%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : GEO202+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Jul 24 01:38:30 PM UTC 2025
% Result : Theorem 0.13s 0.41s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 14 unt; 0 def)
% Number of atoms : 75 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 70 ( 30 ~; 27 |; 5 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,plain,
! [X,Y,Z] :
( ( distinct_points(X,Y)
& distinct_points(X,Z)
& convergent_lines(line_connecting(X,Y),line_connecting(X,Z)) )
=> equal_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(con_negated,plain,
~ ! [X,Y,Z] :
( ( distinct_points(X,Y)
& distinct_points(X,Z)
& convergent_lines(line_connecting(X,Y),line_connecting(X,Z)) )
=> equal_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X) ),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(46,plain,
distinct_points(sK1,sK2),
inference(cnf,[status(esa)],[con_negated]) ).
cnf(l0,plain,
distinct_points(sK1,sK2),
inference(instantiation,[status(thm)],[46]) ).
fof(ci1,plain,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('Axioms/GEO006+0.ax',ci1) ).
cnf(6,plain,
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(cnf,[status(esa)],[ci1]) ).
cnf(l1,plain,
( ~ distinct_points(sK1,sK2)
| ~ apart_point_and_line(sK1,line_connecting(sK1,sK2)) ),
inference(instantiation,[status(thm)],[6]) ).
fof(cu1,plain,
! [X,Y,U,V] :
( ( distinct_points(X,Y)
& distinct_lines(U,V) )
=> ( apart_point_and_line(X,U)
| apart_point_and_line(X,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(Y,V) ) ),
file('Axioms/GEO006+0.ax',cu1) ).
cnf(10,plain,
( ~ distinct_points(X0,X1)
| ~ distinct_lines(X2,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3) ),
inference(cnf,[status(esa)],[cu1]) ).
cnf(l2,plain,
( ~ distinct_points(intersection_point(line_connecting(sK1,sK2),line_connecting(sK1,sK3)),sK1)
| ~ distinct_lines(line_connecting(sK1,sK3),line_connecting(sK1,sK2))
| apart_point_and_line(intersection_point(line_connecting(sK1,sK2),line_connecting(sK1,sK3)),line_connecting(sK1,sK3))
| apart_point_and_line(intersection_point(line_connecting(sK1,sK2),line_connecting(sK1,sK3)),line_connecting(sK1,sK2))
| apart_point_and_line(sK1,line_connecting(sK1,sK3))
| apart_point_and_line(sK1,line_connecting(sK1,sK2)) ),
inference(instantiation,[status(thm)],[10]) ).
fof(ceq3,plain,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( distinct_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('Axioms/GEO006+0.ax',ceq3) ).
cnf(13,plain,
( ~ convergent_lines(X0,X1)
| distinct_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf,[status(esa)],[ceq3]) ).
cnf(l4,plain,
( ~ convergent_lines(line_connecting(sK1,sK2),line_connecting(sK1,sK3))
| distinct_lines(line_connecting(sK1,sK3),line_connecting(sK1,sK2))
| convergent_lines(line_connecting(sK1,sK2),line_connecting(sK1,sK2)) ),
inference(instantiation,[status(thm)],[13]) ).
fof(apart3,plain,
! [X] : ~ convergent_lines(X,X),
file('Axioms/GEO006+0.ax',apart3) ).
cnf(2,plain,
~ convergent_lines(X0,X0),
inference(cnf,[status(esa)],[apart3]) ).
cnf(l24,plain,
~ convergent_lines(line_connecting(sK1,sK2),line_connecting(sK1,sK2)),
inference(instantiation,[status(thm)],[2]) ).
cnf(48,plain,
convergent_lines(line_connecting(sK1,sK2),line_connecting(sK1,sK3)),
inference(cnf,[status(esa)],[con_negated]) ).
cnf(l7,plain,
convergent_lines(line_connecting(sK1,sK2),line_connecting(sK1,sK3)),
inference(instantiation,[status(thm)],[48]) ).
cnf(l8,plain,
( ~ distinct_points(sK1,sK3)
| ~ apart_point_and_line(sK1,line_connecting(sK1,sK3)) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(47,plain,
distinct_points(sK1,sK3),
inference(cnf,[status(esa)],[con_negated]) ).
cnf(l14,plain,
distinct_points(sK1,sK3),
inference(instantiation,[status(thm)],[47]) ).
fof(ci4,plain,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),Y) ),
file('Axioms/GEO006+0.ax',ci4) ).
cnf(9,plain,
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf,[status(esa)],[ci4]) ).
cnf(l19,plain,
( ~ convergent_lines(line_connecting(sK1,sK2),line_connecting(sK1,sK3))
| ~ apart_point_and_line(intersection_point(line_connecting(sK1,sK2),line_connecting(sK1,sK3)),line_connecting(sK1,sK3)) ),
inference(instantiation,[status(thm)],[9]) ).
fof(ci3,plain,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ),
file('Axioms/GEO006+0.ax',ci3) ).
cnf(8,plain,
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf,[status(esa)],[ci3]) ).
cnf(l5,plain,
( ~ convergent_lines(line_connecting(sK1,sK2),line_connecting(sK1,sK3))
| ~ apart_point_and_line(intersection_point(line_connecting(sK1,sK2),line_connecting(sK1,sK3)),line_connecting(sK1,sK2)) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(l17,plain,
convergent_lines(line_connecting(sK1,sK2),line_connecting(sK1,sK3)),
inference(instantiation,[status(thm)],[48]) ).
cnf(l20,plain,
convergent_lines(line_connecting(sK1,sK2),line_connecting(sK1,sK3)),
inference(instantiation,[status(thm)],[48]) ).
fof(ax1,plain,
! [X,Y] :
( equal_points(X,Y)
<=> ~ distinct_points(X,Y) ),
file('Axioms/GEO006+6.ax',ax1) ).
cnf(37,plain,
( distinct_points(X0,X1)
| equal_points(X0,X1) ),
inference(cnf,[status(esa)],[ax1]) ).
cnf(l3,plain,
( distinct_points(intersection_point(line_connecting(sK1,sK2),line_connecting(sK1,sK3)),sK1)
| equal_points(intersection_point(line_connecting(sK1,sK2),line_connecting(sK1,sK3)),sK1) ),
inference(instantiation,[status(thm)],[37]) ).
cnf(49,plain,
~ equal_points(intersection_point(line_connecting(sK1,sK2),line_connecting(sK1,sK3)),sK1),
inference(cnf,[status(esa)],[con_negated]) ).
cnf(l10,plain,
~ equal_points(intersection_point(line_connecting(sK1,sK2),line_connecting(sK1,sK3)),sK1),
inference(instantiation,[status(thm)],[49]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l4,l24,l7,l8,l14,l19,l5,l17,l20,l3,l10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO202+3 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Jul 20 11:41:49 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % launching worker at depth: 2
% 0.13/0.35 % launching worker at depth: 8
% 0.13/0.35 % launching worker at depth: 4
% 0.13/0.35 % launching worker at depth: 6
% 0.13/0.35 % launching worker at depth: 1
% 0.13/0.35 % launching worker at depth: 5
% 0.13/0.35 % launching worker at depth: 7
% 0.13/0.35 % launching worker at depth: 3
% 0.13/0.35 % launching worker at depth: 9
% 0.13/0.36 % launching worker at depth: 10
% 0.13/0.41 % SZS status Theorem for theBenchmark
% 0.13/0.41 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------