%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO201+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 : 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 07:17:26 AM UTC 2026
% Result : Theorem 0.19s 0.48s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 56 ( 21 unt; 0 def)
% Number of atoms : 117 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 99 ( 38 ~; 47 |; 3 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 98 ( 12 sgn 34 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart2,axiom,
! [X] : ~ distinct_lines(X,X),
file('theBenchmark.p',apart2) ).
fof(apart3,axiom,
! [X] : ~ convergent_lines(X,X),
file('theBenchmark.p',apart3) ).
fof(apart5,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(Y,Z)
| distinct_lines(X,Z) ) ),
file('theBenchmark.p',apart5) ).
fof(ax6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('theBenchmark.p',ax6) ).
fof(ci3,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ),
file('theBenchmark.p',ci3) ).
fof(ci4,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),Y) ),
file('theBenchmark.p',ci4) ).
fof(cu1,axiom,
! [X,Y,U,V] :
( ( distinct_lines(U,V)
& distinct_points(X,Y) )
=> ( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U) ) ),
file('theBenchmark.p',cu1) ).
fof(ceq2,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ) ),
file('theBenchmark.p',ceq2) ).
fof(ceq3,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('theBenchmark.p',ceq3) ).
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(cp2,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
file('theBenchmark.p',cp2) ).
fof(ax1,axiom,
! [X,Y] :
( equal_points(X,Y)
<=> ~ distinct_points(X,Y) ),
file('theBenchmark.p',ax1) ).
fof(con,conjecture,
! [X,Y] :
( convergent_lines(X,Y)
=> equal_points(intersection_point(X,Y),intersection_point(Y,X)) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y] :
( convergent_lines(X,Y)
=> equal_points(intersection_point(X,Y),intersection_point(Y,X)) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_37,plain,
( distinct_points(A,B)
| equal_points(A,B) ),
inference(clausify,[status(thm)],[ax1]) ).
fof(nnf_36,plain,
? [X,Y] :
( ~ equal_points(intersection_point(X,Y),intersection_point(Y,X))
& convergent_lines(X,Y) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ~ equal_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0))
& convergent_lines(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_36]) ).
cnf(c_39,negated_conjecture,
~ equal_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0)),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_48,negated_conjecture,
distinct_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0)),
inference(resolve,[status(thm)],[c_39,c_37]) ).
cnf(c_49,negated_conjecture,
convergent_lines(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_67,plain,
~ apart_point_and_line(A,parallel_through_point(B,A)),
inference(clausify,[status(thm)],[cp2]) ).
cnf(c_68,plain,
~ convergent_lines(parallel_through_point(A,B),A),
inference(clausify,[status(thm)],[cp1]) ).
cnf(c_69,plain,
( convergent_lines(A,B)
| ~ distinct_lines(A,B) ),
inference(clausify,[status(thm)],[p1]) ).
cnf(c_70,plain,
( convergent_lines(A,C)
| distinct_lines(B,C)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ceq3]) ).
cnf(c_71,plain,
( apart_point_and_line(A,C)
| distinct_lines(B,C)
| ~ apart_point_and_line(A,B) ),
inference(clausify,[status(thm)],[ceq2]) ).
cnf(c_73,plain,
( apart_point_and_line(B,D)
| apart_point_and_line(B,C)
| apart_point_and_line(A,D)
| apart_point_and_line(A,C)
| ~ distinct_lines(C,D)
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[cu1]) ).
cnf(c_74,plain,
( ~ apart_point_and_line(intersection_point(A,B),B)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ci4]) ).
cnf(c_75,plain,
( ~ apart_point_and_line(intersection_point(A,B),A)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ci3]) ).
cnf(c_78,plain,
( convergent_lines(B,C)
| convergent_lines(A,C)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ax6]) ).
cnf(c_79,plain,
( distinct_lines(B,C)
| distinct_lines(A,C)
| ~ distinct_lines(A,B) ),
inference(clausify,[status(thm)],[apart5]) ).
cnf(c_81,plain,
~ convergent_lines(A,A),
inference(clausify,[status(thm)],[apart3]) ).
cnf(c_82,plain,
~ distinct_lines(A,A),
inference(clausify,[status(thm)],[apart2]) ).
cnf(c_88,plain,
~ distinct_lines(parallel_through_point(A,B),A),
inference(resolve,[status(thm)],[c_69,c_68]) ).
cnf(c_89,plain,
( convergent_lines(sK0,A)
| distinct_lines(sK1,A) ),
inference(resolve,[status(thm)],[c_70,c_49]) ).
cnf(c_90,plain,
( apart_point_and_line(intersection_point(sK1,sK0),B)
| apart_point_and_line(intersection_point(sK1,sK0),A)
| apart_point_and_line(intersection_point(sK0,sK1),B)
| apart_point_and_line(intersection_point(sK0,sK1),A)
| ~ distinct_lines(A,B) ),
inference(resolve,[status(thm)],[c_73,c_48]) ).
