%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO255+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 07:17:43 AM UTC 2026
% Result : Theorem 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 14 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 49 ( 24 ~; 14 |; 7 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 49 ( 1 sgn 19 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a4_defns,axiom,
! [X,Y] :
( equally_directed_lines(X,Y)
<=> ~ unequally_directed_lines(X,Y) ),
file('theBenchmark.p',a4_defns) ).
fof(ax4_defns,axiom,
! [L,A,B] :
( before_on_line(L,A,B)
<=> ( equally_directed_lines(L,line_connecting(A,B))
& incident_point_and_line(B,L)
& incident_point_and_line(A,L)
& distinct_points(A,B) ) ),
file('theBenchmark.p',ax4_defns) ).
fof(ax5_basics,axiom,
! [L] : equally_directed_lines(L,L),
file('theBenchmark.p',ax5_basics) ).
fof(ax6_basics,axiom,
! [L,M,N] :
( unequally_directed_lines(L,M)
=> ( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N) ) ),
file('theBenchmark.p',ax6_basics) ).
fof(ax8_basics,axiom,
! [L,M] :
( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ),
file('theBenchmark.p',ax8_basics) ).
fof(ax9_cons_objs,axiom,
! [A,B] :
( distinct_points(A,B)
=> equally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))) ),
file('theBenchmark.p',ax9_cons_objs) ).
fof(con,conjecture,
! [L,A,B] :
~ ( before_on_line(L,B,A)
& before_on_line(L,A,B) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [L,A,B] :
~ ( before_on_line(L,B,A)
& before_on_line(L,A,B) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_47,plain,
( ~ unequally_directed_lines(A,B)
| ~ equally_directed_lines(A,B) ),
inference(clausify,[status(thm)],[a4_defns]) ).
cnf(c_48,plain,
( equally_directed_lines(A,line_connecting(B,C))
| ~ before_on_line(A,B,C) ),
inference(clausify,[status(thm)],[ax4_defns]) ).
cnf(c_50,plain,
equally_directed_lines(A,A),
inference(clausify,[status(thm)],[ax5_basics]) ).
cnf(c_51,plain,
( equally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A)))
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[ax9_cons_objs]) ).
cnf(c_89,plain,
( ~ unequally_directed_lines(A,line_connecting(B,C))
| ~ before_on_line(A,B,C) ),
inference(resolve,[status(thm)],[c_48,c_47]) ).
fof(nnf_37,plain,
? [L,A,B] :
( before_on_line(L,B,A)
& before_on_line(L,A,B) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( before_on_line(sK0,sK1,sK2)
& before_on_line(sK0,sK2,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK1]),skolemize(L,sK0),skolemize(A,sK2),skolemize(B,sK1)],[nnf_37]) ).
cnf(c_93,negated_conjecture,
before_on_line(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_94,negated_conjecture,
before_on_line(sK0,sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_97,plain,
( distinct_points(B,C)
| ~ before_on_line(A,B,C) ),
inference(clausify,[status(thm)],[ax4_defns]) ).
cnf(c_98,negated_conjecture,
distinct_points(sK1,sK2),
inference(resolve,[status(thm)],[c_97,c_93]) ).
cnf(c_102,negated_conjecture,
~ unequally_directed_lines(sK0,line_connecting(sK2,sK1)),
inference(resolve,[status(thm)],[c_94,c_89]) ).
cnf(c_103,negated_conjecture,
~ unequally_directed_lines(sK0,line_connecting(sK1,sK2)),
inference(resolve,[status(thm)],[c_93,c_89]) ).
cnf(c_115,plain,
( unequally_directed_lines(B,C)
| unequally_directed_lines(A,C)
| ~ unequally_directed_lines(A,B) ),
inference(clausify,[status(thm)],[ax6_basics]) ).
cnf(c_118,plain,
( unequally_directed_lines(A,reverse_line(B))
| unequally_directed_lines(A,B) ),
inference(clausify,[status(thm)],[ax8_basics]) ).
cnf(c_133,plain,
~ unequally_directed_lines(A,A),
inference(resolve,[status(thm)],[c_50,c_47]) ).
cnf(c_134,plain,
( ~ unequally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A)))
| ~ distinct_points(A,B) ),
inference(resolve,[status(thm)],[c_51,c_47]) ).
cnf(c_165,plain,
( unequally_directed_lines(B,A)
| ~ unequally_directed_lines(A,B) ),
inference(resolve,[status(thm)],[c_115,c_133]) ).
cnf(c_145,negated_conjecture,
~ unequally_directed_lines(line_connecting(sK1,sK2),sK0),
inference(resolve,[status(thm)],[c_165,c_103]) ).
cnf(c_166,plain,
( unequally_directed_lines(B,A)
| ~ unequally_directed_lines(A,B) ),
inference(resolve,[status(thm)],[c_115,c_133]) ).
cnf(c_146,negated_conjecture,
~ unequally_directed_lines(line_connecting(sK2,sK1),sK0),
inference(resolve,[status(thm)],[c_166,c_102]) ).
cnf(c_167,negated_conjecture,
~ unequally_directed_lines(line_connecting(sK1,sK2),reverse_line(line_connecting(sK2,sK1))),
inference(resolve,[status(thm)],[c_134,c_98]) ).
cnf(c_150,negated_conjecture,
unequally_directed_lines(line_connecting(sK1,sK2),line_connecting(sK2,sK1)),
inference(resolve,[status(thm)],[c_167,c_118]) ).
cnf(c_168,plain,
( unequally_directed_lines(A,sK0)
| ~ unequally_directed_lines(line_connecting(sK1,sK2),A) ),
inference(resolve,[status(thm)],[c_115,c_145]) ).
cnf(c_169,plain,
~ unequally_directed_lines(line_connecting(sK1,sK2),line_connecting(sK2,sK1)),
inference(resolve,[status(thm)],[c_168,c_146]) ).
cnf(c_164,plain,
$false,
inference(resolve,[status(thm)],[c_150,c_169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO255+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 13:14:12 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1440276 was started by sandbox2 on n015,
% 0.09/0.37 % Fri Sep 25 13:14:12 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.39
% 0.14/0.39 % From the command line: assign(max_seconds, 300).
% 0.14/0.40
% 0.14/0.40 % Assigning unary symbol reverse_line kb_weight 0 and highest precedence (15).
% 0.14/0.40
% 0.14/0.40 % SZS status Theorem for theBenchmark
% 0.14/0.40
% 0.14/0.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/0.40 % Length of proof is 26.
% 0.14/0.40 % Level of proof is 5.
% 0.14/0.40 % Maximum clause weight is 26.000.
% 0.14/0.40 % Given clauses 27.
% 0.14/0.40
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------