%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO257+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 : n002.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 07:17:44 AM UTC 2026
% Result : Theorem 0.15s 5.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 8 ( 3 unt; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 34 ( 9 ~; 1 |; 20 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 19 ( 2 sgn 12 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(oag10,axiom,
! [A,L] :
~ ( left_apart_point(A,reverse_line(L))
| left_apart_point(A,L) ),
file('theBenchmark.p',oag10) ).
fof(con,conjecture,
! [L,A,B,C,D] :
( ( left_apart_point(D,L)
& ~ apart_point_and_line(C,L)
& distinct_points(B,C)
& distinct_points(A,C) )
=> ( ( before_on_line(L,B,C)
& before_on_line(L,A,B) )
=> before_on_line(L,A,C) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [L,A,B,C,D] :
( ( left_apart_point(D,L)
& ~ apart_point_and_line(C,L)
& distinct_points(B,C)
& distinct_points(A,C) )
=> ( ( before_on_line(L,B,C)
& before_on_line(L,A,B) )
=> before_on_line(L,A,C) ) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(nnf_32,plain,
? [L,A,B,C,D] :
( ~ before_on_line(L,A,C)
& before_on_line(L,B,C)
& before_on_line(L,A,B)
& left_apart_point(D,L)
& ~ apart_point_and_line(C,L)
& distinct_points(B,C)
& distinct_points(A,C) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ~ before_on_line(sK1,sK2,sK3)
& before_on_line(sK1,sK4,sK3)
& before_on_line(sK1,sK2,sK4)
& left_apart_point(sK0,sK1)
& ~ apart_point_and_line(sK3,sK1)
& distinct_points(sK4,sK3)
& distinct_points(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK1,sK0]),skolemize(L,sK1),skolemize(A,sK2),skolemize(B,sK4),skolemize(C,sK3),skolemize(D,sK0)],[nnf_32]) ).
cnf(c_88,negated_conjecture,
left_apart_point(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_105,plain,
~ left_apart_point(A,B),
inference(clausify,[status(thm)],[oag10]) ).
cnf(c_106,plain,
$false,
inference(resolve,[status(thm)],[c_105,c_88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO257+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n002.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Fri Sep 25 13:14:12 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 3350467 was started by sandbox on n002,
% 0.10/5.38 % Fri Sep 25 13:14:12 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.39
% 0.10/5.39 % From the command line: assign(max_seconds, 300).
% 0.15/5.40
% 0.15/5.40 % SZS status Theorem for theBenchmark
% 0.15/5.40
% 0.15/5.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/5.40 % Length of proof is 5.
% 0.15/5.40 % Level of proof is 2.
% 0.15/5.40 % Maximum clause weight is 3.000.
% 0.15/5.40 % Given clauses 0.
% 0.15/5.40
% 0.15/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------