%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO222+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 12:24:36 PM UTC 2026
% Result : Theorem 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 15 unt; 1 def)
% Number of atoms : 115 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 116 ( 46 ~; 50 |; 15 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 102 ( 100 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(f19,axiom,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [L,M,N] :
( ( ~ unorthogonal_lines(L,N)
& ~ unorthogonal_lines(L,M) )
=> ~ convergent_lines(M,N) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [X,Y] :
( parallel_lines(X,Y)
<=> ~ convergent_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,conjecture,
! [A,L] : parallel_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [A,L] : parallel_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)),
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(f77,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)],[f20]) ).
fof(f78,definition,
! [L,N] :
( sP0_prd(N,L)
<=> ( unorthogonal_lines(L,N)
& convergent_lines(L,N) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f79,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)],[f77,f78]) ).
fof(f80,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)],[f79]) ).
fof(f82,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)],[f80]) ).
fof(f83,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f96,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| unorthogonal_lines(L,N)
| unorthogonal_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f97,plain,
! [M,N] :
( ~ convergent_lines(M,N)
| ! [L] :
( unorthogonal_lines(L,N)
| unorthogonal_lines(L,M) ) ),
inference(miniscoping,[status(thm)],[f96]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X1,X2)
| unorthogonal_lines(X0,X2)
| unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
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(f118,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| parallel_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f127,plain,
? [A,L] : ~ parallel_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f128,plain,
~ parallel_lines(sK1_skl,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(A,sK0_skl),skolemize(L,sK1_skl)],[f127]) ).
fof(f129,plain,
~ parallel_lines(sK1_skl,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl)),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,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)],[f78]) ).
fof(f131,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)],[f130]) ).
fof(f132,plain,
! [X0,X1] :
( convergent_lines(X1,X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f144,plain,
! [X0,X1,X2] :
( parallel_lines(X0,X2)
| convergent_lines(X2,X1)
| convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f49,f118]) ).
fof(f145,plain,
! [X0] :
( convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X0)
| convergent_lines(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f144,f129]) ).
fof(f148,plain,
convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),sK1_skl),
inference(resolution,[status(thm)],[f145,f40]) ).
fof(f163,plain,
! [X0,X1] : convergent_lines(orthogonal_through_point(X0,X1),X0),
inference(resolution,[status(thm)],[f76,f83]) ).
fof(f164,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(orthogonal_through_point(X0,X1),X2) ),
inference(resolution,[status(thm)],[f163,f49]) ).
fof(f171,plain,
! [X0,X1] : convergent_lines(X0,orthogonal_through_point(X0,X1)),
inference(resolution,[status(thm)],[f164,f40]) ).
fof(f207,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X2,X0)
| unorthogonal_lines(orthogonal_through_point(X0,X1),X2) ),
inference(resolution,[status(thm)],[f98,f83]) ).
fof(f210,plain,
! [X0,X1,X2] :
( sP0_prd(X1,X0)
| ~ unorthogonal_lines(X0,orthogonal_through_point(X1,X2))
| ~ convergent_lines(X0,orthogonal_through_point(X1,X2)) ),
inference(resolution,[status(thm)],[f82,f83]) ).
fof(f226,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,orthogonal_through_point(X1,X2))
| ~ convergent_lines(X0,orthogonal_through_point(X1,X2)) ),
inference(resolution,[status(thm)],[f210,f132]) ).
fof(f248,plain,
! [X0,X1] :
( ~ unorthogonal_lines(X0,orthogonal_through_point(X0,X1))
| ~ convergent_lines(X0,orthogonal_through_point(X0,X1)) ),
inference(resolution,[status(thm)],[f226,f40]) ).
fof(f249,plain,
! [X0,X1] : ~ unorthogonal_lines(X0,orthogonal_through_point(X0,X1)),
inference(forward_subsumption_resolution,[status(thm)],[f248,f171]) ).
fof(f258,plain,
! [X0,X1,X2] : ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(X0,X1),X2),X0),
inference(resolution,[status(thm)],[f249,f207]) ).
fof(f265,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f148,f258]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO222+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n006.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 20 13:50:46 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 0.08/0.38 % Refutation found
% 0.08/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.053132 seconds
% 0.13/0.41 % CPU time: 0.192625 seconds
% 0.13/0.41 % Total memory used: 19.226 MB
% 0.13/0.41 % Net memory used: 19.008 MB
%------------------------------------------------------------------------------