%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : GEO172+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 : n031.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 01:38:19 PM UTC 2025
% Result : Theorem 0.19s 0.46s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of formulae : 42 ( 13 unt; 0 def)
% Number of atoms : 101 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 107 ( 48 ~; 42 |; 7 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 58 ( 3 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,plain,
! [X,Y,Z] :
( ( convergent_lines(X,Y)
& incident_point_and_line(Z,X)
& incident_point_and_line(Z,Y) )
=> equal_points(Z,intersection_point(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(con_negated,plain,
~ ! [X,Y,Z] :
( ( convergent_lines(X,Y)
& incident_point_and_line(Z,X)
& incident_point_and_line(Z,Y) )
=> equal_points(Z,intersection_point(X,Y)) ),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(46,plain,
convergent_lines(sK1,sK2),
inference(cnf,[status(esa)],[con_negated]) ).
cnf(l0,plain,
convergent_lines(sK1,sK2),
inference(instantiation,[status(thm)],[46]) ).
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(l1,plain,
( ~ convergent_lines(sK1,sK2)
| distinct_lines(sK2,sK1)
| convergent_lines(sK1,sK1) ),
inference(instantiation,[status(thm)],[13]) ).
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(l3,plain,
( ~ distinct_points(sK3,intersection_point(sK1,sK2))
| ~ distinct_lines(sK2,sK1)
| apart_point_and_line(sK3,sK2)
| apart_point_and_line(sK3,sK1)
| apart_point_and_line(intersection_point(sK1,sK2),sK2)
| apart_point_and_line(intersection_point(sK1,sK2),sK1) ),
inference(instantiation,[status(thm)],[10]) ).
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(l44,plain,
( ~ convergent_lines(sK1,sK2)
| ~ apart_point_and_line(intersection_point(sK1,sK2),sK2) ),
inference(instantiation,[status(thm)],[9]) ).
fof(a4,plain,
! [X,Y] :
( incident_point_and_line(X,Y)
<=> ~ apart_point_and_line(X,Y) ),
file('Axioms/GEO006+6.ax',a4) ).
cnf(42,plain,
( ~ apart_point_and_line(X0,X1)
| ~ incident_point_and_line(X0,X1) ),
inference(cnf,[status(esa)],[a4]) ).
cnf(l9,plain,
( ~ apart_point_and_line(sK3,sK2)
| ~ incident_point_and_line(sK3,sK2) ),
inference(instantiation,[status(thm)],[42]) ).
cnf(48,plain,
incident_point_and_line(sK3,sK2),
inference(cnf,[status(esa)],[con_negated]) ).
cnf(l49,plain,
incident_point_and_line(sK3,sK2),
inference(instantiation,[status(thm)],[48]) ).
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(l46,plain,
( ~ convergent_lines(sK1,sK2)
| ~ apart_point_and_line(intersection_point(sK1,sK2),sK1) ),
inference(instantiation,[status(thm)],[8]) ).
fof(cotno1,plain,
! [L,M,N] :
( ( ( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M) )
& ( ~ convergent_lines(L,N)
| ~ unorthogonal_lines(L,N) ) )
=> ( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N) ) ),
file('Axioms/GEO006+4.ax',cotno1) ).
cnf(27,plain,
( ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1)
| convergent_lines(X2,X0)
| sP1(X2,X1) ),
inference(cnf,[status(esa)],[cotno1]) ).
cnf(l7,plain,
( ~ convergent_lines(sK1,sK1)
| ~ unorthogonal_lines(sK1,sK1)
| convergent_lines(parallel_through_point(sK1,X1_19),sK1)
| sP1(parallel_through_point(sK1,X1_19),sK1) ),
inference(instantiation,[status(thm)],[27]) ).
fof(cp1,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('Axioms/GEO006+2.ax',cp1) ).
cnf(15,plain,
~ convergent_lines(parallel_through_point(X0,X1),X0),
inference(cnf,[status(esa)],[cp1]) ).
cnf(l12,plain,
~ convergent_lines(parallel_through_point(sK1,X1_19),sK1),
inference(instantiation,[status(thm)],[15]) ).
cnf(30,plain,
( convergent_lines(X0,X1)
| ~ sP1(X0,X1) ),
inference(cnf,[status(esa)],[cotno1]) ).
cnf(l10,plain,
( convergent_lines(parallel_through_point(sK1,X1_19),sK1)
| ~ sP1(parallel_through_point(sK1,X1_19),sK1) ),
inference(instantiation,[status(thm)],[30]) ).
cnf(l19,plain,
~ convergent_lines(parallel_through_point(sK1,X1_19),sK1),
inference(instantiation,[status(thm)],[15]) ).
fof(couo1,plain,
! [L,M,N] :
( ( ~ unorthogonal_lines(L,M)
& ~ unorthogonal_lines(L,N) )
=> ~ convergent_lines(M,N) ),
file('Axioms/GEO006+4.ax',couo1) ).
cnf(31,plain,
( ~ convergent_lines(X0,X1)
| unorthogonal_lines(X2,X0)
| unorthogonal_lines(X2,X1) ),
inference(cnf,[status(esa)],[couo1]) ).
cnf(l35,plain,
( ~ convergent_lines(sK1,sK1)
| unorthogonal_lines(sK1,sK1)
| unorthogonal_lines(sK1,sK1) ),
inference(instantiation,[status(thm)],[31]) ).
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(l6,plain,
( distinct_points(sK3,intersection_point(sK1,sK2))
| equal_points(sK3,intersection_point(sK1,sK2)) ),
inference(instantiation,[status(thm)],[37]) ).
cnf(49,plain,
~ equal_points(sK3,intersection_point(sK1,sK2)),
inference(cnf,[status(esa)],[con_negated]) ).
cnf(l30,plain,
~ equal_points(sK3,intersection_point(sK1,sK2)),
inference(instantiation,[status(thm)],[49]) ).
cnf(l36,plain,
( ~ apart_point_and_line(sK3,sK1)
| ~ incident_point_and_line(sK3,sK1) ),
inference(instantiation,[status(thm)],[42]) ).
cnf(47,plain,
incident_point_and_line(sK3,sK1),
inference(cnf,[status(esa)],[con_negated]) ).
cnf(l47,plain,
incident_point_and_line(sK3,sK1),
inference(instantiation,[status(thm)],[47]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l3,l44,l9,l49,l46,l7,l12,l10,l19,l35,l6,l30,l36,l47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO172+3 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.33 % Computer : n031.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Jul 20 11:36:49 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % launching worker at depth: 1
% 0.13/0.34 % launching worker at depth: 5
% 0.13/0.34 % launching worker at depth: 2
% 0.13/0.34 % launching worker at depth: 4
% 0.13/0.34 % launching worker at depth: 3
% 0.13/0.34 % launching worker at depth: 6
% 0.13/0.34 % launching worker at depth: 7
% 0.13/0.34 % launching worker at depth: 8
% 0.13/0.34 % launching worker at depth: 9
% 0.13/0.34 % launching worker at depth: 10
% 0.13/0.36 % launching worker at depth: 11
% 0.19/0.46 % SZS status Theorem for theBenchmark
% 0.19/0.46 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------