%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO187+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 : n011.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 01:17:21 PM UTC 2026
% Result : Theorem 16.00s 2.43s
% Output : Proof 16.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 15 unt; 0 def)
% Number of atoms : 113 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 100 ( 34 ~; 42 |; 18 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 84 ( 4 sgn 53 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
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]) ).
fof(f35,conjecture,
! [X,Y,U,V] :
( ( incident_point_and_line(Y,line_connecting(U,V))
& incident_point_and_line(X,line_connecting(U,V))
& distinct_points(U,V)
& distinct_points(X,Y) )
=> ( incident_point_and_line(V,line_connecting(X,Y))
& incident_point_and_line(U,line_connecting(X,Y)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f35_neg,negated_conjecture,
~ ! [X,Y,U,V] :
( ( incident_point_and_line(Y,line_connecting(U,V))
& incident_point_and_line(X,line_connecting(U,V))
& distinct_points(U,V)
& distinct_points(X,Y) )
=> ( incident_point_and_line(V,line_connecting(X,Y))
& incident_point_and_line(U,line_connecting(X,Y)) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f35_nnf,plain,
? [X,Y,U,V] :
( ( ~ incident_point_and_line(V,line_connecting(X,Y))
| ~ incident_point_and_line(U,line_connecting(X,Y)) )
& incident_point_and_line(Y,line_connecting(U,V))
& incident_point_and_line(X,line_connecting(U,V))
& distinct_points(U,V)
& distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f35_neg]) ).
fof(f35_sk,plain,
( ( ~ incident_point_and_line(sk3,line_connecting(sk0,sk1))
| ~ incident_point_and_line(sk2,line_connecting(sk0,sk1)) )
& incident_point_and_line(sk1,line_connecting(sk2,sk3))
& incident_point_and_line(sk0,line_connecting(sk2,sk3))
& distinct_points(sk2,sk3)
& distinct_points(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3])],[f35_nnf]) ).
cnf(c50,plain,
( ~ incident_point_and_line(sk3,line_connecting(sk0,sk1))
| ~ incident_point_and_line(sk2,line_connecting(sk0,sk1)) ),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(p430,plain,
( ~ incident_point_and_line(sk3,line_connecting(sk0,sk1))
| apart_point_and_line(sk2,line_connecting(sk0,sk1)) ),
inference(resolution,[status(thm)],[c43,c50]) ).
cnf(p431,plain,
( apart_point_and_line(sk3,line_connecting(sk0,sk1))
| apart_point_and_line(sk2,line_connecting(sk0,sk1)) ),
inference(resolution,[status(thm)],[p430,c43]) ).
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/sandbox2/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]) ).
cnf(p433,plain,
( apart_point_and_line(sk3,X0)
| distinct_lines(line_connecting(sk0,sk1),X0)
| apart_point_and_line(sk2,line_connecting(sk0,sk1)) ),
inference(resolution,[status(thm)],[p431,c12]) ).
fof(f4,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(Y,Z)
| distinct_lines(X,Z) ) ),
file('/export/starexec/sandbox2/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(p652,plain,
( distinct_lines(X0,X1)
| distinct_lines(line_connecting(sk0,sk1),X1)
| apart_point_and_line(sk3,X0)
| apart_point_and_line(sk2,line_connecting(sk0,sk1)) ),
inference(resolution,[status(thm)],[p433,c4]) ).
fof(f1,axiom,
! [X] : ~ distinct_lines(X,X),
file('/export/starexec/sandbox2/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(p4238,plain,
( distinct_lines(X0,line_connecting(sk0,sk1))
| apart_point_and_line(sk3,X0)
| apart_point_and_line(sk2,line_connecting(sk0,sk1)) ),
inference(resolution,[status(thm)],[p652,c1]) ).
fof(f14,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ),
file('/export/starexec/sandbox2/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(p5354,plain,
( convergent_lines(X0,line_connecting(sk0,sk1))
| apart_point_and_line(sk3,X0)
| apart_point_and_line(sk2,line_connecting(sk0,sk1)) ),
inference(resolution,[status(thm)],[p4238,c14]) ).
fof(f15,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('/export/starexec/sandbox2/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(p5683,plain,
( apart_point_and_line(sk3,parallel_through_point(line_connecting(sk0,sk1),X0))
| apart_point_and_line(sk2,line_connecting(sk0,sk1)) ),
inference(resolution,[status(thm)],[p5354,c15]) ).
fof(f16,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
file('/export/starexec/sandbox2/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(p5696,plain,
apart_point_and_line(sk2,line_connecting(sk0,sk1)),
inference(resolution,[status(thm)],[p5683,c16]) ).
cnf(p5712,plain,
( apart_point_and_line(sk2,X0)
| distinct_lines(line_connecting(sk0,sk1),X0) ),
inference(resolution,[status(thm)],[p5696,c12]) ).
cnf(p5766,plain,
( distinct_lines(X0,X1)
| distinct_lines(line_connecting(sk0,sk1),X1)
| apart_point_and_line(sk2,X0) ),
inference(resolution,[status(thm)],[p5712,c4]) ).
cnf(p6852,plain,
( distinct_lines(X0,line_connecting(sk0,sk1))
| apart_point_and_line(sk2,X0) ),
inference(resolution,[status(thm)],[p5766,c1]) ).
cnf(p7038,plain,
( convergent_lines(X0,line_connecting(sk0,sk1))
| apart_point_and_line(sk2,X0) ),
inference(resolution,[status(thm)],[p6852,c14]) ).
cnf(p7039,plain,
apart_point_and_line(sk2,parallel_through_point(line_connecting(sk0,sk1),X0)),
inference(resolution,[status(thm)],[p7038,c15]) ).
cnf(p7050,plain,
$false,
inference(resolution,[status(thm)],[p7039,c16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO187+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n011.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 11:21:41 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 16.00/2.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.00/2.43 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------