%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO185+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 01:17:20 PM UTC 2026
% Result : Theorem 4.96s 1.34s
% Output : Proof 4.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 8 unt; 0 def)
% Number of atoms : 93 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 95 ( 40 ~; 32 |; 16 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 41 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(Z,Y)
| distinct_points(X,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq1) ).
fof(f11_nnf,plain,
! [X,Y,Z] :
( apart_point_and_line(Z,Y)
| distinct_points(X,Z)
| ~ apart_point_and_line(X,Y) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y,Z] :
( apart_point_and_line(Z,Y)
| distinct_points(X,Z)
| ~ apart_point_and_line(X,Y) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( apart_point_and_line(X2,X1)
| distinct_points(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
fof(f35,conjecture,
! [X,Y,U,V] :
( ( equal_points(X,intersection_point(U,V))
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> ( incident_point_and_line(X,V)
& incident_point_and_line(X,U) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f35_neg,negated_conjecture,
~ ! [X,Y,U,V] :
( ( equal_points(X,intersection_point(U,V))
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> ( incident_point_and_line(X,V)
& incident_point_and_line(X,U) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f35_nnf,plain,
? [X,Y,U,V] :
( ( ~ incident_point_and_line(X,V)
| ~ incident_point_and_line(X,U) )
& equal_points(X,intersection_point(U,V))
& convergent_lines(U,V)
& distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f35_neg]) ).
fof(f35_sk,plain,
( ( ~ incident_point_and_line(sk0,sk3)
| ~ incident_point_and_line(sk0,sk2) )
& equal_points(sk0,intersection_point(sk2,sk3))
& convergent_lines(sk2,sk3)
& distinct_points(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3])],[f35_nnf]) ).
cnf(c49,plain,
( ~ incident_point_and_line(sk0,sk3)
| ~ incident_point_and_line(sk0,sk2) ),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
fof(f33,axiom,
! [X,Y] :
( incident_point_and_line(X,Y)
<=> ~ apart_point_and_line(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a4) ).
fof(f33_nnf,plain,
! [X,Y] :
( ( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) )
& ( ~ apart_point_and_line(X,Y)
| ~ incident_point_and_line(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
! [X,Y] :
( ( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) )
& ( ~ apart_point_and_line(X,Y)
| ~ incident_point_and_line(X,Y) ) ),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c43,plain,
( apart_point_and_line(X0,X1)
| incident_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(p61,plain,
( apart_point_and_line(sk0,sk2)
| ~ incident_point_and_line(sk0,sk3) ),
inference(resolution,[status(thm)],[c49,c43]) ).
cnf(p70,plain,
( apart_point_and_line(sk0,sk3)
| apart_point_and_line(sk0,sk2) ),
inference(resolution,[status(thm)],[p61,c43]) ).
cnf(p75,plain,
( apart_point_and_line(sk0,sk2)
| apart_point_and_line(X0,sk3)
| distinct_points(sk0,X0) ),
inference(resolution,[status(thm)],[c11,p70]) ).
fof(f9,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci4) ).
fof(f9_nnf,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(c47,plain,
convergent_lines(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(p59,plain,
~ apart_point_and_line(intersection_point(sk2,sk3),sk3),
inference(resolution,[status(thm)],[c9,c47]) ).
cnf(p292,plain,
( apart_point_and_line(sk0,sk2)
| distinct_points(sk0,intersection_point(sk2,sk3)) ),
inference(resolution,[status(thm)],[p75,p59]) ).
fof(f30,axiom,
! [X,Y] :
( equal_points(X,Y)
<=> ~ distinct_points(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
fof(f30_nnf,plain,
! [X,Y] :
( ( distinct_points(X,Y)
| equal_points(X,Y) )
& ( ~ distinct_points(X,Y)
| ~ equal_points(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [X,Y] :
( ( distinct_points(X,Y)
| equal_points(X,Y) )
& ( ~ distinct_points(X,Y)
| ~ equal_points(X,Y) ) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c36,plain,
( ~ distinct_points(X0,X1)
| ~ equal_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(c48,plain,
equal_points(sk0,intersection_point(sk2,sk3)),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(p54,plain,
~ distinct_points(sk0,intersection_point(sk2,sk3)),
inference(resolution,[status(thm)],[c36,c48]) ).
cnf(p310,plain,
apart_point_and_line(sk0,sk2),
inference(resolution,[status(thm)],[p292,p54]) ).
cnf(p311,plain,
( apart_point_and_line(X0,sk2)
| distinct_points(sk0,X0) ),
inference(resolution,[status(thm)],[p310,c11]) ).
fof(f8,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci3) ).
fof(f8_nnf,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p57,plain,
~ apart_point_and_line(intersection_point(sk2,sk3),sk2),
inference(resolution,[status(thm)],[c8,c47]) ).
cnf(p313,plain,
distinct_points(sk0,intersection_point(sk2,sk3)),
inference(resolution,[status(thm)],[p311,p57]) ).
cnf(p325,plain,
$false,
inference(resolution,[status(thm)],[p313,p54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO185+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n019.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Wed Sep 23 11:20:49 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.96/1.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.96/1.34 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------