%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : GEO195+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n032.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 01:38:28 PM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 9
% Syntax : Number of formulae : 63 ( 22 unt; 0 def)
% Number of atoms : 161 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 165 ( 67 ~; 79 |; 6 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,plain,
! [X,Y,Z] :
( ( convergent_lines(X,Y)
& convergent_lines(Z,Y)
& convergent_lines(X,Z) )
=> ( apart_point_and_line(intersection_point(X,Y),Z)
=> apart_point_and_line(intersection_point(Y,X),Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(con_negated,plain,
~ ! [X,Y,Z] :
( ( convergent_lines(X,Y)
& convergent_lines(Z,Y)
& convergent_lines(X,Z) )
=> ( apart_point_and_line(intersection_point(X,Y),Z)
=> apart_point_and_line(intersection_point(Y,X),Z) ) ),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(14,plain,
convergent_lines(sK1,sK2),
inference(cnf,[status(esa)],[con_negated]) ).
cnf(l0,plain,
convergent_lines(sK1,sK2),
inference(instantiation,[status(thm)],[14]) ).
fof(apart6,plain,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| convergent_lines(Y,Z) ) ),
file('Axioms/GEO008+0.ax',apart6) ).
cnf(5,plain,
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| convergent_lines(X1,X2) ),
inference(cnf,[status(esa)],[apart6]) ).
cnf(l1,plain,
( ~ convergent_lines(sK1,sK2)
| convergent_lines(sK1,sK1)
| convergent_lines(sK2,sK1) ),
inference(instantiation,[status(thm)],[5]) ).
fof(con2,plain,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( ( apart_point_and_line(Z,X)
| apart_point_and_line(Z,Y) )
=> distinct_points(Z,intersection_point(X,Y)) ) ),
file('Axioms/GEO008+0.ax',con2) ).
cnf(9,plain,
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(X2,X1)
| distinct_points(X2,intersection_point(X0,X1)) ),
inference(cnf,[status(esa)],[con2]) ).
cnf(l2,plain,
( ~ convergent_lines(sK1,sK1)
| ~ apart_point_and_line(intersection_point(sK1,sK2),sK1)
| distinct_points(intersection_point(sK1,sK2),intersection_point(sK1,sK1)) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(l3,plain,
( ~ convergent_lines(sK2,sK1)
| ~ apart_point_and_line(intersection_point(sK2,sK1),sK1)
| distinct_points(intersection_point(sK2,sK1),intersection_point(sK2,sK1)) ),
inference(instantiation,[status(thm)],[9]) ).
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/GEO008+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(l6,plain,
( ~ distinct_points(intersection_point(sK1,sK2),intersection_point(sK1,sK3))
| ~ distinct_lines(sK1,sK1)
| apart_point_and_line(intersection_point(sK1,sK2),sK1)
| apart_point_and_line(intersection_point(sK1,sK2),sK1)
| apart_point_and_line(intersection_point(sK1,sK3),sK1)
| apart_point_and_line(intersection_point(sK1,sK3),sK1) ),
inference(instantiation,[status(thm)],[10]) ).
fof(ceq3,plain,
! [X,Y] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ),
file('Axioms/GEO008+0.ax',ceq3) ).
cnf(13,plain,
( ~ convergent_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf,[status(esa)],[ceq3]) ).
cnf(l10,plain,
( ~ convergent_lines(sK1,sK1)
| distinct_lines(sK1,sK1) ),
inference(instantiation,[status(thm)],[13]) ).
fof(apart1,plain,
! [X] : ~ distinct_points(X,X),
file('Axioms/GEO008+0.ax',apart1) ).
cnf(0,plain,
~ distinct_points(X0,X0),
inference(cnf,[status(esa)],[apart1]) ).
cnf(l5,plain,
~ distinct_points(intersection_point(sK2,sK1),intersection_point(sK2,sK1)),
inference(instantiation,[status(thm)],[0]) ).
cnf(8,plain,
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(X2,X0)
| distinct_points(X2,intersection_point(X0,X1)) ),
inference(cnf,[status(esa)],[con2]) ).
cnf(l50,plain,
( ~ convergent_lines(sK1,sK3)
| ~ apart_point_and_line(intersection_point(sK1,sK3),sK1)
| distinct_points(intersection_point(sK1,sK3),intersection_point(sK1,sK3)) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(l7,plain,
( ~ distinct_points(intersection_point(sK1,sK2),intersection_point(sK2,sK1))
| ~ distinct_lines(sK2,sK1)
| apart_point_and_line(intersection_point(sK1,sK2),sK2)
| apart_point_and_line(intersection_point(sK1,sK2),sK1)
| apart_point_and_line(intersection_point(sK2,sK1),sK2)
| apart_point_and_line(intersection_point(sK2,sK1),sK1) ),
inference(instantiation,[status(thm)],[10]) ).
