%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO206+3 : TPTP v9.3.1. Bugfixed v4.0.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 07:17:28 AM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 9 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 15 ~; 7 |; 6 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 2 sgn 17 !; 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(p1,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ),
file('theBenchmark.p',p1) ).
fof(cp1,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('theBenchmark.p',cp1) ).
fof(ax2,axiom,
! [X,Y] :
( equal_lines(X,Y)
<=> ~ distinct_lines(X,Y) ),
file('theBenchmark.p',ax2) ).
fof(a3,axiom,
! [X,Y] :
( parallel_lines(X,Y)
<=> ~ convergent_lines(X,Y) ),
file('theBenchmark.p',a3) ).
fof(con,conjecture,
! [X,Y,Z] :
( ( parallel_lines(Y,Z)
& incident_point_and_line(X,Y) )
=> equal_lines(Y,parallel_through_point(Z,X)) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( parallel_lines(Y,Z)
& incident_point_and_line(X,Y) )
=> equal_lines(Y,parallel_through_point(Z,X)) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_39,plain,
( distinct_lines(A,B)
| equal_lines(A,B) ),
inference(clausify,[status(thm)],[ax2]) ).
fof(nnf_36,plain,
? [X,Y,Z] :
( ~ equal_lines(Y,parallel_through_point(Z,X))
& parallel_lines(Y,Z)
& incident_point_and_line(X,Y) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ~ equal_lines(sK0,parallel_through_point(sK1,sK2))
& parallel_lines(sK0,sK1)
& incident_point_and_line(sK2,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK0,sK1]),skolemize(X,sK2),skolemize(Y,sK0),skolemize(Z,sK1)],[nnf_36]) ).
cnf(c_40,negated_conjecture,
~ equal_lines(sK0,parallel_through_point(sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_43,plain,
( ~ convergent_lines(A,B)
| ~ parallel_lines(A,B) ),
inference(clausify,[status(thm)],[a3]) ).
cnf(c_44,negated_conjecture,
parallel_lines(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_50,negated_conjecture,
~ convergent_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_44,c_43]) ).
cnf(c_69,plain,
~ convergent_lines(parallel_through_point(A,B),A),
inference(clausify,[status(thm)],[cp1]) ).
cnf(c_70,plain,
( convergent_lines(A,B)
| ~ distinct_lines(A,B) ),
inference(clausify,[status(thm)],[p1]) ).
cnf(c_79,plain,
( convergent_lines(B,C)
| convergent_lines(A,C)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ax6]) ).
cnf(c_85,negated_conjecture,
distinct_lines(sK0,parallel_through_point(sK1,sK2)),
inference(resolve,[status(thm)],[c_39,c_40]) ).
cnf(c_97,negated_conjecture,
( convergent_lines(A,sK1)
| ~ convergent_lines(sK0,A) ),
inference(resolve,[status(thm)],[c_79,c_50]) ).
cnf(c_92,negated_conjecture,
~ convergent_lines(sK0,parallel_through_point(sK1,A)),
inference(resolve,[status(thm)],[c_97,c_69]) ).
cnf(c_98,negated_conjecture,
convergent_lines(sK0,parallel_through_point(sK1,sK2)),
inference(resolve,[status(thm)],[c_85,c_70]) ).
cnf(c_96,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_92,c_98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO206+3 : TPTP v9.3.1. Bugfixed v4.0.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 13:08:36 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 3330954 was started by sandbox2 on n002,
% 0.13/0.36 % Fri Sep 25 13:08:36 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 17.
% 0.13/0.38 % Level of proof is 4.
% 0.13/0.38 % Maximum clause weight is 9.000.
% 0.13/0.38 % Given clauses 34.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------