%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO218+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 0.17s 10.47s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 13 unt; 0 def)
% Number of atoms : 64 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 67 ( 35 ~; 18 |; 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 : 41 ( 0 sgn 19 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart3,axiom,
! [X] : ~ convergent_lines(X,X),
file('theBenchmark.p',apart3) ).
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] :
( ( orthogonal_lines(L,N)
& parallel_lines(L,M) )
=> orthogonal_lines(M,N) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [L,M,N] :
( ( orthogonal_lines(L,N)
& parallel_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)
& orthogonal_lines(L,N)
& parallel_lines(L,M) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ~ orthogonal_lines(sK1,sK2)
& orthogonal_lines(sK0,sK2)
& parallel_lines(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(L,sK0),skolemize(M,sK1),skolemize(N,sK2)],[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(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_50,negated_conjecture,
unorthogonal_lines(sK1,sK2),
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_59,plain,
( ~ unorthogonal_lines(B,C)
| ~ convergent_lines(B,C)
| unorthogonal_lines(A,C)
| convergent_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_84,plain,
~ convergent_lines(A,A),
inference(clausify,[status(thm)],[apart3]) ).
cnf(c_139,negated_conjecture,
( ~ unorthogonal_lines(sK1,A)
| ~ convergent_lines(sK1,A)
| unorthogonal_lines(sK0,A) ),
inference(resolve,[status(thm)],[c_59,c_52]) ).
cnf(c_140,negated_conjecture,
( ~ unorthogonal_lines(sK1,sK2)
| ~ convergent_lines(sK1,sK2) ),
inference(resolve,[status(thm)],[c_139,c_51]) ).
cnf(c_89,negated_conjecture,
~ convergent_lines(sK1,sK2),
inference(resolve,[status(thm)],[c_140,c_50]) ).
cnf(c_93,plain,
convergent_lines(sK0,sK2),
inference(resolve,[status(thm)],[c_61,c_51]) ).
cnf(c_141,plain,
( convergent_lines(B,A)
| ~ convergent_lines(A,B) ),
inference(resolve,[status(thm)],[c_81,c_84]) ).
cnf(c_108,plain,
~ convergent_lines(sK2,sK1),
inference(resolve,[status(thm)],[c_141,c_89]) ).
cnf(c_142,negated_conjecture,
( convergent_lines(A,sK1)
| ~ convergent_lines(sK0,A) ),
inference(resolve,[status(thm)],[c_81,c_52]) ).
cnf(c_143,negated_conjecture,
~ convergent_lines(sK0,sK2),
inference(resolve,[status(thm)],[c_142,c_108]) ).
cnf(c_138,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_93,c_143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO218+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/10.44 % Computer : n006.cluster.edu
% 0.17/10.44 % Model : x86_64 x86_64
% 0.17/10.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/10.44 % Memory : 8046.5625MB
% 0.17/10.44 % OS : Linux 6.8.0-71-generic
% 0.17/10.44 % CPULimit : 300
% 0.17/10.44 % WCLimit : 300
% 0.17/10.44 % DateTime : Fri Sep 25 13:07:22 UTC 2026
% 0.17/10.45 % CPUTime :
% 0.17/10.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/10.45 % Process 2993175 was started by sandbox2 on n006,
% 0.17/10.45 % Fri Sep 25 13:07:22 2026
% 0.17/10.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/10.46
% 0.17/10.46 % From the command line: assign(max_seconds, 300).
% 0.17/10.47
% 0.17/10.47 % SZS status Theorem for theBenchmark
% 0.17/10.47
% 0.17/10.47 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.17/10.47 % Length of proof is 24.
% 0.17/10.47 % Level of proof is 5.
% 0.17/10.47 % Maximum clause weight is 14.000.
% 0.17/10.47 % Given clauses 40.
% 0.17/10.47
% 0.17/10.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------