fof(ceq1,plain,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( distinct_points(X,Z)
| apart_point_and_line(Z,Y) ) ),
file('Axioms/GEO008+0.ax',ceq1) ).
cnf(11,plain,
( ~ apart_point_and_line(X0,X1)
| distinct_points(X0,X2)
| apart_point_and_line(X2,X1) ),
inference(cnf,[status(esa)],[ceq1]) ).
cnf(l41,plain,
( ~ apart_point_and_line(intersection_point(sK1,sK2),sK3)
| distinct_points(intersection_point(sK1,sK2),intersection_point(sK2,sK1))
| apart_point_and_line(intersection_point(sK2,sK1),sK3) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l39,plain,
( ~ convergent_lines(sK2,sK1)
| distinct_lines(sK2,sK1) ),
inference(instantiation,[status(thm)],[13]) ).
cnf(l61,plain,
( ~ convergent_lines(sK1,sK1)
| convergent_lines(sK1,sK3)
| convergent_lines(sK1,sK3) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l51,plain,
~ distinct_points(intersection_point(sK1,sK3),intersection_point(sK1,sK3)),
inference(instantiation,[status(thm)],[0]) ).
cnf(l47,plain,
( ~ convergent_lines(sK1,sK2)
| ~ apart_point_and_line(intersection_point(sK1,sK2),sK1)
| distinct_points(intersection_point(sK1,sK2),intersection_point(sK1,sK2)) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(l54,plain,
( ~ convergent_lines(sK1,sK3)
| ~ apart_point_and_line(intersection_point(sK1,sK3),sK1)
| distinct_points(intersection_point(sK1,sK3),intersection_point(sK1,sK3)) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(18,plain,
~ apart_point_and_line(intersection_point(sK2,sK1),sK3),
inference(cnf,[status(esa)],[con_negated]) ).
cnf(l58,plain,
~ apart_point_and_line(intersection_point(sK2,sK1),sK3),
inference(instantiation,[status(thm)],[18]) ).
cnf(l56,plain,
~ distinct_points(intersection_point(sK1,sK3),intersection_point(sK1,sK3)),
inference(instantiation,[status(thm)],[0]) ).
cnf(l23,plain,
( ~ convergent_lines(sK1,sK3)
| ~ apart_point_and_line(intersection_point(sK1,sK2),sK3)
| distinct_points(intersection_point(sK1,sK2),intersection_point(sK1,sK3)) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(l48,plain,
~ distinct_points(intersection_point(sK1,sK2),intersection_point(sK1,sK2)),
inference(instantiation,[status(thm)],[0]) ).
cnf(l40,plain,
( ~ convergent_lines(sK1,sK2)
| ~ apart_point_and_line(intersection_point(sK1,sK2),sK2)
| distinct_points(intersection_point(sK1,sK2),intersection_point(sK1,sK2)) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(l4,plain,
( ~ distinct_points(intersection_point(sK1,sK2),intersection_point(sK1,sK1))
| ~ distinct_lines(sK1,line_connecting(intersection_point(sK1,sK2),intersection_point(sK1,sK1)))
| apart_point_and_line(intersection_point(sK1,sK2),sK1)
| apart_point_and_line(intersection_point(sK1,sK2),line_connecting(intersection_point(sK1,sK2),intersection_point(sK1,sK1)))
| apart_point_and_line(intersection_point(sK1,sK1),sK1)
| apart_point_and_line(intersection_point(sK1,sK1),line_connecting(intersection_point(sK1,sK2),intersection_point(sK1,sK1))) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(16,plain,
convergent_lines(sK1,sK3),
inference(cnf,[status(esa)],[con_negated]) ).
cnf(l55,plain,
convergent_lines(sK1,sK3),
inference(instantiation,[status(thm)],[16]) ).
cnf(l82,plain,
~ distinct_points(intersection_point(sK1,sK2),intersection_point(sK1,sK2)),
inference(instantiation,[status(thm)],[0]) ).
cnf(l32,plain,
( ~ convergent_lines(sK1,sK1)
| convergent_lines(sK1,sK3)
| convergent_lines(sK1,sK3) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(17,plain,
apart_point_and_line(intersection_point(sK1,sK2),sK3),
inference(cnf,[status(esa)],[con_negated]) ).
cnf(l42,plain,
apart_point_and_line(intersection_point(sK1,sK2),sK3),
inference(instantiation,[status(thm)],[17]) ).
fof(con1,plain,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(X,Y))
=> ( distinct_points(Z,X)
& distinct_points(Z,Y) ) ) ),
file('Axioms/GEO008+0.ax',con1) ).
