%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO193+3 : TPTP v9.3.1. Released v4.0.0.
% 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 01:17:24 PM UTC 2026
% Result : Theorem 5.01s 1.21s
% Output : Proof 5.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 17 unt; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 62 ( 24 ~; 19 |; 12 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 67 ( 6 sgn 45 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,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(f12_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)],[f12]) ).
fof(f12_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)],[f12_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)],[f12_sk]) ).
fof(f35,conjecture,
! [X,Y,Z] :
( ( convergent_lines(X,Z)
& convergent_lines(Z,Y)
& convergent_lines(X,Y) )
=> ( apart_point_and_line(intersection_point(X,Y),Z)
=> apart_point_and_line(intersection_point(Z,Y),X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f35_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( convergent_lines(X,Z)
& convergent_lines(Z,Y)
& convergent_lines(X,Y) )
=> ( apart_point_and_line(intersection_point(X,Y),Z)
=> apart_point_and_line(intersection_point(Z,Y),X) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f35_nnf,plain,
? [X,Y,Z] :
( ~ apart_point_and_line(intersection_point(Z,Y),X)
& apart_point_and_line(intersection_point(X,Y),Z)
& convergent_lines(X,Z)
& convergent_lines(Z,Y)
& convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f35_neg]) ).
fof(f35_sk,plain,
( ~ apart_point_and_line(intersection_point(sk2,sk1),sk0)
& apart_point_and_line(intersection_point(sk0,sk1),sk2)
& convergent_lines(sk0,sk2)
& convergent_lines(sk2,sk1)
& convergent_lines(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f35_nnf]) ).
cnf(c49,plain,
apart_point_and_line(intersection_point(sk0,sk1),sk2),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(p129,plain,
( apart_point_and_line(intersection_point(sk0,sk1),X0)
| distinct_lines(sk2,X0) ),
inference(resolution,[status(thm)],[c12,c49]) ).
fof(f16,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp2) ).
fof(f16_nnf,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p326,plain,
distinct_lines(sk2,parallel_through_point(X0,intersection_point(sk0,sk1))),
inference(resolution,[status(thm)],[p129,c16]) ).
fof(f14,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f14_nnf,plain,
! [X,Y] :
( convergent_lines(X,Y)
| ~ distinct_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X,Y] :
( convergent_lines(X,Y)
| ~ distinct_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p330,plain,
convergent_lines(sk2,parallel_through_point(X0,intersection_point(sk0,sk1))),
inference(resolution,[status(thm)],[p326,c14]) ).
fof(f5,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).
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(p367,plain,
( convergent_lines(parallel_through_point(X1,intersection_point(sk0,sk1)),X0)
| convergent_lines(sk2,X0) ),
inference(resolution,[status(thm)],[p330,c5]) ).
fof(f15,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp1) ).
fof(f15_nnf,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [Y,X] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p2305,plain,
convergent_lines(sk2,X0),
inference(resolution,[status(thm)],[p367,c15]) ).
fof(f2,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart3) ).
fof(f2_nnf,plain,
! [X] : ~ convergent_lines(X,X),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] : ~ convergent_lines(X,X),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p2306,plain,
$false,
inference(resolution,[status(thm)],[p2305,c2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO193+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 11:27:24 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.01/1.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.01/1.21 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------