%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO237+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 07:17:38 AM UTC 2026
% Result : Theorem 0.14s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 4 unt; 0 def)
% Number of atoms : 30 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 26 ( 8 ~; 7 |; 6 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 20 ( 2 sgn 12 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apt_def,axiom,
! [A,L] :
( apart_point_and_line(A,L)
<=> ( left_apart_point(A,reverse_line(L))
| left_apart_point(A,L) ) ),
file('theBenchmark.p',apt_def) ).
fof(oag10,axiom,
! [A,L] :
~ ( left_apart_point(A,reverse_line(L))
| left_apart_point(A,L) ),
file('theBenchmark.p',oag10) ).
fof(con,conjecture,
! [A,B,C,L] :
( apart_point_and_line(C,L)
=> ( divides_points(L,A,B)
=> ( divides_points(L,B,C)
| divides_points(L,A,C) ) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [A,B,C,L] :
( apart_point_and_line(C,L)
=> ( divides_points(L,A,B)
=> ( divides_points(L,B,C)
| divides_points(L,A,C) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_34,plain,
( left_apart_point(A,reverse_line(B))
| left_apart_point(A,B)
| ~ apart_point_and_line(A,B) ),
inference(clausify,[status(thm)],[apt_def]) ).
fof(nnf_32,plain,
? [A,B,C,L] :
( ~ divides_points(L,B,C)
& ~ divides_points(L,A,C)
& divides_points(L,A,B)
& apart_point_and_line(C,L) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ~ divides_points(sK1,sK3,sK0)
& ~ divides_points(sK1,sK2,sK0)
& divides_points(sK1,sK2,sK3)
& apart_point_and_line(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(A,sK2),skolemize(B,sK3),skolemize(C,sK0),skolemize(L,sK1)],[nnf_32]) ).
cnf(c_41,negated_conjecture,
apart_point_and_line(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_75,negated_conjecture,
( left_apart_point(sK0,reverse_line(sK1))
| left_apart_point(sK0,sK1) ),
inference(resolve,[status(thm)],[c_41,c_34]) ).
cnf(c_101,plain,
~ left_apart_point(A,B),
inference(clausify,[status(thm)],[oag10]) ).
cnf(c_114,negated_conjecture,
left_apart_point(sK0,reverse_line(sK1)),
inference(resolve,[status(thm)],[c_101,c_75]) ).
cnf(c_113,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_101,c_114]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO237+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 13:09:36 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3236672 was started by sandbox2 on n004,
% 0.10/0.37 % Fri Sep 25 13:09:36 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 0.14/0.41
% 0.14/0.41 % SZS status Theorem for theBenchmark
% 0.14/0.41
% 0.14/0.41 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/0.41 % Length of proof is 8.
% 0.14/0.41 % Level of proof is 3.
% 0.14/0.41 % Maximum clause weight is 17.000.
% 0.14/0.41 % Given clauses 0.
% 0.14/0.41
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------