%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : GEO212+1 : 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 : n018.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 01:38:34 PM UTC 2025
% Result : Theorem 2.44s 0.63s
% Output : CNFRefutation 2.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of formulae : 50 ( 18 unt; 0 def)
% Number of atoms : 113 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 110 ( 47 ~; 52 |; 3 &)
% ( 0 <=>; 8 =>; 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 : 67 ( 3 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,plain,
! [L,M,N] :
( unorthogonal_lines(L,M)
=> ( convergent_lines(L,N)
| unorthogonal_lines(M,N) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(con_negated,plain,
~ ! [L,M,N] :
( unorthogonal_lines(L,M)
=> ( convergent_lines(L,N)
| unorthogonal_lines(M,N) ) ),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(25,plain,
unorthogonal_lines(sK1,sK2),
inference(cnf,[status(esa)],[con_negated]) ).
cnf(l0,plain,
unorthogonal_lines(sK1,sK2),
inference(instantiation,[status(thm)],[25]) ).
fof(oac1,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+3.ax',oac1) ).
cnf(18,plain,
( ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1)
| convergent_lines(X0,X2)
| sP0(X1,X2) ),
inference(cnf,[status(esa)],[oac1]) ).
cnf(l1,plain,
( ~ convergent_lines(sK1,sK2)
| ~ unorthogonal_lines(sK1,sK2)
| convergent_lines(sK1,sK1)
| sP0(sK2,sK1) ),
inference(instantiation,[status(thm)],[18]) ).
cnf(21,plain,
( convergent_lines(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf,[status(esa)],[oac1]) ).
cnf(l4,plain,
( convergent_lines(sK2,sK1)
| ~ sP0(sK2,sK1) ),
inference(instantiation,[status(thm)],[21]) ).
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(l2,plain,
( ~ convergent_lines(orthogonal_through_point(sK3,X1_74),sK1)
| convergent_lines(orthogonal_through_point(sK3,X1_74),sK2)
| convergent_lines(sK1,sK2) ),
inference(instantiation,[status(thm)],[5]) ).
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(l3,plain,
~ convergent_lines(sK1,sK1),
inference(instantiation,[status(thm)],[2]) ).
cnf(l8,plain,
( ~ convergent_lines(orthogonal_through_point(sK3,X1_74),sK3)
| convergent_lines(orthogonal_through_point(sK3,X1_74),sK1)
| convergent_lines(sK3,sK1) ),
inference(instantiation,[status(thm)],[5]) ).
fof(occu1,plain,
! [L,M] :
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
file('Axioms/GEO006+3.ax',occu1) ).
cnf(17,plain,
( convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
inference(cnf,[status(esa)],[occu1]) ).
cnf(l11,plain,
( convergent_lines(orthogonal_through_point(sK3,X1_74),sK3)
| unorthogonal_lines(orthogonal_through_point(sK3,X1_74),sK3) ),
inference(instantiation,[status(thm)],[17]) ).
fof(ooc1,plain,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('Axioms/GEO006+3.ax',ooc1) ).
cnf(22,plain,
~ unorthogonal_lines(orthogonal_through_point(X0,X1),X0),
inference(cnf,[status(esa)],[ooc1]) ).
cnf(l36,plain,
~ unorthogonal_lines(orthogonal_through_point(sK3,X1_74),sK3),
inference(instantiation,[status(thm)],[22]) ).
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(l62,plain,
( ~ convergent_lines(orthogonal_through_point(sK3,X1_74),sK2)
| distinct_lines(sK2,orthogonal_through_point(sK3,X1_74))
| convergent_lines(orthogonal_through_point(sK3,X1_74),orthogonal_through_point(sK3,X1_74)) ),
inference(instantiation,[status(thm)],[13]) ).
cnf(19,plain,
( ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1)
| unorthogonal_lines(X0,X2)
| sP0(X1,X2) ),
inference(cnf,[status(esa)],[oac1]) ).
cnf(l6,plain,
( ~ convergent_lines(sK2,sK1)
| ~ unorthogonal_lines(sK2,sK1)
| unorthogonal_lines(sK2,sK3)
| sP0(sK1,sK3) ),
inference(instantiation,[status(thm)],[19]) ).
cnf(20,plain,
( unorthogonal_lines(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf,[status(esa)],[oac1]) ).
