%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO219+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 : n004.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 07:17:33 AM UTC 2026
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 10 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 62 ( 31 ~; 17 |; 8 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 37 ( 0 sgn 18 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('theBenchmark.p',ax6) ).
fof(coipo1,axiom,
! [L,M] :
~ ( ~ unorthogonal_lines(L,M)
& ~ convergent_lines(L,M) ),
file('theBenchmark.p',coipo1) ).
fof(cotno1,axiom,
! [L,M,N] :
( ( ( ~ unorthogonal_lines(L,N)
| ~ convergent_lines(L,N) )
& ( ~ unorthogonal_lines(L,M)
| ~ convergent_lines(L,M) ) )
=> ( ~ unorthogonal_lines(M,N)
| ~ convergent_lines(M,N) ) ),
file('theBenchmark.p',cotno1) ).
fof(a3,axiom,
! [X,Y] :
( parallel_lines(X,Y)
<=> ~ convergent_lines(X,Y) ),
file('theBenchmark.p',a3) ).
fof(a5,axiom,
! [X,Y] :
( orthogonal_lines(X,Y)
<=> ~ unorthogonal_lines(X,Y) ),
file('theBenchmark.p',a5) ).
fof(con,conjecture,
! [L,M,N] :
( ( parallel_lines(L,N)
& orthogonal_lines(L,M) )
=> orthogonal_lines(M,N) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [L,M,N] :
( ( parallel_lines(L,N)
& orthogonal_lines(L,M) )
=> orthogonal_lines(M,N) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_42,plain,
( ~ convergent_lines(A,B)
| ~ parallel_lines(A,B) ),
inference(clausify,[status(thm)],[a3]) ).
fof(nnf_36,plain,
? [L,M,N] :
( ~ orthogonal_lines(M,N)
& parallel_lines(L,N)
& orthogonal_lines(L,M) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ~ orthogonal_lines(sK2,sK1)
& parallel_lines(sK0,sK1)
& orthogonal_lines(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK1]),skolemize(L,sK0),skolemize(M,sK2),skolemize(N,sK1)],[nnf_36]) ).
cnf(c_43,negated_conjecture,
parallel_lines(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_46,plain,
( unorthogonal_lines(A,B)
| orthogonal_lines(A,B) ),
inference(clausify,[status(thm)],[a5]) ).
cnf(c_47,plain,
( ~ unorthogonal_lines(A,B)
| ~ orthogonal_lines(A,B) ),
inference(clausify,[status(thm)],[a5]) ).
cnf(c_48,negated_conjecture,
orthogonal_lines(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_49,negated_conjecture,
~ orthogonal_lines(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_50,negated_conjecture,
unorthogonal_lines(sK2,sK1),
inference(resolve,[status(thm)],[c_49,c_46]) ).
cnf(c_51,negated_conjecture,
~ unorthogonal_lines(sK0,sK2),
inference(resolve,[status(thm)],[c_48,c_47]) ).
cnf(c_52,negated_conjecture,
~ convergent_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_43,c_42]) ).
cnf(c_58,plain,
( ~ unorthogonal_lines(B,C)
| ~ convergent_lines(B,C)
| convergent_lines(A,C)
| unorthogonal_lines(A,B) ),
inference(clausify,[status(thm)],[cotno1]) ).
cnf(c_61,plain,
( unorthogonal_lines(A,B)
| convergent_lines(A,B) ),
inference(clausify,[status(thm)],[coipo1]) ).
cnf(c_81,plain,
( convergent_lines(B,C)
| convergent_lines(A,C)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ax6]) ).
cnf(c_101,negated_conjecture,
( ~ unorthogonal_lines(sK2,A)
| ~ convergent_lines(sK2,A)
| convergent_lines(sK0,A) ),
inference(resolve,[status(thm)],[c_58,c_51]) ).
cnf(c_102,negated_conjecture,
( ~ unorthogonal_lines(sK2,sK1)
| ~ convergent_lines(sK2,sK1) ),
inference(resolve,[status(thm)],[c_101,c_52]) ).
cnf(c_88,negated_conjecture,
~ convergent_lines(sK2,sK1),
inference(resolve,[status(thm)],[c_102,c_50]) ).
cnf(c_89,plain,
convergent_lines(sK0,sK2),
inference(resolve,[status(thm)],[c_61,c_51]) ).
cnf(c_103,negated_conjecture,
( convergent_lines(A,sK1)
| ~ convergent_lines(sK0,A) ),
inference(resolve,[status(thm)],[c_81,c_52]) ).
cnf(c_104,negated_conjecture,
~ convergent_lines(sK0,sK2),
inference(resolve,[status(thm)],[c_103,c_88]) ).
cnf(c_100,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_89,c_104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO219+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n004.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 25 13:07:51 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 3232533 was started by sandbox on n004,
% 0.08/0.35 % Fri Sep 25 13:07:51 2026
% 0.08/0.35 % 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 0.01 (+ 0.00) seconds.
% 0.13/0.37 % Length of proof is 21.
% 0.13/0.37 % Level of proof is 4.
% 0.13/0.37 % Maximum clause weight is 12.000.
% 0.13/0.37 % Given clauses 36.
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------