%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO215+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 : 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 07:17:32 AM UTC 2026
% Result : Theorem 0.10s 0.45s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 10 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 56 ( 23 ~; 23 |; 4 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 16 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X),
file('theBenchmark.p',apart1) ).
fof(con2,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( ( apart_point_and_line(Z,Y)
| apart_point_and_line(Z,X) )
=> distinct_points(Z,intersection_point(X,Y)) ) ),
file('theBenchmark.p',con2) ).
fof(ceq3,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ),
file('theBenchmark.p',ceq3) ).
fof(ouo1,axiom,
! [A,L,M,N] :
( distinct_lines(L,M)
=> ( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N)
| apart_point_and_line(A,M)
| apart_point_and_line(A,L) ) ),
file('theBenchmark.p',ouo1) ).
fof(con,conjecture,
! [L,M,N] :
( convergent_lines(L,M)
=> ( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [L,M,N] :
( convergent_lines(L,M)
=> ( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N) ) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_22,plain,
~ distinct_points(A,A),
inference(clausify,[status(thm)],[apart1]) ).
cnf(c_30,plain,
( distinct_points(C,intersection_point(A,B))
| ~ apart_point_and_line(C,A)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[con2]) ).
cnf(c_31,plain,
( distinct_points(C,intersection_point(A,B))
| ~ apart_point_and_line(C,B)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[con2]) ).
cnf(c_35,plain,
( distinct_lines(A,B)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ceq3]) ).
cnf(c_45,plain,
( unorthogonal_lines(B,D)
| unorthogonal_lines(A,D)
| apart_point_and_line(C,B)
| apart_point_and_line(C,A)
| ~ distinct_lines(A,B) ),
inference(clausify,[status(thm)],[ouo1]) ).
fof(nnf_21,plain,
? [L,M,N] :
( ~ unorthogonal_lines(M,N)
& ~ unorthogonal_lines(L,N)
& convergent_lines(L,M) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ~ unorthogonal_lines(sK1,sK2)
& ~ unorthogonal_lines(sK0,sK2)
& convergent_lines(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(L,sK0),skolemize(M,sK1),skolemize(N,sK2)],[nnf_21]) ).
cnf(c_46,negated_conjecture,
convergent_lines(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_47,negated_conjecture,
~ unorthogonal_lines(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_48,negated_conjecture,
~ unorthogonal_lines(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_54,plain,
distinct_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_46,c_35]) ).
cnf(c_75,negated_conjecture,
( distinct_points(A,intersection_point(sK0,sK1))
| ~ apart_point_and_line(A,sK1) ),
inference(resolve,[status(thm)],[c_31,c_46]) ).
cnf(c_56,negated_conjecture,
~ apart_point_and_line(intersection_point(sK0,sK1),sK1),
inference(resolve,[status(thm)],[c_75,c_22]) ).
cnf(c_76,negated_conjecture,
( distinct_points(A,intersection_point(sK0,sK1))
| ~ apart_point_and_line(A,sK0) ),
inference(resolve,[status(thm)],[c_30,c_46]) ).
cnf(c_57,negated_conjecture,
~ apart_point_and_line(intersection_point(sK0,sK1),sK0),
inference(resolve,[status(thm)],[c_76,c_22]) ).
cnf(c_77,plain,
( unorthogonal_lines(A,B)
| unorthogonal_lines(sK0,B)
| apart_point_and_line(intersection_point(sK0,sK1),A)
| ~ distinct_lines(sK0,A) ),
inference(resolve,[status(thm)],[c_45,c_57]) ).
cnf(c_78,plain,
( unorthogonal_lines(sK1,A)
| unorthogonal_lines(sK0,A)
| ~ distinct_lines(sK0,sK1) ),
inference(resolve,[status(thm)],[c_77,c_56]) ).
cnf(c_79,negated_conjecture,
( unorthogonal_lines(sK1,sK2)
| ~ distinct_lines(sK0,sK1) ),
inference(resolve,[status(thm)],[c_78,c_47]) ).
cnf(c_80,negated_conjecture,
~ distinct_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_79,c_48]) ).
cnf(c_74,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_54,c_80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO215+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.41 % Computer : n017.cluster.edu
% 0.10/0.41 % Model : x86_64 x86_64
% 0.10/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.41 % Memory : 8046.5625MB
% 0.10/0.41 % OS : Linux 6.8.0-71-generic
% 0.10/0.41 % CPULimit : 300
% 0.10/0.41 % WCLimit : 300
% 0.10/0.41 % DateTime : Fri Sep 25 13:02:17 UTC 2026
% 0.10/0.41 % CPUTime :
% 0.10/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.41 % Process 2333224 was started by sandbox on n017,
% 0.10/0.41 % Fri Sep 25 13:02:17 2026
% 0.10/0.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.42
% 0.10/0.42 % From the command line: assign(max_seconds, 300).
% 0.10/0.45
% 0.10/0.45 % SZS status Theorem for theBenchmark
% 0.10/0.45
% 0.10/0.45 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.45 % Length of proof is 17.
% 0.10/0.45 % Level of proof is 3.
% 0.10/0.45 % Maximum clause weight is 15.000.
% 0.10/0.45 % Given clauses 32.
% 0.10/0.45
% 0.10/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------