%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO213+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 : n011.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 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 12 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 53 ( 23 ~; 18 |; 7 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 37 ( 0 sgn 17 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart3,axiom,
! [X] : ~ convergent_lines(X,X),
file('theBenchmark.p',apart3) ).
fof(apart6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('theBenchmark.p',apart6) ).
fof(ceq3,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ),
file('theBenchmark.p',ceq3) ).
fof(occu1,axiom,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
file('theBenchmark.p',occu1) ).
fof(oac1,axiom,
! [L,M,N] :
( ( unorthogonal_lines(L,M)
& convergent_lines(L,M) )
=> ( ( unorthogonal_lines(M,N)
& convergent_lines(M,N) )
| ( unorthogonal_lines(L,N)
& convergent_lines(L,N) ) ) ),
file('theBenchmark.p',oac1) ).
fof(con,conjecture,
! [L,M,N] :
( unorthogonal_lines(L,M)
=> ( unorthogonal_lines(M,N)
| distinct_lines(L,N) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [L,M,N] :
( unorthogonal_lines(L,M)
=> ( unorthogonal_lines(M,N)
| distinct_lines(L,N) ) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_24,plain,
~ convergent_lines(A,A),
inference(clausify,[status(thm)],[apart3]) ).
cnf(c_27,plain,
( convergent_lines(B,C)
| convergent_lines(A,C)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[apart6]) ).
cnf(c_35,plain,
( distinct_lines(A,B)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ceq3]) ).
cnf(c_39,plain,
( unorthogonal_lines(A,B)
| convergent_lines(A,B) ),
inference(clausify,[status(thm)],[occu1]) ).
cnf(c_40,plain,
( unorthogonal_lines(B,C)
| convergent_lines(A,C)
| ~ unorthogonal_lines(A,B)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[oac1]) ).
fof(nnf_21,plain,
? [L,M,N] :
( ~ unorthogonal_lines(M,N)
& ~ distinct_lines(L,N)
& unorthogonal_lines(L,M) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ~ unorthogonal_lines(sK1,sK2)
& ~ distinct_lines(sK0,sK2)
& unorthogonal_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,
unorthogonal_lines(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_47,negated_conjecture,
~ distinct_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_57,negated_conjecture,
~ convergent_lines(sK0,sK2),
inference(resolve,[status(thm)],[c_35,c_47]) ).
cnf(c_59,plain,
convergent_lines(sK1,sK2),
inference(resolve,[status(thm)],[c_48,c_39]) ).
cnf(c_96,negated_conjecture,
( unorthogonal_lines(sK1,A)
| convergent_lines(sK0,A)
| ~ convergent_lines(sK0,sK1) ),
inference(resolve,[status(thm)],[c_40,c_46]) ).
cnf(c_97,negated_conjecture,
( unorthogonal_lines(sK1,sK2)
| ~ convergent_lines(sK0,sK1) ),
inference(resolve,[status(thm)],[c_96,c_57]) ).
cnf(c_62,negated_conjecture,
~ convergent_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_97,c_48]) ).
cnf(c_98,plain,
( convergent_lines(B,A)
| ~ convergent_lines(A,B) ),
inference(resolve,[status(thm)],[c_27,c_24]) ).
cnf(c_64,plain,
~ convergent_lines(sK2,sK0),
inference(resolve,[status(thm)],[c_98,c_57]) ).
cnf(c_99,plain,
( convergent_lines(B,A)
| ~ convergent_lines(A,B) ),
inference(resolve,[status(thm)],[c_27,c_24]) ).
cnf(c_67,plain,
~ convergent_lines(sK1,sK0),
inference(resolve,[status(thm)],[c_99,c_62]) ).
cnf(c_100,plain,
( convergent_lines(A,sK0)
| ~ convergent_lines(sK1,A) ),
inference(resolve,[status(thm)],[c_27,c_67]) ).
cnf(c_101,plain,
~ convergent_lines(sK1,sK2),
inference(resolve,[status(thm)],[c_100,c_64]) ).
cnf(c_95,plain,
$false,
inference(resolve,[status(thm)],[c_59,c_101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO213+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n011.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Fri Sep 25 13:06:44 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 2082311 was started by sandbox on n011,
% 0.07/0.35 % Fri Sep 25 13:06:44 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.37
% 0.13/0.37 % SZS status Theorem for theBenchmark
% 0.13/0.37
% 0.13/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.37 % Length of proof is 20.
% 0.13/0.37 % Level of proof is 5.
% 0.13/0.37 % Maximum clause weight is 12.000.
% 0.13/0.37 % Given clauses 38.
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------