%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO262+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 0.46s
% 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 : 62 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 57 ( 16 ~; 12 |; 24 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 42 ( 2 sgn 20 !; 6 ?)
% 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,N,A,B,C] :
( ( incident_point_and_line(B,N)
& convergent_lines(M,N)
& convergent_lines(L,N)
& incident_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] :
( ( incident_point_and_line(B,N)
& convergent_lines(M,N)
& convergent_lines(L,N)
& incident_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_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,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)))
& incident_point_and_line(B,N)
& convergent_lines(M,N)
& convergent_lines(L,N)
& 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,
( ~ between_on_line(sK0,intersection_point(sK0,parallel_through_point(sK1,sK3)),sK4,intersection_point(sK0,parallel_through_point(sK1,sK5)))
& incident_point_and_line(sK4,sK1)
& convergent_lines(sK0,sK1)
& convergent_lines(sK2,sK1)
& incident_point_and_line(sK4,sK0)
& convergent_lines(sK2,sK0)
& between_on_line(sK2,sK3,sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK0,sK1]),skolemize(L,sK2),skolemize(M,sK0),skolemize(N,sK1),skolemize(A,sK3),skolemize(B,sK4),skolemize(C,sK5)],[nnf_37]) ).
cnf(c_67,negated_conjecture,
convergent_lines(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_70,plain,
( unequally_directed_lines(A,B)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[a7_defns]) ).
cnf(c_125,plain,
~ left_convergent_lines(A,B),
inference(clausify,[status(thm)],[ax11_basics]) ).
cnf(c_128,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_175,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_125,c_128]) ).
cnf(c_129,plain,
( ~ unequally_directed_lines(A,reverse_line(B))
| ~ unequally_directed_lines(A,B) ),
inference(resolve,[status(thm)],[c_125,c_175]) ).
cnf(c_139,negated_conjecture,
unequally_directed_lines(sK0,reverse_line(sK1)),
inference(resolve,[status(thm)],[c_67,c_65]) ).
cnf(c_144,negated_conjecture,
unequally_directed_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_70,c_67]) ).
cnf(c_176,negated_conjecture,
~ unequally_directed_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_139,c_129]) ).
cnf(c_174,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_144,c_176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO262+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.41 % Computer : n026.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Fri Sep 25 13:14:24 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.42 % Process 2596771 was started by sandbox on n026,
% 0.14/0.42 % Fri Sep 25 13:14:24 2026
% 0.14/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.43
% 0.14/0.43 % From the command line: assign(max_seconds, 300).
% 0.14/0.46
% 0.14/0.46 % SZS status Theorem for theBenchmark
% 0.14/0.46
% 0.14/0.46 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.14/0.46 % Length of proof is 16.
% 0.14/0.46 % Level of proof is 4.
% 0.14/0.46 % Maximum clause weight is 7.000.
% 0.14/0.46 % Given clauses 32.
% 0.14/0.46
% 0.14/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------