%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : GEO187+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n021.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 01:38:24 PM UTC 2025
% Result : Theorem 0.20s 0.50s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 14
% Syntax : Number of formulae : 45 ( 19 unt; 0 def)
% Number of atoms : 100 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 97 ( 42 ~; 36 |; 10 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 68 ( 4 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,plain,
! [X,Y,U,V] :
( ( distinct_points(X,Y)
& distinct_points(U,V)
& incident_point_and_line(X,line_connecting(U,V))
& incident_point_and_line(Y,line_connecting(U,V)) )
=> ( incident_point_and_line(U,line_connecting(X,Y))
& incident_point_and_line(V,line_connecting(X,Y)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(con_negated,plain,
~ ! [X,Y,U,V] :
( ( distinct_points(X,Y)
& distinct_points(U,V)
& incident_point_and_line(X,line_connecting(U,V))
& incident_point_and_line(Y,line_connecting(U,V)) )
=> ( incident_point_and_line(U,line_connecting(X,Y))
& incident_point_and_line(V,line_connecting(X,Y)) ) ),
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(ci2,plain,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
file('Axioms/GEO006+0.ax',ci2) ).
cnf(7,plain,
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
inference(cnf,[status(esa)],[ci2]) ).
cnf(l1,plain,
( ~ distinct_points(sK1,sK2)
| ~ apart_point_and_line(sK2,line_connecting(sK1,sK2)) ),
inference(instantiation,[status(thm)],[7]) ).
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(sK1,sK2)
| ~ distinct_lines(line_connecting(sK1,sK2),parallel_through_point(orthogonal_through_point(line_connecting(sK1,sK2),sK1),sK2))
| apart_point_and_line(sK1,line_connecting(sK1,sK2))
| apart_point_and_line(sK1,parallel_through_point(orthogonal_through_point(line_connecting(sK1,sK2),sK1),sK2))
| apart_point_and_line(sK2,line_connecting(sK1,sK2))
| apart_point_and_line(sK2,parallel_through_point(orthogonal_through_point(line_connecting(sK1,sK2),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(orthogonal_through_point(line_connecting(sK1,sK2),sK1),line_connecting(sK1,sK2))
| distinct_lines(line_connecting(sK1,sK2),parallel_through_point(orthogonal_through_point(line_connecting(sK1,sK2),sK1),sK2))
| convergent_lines(orthogonal_through_point(line_connecting(sK1,sK2),sK1),parallel_through_point(orthogonal_through_point(line_connecting(sK1,sK2),sK1),sK2)) ),
inference(instantiation,[status(thm)],[13]) ).
fof(cp2,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
file('Axioms/GEO006+2.ax',cp2) ).
cnf(16,plain,
~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf,[status(esa)],[cp2]) ).
cnf(l78,plain,
~ apart_point_and_line(sK2,parallel_through_point(orthogonal_through_point(line_connecting(sK1,sK2),sK1),sK2)),
inference(instantiation,[status(thm)],[16]) ).
fof(coipo1,plain,
! [L,M] :
~ ( ~ convergent_lines(L,M)
& ~ unorthogonal_lines(L,M) ),
file('Axioms/GEO006+4.ax',coipo1) ).
cnf(26,plain,
( convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
inference(cnf,[status(esa)],[coipo1]) ).
cnf(l8,plain,
( convergent_lines(orthogonal_through_point(line_connecting(sK1,sK2),sK1),line_connecting(sK1,sK2))
| unorthogonal_lines(orthogonal_through_point(line_connecting(sK1,sK2),sK1),line_connecting(sK1,sK2)) ),
inference(instantiation,[status(thm)],[26]) ).
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(l55,plain,
( ~ distinct_points(sK1,sK2)
| ~ apart_point_and_line(sK1,line_connecting(sK1,sK2)) ),
inference(instantiation,[status(thm)],[6]) ).
fof(ooc1,plain,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('Axioms/GEO006+3.ax',ooc1) ).
cnf(23,plain,
~ unorthogonal_lines(orthogonal_through_point(X0,X1),X0),
inference(cnf,[status(esa)],[ooc1]) ).
cnf(l30,plain,
~ unorthogonal_lines(orthogonal_through_point(line_connecting(sK1,sK2),sK1),line_connecting(sK1,sK2)),
inference(instantiation,[status(thm)],[23]) ).
