%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO262+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 0.08s 0.36s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 6 unt; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 60 ( 22 ~; 10 |; 24 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 36 ( 2 sgn 18 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con_def,axiom,
! [L,M] :
( convergent_lines(L,M)
<=> ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) ) ),
file('theBenchmark.p',con_def) ).
fof(oag9,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',oag9) ).
fof(oag11,axiom,
! [L,M] :
~ ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ),
file('theBenchmark.p',oag11) ).
fof(con,conjecture,
! [L,M,N,A,B,C] :
( ( ~ apart_point_and_line(B,N)
& convergent_lines(M,N)
& convergent_lines(L,N)
& ~ apart_point_and_line(B,M)
& convergent_lines(L,M)
& between_on_line(L,A,B,C) )
=> between_on_line(M,intersection_point(M,parallel_through_point(N,A)),B,intersection_point(M,parallel_through_point(N,C))) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [L,M,N,A,B,C] :
( ( ~ apart_point_and_line(B,N)
& convergent_lines(M,N)
& convergent_lines(L,N)
& ~ apart_point_and_line(B,M)
& convergent_lines(L,M)
& between_on_line(L,A,B,C) )
=> between_on_line(M,intersection_point(M,parallel_through_point(N,A)),B,intersection_point(M,parallel_through_point(N,C))) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_43,plain,
( unequally_directed_lines(A,reverse_line(B))
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[con_def]) ).
fof(nnf_32,plain,
? [L,M,N,A,B,C] :
( ~ between_on_line(M,intersection_point(M,parallel_through_point(N,A)),B,intersection_point(M,parallel_through_point(N,C)))
& ~ apart_point_and_line(B,N)
& convergent_lines(M,N)
& convergent_lines(L,N)
& ~ apart_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,
( ~ between_on_line(sK1,intersection_point(sK1,parallel_through_point(sK5,sK2)),sK3,intersection_point(sK1,parallel_through_point(sK5,sK4)))
& ~ apart_point_and_line(sK3,sK5)
& convergent_lines(sK1,sK5)
& convergent_lines(sK0,sK5)
& ~ apart_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,sK5]),skolemize(L,sK0),skolemize(M,sK1),skolemize(N,sK5),skolemize(A,sK2),skolemize(B,sK3),skolemize(C,sK4)],[nnf_32]) ).
cnf(c_45,negated_conjecture,
convergent_lines(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_48,plain,
( unequally_directed_lines(A,B)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[con_def]) ).
cnf(c_71,negated_conjecture,
unequally_directed_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_48,c_45]) ).
cnf(c_74,negated_conjecture,
unequally_directed_lines(sK0,reverse_line(sK1)),
inference(resolve,[status(thm)],[c_43,c_45]) ).
cnf(c_91,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)],[oag9]) ).
cnf(c_93,plain,
~ left_convergent_lines(A,B),
inference(clausify,[status(thm)],[oag11]) ).
cnf(c_133,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_93,c_91]) ).
cnf(c_109,plain,
( ~ unequally_directed_lines(A,reverse_line(B))
| ~ unequally_directed_lines(A,B) ),
inference(resolve,[status(thm)],[c_93,c_133]) ).
cnf(c_134,negated_conjecture,
~ unequally_directed_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_109,c_74]) ).
cnf(c_132,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_71,c_134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO262+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n010.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 25 13:11:14 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.34 % Process 832839 was started by sandbox on n010,
% 0.08/0.34 % Fri Sep 25 13:11:14 2026
% 0.08/0.34 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 0.08/0.36
% 0.08/0.36 % SZS status Theorem for theBenchmark
% 0.08/0.36
% 0.08/0.36 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.08/0.36 % Length of proof is 13.
% 0.08/0.36 % Level of proof is 3.
% 0.08/0.36 % Maximum clause weight is 14.000.
% 0.08/0.36 % Given clauses 33.
% 0.08/0.36
% 0.08/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------