%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO255+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 : n017.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 01:17:45 PM UTC 2026
% Result : Theorem 4.77s 1.37s
% Output : Proof 4.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 52 ( 18 unt; 0 def)
% Number of atoms : 118 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 104 ( 38 ~; 42 |; 19 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 81 ( 1 sgn 51 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f29,axiom,
! [A,B] :
( distinct_points(A,B)
=> equally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax9_cons_objs) ).
fof(f29_nnf,plain,
! [A,B] :
( equally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A)))
| ~ distinct_points(A,B) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [A,B] :
( equally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A)))
| ~ distinct_points(A,B) ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c59,plain,
( equally_directed_lines(line_connecting(X0,X1),reverse_line(line_connecting(X1,X0)))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
fof(f8,axiom,
! [L,A,B] :
( before_on_line(L,A,B)
<=> ( equally_directed_lines(L,line_connecting(A,B))
& incident_point_and_line(B,L)
& incident_point_and_line(A,L)
& distinct_points(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4_defns) ).
fof(f8_nnf,plain,
! [L,A,B] :
( ( ~ equally_directed_lines(L,line_connecting(A,B))
| ~ incident_point_and_line(B,L)
| ~ incident_point_and_line(A,L)
| ~ distinct_points(A,B)
| before_on_line(L,A,B) )
& ( ( equally_directed_lines(L,line_connecting(A,B))
& incident_point_and_line(B,L)
& incident_point_and_line(A,L)
& distinct_points(A,B) )
| ~ before_on_line(L,A,B) ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [L,A,B] :
( ( ~ equally_directed_lines(L,line_connecting(A,B))
| ~ incident_point_and_line(B,L)
| ~ incident_point_and_line(A,L)
| ~ distinct_points(A,B)
| before_on_line(L,A,B) )
& ( ( equally_directed_lines(L,line_connecting(A,B))
& incident_point_and_line(B,L)
& incident_point_and_line(A,L)
& distinct_points(A,B) )
| ~ before_on_line(L,A,B) ) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c22,plain,
( distinct_points(X1,X2)
| ~ before_on_line(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f36,conjecture,
! [L,A,B] :
~ ( before_on_line(L,B,A)
& before_on_line(L,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f36_neg,negated_conjecture,
~ ! [L,A,B] :
~ ( before_on_line(L,B,A)
& before_on_line(L,A,B) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f36_nnf,plain,
? [L,A,B] :
( before_on_line(L,B,A)
& before_on_line(L,A,B) ),
inference(nnf_transformation,[status(thm)],[f36_neg]) ).
fof(f36_sk,plain,
( before_on_line(sk0,sk2,sk1)
& before_on_line(sk0,sk1,sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f36_nnf]) ).
cnf(c67,plain,
before_on_line(sk0,sk2,sk1),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(p71,plain,
distinct_points(sk2,sk1),
inference(resolution,[status(thm)],[c22,c67]) ).
cnf(p290,plain,
equally_directed_lines(line_connecting(sk2,sk1),reverse_line(line_connecting(sk1,sk2))),
inference(resolution,[status(thm)],[c59,p71]) ).
fof(f3,axiom,
! [X,Y] :
( equally_directed_lines(X,Y)
<=> ~ unequally_directed_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a4_defns) ).
fof(f3_nnf,plain,
! [X,Y] :
( ( unequally_directed_lines(X,Y)
| equally_directed_lines(X,Y) )
& ( ~ unequally_directed_lines(X,Y)
| ~ equally_directed_lines(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] :
( ( unequally_directed_lines(X,Y)
| equally_directed_lines(X,Y) )
& ( ~ unequally_directed_lines(X,Y)
| ~ equally_directed_lines(X,Y) ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c6,plain,
( ~ unequally_directed_lines(X0,X1)
| ~ equally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p310,plain,
~ unequally_directed_lines(line_connecting(sk2,sk1),reverse_line(line_connecting(sk1,sk2))),
inference(resolution,[status(thm)],[p290,c6]) ).