fof(ceq2,plain,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( distinct_lines(Y,Z)
| apart_point_and_line(X,Z) ) ),
file('Axioms/GEO006+0.ax',ceq2) ).
cnf(12,plain,
( ~ apart_point_and_line(X0,X1)
| distinct_lines(X1,X2)
| apart_point_and_line(X0,X2) ),
inference(cnf,[status(esa)],[ceq2]) ).
cnf(l5,plain,
( ~ apart_point_and_line(sK1,parallel_through_point(orthogonal_through_point(line_connecting(sK1,sK2),sK1),sK2))
| distinct_lines(parallel_through_point(orthogonal_through_point(line_connecting(sK1,sK2),sK1),sK2),orthogonal_through_point(line_connecting(sK1,sK2),sK1))
| apart_point_and_line(sK1,orthogonal_through_point(line_connecting(sK1,sK2),sK1)) ),
inference(instantiation,[status(thm)],[12]) ).
fof(ax6,plain,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| convergent_lines(Y,Z) ) ),
file('Axioms/GEO006+0.ax',ax6) ).
cnf(5,plain,
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| convergent_lines(X1,X2) ),
inference(cnf,[status(esa)],[ax6]) ).
cnf(l54,plain,
( ~ convergent_lines(orthogonal_through_point(line_connecting(sK1,sK2),sK1),parallel_through_point(orthogonal_through_point(line_connecting(sK1,sK2),sK1),sK2))
| convergent_lines(orthogonal_through_point(line_connecting(sK1,sK2),sK1),orthogonal_through_point(line_connecting(sK1,sK2),sK1))
| convergent_lines(parallel_through_point(orthogonal_through_point(line_connecting(sK1,sK2),sK1),sK2),orthogonal_through_point(line_connecting(sK1,sK2),sK1)) ),
inference(instantiation,[status(thm)],[5]) ).
fof(p1,plain,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ),
file('Axioms/GEO006+1.ax',p1) ).
cnf(14,plain,
( ~ distinct_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf,[status(esa)],[p1]) ).
cnf(l10,plain,
( ~ distinct_lines(parallel_through_point(orthogonal_through_point(line_connecting(sK1,sK2),sK1),sK2),orthogonal_through_point(line_connecting(sK1,sK2),sK1))
| convergent_lines(parallel_through_point(orthogonal_through_point(line_connecting(sK1,sK2),sK1),sK2),orthogonal_through_point(line_connecting(sK1,sK2),sK1)) ),
inference(instantiation,[status(thm)],[14]) ).
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(l67,plain,
~ convergent_lines(orthogonal_through_point(line_connecting(sK1,sK2),sK1),orthogonal_through_point(line_connecting(sK1,sK2),sK1)),
inference(instantiation,[status(thm)],[2]) ).
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(l68,plain,
~ convergent_lines(parallel_through_point(orthogonal_through_point(line_connecting(sK1,sK2),sK1),sK2),orthogonal_through_point(line_connecting(sK1,sK2),sK1)),
inference(instantiation,[status(thm)],[15]) ).
fof(ooc2,plain,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
file('Axioms/GEO006+3.ax',ooc2) ).
cnf(24,plain,
~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf,[status(esa)],[ooc2]) ).
cnf(l23,plain,
~ apart_point_and_line(sK1,orthogonal_through_point(line_connecting(sK1,sK2),sK1)),
inference(instantiation,[status(thm)],[24]) ).
cnf(l84,plain,
~ convergent_lines(parallel_through_point(orthogonal_through_point(line_connecting(sK1,sK2),sK1),sK2),orthogonal_through_point(line_connecting(sK1,sK2),sK1)),
inference(instantiation,[status(thm)],[15]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l4,l78,l8,l55,l30,l5,l54,l10,l67,l68,l23,l84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO187+3 : TPTP v9.0.0. Released v4.0.0.
% 0.10/0.13 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Computer : n021.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 11:39:49 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % launching worker at depth: 5
% 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: 4
% 0.13/0.34 % launching worker at depth: 1
% 0.13/0.34 % launching worker at depth: 3
% 0.13/0.34 % launching worker at depth: 2
% 0.13/0.34 % launching worker at depth: 8
% 0.13/0.35 % launching worker at depth: 9
% 0.13/0.35 % launching worker at depth: 10
% 0.13/0.36 % launching worker at depth: 11
% 0.20/0.50 % SZS status Theorem for theBenchmark
% 0.20/0.50 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------