cnf(6,plain,
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| distinct_points(X2,X0) ),
inference(cnf,[status(esa)],[con1]) ).
cnf(l59,plain,
( ~ distinct_points(intersection_point(sK1,sK2),intersection_point(sK1,sK1))
| ~ apart_point_and_line(intersection_point(sK1,sK2),line_connecting(intersection_point(sK1,sK2),intersection_point(sK1,sK1)))
| distinct_points(intersection_point(sK1,sK2),intersection_point(sK1,sK2)) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(l69,plain,
( ~ convergent_lines(sK2,sK1)
| ~ apart_point_and_line(intersection_point(sK2,sK1),sK2)
| distinct_points(intersection_point(sK2,sK1),intersection_point(sK2,sK1)) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(l77,plain,
~ distinct_points(intersection_point(sK1,sK2),intersection_point(sK1,sK2)),
inference(instantiation,[status(thm)],[0]) ).
cnf(l33,plain,
apart_point_and_line(intersection_point(sK1,sK2),sK3),
inference(instantiation,[status(thm)],[17]) ).
cnf(l49,plain,
( ~ convergent_lines(sK1,sK1)
| ~ apart_point_and_line(intersection_point(sK1,sK1),sK1)
| distinct_points(intersection_point(sK1,sK1),intersection_point(sK1,sK1)) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(7,plain,
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| distinct_points(X2,X1) ),
inference(cnf,[status(esa)],[con1]) ).
cnf(l57,plain,
( ~ distinct_points(intersection_point(sK1,sK2),intersection_point(sK1,sK1))
| ~ apart_point_and_line(intersection_point(sK1,sK1),line_connecting(intersection_point(sK1,sK2),intersection_point(sK1,sK1)))
| distinct_points(intersection_point(sK1,sK1),intersection_point(sK1,sK1)) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l75,plain,
~ distinct_points(intersection_point(sK2,sK1),intersection_point(sK2,sK1)),
inference(instantiation,[status(thm)],[0]) ).
cnf(l14,plain,
( ~ convergent_lines(sK1,sK2)
| ~ apart_point_and_line(intersection_point(sK1,sK2),sK1)
| distinct_points(intersection_point(sK1,sK2),intersection_point(sK1,sK2)) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(l81,plain,
~ distinct_points(intersection_point(sK1,sK1),intersection_point(sK1,sK1)),
inference(instantiation,[status(thm)],[0]) ).
fof(apart5,plain,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('Axioms/GEO008+0.ax',apart5) ).
cnf(4,plain,
( ~ distinct_lines(X0,X1)
| distinct_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf,[status(esa)],[apart5]) ).
cnf(l8,plain,
( ~ distinct_lines(sK1,sK1)
| distinct_lines(sK1,line_connecting(intersection_point(sK1,sK2),intersection_point(sK1,sK1)))
| distinct_lines(sK1,line_connecting(intersection_point(sK1,sK2),intersection_point(sK1,sK1))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l65,plain,
( ~ convergent_lines(sK1,sK1)
| distinct_lines(sK1,sK1) ),
inference(instantiation,[status(thm)],[13]) ).
cnf(l16,plain,
~ distinct_points(intersection_point(sK1,sK2),intersection_point(sK1,sK2)),
inference(instantiation,[status(thm)],[0]) ).
cnf(l64,plain,
~ distinct_points(intersection_point(sK1,sK1),intersection_point(sK1,sK1)),
inference(instantiation,[status(thm)],[0]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l3,l6,l10,l5,l50,l7,l41,l39,l61,l51,l47,l54,l58,l56,l23,l48,l40,l4,l55,l82,l32,l42,l59,l69,l77,l33,l49,l57,l75,l14,l81,l8,l65,l16,l64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : GEO195+2 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.08 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.27 % Computer : n032.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 300
% 0.08/0.27 % DateTime : Sun Jul 20 11:40:49 EDT 2025
% 0.08/0.27 % CPUTime :
% 0.08/0.27 % launching worker at depth: 6
% 0.08/0.27 % launching worker at depth: 7
% 0.08/0.27 % launching worker at depth: 3
% 0.08/0.27 % launching worker at depth: 2
% 0.08/0.27 % launching worker at depth: 4
% 0.08/0.27 % launching worker at depth: 8
% 0.08/0.27 % launching worker at depth: 1
% 0.08/0.27 % launching worker at depth: 5
% 0.08/0.27 % launching worker at depth: 9
% 0.08/0.27 % launching worker at depth: 10
% 0.08/0.29 % launching worker at depth: 11
% 0.12/0.37 % SZS status Theorem for theBenchmark
% 0.12/0.37 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------