L,M,N] :
( ~ unorthogonal_lines(M,N)
| ~ convergent_lines(M,N)
| ( unorthogonal_lines(L,N)
& convergent_lines(L,N) )
| sP1_prd(M,L) ),
inference(formula_renaming,[status(thm)],[f90,f91]) ).
fof(f93,plain,
! [M,N] :
( ~ unorthogonal_lines(M,N)
| ~ convergent_lines(M,N)
| ! [L] :
( ( unorthogonal_lines(L,N)
& convergent_lines(L,N) )
| sP1_prd(M,L) ) ),
inference(miniscoping,[status(thm)],[f92]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ~ unorthogonal_lines(X0,X2)
| ~ convergent_lines(X0,X2)
| unorthogonal_lines(X1,X2)
| sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f115,plain,
! [X,Y] :
( ( convergent_lines(X,Y)
| parallel_lines(X,Y) )
& ( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f33]) ).
fof(f116,plain,
( ! [X,Y] :
( convergent_lines(X,Y)
| parallel_lines(X,Y) )
& ! [X,Y] :
( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f117,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ parallel_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f123,plain,
! [X,Y] :
( ( unorthogonal_lines(X,Y)
| orthogonal_lines(X,Y) )
& ( ~ unorthogonal_lines(X,Y)
| ~ orthogonal_lines(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f35]) ).
fof(f124,plain,
( ! [X,Y] :
( unorthogonal_lines(X,Y)
| orthogonal_lines(X,Y) )
& ! [X,Y] :
( ~ unorthogonal_lines(X,Y)
| ~ orthogonal_lines(X,Y) ) ),
inference(miniscoping,[status(thm)],[f123]) ).
fof(f125,plain,
! [X0,X1] :
( ~ unorthogonal_lines(X0,X1)
| ~ orthogonal_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f126,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| orthogonal_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f127,plain,
? [L,M,N] :
( ~ orthogonal_lines(M,N)
& orthogonal_lines(L,N)
& parallel_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f128,plain,
? [M,N] :
( ~ orthogonal_lines(M,N)
& ? [L] :
( orthogonal_lines(L,N)
& parallel_lines(L,M) ) ),
inference(miniscoping,[status(thm)],[f127]) ).
fof(f129,plain,
( ~ orthogonal_lines(sK0_skl,sK1_skl)
& orthogonal_lines(sK2_skl,sK1_skl)
& parallel_lines(sK2_skl,sK0_skl) ),
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]) ).
fof(f130,plain,
parallel_lines(sK2_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f131,plain,
orthogonal_lines(sK2_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f132,plain,
~ orthogonal_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f138,plain,
! [L,M] :
( ( ~ unorthogonal_lines(L,M)
| ~ convergent_lines(L,M)
| sP1_prd(M,L) )
& ( ( unorthogonal_lines(L,M)
& convergent_lines(L,M) )
| ~ sP1_prd(M,L) ) ),
inference(NNF_transformation,[status(thm)],[f91]) ).
fof(f139,plain,
( ! [L,M] :
( ~ unorthogonal_lines(L,M)
| ~ convergent_lines(L,M)
| sP1_prd(M,L) )
& ! [L,M] :
( ( unorthogonal_lines(L,M)
& convergent_lines(L,M) )
| ~ sP1_prd(M,L) ) ),
inference(miniscoping,[status(thm)],[f138]) ).
fof(f140,plain,
! [X0,X1] :
( convergent_lines(X1,X0)
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f143,plain,
unorthogonal_lines(sK0_skl,sK1_skl),
inference(resolution,[status(thm)],[f126,f132]) ).
fof(f146,plain,
! [X0,X1] :
( ~ orthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f76,f125]) ).
fof(f150,plain,
convergent_lines(sK2_skl,sK1_skl),
inference(resolution,[status(thm)],[f146,f131]) ).
fof(f152,plain,
! [X0] :
( convergent_lines(sK1_skl,X0)
| convergent_lines(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f150,f49]) ).
fof(f157,plain,
! [X0] :
( ~ parallel_lines(sK2_skl,X0)
| convergent_lines(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f152,f117]) ).
fof(f161,plain,
convergent_lines(sK1_skl,sK0_skl),
inference(resolution,[status(thm)],[f157,f130]) ).
fof(f163,plain,
! [X0] :
( convergent_lines(sK0_skl,X0)
| convergent_lines(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f161,f49]) ).
fof(f167,plain,
convergent_lines(sK0_skl,sK1_skl),
inference(resolution,[status(thm)],[f163,f40]) ).
fof(f388,definition,
( sQ15_spl
<=> convergent_lines(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f390,plain,
( sQ15_spl
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f388]) ).
fof(f597,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f390,f167]) ).
fof(f598,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f597]) ).
fof(f698,plain,
! [X0] :
( ~ convergent_lines(sK0_skl,sK1_skl)
| unorthogonal_lines(X0,sK1_skl)
| sP1_prd(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f95,f143]) ).
fof(f701,definition,
! [X0] :
( sQ36_spl
<=> ( unorthogonal_lines(X0,sK1_skl)
| sP1_prd(sK0_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f702,plain,
! [X0] :
( ~ sQ36_spl
| unorthogonal_lines(X0,sK1_skl)
| sP1_prd(sK0_skl,X0) ),
inference(component_clause,[status(thm)],[f701]) ).
fof(f704,plain,
( ~ sQ15_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f698,f701,f388]) ).
fof(f763,plain,
! [X0] :
( ~ sQ36_spl
| ~ orthogonal_lines(X0,sK1_skl)
| sP1_prd(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f702,f125]) ).
fof(f1027,plain,
( ~ sQ36_spl
| sP1_prd(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f763,f131]) ).
fof(f1030,plain,
( ~ sQ36_spl
| convergent_lines(sK2_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f1027,f140]) ).
fof(f1088,plain,
( ~ sQ36_spl
| ~ parallel_lines(sK2_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f1030,f117]) ).
fof(f1089,plain,
( ~ sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1088,f130]) ).
fof(f1090,plain,
~ sQ36_spl,
inference(contradiction_clause,[status(thm)],[f1089]) ).
fof(f1091,plain,
$false,
inference(sat_refutation,[status(thm)],[f598,f704,f1090]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO218+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 13:37:35 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.12/0.37 % 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
% 0.12/0.47 % Elapsed time: 0.092861 seconds
% 0.12/0.47 % CPU time: 0.515263 seconds
% 0.12/0.47 % Total memory used: 22.845 MB
% 0.12/0.47 % Net memory used: 22.001 MB
%------------------------------------------------------------------------------