cnf(l14,plain,
( unorthogonal_lines(sK2,sK1)
| ~ sP0(sK2,sK1) ),
inference(instantiation,[status(thm)],[20]) ).
cnf(l64,plain,
~ convergent_lines(orthogonal_through_point(sK3,X1_74),orthogonal_through_point(sK3,X1_74)),
inference(instantiation,[status(thm)],[2]) ).
cnf(27,plain,
~ unorthogonal_lines(sK2,sK3),
inference(cnf,[status(esa)],[con_negated]) ).
cnf(l50,plain,
~ unorthogonal_lines(sK2,sK3),
inference(instantiation,[status(thm)],[27]) ).
cnf(l65,plain,
( convergent_lines(sK1,sK3)
| ~ sP0(sK1,sK3) ),
inference(instantiation,[status(thm)],[21]) ).
fof(ouo1,plain,
! [A,L,M,N] :
( distinct_lines(L,M)
=> ( apart_point_and_line(A,L)
| apart_point_and_line(A,M)
| unorthogonal_lines(L,N)
| unorthogonal_lines(M,N) ) ),
file('Axioms/GEO006+3.ax',ouo1) ).
cnf(24,plain,
( ~ distinct_lines(X0,X1)
| unorthogonal_lines(X0,X2)
| unorthogonal_lines(X1,X2)
| apart_point_and_line(X3,X0)
| apart_point_and_line(X3,X1) ),
inference(cnf,[status(esa)],[ouo1]) ).
cnf(l68,plain,
( ~ distinct_lines(sK2,orthogonal_through_point(sK3,X1_74))
| unorthogonal_lines(sK2,sK3)
| unorthogonal_lines(orthogonal_through_point(sK3,X1_74),sK3)
| apart_point_and_line(intersection_point(orthogonal_through_point(sK3,X1_74),sK2),sK2)
| apart_point_and_line(intersection_point(orthogonal_through_point(sK3,X1_74),sK2),orthogonal_through_point(sK3,X1_74)) ),
inference(instantiation,[status(thm)],[24]) ).
cnf(l74,plain,
~ unorthogonal_lines(orthogonal_through_point(sK3,X1_74),sK3),
inference(instantiation,[status(thm)],[22]) ).
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(l71,plain,
( ~ convergent_lines(orthogonal_through_point(sK3,X1_74),sK2)
| ~ apart_point_and_line(intersection_point(orthogonal_through_point(sK3,X1_74),sK2),orthogonal_through_point(sK3,X1_74)) ),
inference(instantiation,[status(thm)],[8]) ).
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(l77,plain,
( ~ convergent_lines(orthogonal_through_point(sK3,X1_74),sK2)
| ~ apart_point_and_line(intersection_point(orthogonal_through_point(sK3,X1_74),sK2),sK2) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(26,plain,
~ convergent_lines(sK1,sK3),
inference(cnf,[status(esa)],[con_negated]) ).
cnf(l66,plain,
~ convergent_lines(sK1,sK3),
inference(instantiation,[status(thm)],[26]) ).
cnf(l69,plain,
~ unorthogonal_lines(sK2,sK3),
inference(instantiation,[status(thm)],[27]) ).
cnf(l46,plain,
( ~ convergent_lines(sK3,sK1)
| convergent_lines(sK3,sK3)
| convergent_lines(sK1,sK3) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l54,plain,
~ convergent_lines(sK3,sK3),
inference(instantiation,[status(thm)],[2]) ).
cnf(l49,plain,
~ convergent_lines(sK1,sK3),
inference(instantiation,[status(thm)],[26]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l4,l2,l3,l8,l11,l36,l62,l6,l14,l64,l50,l65,l68,l74,l71,l77,l66,l69,l46,l54,l49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO212+1 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.33 % Computer : n018.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 11:42:49 EDT 2025
% 0.13/0.34 % 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: 3
% 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: 4
% 0.13/0.34 % launching worker at depth: 6
% 0.13/0.34 % launching worker at depth: 9
% 0.13/0.34 % launching worker at depth: 10
% 0.13/0.35 % launching worker at depth: 11
% 0.19/0.45 % launching worker at depth: 12
% 2.44/0.63 % SZS status Theorem for theBenchmark
% 2.44/0.63 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------