%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO192+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 01:17:23 PM UTC 2026
% Result : Theorem 4.00s 6.32s
% Output : Proof 4.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 16 unt; 0 def)
% Number of atoms : 90 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 83 ( 34 ~; 33 |; 8 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 39 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq2) ).
fof(f10_nnf,plain,
! [X,Y,Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z)
| ~ apart_point_and_line(X,Y) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Y,Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z)
| ~ apart_point_and_line(X,Y) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c12,plain,
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
fof(f12,conjecture,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( apart_point_and_line(intersection_point(X,Y),Z)
=> ( distinct_lines(Y,Z)
& distinct_lines(X,Z) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f12_neg,negated_conjecture,
~ ! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( apart_point_and_line(intersection_point(X,Y),Z)
=> ( distinct_lines(Y,Z)
& distinct_lines(X,Z) ) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f12_nnf,plain,
? [X,Y,Z] :
( ( ~ distinct_lines(Y,Z)
| ~ distinct_lines(X,Z) )
& apart_point_and_line(intersection_point(X,Y),Z)
& convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f12_neg]) ).
fof(f12_sk,plain,
( ( ~ distinct_lines(sk1,sk2)
| ~ distinct_lines(sk0,sk2) )
& apart_point_and_line(intersection_point(sk0,sk1),sk2)
& convergent_lines(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f12_nnf]) ).
cnf(c15,plain,
apart_point_and_line(intersection_point(sk0,sk1),sk2),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p137,plain,
( apart_point_and_line(intersection_point(sk0,sk1),X0)
| distinct_lines(sk2,X0) ),
inference(resolution,[status(thm)],[c12,c15]) ).
fof(f7,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( ( apart_point_and_line(Z,Y)
| apart_point_and_line(Z,X) )
=> distinct_points(Z,intersection_point(X,Y)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con2) ).
fof(f7_nnf,plain,
! [X,Y,Z] :
( distinct_points(Z,intersection_point(X,Y))
| ( ~ apart_point_and_line(Z,Y)
& ~ apart_point_and_line(Z,X) )
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y,Z] :
( distinct_points(Z,intersection_point(X,Y))
| ( ~ apart_point_and_line(Z,Y)
& ~ apart_point_and_line(Z,X) )
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c9,plain,
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(c14,plain,
convergent_lines(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p74,plain,
( distinct_points(X0,intersection_point(sk0,sk1))
| ~ apart_point_and_line(X0,sk1) ),
inference(resolution,[status(thm)],[c9,c14]) ).
cnf(p139,plain,
( distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk1))
| distinct_lines(sk2,sk1) ),
inference(resolution,[status(thm)],[p137,p74]) ).
fof(f0,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).
fof(f0_nnf,plain,
! [X] : ~ distinct_points(X,X),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : ~ distinct_points(X,X),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
~ distinct_points(X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p314,plain,
distinct_lines(sk2,sk1),
inference(resolution,[status(thm)],[p139,c0]) ).
fof(f4,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(Y,Z)
| distinct_lines(X,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart5) ).
fof(f4_nnf,plain,
! [X,Y,Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z)
| ~ distinct_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y,Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z)
| ~ distinct_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p315,plain,
( distinct_lines(sk1,X0)
| distinct_lines(sk2,X0) ),
inference(resolution,[status(thm)],[p314,c4]) ).
fof(f1,axiom,
! [X] : ~ distinct_lines(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart2) ).
fof(f1_nnf,plain,
! [X] : ~ distinct_lines(X,X),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] : ~ distinct_lines(X,X),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
~ distinct_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p316,plain,
distinct_lines(sk1,sk2),
inference(resolution,[status(thm)],[p315,c1]) ).
cnf(c8,plain,
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p55,plain,
( distinct_points(X0,intersection_point(sk0,sk1))
| ~ apart_point_and_line(X0,sk0) ),
inference(resolution,[status(thm)],[c8,c14]) ).
cnf(p138,plain,
( distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk1))
| distinct_lines(sk2,sk0) ),
inference(resolution,[status(thm)],[p137,p55]) ).
cnf(p241,plain,
distinct_lines(sk2,sk0),
inference(resolution,[status(thm)],[p138,c0]) ).
cnf(p242,plain,
( distinct_lines(sk0,X0)
| distinct_lines(sk2,X0) ),
inference(resolution,[status(thm)],[p241,c4]) ).
cnf(p243,plain,
distinct_lines(sk0,sk2),
inference(resolution,[status(thm)],[p242,c1]) ).
cnf(c16,plain,
( ~ distinct_lines(sk1,sk2)
| ~ distinct_lines(sk0,sk2) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p247,plain,
~ distinct_lines(sk1,sk2),
inference(resolution,[status(thm)],[p243,c16]) ).
cnf(p330,plain,
$false,
inference(resolution,[status(thm)],[p316,p247]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO192+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/5.59 % Computer : n015.cluster.edu
% 0.12/5.59 % Model : x86_64 x86_64
% 0.12/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.59 % Memory : 8046.5625MB
% 0.12/5.59 % OS : Linux 6.8.0-71-generic
% 0.12/5.59 % CPULimit : 300
% 0.12/5.59 % WCLimit : 300
% 0.12/5.59 % DateTime : Wed Sep 23 11:27:16 UTC 2026
% 0.12/5.60 % CPUTime :
% 0.15/5.60 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.00/6.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.00/6.32 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------