%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO206+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 01:17:29 PM UTC 2026
% Result : Theorem 4.55s 1.22s
% Output : Proof 4.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 13 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 61 ( 27 ~; 24 |; 6 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 51 ( 2 sgn 36 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,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/sandbox2/benchmark/theBenchmark.p',cup1) ).
fof(f14_nnf,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(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [Y,Z,X] :
( convergent_lines(Y,Z)
| apart_point_and_line(X,Z)
| apart_point_and_line(X,Y)
| ~ distinct_lines(Y,Z) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c16,plain,
( convergent_lines(X1,X2)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1)
| ~ distinct_lines(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
fof(f15,conjecture,
! [X,Y,Z] :
( ( ~ convergent_lines(Y,Z)
& ~ apart_point_and_line(X,Y) )
=> ~ distinct_lines(Y,parallel_through_point(Z,X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f15_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( ~ convergent_lines(Y,Z)
& ~ apart_point_and_line(X,Y) )
=> ~ distinct_lines(Y,parallel_through_point(Z,X)) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f15_nnf,plain,
? [X,Y,Z] :
( distinct_lines(Y,parallel_through_point(Z,X))
& ~ convergent_lines(Y,Z)
& ~ apart_point_and_line(X,Y) ),
inference(nnf_transformation,[status(thm)],[f15_neg]) ).
fof(f15_sk,plain,
( distinct_lines(sk1,parallel_through_point(sk2,sk0))
& ~ convergent_lines(sk1,sk2)
& ~ apart_point_and_line(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f15_nnf]) ).
cnf(c19,plain,
distinct_lines(sk1,parallel_through_point(sk2,sk0)),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p26,plain,
( convergent_lines(sk1,parallel_through_point(sk2,sk0))
| apart_point_and_line(X0,parallel_through_point(sk2,sk0))
| apart_point_and_line(X0,sk1) ),
inference(resolution,[status(thm)],[c16,c19]) ).
fof(f13,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp2) ).
fof(f13_nnf,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c15,plain,
~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p32,plain,
( convergent_lines(sk1,parallel_through_point(sk2,sk0))
| apart_point_and_line(sk0,sk1) ),
inference(resolution,[status(thm)],[p26,c15]) ).
fof(f5,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart6) ).
fof(f5_nnf,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z)
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z)
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p46,plain,
( convergent_lines(parallel_through_point(sk2,sk0),X0)
| convergent_lines(sk1,X0)
| apart_point_and_line(sk0,sk1) ),
inference(resolution,[status(thm)],[p32,c5]) ).
fof(f12,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp1) ).
fof(f12_nnf,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [Y,X] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c14,plain,
~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p76,plain,
( convergent_lines(sk1,sk2)
| apart_point_and_line(sk0,sk1) ),
inference(resolution,[status(thm)],[p46,c14]) ).
cnf(c17,plain,
~ apart_point_and_line(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p86,plain,
convergent_lines(sk1,sk2),
inference(resolution,[status(thm)],[p76,c17]) ).
cnf(c18,plain,
~ convergent_lines(sk1,sk2),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p87,plain,
$false,
inference(resolution,[status(thm)],[p86,c18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO206+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.02/0.36 % CPULimit : 300
% 0.02/0.36 % WCLimit : 300
% 0.02/0.36 % DateTime : Wed Sep 23 11:28:26 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.55/1.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.55/1.22 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------