%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO219+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 : n020.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 0.07s 0.36s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 7 unt; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 58 ( 32 ~; 14 |; 8 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 27 ( 0 sgn 14 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('theBenchmark.p',apart6) ).
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(con,conjecture,
! [L,M,N] :
( ( ~ convergent_lines(L,N)
& ~ unorthogonal_lines(L,M) )
=> ~ unorthogonal_lines(M,N) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [L,M,N] :
( ( ~ convergent_lines(L,N)
& ~ unorthogonal_lines(L,M) )
=> ~ unorthogonal_lines(M,N) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_22,plain,
( convergent_lines(B,C)
| convergent_lines(A,C)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[apart6]) ).
cnf(c_31,plain,
( unorthogonal_lines(A,B)
| convergent_lines(A,B) ),
inference(clausify,[status(thm)],[coipo1]) ).
cnf(c_34,plain,
( ~ unorthogonal_lines(B,C)
| ~ convergent_lines(B,C)
| convergent_lines(A,C)
| unorthogonal_lines(A,B) ),
inference(clausify,[status(thm)],[cotno1]) ).
fof(nnf_16,plain,
? [L,M,N] :
( unorthogonal_lines(M,N)
& ~ convergent_lines(L,N)
& ~ unorthogonal_lines(L,M) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( unorthogonal_lines(sK1,sK2)
& ~ convergent_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_16]) ).
cnf(c_37,negated_conjecture,
~ unorthogonal_lines(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_38,negated_conjecture,
~ convergent_lines(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_39,negated_conjecture,
unorthogonal_lines(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_40,plain,
convergent_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_37,c_31]) ).
cnf(c_52,negated_conjecture,
( ~ unorthogonal_lines(sK1,A)
| ~ convergent_lines(sK1,A)
| convergent_lines(sK0,A) ),
inference(resolve,[status(thm)],[c_34,c_37]) ).
cnf(c_53,negated_conjecture,
( ~ unorthogonal_lines(sK1,sK2)
| ~ convergent_lines(sK1,sK2) ),
inference(resolve,[status(thm)],[c_52,c_38]) ).
cnf(c_45,negated_conjecture,
~ convergent_lines(sK1,sK2),
inference(resolve,[status(thm)],[c_53,c_39]) ).
cnf(c_54,negated_conjecture,
( convergent_lines(A,sK2)
| ~ convergent_lines(sK0,A) ),
inference(resolve,[status(thm)],[c_22,c_38]) ).
cnf(c_55,negated_conjecture,
~ convergent_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_54,c_45]) ).
cnf(c_51,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_40,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO219+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n020.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 25 13:08:48 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 2987590 was started by sandbox on n020,
% 0.07/0.35 % Fri Sep 25 13:08:48 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.35
% 0.07/0.35 % From the command line: assign(max_seconds, 300).
% 0.07/0.36
% 0.07/0.36 % SZS status Theorem for theBenchmark
% 0.07/0.36
% 0.07/0.36 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.07/0.36 % Length of proof is 13.
% 0.07/0.36 % Level of proof is 3.
% 0.07/0.36 % Maximum clause weight is 12.000.
% 0.07/0.36 % Given clauses 25.
% 0.07/0.36
% 0.07/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------