%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO217+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 : n016.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 07:17:32 AM UTC 2026
% Result : Theorem 0.07s 15.46s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 12 unt; 0 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 18 ~; 8 |; 6 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 28 ( 0 sgn 12 !; 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(a3,axiom,
! [X,Y] :
( parallel_lines(X,Y)
<=> ~ convergent_lines(X,Y) ),
file('theBenchmark.p',a3) ).
fof(con,conjecture,
! [L,M,N] :
( ( parallel_lines(L,N)
& parallel_lines(L,M) )
=> parallel_lines(M,N) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [L,M,N] :
( ( parallel_lines(L,N)
& parallel_lines(L,M) )
=> parallel_lines(M,N) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_41,plain,
( convergent_lines(A,B)
| parallel_lines(A,B) ),
inference(clausify,[status(thm)],[a3]) ).
cnf(c_42,plain,
( ~ convergent_lines(A,B)
| ~ parallel_lines(A,B) ),
inference(clausify,[status(thm)],[a3]) ).
fof(nnf_36,plain,
? [L,M,N] :
( ~ parallel_lines(M,N)
& parallel_lines(L,N)
& parallel_lines(L,M) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ~ parallel_lines(sK1,sK2)
& parallel_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_44,negated_conjecture,
parallel_lines(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_45,negated_conjecture,
~ parallel_lines(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_50,negated_conjecture,
convergent_lines(sK1,sK2),
inference(resolve,[status(thm)],[c_45,c_41]) ).
cnf(c_51,negated_conjecture,
~ convergent_lines(sK0,sK2),
inference(resolve,[status(thm)],[c_44,c_42]) ).
cnf(c_52,negated_conjecture,
~ convergent_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_43,c_42]) ).
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_124,plain,
( convergent_lines(B,A)
| ~ convergent_lines(A,B) ),
inference(resolve,[status(thm)],[c_81,c_84]) ).
cnf(c_107,negated_conjecture,
~ convergent_lines(sK1,sK0),
inference(resolve,[status(thm)],[c_124,c_52]) ).
cnf(c_125,plain,
( convergent_lines(B,A)
| ~ convergent_lines(A,B) ),
inference(resolve,[status(thm)],[c_81,c_84]) ).
cnf(c_108,negated_conjecture,
~ convergent_lines(sK2,sK0),
inference(resolve,[status(thm)],[c_125,c_51]) ).
cnf(c_126,plain,
( convergent_lines(A,sK0)
| ~ convergent_lines(sK1,A) ),
inference(resolve,[status(thm)],[c_81,c_107]) ).
cnf(c_127,plain,
~ convergent_lines(sK1,sK2),
inference(resolve,[status(thm)],[c_126,c_108]) ).
cnf(c_123,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_50,c_127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO217+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.07/15.43 % CPULimit : 300
% 0.07/15.43 % WCLimit : 300
% 0.07/15.43 % DateTime : Fri Sep 25 13:07:06 UTC 2026
% 0.07/15.44 % CPUTime :
% 0.07/15.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/15.44 % Process 494734 was started by sandbox on n013,
% 0.07/15.44 % Fri Sep 25 13:07:06 2026
% 0.07/15.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/15.45
% 0.07/15.45 % From the command line: assign(max_seconds, 300).
% 0.07/15.46
% 0.07/15.46 % SZS status Theorem for theBenchmark
% 0.07/15.46
% 0.07/15.46 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.07/15.46 % Length of proof is 17.
% 0.07/15.46 % Level of proof is 4.
% 0.07/15.46 % Maximum clause weight is 14.000.
% 0.07/15.46 % Given clauses 42.
% 0.07/15.46
% 0.07/15.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------