%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO264+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 : n014.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 0.18s 0.48s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 8 ( 3 unt; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 18 ( 5 ~; 1 |; 8 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 16 ( 2 sgn 10 !; 4 ?)
% 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,
! [A,B,C,D] :
( left_apart_point(C,line_connecting(A,B))
=> ( ( left_apart_point(D,reverse_line(line_connecting(C,A)))
& left_apart_point(D,reverse_line(line_connecting(B,C))) )
=> left_apart_point(D,line_connecting(A,B)) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [A,B,C,D] :
( left_apart_point(C,line_connecting(A,B))
=> ( ( left_apart_point(D,reverse_line(line_connecting(C,A)))
& left_apart_point(D,reverse_line(line_connecting(B,C))) )
=> left_apart_point(D,line_connecting(A,B)) ) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(nnf_32,plain,
? [A,B,C,D] :
( ~ left_apart_point(D,line_connecting(A,B))
& left_apart_point(D,reverse_line(line_connecting(C,A)))
& left_apart_point(D,reverse_line(line_connecting(B,C)))
& left_apart_point(C,line_connecting(A,B)) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ~ left_apart_point(sK0,line_connecting(sK3,sK1))
& left_apart_point(sK0,reverse_line(line_connecting(sK2,sK3)))
& left_apart_point(sK0,reverse_line(line_connecting(sK1,sK2)))
& left_apart_point(sK2,line_connecting(sK3,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK1,sK0]),skolemize(A,sK3),skolemize(B,sK1),skolemize(C,sK2),skolemize(D,sK0)],[nnf_32]) ).
cnf(c_75,negated_conjecture,
left_apart_point(sK0,reverse_line(line_connecting(sK1,sK2))),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_91,plain,
~ left_apart_point(A,reverse_line(B)),
inference(clausify,[status(thm)],[oag10]) ).
cnf(c_92,plain,
$false,
inference(resolve,[status(thm)],[c_91,c_75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO264+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n014.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 13:11:32 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 299291 was started by sandbox2 on n014,
% 0.18/0.44 % Fri Sep 25 13:11:32 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 0.18/0.48
% 0.18/0.48 % SZS status Theorem for theBenchmark
% 0.18/0.48
% 0.18/0.48 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.18/0.48 % Length of proof is 5.
% 0.18/0.48 % Level of proof is 2.
% 0.18/0.48 % Maximum clause weight is 6.000.
% 0.18/0.48 % Given clauses 0.
% 0.18/0.48
% 0.18/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------