%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO224+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 12 unt; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 51 ( 23 ~; 14 |; 8 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 53 ( 7 sgn 21 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart2,axiom,
! [X] : ~ distinct_lines(X,X),
file('theBenchmark.p',apart2) ).
fof(apart5,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(Y,Z)
| distinct_lines(X,Z) ) ),
file('theBenchmark.p',apart5) ).
fof(ceq2,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ) ),
file('theBenchmark.p',ceq2) ).
fof(p1,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ),
file('theBenchmark.p',p1) ).
fof(cp1,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('theBenchmark.p',cp1) ).
fof(cp2,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
file('theBenchmark.p',cp2) ).
fof(a4,axiom,
! [X,Y] :
( incident_point_and_line(X,Y)
<=> ~ apart_point_and_line(X,Y) ),
file('theBenchmark.p',a4) ).
fof(con,conjecture,
! [X,Y] :
( ( line(Y)
& point(X) )
=> ? [Z] :
( incident_point_and_line(Z,Y)
& point(Z) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y] :
( ( line(Y)
& point(X) )
=> ? [Z] :
( incident_point_and_line(Z,Y)
& point(Z) ) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_43,plain,
( apart_point_and_line(A,B)
| incident_point_and_line(A,B) ),
inference(clausify,[status(thm)],[a4]) ).
fof(nnf_36,plain,
? [X,Y] :
( ! [Z] :
( ~ incident_point_and_line(Z,Y)
| ~ point(Z) )
& line(Y)
& point(X) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ! [Z] :
( ~ incident_point_and_line(Z,sK0)
| ~ point(Z) )
& line(sK0)
& point(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(X,sK1),skolemize(Y,sK0)],[nnf_36]) ).
cnf(c_44,negated_conjecture,
( ~ incident_point_and_line(A,sK0)
| ~ point(A) ),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_49,negated_conjecture,
point(sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_67,plain,
~ apart_point_and_line(A,parallel_through_point(B,A)),
inference(clausify,[status(thm)],[cp2]) ).
cnf(c_68,plain,
~ convergent_lines(parallel_through_point(A,B),A),
inference(clausify,[status(thm)],[cp1]) ).
cnf(c_69,plain,
( convergent_lines(A,B)
| ~ distinct_lines(A,B) ),
inference(clausify,[status(thm)],[p1]) ).
cnf(c_71,plain,
( apart_point_and_line(A,C)
| distinct_lines(B,C)
| ~ apart_point_and_line(A,B) ),
inference(clausify,[status(thm)],[ceq2]) ).
cnf(c_79,plain,
( distinct_lines(B,C)
| distinct_lines(A,C)
| ~ distinct_lines(A,B) ),
inference(clausify,[status(thm)],[apart5]) ).
cnf(c_82,plain,
~ distinct_lines(A,A),
inference(clausify,[status(thm)],[apart2]) ).
cnf(c_84,negated_conjecture,
( ~ point(A)
| apart_point_and_line(A,sK0) ),
inference(resolve,[status(thm)],[c_43,c_44]) ).
cnf(c_88,plain,
~ distinct_lines(parallel_through_point(A,B),A),
inference(resolve,[status(thm)],[c_69,c_68]) ).
cnf(c_91,plain,
apart_point_and_line(sK1,sK0),
inference(resolve,[status(thm)],[c_84,c_49]) ).
cnf(c_103,plain,
( distinct_lines(B,A)
| ~ distinct_lines(A,B) ),
inference(resolve,[status(thm)],[c_79,c_82]) ).
cnf(c_94,plain,
~ distinct_lines(A,parallel_through_point(A,B)),
inference(resolve,[status(thm)],[c_103,c_88]) ).
cnf(c_104,plain,
( apart_point_and_line(A,parallel_through_point(B,C))
| ~ apart_point_and_line(A,B) ),
inference(resolve,[status(thm)],[c_71,c_94]) ).
cnf(c_101,plain,
~ apart_point_and_line(A,B),
inference(resolve,[status(thm)],[c_104,c_67]) ).
cnf(c_102,plain,
$false,
inference(resolve,[status(thm)],[c_101,c_91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO224+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n009.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 13:08:29 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 1668639 was started by sandbox on n009,
% 0.10/0.37 % Fri Sep 25 13:08:29 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.14/0.40
% 0.14/0.40 % SZS status Theorem for theBenchmark
% 0.14/0.40
% 0.14/0.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.40 % Length of proof is 23.
% 0.14/0.40 % Level of proof is 5.
% 0.14/0.40 % Maximum clause weight is 9.000.
% 0.14/0.40 % Given clauses 39.
% 0.14/0.40
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------