%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO222+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 07:17:34 AM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 15 unt; 0 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 47 ( 22 ~; 16 |; 5 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 53 ( 5 sgn 20 !; 2 ?)
% 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(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(ooc1,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('theBenchmark.p',ooc1) ).
fof(coipo1,axiom,
! [L,M] :
~ ( ~ unorthogonal_lines(L,M)
& ~ convergent_lines(L,M) ),
file('theBenchmark.p',coipo1) ).
fof(couo1,axiom,
! [L,M,N] :
( ( ~ unorthogonal_lines(L,N)
& ~ unorthogonal_lines(L,M) )
=> ~ convergent_lines(M,N) ),
file('theBenchmark.p',couo1) ).
fof(a3,axiom,
! [X,Y] :
( parallel_lines(X,Y)
<=> ~ convergent_lines(X,Y) ),
file('theBenchmark.p',a3) ).
fof(con,conjecture,
! [A,L] : parallel_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [A,L] : parallel_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_41,plain,
( convergent_lines(A,B)
| parallel_lines(A,B) ),
inference(clausify,[status(thm)],[a3]) ).
fof(nnf_36,plain,
? [A,L] : ~ parallel_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
~ parallel_lines(sK0,orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK1),skolemize(L,sK0)],[nnf_36]) ).
cnf(c_43,negated_conjecture,
~ parallel_lines(sK0,orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1)),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_48,negated_conjecture,
convergent_lines(sK0,orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1)),
inference(resolve,[status(thm)],[c_43,c_41]) ).
cnf(c_53,plain,
( ~ convergent_lines(B,C)
| unorthogonal_lines(A,C)
| unorthogonal_lines(A,B) ),
inference(clausify,[status(thm)],[couo1]) ).
cnf(c_57,plain,
( unorthogonal_lines(A,B)
| convergent_lines(A,B) ),
inference(clausify,[status(thm)],[coipo1]) ).
cnf(c_60,plain,
~ unorthogonal_lines(orthogonal_through_point(A,B),A),
inference(clausify,[status(thm)],[ooc1]) ).
cnf(c_63,plain,
( unorthogonal_lines(B,C)
| convergent_lines(A,C)
| ~ unorthogonal_lines(A,B)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[oac1]) ).
cnf(c_77,plain,
( convergent_lines(B,C)
| convergent_lines(A,C)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ax6]) ).
cnf(c_80,plain,
~ convergent_lines(A,A),
inference(clausify,[status(thm)],[apart3]) ).
cnf(c_84,plain,
( unorthogonal_lines(A,orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1))
| unorthogonal_lines(A,sK0) ),
inference(resolve,[status(thm)],[c_53,c_48]) ).
cnf(c_85,plain,
convergent_lines(orthogonal_through_point(A,B),A),
inference(resolve,[status(thm)],[c_60,c_57]) ).
cnf(c_102,plain,
( convergent_lines(A,C)
| convergent_lines(orthogonal_through_point(A,B),C) ),
inference(resolve,[status(thm)],[c_85,c_77]) ).
cnf(c_121,plain,
convergent_lines(A,orthogonal_through_point(A,B)),
inference(resolve,[status(thm)],[c_102,c_80]) ).
cnf(c_134,plain,
( unorthogonal_lines(orthogonal_through_point(A,B),C)
| convergent_lines(A,C)
| ~ unorthogonal_lines(A,orthogonal_through_point(A,B)) ),
inference(resolve,[status(thm)],[c_63,c_121]) ).
cnf(c_135,plain,
( unorthogonal_lines(orthogonal_through_point(A,B),A)
| ~ unorthogonal_lines(A,orthogonal_through_point(A,B)) ),
inference(resolve,[status(thm)],[c_134,c_80]) ).
cnf(c_128,plain,
~ unorthogonal_lines(A,orthogonal_through_point(A,B)),
inference(resolve,[status(thm)],[c_135,c_60]) ).
cnf(c_136,plain,
unorthogonal_lines(orthogonal_through_point(sK0,sK1),sK0),
inference(resolve,[status(thm)],[c_128,c_84]) ).
cnf(c_133,plain,
$false,
inference(resolve,[status(thm)],[c_60,c_136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO222+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n004.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 13:08:07 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 3233363 was started by sandbox on n004,
% 0.08/0.35 % Fri Sep 25 13:08:07 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.38
% 0.12/0.38 % SZS status Theorem for theBenchmark
% 0.12/0.38
% 0.12/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.38 % Length of proof is 23.
% 0.12/0.38 % Level of proof is 6.
% 0.12/0.38 % Maximum clause weight is 27.000.
% 0.12/0.38 % Given clauses 46.
% 0.12/0.38
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------