%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO219+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 65 ( 13 unt; 7 def)
% Number of atoms : 155 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 159 ( 69 ~; 59 |; 19 &)
% ( 7 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 74 ( 68 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X] : ~ distinct_lines(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [L,M] :
~ ( ~ unorthogonal_lines(L,M)
& ~ convergent_lines(L,M) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,conjecture,
! [L,M,N] :
( ( ~ convergent_lines(L,N)
& ~ unorthogonal_lines(L,M) )
=> ~ unorthogonal_lines(M,N) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
~ ! [L,M,N] :
( ( ~ convergent_lines(L,N)
& ~ unorthogonal_lines(L,M) )
=> ~ unorthogonal_lines(M,N) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f19,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f20,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f27,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f28,plain,
! [X,Y] :
( ! [Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z) )
| ~ convergent_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f46,plain,
! [X,Y] :
( distinct_lines(X,Y)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f49,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,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)],[f14]) ).
fof(f51,definition,
! [L,M] :
( sP0_prd(M,L)
<=> ( unorthogonal_lines(L,M)
& convergent_lines(L,M) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f52,plain,
! [L,M,N] :
( ~ unorthogonal_lines(M,N)
| ~ convergent_lines(M,N)
| ( unorthogonal_lines(L,N)
& convergent_lines(L,N) )
| sP0_prd(M,L) ),
inference(formula_renaming,[status(thm)],[f50,f51]) ).
fof(f53,plain,
! [M,N] :
( ~ unorthogonal_lines(M,N)
| ~ convergent_lines(M,N)
| ! [L] :
( ( unorthogonal_lines(L,N)
& convergent_lines(L,N) )
| sP0_prd(M,L) ) ),
inference(miniscoping,[status(thm)],[f52]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ~ unorthogonal_lines(X0,X2)
| ~ convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f59,plain,
? [L,M,N] :
( unorthogonal_lines(M,N)
& ~ convergent_lines(L,N)
& ~ unorthogonal_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f60,plain,
? [M,N] :
( unorthogonal_lines(M,N)
& ? [L] :
( ~ convergent_lines(L,N)
& ~ unorthogonal_lines(L,M) ) ),
inference(miniscoping,[status(thm)],[f59]) ).
fof(f61,plain,
( unorthogonal_lines(sK0_skl,sK1_skl)
& ~ convergent_lines(sK2_skl,sK1_skl)
& ~ unorthogonal_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)],[f60]) ).
fof(f62,plain,
~ unorthogonal_lines(sK2_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
~ convergent_lines(sK2_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f64,plain,
unorthogonal_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f65,plain,
! [L,M] :
( ( ~ unorthogonal_lines(L,M)
| ~ convergent_lines(L,M)
| sP0_prd(M,L) )
& ( ( unorthogonal_lines(L,M)
& convergent_lines(L,M) )
| ~ sP0_prd(M,L) ) ),
inference(NNF_transformation,[status(thm)],[f51]) ).
fof(f66,plain,
( ! [L,M] :
( ~ unorthogonal_lines(L,M)
| ~ convergent_lines(L,M)
| sP0_prd(M,L) )
& ! [L,M] :
( ( unorthogonal_lines(L,M)
& convergent_lines(L,M) )
| ~ sP0_prd(M,L) ) ),
inference(miniscoping,[status(thm)],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( convergent_lines(X1,X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( unorthogonal_lines(X1,X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f70,plain,
convergent_lines(sK2_skl,sK0_skl),
inference(resolution,[status(thm)],[f49,f62]) ).
fof(f71,plain,
! [X0] :
( convergent_lines(sK0_skl,X0)
| convergent_lines(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f29,f70]) ).
fof(f84,plain,
! [X0] :
( convergent_lines(sK0_skl,X0)
| distinct_lines(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f47,f71]) ).
fof(f94,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| convergent_lines(sK0_skl,X1)
| distinct_lines(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f84,f29]) ).
fof(f176,definition,
( sQ12_spl
<=> unorthogonal_lines(sK2_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f177,plain,
( ~ sQ12_spl
| unorthogonal_lines(sK2_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f176]) ).
fof(f227,plain,
( convergent_lines(sK0_skl,sK1_skl)
| distinct_lines(sK2_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f94,f63]) ).
fof(f244,definition,
( sQ16_spl
<=> distinct_lines(sK2_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f245,plain,
( ~ sQ16_spl
| distinct_lines(sK2_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f244]) ).
fof(f247,definition,
( sQ17_spl
<=> convergent_lines(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f250,plain,
( sQ17_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f227,f244,f247]) ).
fof(f251,plain,
( ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f245,f19]) ).
fof(f252,plain,
~ sQ16_spl,
inference(contradiction_clause,[status(thm)],[f251]) ).
fof(f323,plain,
( ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f177,f62]) ).
fof(f324,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f323]) ).
fof(f353,definition,
( sQ22_spl
<=> sP0_prd(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f354,plain,
( ~ sQ22_spl
| sP0_prd(sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f353]) ).
fof(f357,definition,
( sQ23_spl
<=> sP0_prd(sK2_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f358,plain,
( ~ sQ23_spl
| sP0_prd(sK2_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f357]) ).
fof(f388,plain,
( ~ sQ23_spl
| convergent_lines(sK2_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f358,f67]) ).
fof(f389,plain,
( ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f388,f20]) ).
fof(f390,plain,
~ sQ23_spl,
inference(contradiction_clause,[status(thm)],[f389]) ).
fof(f437,plain,
! [X0] :
( ~ convergent_lines(sK0_skl,sK1_skl)
| convergent_lines(X0,sK1_skl)
| sP0_prd(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f54,f64]) ).
fof(f465,definition,
! [X0] :
( sQ36_spl
<=> ( convergent_lines(X0,sK1_skl)
| sP0_prd(sK0_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f466,plain,
! [X0] :
( ~ sQ36_spl
| convergent_lines(X0,sK1_skl)
| sP0_prd(sK0_skl,X0) ),
inference(component_clause,[status(thm)],[f465]) ).
fof(f468,plain,
( ~ sQ17_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f437,f465,f247]) ).
fof(f542,plain,
( ~ sQ22_spl
| convergent_lines(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f354,f67]) ).
fof(f543,plain,
( ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f542,f63]) ).
fof(f544,plain,
~ sQ22_spl,
inference(contradiction_clause,[status(thm)],[f543]) ).
fof(f545,plain,
( ~ sQ36_spl
| sP0_prd(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f466,f63]) ).
fof(f550,plain,
( ~ sQ36_spl
| unorthogonal_lines(sK2_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f545,f68]) ).
fof(f552,plain,
( ~ sQ36_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f550,f176,f465]) ).
fof(f553,plain,
$false,
inference(sat_refutation,[status(thm)],[f250,f252,f324,f390,f468,f544,f552]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO219+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n020.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 20 13:39:47 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 0.10/0.41 % Refutation found
% 0.10/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.44 % Elapsed time: 0.042254 seconds
% 0.10/0.44 % CPU time: 0.126632 seconds
% 0.10/0.44 % Total memory used: 11.873 MB
% 0.10/0.44 % Net memory used: 11.621 MB
%------------------------------------------------------------------------------