%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO209+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 : n018.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 01:17:30 PM UTC 2026
% Result : Theorem 4.30s 1.10s
% Output : Proof 4.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 8 unt; 0 def)
% Number of atoms : 67 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 73 ( 29 ~; 22 |; 18 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 38 ( 0 sgn 26 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X,Y,Z] :
( distinct_lines(Y,Z)
=> ( convergent_lines(Y,Z)
| apart_point_and_line(X,Z)
| apart_point_and_line(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cup1) ).
fof(f14_nnf,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| apart_point_and_line(X,Z)
| apart_point_and_line(X,Y)
| ~ distinct_lines(Y,Z) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [Y,Z,X] :
( convergent_lines(Y,Z)
| apart_point_and_line(X,Z)
| apart_point_and_line(X,Y)
| ~ distinct_lines(Y,Z) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c16,plain,
( convergent_lines(X1,X2)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1)
| ~ distinct_lines(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
fof(f15,conjecture,
! [A,L,M,N] :
( ( ~ convergent_lines(N,L)
& ~ convergent_lines(M,L)
& ~ apart_point_and_line(A,N)
& ~ apart_point_and_line(A,M)
& apart_point_and_line(A,L) )
=> ~ distinct_lines(M,N) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f15_neg,negated_conjecture,
~ ! [A,L,M,N] :
( ( ~ convergent_lines(N,L)
& ~ convergent_lines(M,L)
& ~ apart_point_and_line(A,N)
& ~ apart_point_and_line(A,M)
& apart_point_and_line(A,L) )
=> ~ distinct_lines(M,N) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f15_nnf,plain,
? [A,L,M,N] :
( distinct_lines(M,N)
& ~ convergent_lines(N,L)
& ~ convergent_lines(M,L)
& ~ apart_point_and_line(A,N)
& ~ apart_point_and_line(A,M)
& apart_point_and_line(A,L) ),
inference(nnf_transformation,[status(thm)],[f15_neg]) ).
fof(f15_sk,plain,
( distinct_lines(sk2,sk3)
& ~ convergent_lines(sk3,sk1)
& ~ convergent_lines(sk2,sk1)
& ~ apart_point_and_line(sk0,sk3)
& ~ apart_point_and_line(sk0,sk2)
& apart_point_and_line(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3])],[f15_nnf]) ).
cnf(c22,plain,
distinct_lines(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p76,plain,
( convergent_lines(sk2,sk3)
| apart_point_and_line(X0,sk3)
| apart_point_and_line(X0,sk2) ),
inference(resolution,[status(thm)],[c16,c22]) ).
cnf(c19,plain,
~ apart_point_and_line(sk0,sk3),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p151,plain,
( convergent_lines(sk2,sk3)
| apart_point_and_line(sk0,sk2) ),
inference(resolution,[status(thm)],[p76,c19]) ).
cnf(c18,plain,
~ apart_point_and_line(sk0,sk2),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p154,plain,
convergent_lines(sk2,sk3),
inference(resolution,[status(thm)],[p151,c18]) ).
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',apart6) ).
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(p155,plain,
( convergent_lines(sk3,X0)
| convergent_lines(sk2,X0) ),
inference(resolution,[status(thm)],[p154,c5]) ).
cnf(c21,plain,
~ convergent_lines(sk3,sk1),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p165,plain,
convergent_lines(sk2,sk1),
inference(resolution,[status(thm)],[p155,c21]) ).
cnf(c20,plain,
~ convergent_lines(sk2,sk1),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p170,plain,
$false,
inference(resolution,[status(thm)],[p165,c20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO209+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.38 % Computer : n018.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Wed Sep 23 11:32:17 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.30/1.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.30/1.10 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------