%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO215+1 : 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 : n008.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 07:17:31 AM UTC 2026
% Result : Theorem 0.19s 0.47s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 10 unt; 0 def)
% Number of atoms : 57 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 54 ( 23 ~; 21 |; 4 &)
% ( 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 18 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart3,axiom,
! [X] : ~ convergent_lines(X,X),
file('theBenchmark.p',apart3) ).
fof(ci3,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ),
file('theBenchmark.p',ci3) ).
fof(ci4,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),Y) ),
file('theBenchmark.p',ci4) ).
fof(ceq3,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
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_26,plain,
~ convergent_lines(A,A),
inference(clausify,[status(thm)],[apart3]) ).
cnf(c_32,plain,
( ~ apart_point_and_line(intersection_point(A,B),A)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ci3]) ).
cnf(c_33,plain,
( ~ apart_point_and_line(intersection_point(A,B),B)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ci4]) ).
cnf(c_37,plain,
( convergent_lines(A,C)
| distinct_lines(B,C)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ceq3]) ).
cnf(c_47,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_23,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_23]) ).
cnf(c_48,negated_conjecture,
convergent_lines(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_49,negated_conjecture,
~ unorthogonal_lines(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_50,negated_conjecture,
~ unorthogonal_lines(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_59,plain,
( convergent_lines(sK0,A)
| distinct_lines(sK1,A) ),
inference(resolve,[status(thm)],[c_48,c_37]) ).
cnf(c_60,plain,
~ apart_point_and_line(intersection_point(sK0,sK1),sK1),
inference(resolve,[status(thm)],[c_48,c_33]) ).
cnf(c_61,plain,
~ apart_point_and_line(intersection_point(sK0,sK1),sK0),
inference(resolve,[status(thm)],[c_48,c_32]) ).
cnf(c_105,plain,
( unorthogonal_lines(A,B)
| unorthogonal_lines(sK1,B)
| apart_point_and_line(intersection_point(sK0,sK1),A)
| ~ distinct_lines(sK1,A) ),
inference(resolve,[status(thm)],[c_47,c_60]) ).
cnf(c_106,plain,
( unorthogonal_lines(sK0,A)
| unorthogonal_lines(sK1,A)
| ~ distinct_lines(sK1,sK0) ),
inference(resolve,[status(thm)],[c_105,c_61]) ).
cnf(c_107,negated_conjecture,
( unorthogonal_lines(sK0,sK2)
| ~ distinct_lines(sK1,sK0) ),
inference(resolve,[status(thm)],[c_106,c_50]) ).
cnf(c_76,negated_conjecture,
~ distinct_lines(sK1,sK0),
inference(resolve,[status(thm)],[c_107,c_49]) ).
cnf(c_108,plain,
convergent_lines(sK0,sK0),
inference(resolve,[status(thm)],[c_76,c_59]) ).
cnf(c_104,plain,
$false,
inference(resolve,[status(thm)],[c_26,c_108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO215+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n008.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Fri Sep 25 13:07:54 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 1119205 was started by sandbox on n008,
% 0.19/0.45 % Fri Sep 25 13:07:54 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.45
% 0.19/0.45 % From the command line: assign(max_seconds, 300).
% 0.19/0.47
% 0.19/0.47 % SZS status Theorem for theBenchmark
% 0.19/0.47
% 0.19/0.47 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.19/0.47 % Length of proof is 19.
% 0.19/0.47 % Level of proof is 4.
% 0.19/0.47 % Maximum clause weight is 20.000.
% 0.19/0.47 % Given clauses 37.
% 0.19/0.47
% 0.19/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------