%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO209+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 12:24:31 PM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 8 unt; 2 def)
% Number of atoms : 92 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 102 ( 42 ~; 31 |; 23 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 44 ( 36 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
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(f15,axiom,
! [X,Y,Z] :
( distinct_lines(Y,Z)
=> ( convergent_lines(Y,Z)
| apart_point_and_line(X,Z)
| apart_point_and_line(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,conjecture,
! [A,L,M,N] :
( ( ~ convergent_lines(N,L)
& ~ convergent_lines(M,L)
& ~ apart_point_and_line(A,N)
& ~ apart_point_and_line(A,M)
& apart_point_and_line(A,L) )
=> ~ distinct_lines(M,N) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
~ ! [A,L,M,N] :
( ( ~ convergent_lines(N,L)
& ~ convergent_lines(M,L)
& ~ apart_point_and_line(A,N)
& ~ apart_point_and_line(A,M)
& apart_point_and_line(A,L) )
=> ~ distinct_lines(M,N) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
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(f50,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| apart_point_and_line(X,Z)
| apart_point_and_line(X,Y)
| ~ distinct_lines(Y,Z) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f51,plain,
! [Y,Z] :
( convergent_lines(Y,Z)
| ! [X] :
( apart_point_and_line(X,Z)
| apart_point_and_line(X,Y) )
| ~ distinct_lines(Y,Z) ),
inference(miniscoping,[status(thm)],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
? [A,L,M,N] :
( distinct_lines(M,N)
& ~ convergent_lines(N,L)
& ~ convergent_lines(M,L)
& ~ apart_point_and_line(A,N)
& ~ apart_point_and_line(A,M)
& apart_point_and_line(A,L) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f54,plain,
? [M,N] :
( distinct_lines(M,N)
& ? [L] :
( ~ convergent_lines(N,L)
& ~ convergent_lines(M,L)
& ? [A] :
( ~ apart_point_and_line(A,N)
& ~ apart_point_and_line(A,M)
& apart_point_and_line(A,L) ) ) ),
inference(miniscoping,[status(thm)],[f53]) ).
fof(f55,plain,
( distinct_lines(sK0_skl,sK1_skl)
& ~ convergent_lines(sK1_skl,sK2_skl)
& ~ convergent_lines(sK0_skl,sK2_skl)
& ~ apart_point_and_line(sK3_skl,sK1_skl)
& ~ apart_point_and_line(sK3_skl,sK0_skl)
& apart_point_and_line(sK3_skl,sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(M,sK0_skl),skolemize(N,sK1_skl),skolemize(L,sK2_skl),skolemize(A,sK3_skl)],[f54]) ).
fof(f57,plain,
~ apart_point_and_line(sK3_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f58,plain,
~ apart_point_and_line(sK3_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f59,plain,
~ convergent_lines(sK0_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f60,plain,
~ convergent_lines(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f61,plain,
distinct_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f68,plain,
! [X0] :
( convergent_lines(sK0_skl,sK1_skl)
| apart_point_and_line(X0,sK1_skl)
| apart_point_and_line(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f52,f61]) ).
fof(f75,definition,
! [X0] :
( sQ0_spl
<=> ( apart_point_and_line(X0,sK1_skl)
| apart_point_and_line(X0,sK0_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f76,plain,
! [X0] :
( ~ sQ0_spl
| apart_point_and_line(X0,sK1_skl)
| apart_point_and_line(X0,sK0_skl) ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f78,definition,
( sQ1_spl
<=> convergent_lines(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f79,plain,
( ~ sQ1_spl
| convergent_lines(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f81,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f68,f75,f78]) ).
fof(f82,plain,
( ~ sQ0_spl
| apart_point_and_line(sK3_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f76,f58]) ).
fof(f83,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f82,f57]) ).
fof(f84,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f83]) ).
fof(f85,plain,
! [X0] :
( ~ sQ1_spl
| convergent_lines(sK1_skl,X0)
| convergent_lines(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f79,f29]) ).
fof(f89,plain,
( ~ sQ1_spl
| convergent_lines(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f85,f60]) ).
fof(f95,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f89,f59]) ).
fof(f96,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f95]) ).
fof(f97,plain,
$false,
inference(sat_refutation,[status(thm)],[f81,f84,f96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO209+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n014.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sun Sep 20 13:24:36 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.40 % Elapsed time: 0.041480 seconds
% 0.12/0.40 % CPU time: 0.114782 seconds
% 0.12/0.40 % Total memory used: 16.715 MB
% 0.12/0.40 % Net memory used: 16.379 MB
%------------------------------------------------------------------------------