fof(f15,axiom,
! [L,M,N] :
( unequally_directed_lines(L,M)
=> ( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6_basics) ).
fof(f15_nnf,plain,
! [L,M,N] :
( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N)
| ~ unequally_directed_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [L,M,N] :
( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N)
| ~ unequally_directed_lines(L,M) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c38,plain,
( unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2)
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(c25,plain,
( equally_directed_lines(X0,line_connecting(X1,X2))
| ~ before_on_line(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(c66,plain,
before_on_line(sk0,sk1,sk2),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(p97,plain,
equally_directed_lines(sk0,line_connecting(sk1,sk2)),
inference(resolution,[status(thm)],[c25,c66]) ).
cnf(p99,plain,
~ unequally_directed_lines(sk0,line_connecting(sk1,sk2)),
inference(resolution,[status(thm)],[p97,c6]) ).
fof(f17,axiom,
! [L,M] :
( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax8_basics) ).
fof(f17_nnf,plain,
! [L,M] :
( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [L,M] :
( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c43,plain,
( unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
fof(f0,axiom,
! [X,Y] :
( unequally_directed_opposite_lines(X,Y)
<=> unequally_directed_lines(X,reverse_line(Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1_defns) ).
fof(f0_nnf,plain,
! [X,Y] :
( ( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) )
& ( unequally_directed_lines(X,reverse_line(Y))
| ~ unequally_directed_opposite_lines(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( ( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) )
& ( unequally_directed_lines(X,reverse_line(Y))
| ~ unequally_directed_opposite_lines(X,Y) ) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c1,plain,
( ~ unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p74,plain,
( unequally_directed_opposite_lines(X0,X1)
| unequally_directed_lines(X0,X1) ),
inference(resolution,[status(thm)],[c43,c1]) ).
cnf(p103,plain,
unequally_directed_opposite_lines(sk0,line_connecting(sk1,sk2)),
inference(resolution,[status(thm)],[p99,p74]) ).
cnf(c0,plain,
( unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p105,plain,
unequally_directed_lines(sk0,reverse_line(line_connecting(sk1,sk2))),
inference(resolution,[status(thm)],[p103,c0]) ).
cnf(p167,plain,
( unequally_directed_lines(reverse_line(line_connecting(sk1,sk2)),X0)
| unequally_directed_lines(sk0,X0) ),
inference(resolution,[status(thm)],[c38,p105]) ).
cnf(p171,plain,
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(reverse_line(line_connecting(sk1,sk2)),X1)
| unequally_directed_lines(sk0,X0) ),
inference(resolution,[status(thm)],[p167,c38]) ).
fof(f14,axiom,
! [L] : equally_directed_lines(L,L),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5_basics) ).
fof(f14_nnf,plain,
! [L] : equally_directed_lines(L,L),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [L] : equally_directed_lines(L,L),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c37,plain,
equally_directed_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p68,plain,
~ unequally_directed_lines(X0,X0),
inference(resolution,[status(thm)],[c6,c37]) ).
cnf(p249,plain,
( unequally_directed_lines(X0,reverse_line(line_connecting(sk1,sk2)))
| unequally_directed_lines(sk0,X0) ),
inference(resolution,[status(thm)],[p171,p68]) ).
cnf(p335,plain,
unequally_directed_lines(sk0,line_connecting(sk2,sk1)),
inference(resolution,[status(thm)],[p310,p249]) ).
cnf(p98,plain,
equally_directed_lines(sk0,line_connecting(sk2,sk1)),
inference(resolution,[status(thm)],[c25,c67]) ).
cnf(p100,plain,
~ unequally_directed_lines(sk0,line_connecting(sk2,sk1)),
inference(resolution,[status(thm)],[p98,c6]) ).
cnf(p337,plain,
$false,
inference(resolution,[status(thm)],[p335,p100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO255+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.58 % Computer : n017.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Wed Sep 23 11:37:59 UTC 2026
% 0.10/0.58 % CPUTime :
% 0.10/0.58 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.77/1.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.77/1.37 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------