%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO226+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.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 01:17:37 PM UTC 2026
% Result : Theorem 4.74s 1.10s
% Output : Proof 4.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 10 unt; 0 def)
% Number of atoms : 92 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 90 ( 36 ~; 30 |; 16 &)
% ( 1 <=>; 7 =>; 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 36 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f33,axiom,
! [X,Y] :
( incident_point_and_line(X,Y)
<=> ~ apart_point_and_line(X,Y) ),
file('/export/starexec/sandbox/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,
! [L,M] :
( ( convergent_lines(L,M)
& line(M)
& line(L) )
=> ? [X] :
( point(X)
=> ( incident_point_and_line(X,M)
& incident_point_and_line(X,L) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f35_neg,negated_conjecture,
~ ! [L,M] :
( ( convergent_lines(L,M)
& line(M)
& line(L) )
=> ? [X] :
( point(X)
=> ( incident_point_and_line(X,M)
& incident_point_and_line(X,L) ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f35_nnf,plain,
? [L,M] :
( ! [X] :
( ( ~ incident_point_and_line(X,M)
| ~ incident_point_and_line(X,L) )
& point(X) )
& convergent_lines(L,M)
& line(M)
& line(L) ),
inference(nnf_transformation,[status(thm)],[f35_neg]) ).
fof(f35_sk,plain,
! [X] :
( ( ~ incident_point_and_line(X,sk1)
| ~ incident_point_and_line(X,sk0) )
& point(X)
& convergent_lines(sk0,sk1)
& line(sk1)
& line(sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f35_nnf]) ).
cnf(c50,plain,
( ~ incident_point_and_line(X2,sk1)
| ~ incident_point_and_line(X2,sk0) ),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(p745,plain,
( ~ incident_point_and_line(X0,sk1)
| apart_point_and_line(X0,sk0) ),
inference(resolution,[status(thm)],[c43,c50]) ).
cnf(p746,plain,
( apart_point_and_line(X0,sk1)
| apart_point_and_line(X0,sk0) ),
inference(resolution,[status(thm)],[p745,c43]) ).
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]) ).
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',ax6) ).
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(c48,plain,
convergent_lines(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(p52,plain,
( convergent_lines(sk1,X0)
| convergent_lines(sk0,X0) ),
inference(resolution,[status(thm)],[c5,c48]) ).
cnf(p54,plain,
( convergent_lines(X0,X1)
| convergent_lines(sk1,X1)
| convergent_lines(sk0,X0) ),
inference(resolution,[status(thm)],[p52,c5]) ).
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(p55,plain,
( convergent_lines(X0,sk1)
| convergent_lines(sk0,X0) ),
inference(resolution,[status(thm)],[p54,c2]) ).
cnf(p61,plain,
( convergent_lines(X0,X1)
| convergent_lines(sk0,X1)
| convergent_lines(X0,sk1) ),
inference(resolution,[status(thm)],[p55,c5]) ).
cnf(p65,plain,
( convergent_lines(X0,sk0)
| convergent_lines(X0,sk1) ),
inference(resolution,[status(thm)],[p61,c2]) ).
cnf(p69,plain,
convergent_lines(sk1,sk0),
inference(resolution,[status(thm)],[p65,c2]) ).
cnf(p93,plain,
~ apart_point_and_line(intersection_point(sk1,sk0),sk1),
inference(resolution,[status(thm)],[c8,p69]) ).
cnf(p747,plain,
apart_point_and_line(intersection_point(sk1,sk0),sk0),
inference(resolution,[status(thm)],[p746,p93]) ).
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(p119,plain,
~ apart_point_and_line(intersection_point(sk1,sk0),sk0),
inference(resolution,[status(thm)],[c9,p69]) ).
cnf(p761,plain,
$false,
inference(resolution,[status(thm)],[p747,p119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO226+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 11:34:58 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.74/1.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.74/1.10 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------