%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO238+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 : n017.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 07:17:39 AM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 4 unt; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 22 ( 6 ~; 5 |; 8 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 22 ( 3 sgn 13 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(div_def,axiom,
! [A,B,L] :
( divides_points(L,A,B)
<=> ( ( left_apart_point(B,L)
& left_apart_point(A,reverse_line(L)) )
| ( left_apart_point(B,reverse_line(L))
& left_apart_point(A,L) ) ) ),
file('theBenchmark.p',div_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] :
( ( divides_points(L,A,C)
& divides_points(L,A,B) )
=> ~ divides_points(L,B,C) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [A,B,C,L] :
( ( divides_points(L,A,C)
& divides_points(L,A,B) )
=> ~ divides_points(L,B,C) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_45,plain,
( left_apart_point(C,A)
| left_apart_point(C,reverse_line(A))
| ~ divides_points(A,B,C) ),
inference(clausify,[status(thm)],[div_def]) ).
fof(nnf_32,plain,
? [A,B,C,L] :
( divides_points(L,B,C)
& divides_points(L,A,C)
& divides_points(L,A,B) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( divides_points(sK0,sK2,sK3)
& divides_points(sK0,sK1,sK3)
& divides_points(sK0,sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(A,sK1),skolemize(B,sK2),skolemize(C,sK3),skolemize(L,sK0)],[nnf_32]) ).
cnf(c_50,negated_conjecture,
divides_points(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_74,negated_conjecture,
( left_apart_point(sK2,sK0)
| left_apart_point(sK2,reverse_line(sK0)) ),
inference(resolve,[status(thm)],[c_50,c_45]) ).
cnf(c_100,plain,
~ left_apart_point(A,B),
inference(clausify,[status(thm)],[oag10]) ).
cnf(c_113,negated_conjecture,
left_apart_point(sK2,sK0),
inference(resolve,[status(thm)],[c_100,c_74]) ).
cnf(c_112,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_100,c_113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO238+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n017.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 13:04:47 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 2338918 was started by sandbox2 on n017,
% 0.17/0.45 % Fri Sep 25 13:04:47 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 0.17/0.48
% 0.17/0.48 % SZS status Theorem for theBenchmark
% 0.17/0.48
% 0.17/0.48 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.17/0.48 % Length of proof is 8.
% 0.17/0.48 % Level of proof is 3.
% 0.17/0.48 % Maximum clause weight is 17.000.
% 0.17/0.48 % Given clauses 0.
% 0.17/0.48
% 0.17/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------