cnf(c_91,negated_conjecture,
~ apart_point_and_line(intersection_point(sK0,sK1),sK1),
inference(resolve,[status(thm)],[c_74,c_49]) ).
cnf(c_95,plain,
( convergent_lines(sK1,A)
| convergent_lines(sK0,A) ),
inference(resolve,[status(thm)],[c_78,c_49]) ).
cnf(c_152,plain,
( convergent_lines(B,A)
| ~ convergent_lines(A,B) ),
inference(resolve,[status(thm)],[c_78,c_81]) ).
cnf(c_98,plain,
~ convergent_lines(A,parallel_through_point(A,B)),
inference(resolve,[status(thm)],[c_152,c_68]) ).
cnf(c_153,plain,
( distinct_lines(B,A)
| ~ distinct_lines(A,B) ),
inference(resolve,[status(thm)],[c_79,c_82]) ).
cnf(c_109,plain,
~ distinct_lines(A,parallel_through_point(A,B)),
inference(resolve,[status(thm)],[c_153,c_88]) ).
cnf(c_154,plain,
( convergent_lines(B,parallel_through_point(A,C))
| ~ convergent_lines(A,B) ),
inference(resolve,[status(thm)],[c_78,c_98]) ).
cnf(c_115,plain,
~ convergent_lines(A,parallel_through_point(parallel_through_point(A,B),C)),
inference(resolve,[status(thm)],[c_154,c_68]) ).
cnf(c_119,plain,
( convergent_lines(A,B)
| convergent_lines(sK1,B)
| convergent_lines(sK0,A) ),
inference(resolve,[status(thm)],[c_95,c_78]) ).
cnf(c_155,plain,
( convergent_lines(sK1,sK0)
| convergent_lines(sK0,sK0) ),
inference(factor,[status(thm)],[c_119]) ).
cnf(c_123,plain,
convergent_lines(sK1,sK0),
inference(resolve,[status(thm)],[c_81,c_155]) ).
cnf(c_126,plain,
~ apart_point_and_line(intersection_point(sK1,sK0),sK1),
inference(resolve,[status(thm)],[c_75,c_123]) ).
cnf(c_156,plain,
( convergent_lines(sK0,A)
| apart_point_and_line(intersection_point(sK1,sK0),A)
| apart_point_and_line(intersection_point(sK1,sK0),sK1)
| apart_point_and_line(intersection_point(sK0,sK1),A)
| apart_point_and_line(intersection_point(sK0,sK1),sK1) ),
inference(resolve,[status(thm)],[c_90,c_89]) ).
cnf(c_157,plain,
( convergent_lines(sK0,A)
| apart_point_and_line(intersection_point(sK1,sK0),A)
| apart_point_and_line(intersection_point(sK1,sK0),sK1)
| apart_point_and_line(intersection_point(sK0,sK1),A) ),
inference(resolve,[status(thm)],[c_91,c_156]) ).
cnf(c_144,plain,
( convergent_lines(sK0,A)
| apart_point_and_line(intersection_point(sK1,sK0),A)
| apart_point_and_line(intersection_point(sK0,sK1),A) ),
inference(resolve,[status(thm)],[c_126,c_157]) ).
cnf(c_158,plain,
( apart_point_and_line(A,parallel_through_point(B,C))
| ~ apart_point_and_line(A,B) ),
inference(resolve,[status(thm)],[c_71,c_109]) ).
cnf(c_149,plain,
~ apart_point_and_line(A,B),
inference(resolve,[status(thm)],[c_158,c_67]) ).
cnf(c_159,plain,
( convergent_lines(sK0,A)
| apart_point_and_line(intersection_point(sK1,sK0),A) ),
inference(resolve,[status(thm)],[c_149,c_144]) ).
cnf(c_150,plain,
convergent_lines(sK0,A),
inference(resolve,[status(thm)],[c_149,c_159]) ).
cnf(c_151,plain,
$false,
inference(resolve,[status(thm)],[c_150,c_115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO201+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n007.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Fri Sep 25 13:03:09 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 1064002 was started by sandbox2 on n007,
% 0.19/0.45 % Fri Sep 25 13:03:09 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.47
% 0.19/0.47 % From the command line: assign(max_seconds, 300).
% 0.19/0.48
% 0.19/0.48 % SZS status Theorem for theBenchmark
% 0.19/0.48
% 0.19/0.48 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.19/0.48 % Length of proof is 45.
% 0.19/0.48 % Level of proof is 8.
% 0.19/0.48 % Maximum clause weight is 33.000.
% 0.19/0.48 % Given clauses 51.
% 0.19/0.48
% 0.19/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------