%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO175+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 01:17:16 PM UTC 2026
% Result : Theorem 7.12s 1.44s
% Output : Proof 7.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 13 unt; 0 def)
% Number of atoms : 101 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 100 ( 37 ~; 44 |; 13 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 44 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X,Y,U,V] :
( ( distinct_lines(U,V)
& distinct_points(X,Y) )
=> ( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cu1) ).
fof(f10_nnf,plain,
! [X,Y,U,V] :
( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U)
| ~ distinct_lines(U,V)
| ~ distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Y,U,V] :
( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U)
| ~ distinct_lines(U,V)
| ~ distinct_points(X,Y) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
fof(f14,conjecture,
! [X,Y,U,V] :
( ( distinct_points(X,intersection_point(U,V))
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> ( apart_point_and_line(X,V)
| apart_point_and_line(X,U) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f14_neg,negated_conjecture,
~ ! [X,Y,U,V] :
( ( distinct_points(X,intersection_point(U,V))
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> ( apart_point_and_line(X,V)
| apart_point_and_line(X,U) ) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f14_nnf,plain,
? [X,Y,U,V] :
( ~ apart_point_and_line(X,V)
& ~ apart_point_and_line(X,U)
& distinct_points(X,intersection_point(U,V))
& convergent_lines(U,V)
& distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f14_neg]) ).
fof(f14_sk,plain,
( ~ apart_point_and_line(sk0,sk3)
& ~ apart_point_and_line(sk0,sk2)
& distinct_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])],[f14_nnf]) ).
cnf(c16,plain,
distinct_points(sk0,intersection_point(sk2,sk3)),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p38,plain,
( apart_point_and_line(intersection_point(sk2,sk3),X1)
| apart_point_and_line(intersection_point(sk2,sk3),X0)
| apart_point_and_line(sk0,X1)
| apart_point_and_line(sk0,X0)
| ~ distinct_lines(X0,X1) ),
inference(resolution,[status(thm)],[c10,c16]) ).
fof(f13,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq3) ).
fof(f13_nnf,plain,
! [X,Y,Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z)
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X,Y,Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z)
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(c15,plain,
convergent_lines(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p41,plain,
( convergent_lines(sk2,X0)
| distinct_lines(sk3,X0) ),
inference(resolution,[status(thm)],[c13,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(p43,plain,
distinct_lines(sk3,sk2),
inference(resolution,[status(thm)],[p41,c2]) ).
cnf(p127,plain,
( apart_point_and_line(intersection_point(sk2,sk3),sk2)
| apart_point_and_line(intersection_point(sk2,sk3),sk3)
| apart_point_and_line(sk0,sk2)
| apart_point_and_line(sk0,sk3) ),
inference(resolution,[status(thm)],[p38,p43]) ).
fof(f9,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),Y) ),
file('/export/starexec/sandbox/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(p32,plain,
~ apart_point_and_line(intersection_point(sk2,sk3),sk3),
inference(resolution,[status(thm)],[c9,c15]) ).
cnf(p1008,plain,
( apart_point_and_line(intersection_point(sk2,sk3),sk2)
| apart_point_and_line(sk0,sk2)
| apart_point_and_line(sk0,sk3) ),
inference(resolution,[status(thm)],[p127,p32]) ).
fof(f8,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ),
file('/export/starexec/sandbox/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(p30,plain,
~ apart_point_and_line(intersection_point(sk2,sk3),sk2),
inference(resolution,[status(thm)],[c8,c15]) ).
cnf(p1697,plain,
( apart_point_and_line(sk0,sk2)
| apart_point_and_line(sk0,sk3) ),
inference(resolution,[status(thm)],[p1008,p30]) ).
cnf(c18,plain,
~ apart_point_and_line(sk0,sk3),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p1698,plain,
apart_point_and_line(sk0,sk2),
inference(resolution,[status(thm)],[p1697,c18]) ).
cnf(c17,plain,
~ apart_point_and_line(sk0,sk2),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p1699,plain,
$false,
inference(resolution,[status(thm)],[p1698,c17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO175+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 11:22:37 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.12/1.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.12/1.44 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------