%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO223+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 : n018.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 0.12s 0.44s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 55 ( 19 unt; 1 def)
% Number of atoms : 131 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 126 ( 50 ~; 55 |; 15 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 115 ( 113 !; 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(f15,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
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(f32,axiom,
! [X,Y] :
( equal_lines(X,Y)
<=> ~ distinct_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,conjecture,
! [A,L] : equal_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [A,L] : equal_lines(parallel_through_point(L,A),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(f69,plain,
! [X,Y] :
( convergent_lines(X,Y)
| ~ distinct_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f70,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f71,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f16]) ).
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(f111,plain,
! [X,Y] :
( ( distinct_lines(X,Y)
| equal_lines(X,Y) )
& ( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f32]) ).
fof(f112,plain,
( ! [X,Y] :
( distinct_lines(X,Y)
| equal_lines(X,Y) )
& ! [X,Y] :
( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) ) ),
inference(miniscoping,[status(thm)],[f111]) ).
fof(f114,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| equal_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f127,plain,
? [A,L] : ~ equal_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f128,plain,
~ equal_lines(parallel_through_point(sK1_skl,sK0_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,
~ equal_lines(parallel_through_point(sK1_skl,sK0_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(f142,plain,
! [X0,X1] :
( equal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f70,f114]) ).
fof(f143,plain,
convergent_lines(parallel_through_point(sK1_skl,sK0_skl),orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl)),
inference(resolution,[status(thm)],[f142,f129]) ).
fof(f146,plain,
! [X0] :
( convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X0)
| convergent_lines(parallel_through_point(sK1_skl,sK0_skl),X0) ),
inference(resolution,[status(thm)],[f143,f49]) ).
fof(f147,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X1)
| convergent_lines(parallel_through_point(sK1_skl,sK0_skl),X0) ),
inference(resolution,[status(thm)],[f146,f49]) ).
fof(f150,plain,
! [X0] :
( convergent_lines(X0,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))
| convergent_lines(parallel_through_point(sK1_skl,sK0_skl),X0) ),
inference(resolution,[status(thm)],[f147,f40]) ).
fof(f153,plain,
convergent_lines(sK1_skl,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl)),
inference(resolution,[status(thm)],[f150,f71]) ).
fof(f156,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)],[f153,f49]) ).
fof(f158,plain,
convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),sK1_skl),
inference(resolution,[status(thm)],[f156,f40]) ).
fof(f165,plain,
! [X0,X1] : convergent_lines(orthogonal_through_point(X0,X1),X0),
inference(resolution,[status(thm)],[f76,f83]) ).
fof(f166,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(orthogonal_through_point(X0,X1),X2) ),
inference(resolution,[status(thm)],[f165,f49]) ).
fof(f175,plain,
! [X0,X1] : convergent_lines(X0,orthogonal_through_point(X0,X1)),
inference(resolution,[status(thm)],[f166,f40]) ).
fof(f214,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X2,X0)
| unorthogonal_lines(orthogonal_through_point(X0,X1),X2) ),
inference(resolution,[status(thm)],[f98,f83]) ).
fof(f217,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(f233,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)],[f217,f132]) ).
fof(f259,plain,
! [X0,X1] :
( ~ unorthogonal_lines(X0,orthogonal_through_point(X0,X1))
| ~ convergent_lines(X0,orthogonal_through_point(X0,X1)) ),
inference(resolution,[status(thm)],[f233,f40]) ).
fof(f260,plain,
! [X0,X1] : ~ unorthogonal_lines(X0,orthogonal_through_point(X0,X1)),
inference(forward_subsumption_resolution,[status(thm)],[f259,f175]) ).
fof(f261,plain,
! [X0,X1,X2] : ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(X0,X1),X2),X0),
inference(resolution,[status(thm)],[f260,f214]) ).
fof(f269,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f158,f261]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO223+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 13:51:43 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % 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
% 0.12/0.45 % Elapsed time: 0.090702 seconds
% 0.12/0.45 % CPU time: 0.550787 seconds
% 0.12/0.45 % Total memory used: 25.603 MB
% 0.12/0.45 % Net memory used: 24.272 MB
%------------------------------------------------------------------------------