%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO225+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 07:17:35 AM UTC 2026
% Result : Theorem 0.09s 0.54s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 6 unt; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 45 ( 14 ~; 10 |; 15 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 10 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X),
file('theBenchmark.p',apart1) ).
fof(con1,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(X,Y))
=> ( distinct_points(Z,Y)
& distinct_points(Z,X) ) ) ),
file('theBenchmark.p',con1) ).
fof(con,conjecture,
! [A,B] :
( ( distinct_points(A,B)
& point(B)
& point(A) )
=> ? [X] :
( line(X)
=> ( ~ apart_point_and_line(B,X)
& ~ apart_point_and_line(A,X) ) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [A,B] :
( ( distinct_points(A,B)
& point(B)
& point(A) )
=> ? [X] :
( line(X)
=> ( ~ apart_point_and_line(B,X)
& ~ apart_point_and_line(A,X) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_18,plain,
~ distinct_points(A,A),
inference(clausify,[status(thm)],[apart1]) ).
cnf(c_24,plain,
( distinct_points(C,A)
| ~ apart_point_and_line(C,line_connecting(A,B))
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[con1]) ).
cnf(c_25,plain,
( distinct_points(C,B)
| ~ apart_point_and_line(C,line_connecting(A,B))
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[con1]) ).
fof(nnf_17,plain,
? [A,B] :
( ! [X] :
( ( apart_point_and_line(B,X)
| apart_point_and_line(A,X) )
& line(X) )
& distinct_points(A,B)
& point(B)
& point(A) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ! [X] :
( ( apart_point_and_line(sK1,X)
| apart_point_and_line(sK0,X) )
& line(X) )
& distinct_points(sK0,sK1)
& point(sK1)
& point(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_17]) ).
cnf(c_38,negated_conjecture,
distinct_points(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_40,negated_conjecture,
( apart_point_and_line(sK1,A)
| apart_point_and_line(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_42,plain,
( distinct_points(A,sK1)
| ~ apart_point_and_line(A,line_connecting(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_38,c_25]) ).
cnf(c_51,negated_conjecture,
( distinct_points(A,sK0)
| ~ apart_point_and_line(A,line_connecting(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_24,c_38]) ).
cnf(c_46,negated_conjecture,
~ apart_point_and_line(sK0,line_connecting(sK0,sK1)),
inference(resolve,[status(thm)],[c_51,c_18]) ).
cnf(c_52,negated_conjecture,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| distinct_points(sK1,sK1) ),
inference(resolve,[status(thm)],[c_42,c_40]) ).
cnf(c_53,negated_conjecture,
apart_point_and_line(sK0,line_connecting(sK0,sK1)),
inference(resolve,[status(thm)],[c_18,c_52]) ).
cnf(c_50,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_46,c_53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO225+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.51 % Computer : n001.cluster.edu
% 0.09/0.51 % Model : x86_64 x86_64
% 0.09/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.51 % Memory : 8046.5625MB
% 0.09/0.51 % OS : Linux 6.8.0-71-generic
% 0.09/0.51 % CPULimit : 300
% 0.09/0.51 % WCLimit : 300
% 0.09/0.52 % DateTime : Fri Sep 25 13:14:10 UTC 2026
% 0.09/0.52 % CPUTime :
% 0.09/0.52 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.52 % Process 3352703 was started by sandbox on n001,
% 0.09/0.52 % Fri Sep 25 13:14:10 2026
% 0.09/0.52 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.53
% 0.09/0.53 % From the command line: assign(max_seconds, 300).
% 0.09/0.54
% 0.09/0.54 % SZS status Theorem for theBenchmark
% 0.09/0.54
% 0.09/0.54 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.54 % Length of proof is 11.
% 0.09/0.54 % Level of proof is 3.
% 0.09/0.54 % Maximum clause weight is 11.000.
% 0.09/0.54 % Given clauses 21.
% 0.09/0.54
% 0.09/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------