%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO208+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 : n007.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 07:17:29 AM UTC 2026
% Result : Theorem 0.08s 0.37s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 6 unt; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 29 ( 11 ~; 3 |; 10 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 21 ( 0 sgn 12 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ),
file('theBenchmark.p',p1) ).
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,Z)
& incident_point_and_line(X,Y) )
=> equal_lines(Y,Z) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( parallel_lines(Y,Z)
& incident_point_and_line(X,Z)
& incident_point_and_line(X,Y) )
=> equal_lines(Y,Z) ),
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,Z)
& parallel_lines(Y,Z)
& incident_point_and_line(X,Z)
& incident_point_and_line(X,Y) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ~ equal_lines(sK0,sK1)
& parallel_lines(sK0,sK1)
& incident_point_and_line(sK2,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,sK1),
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_51,negated_conjecture,
~ convergent_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_44,c_43]) ).
cnf(c_71,plain,
( convergent_lines(A,B)
| ~ distinct_lines(A,B) ),
inference(clausify,[status(thm)],[p1]) ).
cnf(c_86,negated_conjecture,
distinct_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_39,c_40]) ).
cnf(c_92,negated_conjecture,
~ distinct_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_71,c_51]) ).
cnf(c_91,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_86,c_92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO208+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n007.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 25 13:04:08 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 1067456 was started by sandbox on n007,
% 0.08/0.35 % Fri Sep 25 13:04:08 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.08/0.37
% 0.08/0.37 % SZS status Theorem for theBenchmark
% 0.08/0.37
% 0.08/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.08/0.37 % Length of proof is 12.
% 0.08/0.37 % Level of proof is 3.
% 0.08/0.37 % Maximum clause weight is 6.000.
% 0.08/0.37 % Given clauses 19.
% 0.08/0.37
% 0.08/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------