%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO261+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:17:45 AM UTC 2026
% Result : Theorem 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 6 unt; 0 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 45 ( 16 ~; 12 |; 12 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 39 ( 2 sgn 18 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a1_defns,axiom,
! [X,Y] :
( unequally_directed_opposite_lines(X,Y)
<=> unequally_directed_lines(X,reverse_line(Y)) ),
file('theBenchmark.p',a1_defns) ).
fof(a7_defns,axiom,
! [L,M] :
( convergent_lines(L,M)
<=> ( unequally_directed_opposite_lines(L,M)
& unequally_directed_lines(L,M) ) ),
file('theBenchmark.p',a7_defns) ).
fof(ax9_basics,axiom,
! [L,M] :
( ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) )
=> ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ) ),
file('theBenchmark.p',ax9_basics) ).
fof(ax11_basics,axiom,
! [L,M] :
~ ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ),
file('theBenchmark.p',ax11_basics) ).
fof(con,conjecture,
! [L,M,A,B,C] :
( ( incident_point_and_line(B,M)
& convergent_lines(L,M)
& between_on_line(L,A,B,C) )
=> divides_points(M,A,C) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [L,M,A,B,C] :
( ( incident_point_and_line(B,M)
& convergent_lines(L,M)
& between_on_line(L,A,B,C) )
=> divides_points(M,A,C) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_39,plain,
( unequally_directed_lines(A,reverse_line(B))
| ~ unequally_directed_opposite_lines(A,B) ),
inference(clausify,[status(thm)],[a1_defns]) ).
cnf(c_42,plain,
( unequally_directed_opposite_lines(A,B)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[a7_defns]) ).
cnf(c_65,plain,
( unequally_directed_lines(A,reverse_line(B))
| ~ convergent_lines(A,B) ),
inference(resolve,[status(thm)],[c_42,c_39]) ).
fof(nnf_37,plain,
? [L,M,A,B,C] :
( ~ divides_points(M,A,C)
& incident_point_and_line(B,M)
& convergent_lines(L,M)
& between_on_line(L,A,B,C) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ~ divides_points(sK1,sK2,sK4)
& incident_point_and_line(sK3,sK1)
& convergent_lines(sK0,sK1)
& between_on_line(sK0,sK2,sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK3,sK4,sK1]),skolemize(L,sK0),skolemize(M,sK1),skolemize(A,sK2),skolemize(B,sK3),skolemize(C,sK4)],[nnf_37]) ).
cnf(c_67,negated_conjecture,
convergent_lines(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_68,plain,
( unequally_directed_lines(A,B)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[a7_defns]) ).
cnf(c_122,plain,
~ left_convergent_lines(A,B),
inference(clausify,[status(thm)],[ax11_basics]) ).
cnf(c_125,plain,
( left_convergent_lines(A,reverse_line(B))
| left_convergent_lines(A,B)
| ~ unequally_directed_lines(A,reverse_line(B))
| ~ unequally_directed_lines(A,B) ),
inference(clausify,[status(thm)],[ax9_basics]) ).
cnf(c_166,plain,
( left_convergent_lines(A,reverse_line(B))
| ~ unequally_directed_lines(A,reverse_line(B))
| ~ unequally_directed_lines(A,B) ),
inference(resolve,[status(thm)],[c_122,c_125]) ).
cnf(c_126,plain,
( ~ unequally_directed_lines(A,reverse_line(B))
| ~ unequally_directed_lines(A,B) ),
inference(resolve,[status(thm)],[c_122,c_166]) ).
cnf(c_136,negated_conjecture,
unequally_directed_lines(sK0,reverse_line(sK1)),
inference(resolve,[status(thm)],[c_67,c_65]) ).
cnf(c_137,negated_conjecture,
unequally_directed_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_68,c_67]) ).
cnf(c_167,negated_conjecture,
~ unequally_directed_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_136,c_126]) ).
cnf(c_165,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_137,c_167]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO261+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 13:10:40 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3000801 was started by sandbox2 on n006,
% 0.09/0.37 % Fri Sep 25 13:10:40 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.39
% 0.09/0.39 % From the command line: assign(max_seconds, 300).
% 0.14/0.40
% 0.14/0.40 % Assigning unary symbol reverse_line kb_weight 0 and highest precedence (18).
% 0.14/0.40
% 0.14/0.40 % SZS status Theorem for theBenchmark
% 0.14/0.40
% 0.14/0.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/0.40 % Length of proof is 16.
% 0.14/0.40 % Level of proof is 4.
% 0.14/0.40 % Maximum clause weight is 17.000.
% 0.14/0.40 % Given clauses 29.
% 0.14/0.40
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------