%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO198+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 07:17:25 AM UTC 2026
% Result : Theorem 0.13s 5.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 13 unt; 0 def)
% Number of atoms : 81 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 78 ( 29 ~; 28 |; 15 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 16 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X),
file('theBenchmark.p',apart1) ).
fof(con2,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( ( apart_point_and_line(Z,Y)
| apart_point_and_line(Z,X) )
=> distinct_points(Z,intersection_point(X,Y)) ) ),
file('theBenchmark.p',con2) ).
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(ceq3,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ),
file('theBenchmark.p',ceq3) ).
fof(con,conjecture,
! [X,Y,Z] :
( ( ~ apart_point_and_line(intersection_point(X,Y),Z)
& convergent_lines(X,Z)
& convergent_lines(Z,Y)
& convergent_lines(X,Y) )
=> ~ apart_point_and_line(intersection_point(X,Z),Y) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( ~ apart_point_and_line(intersection_point(X,Y),Z)
& convergent_lines(X,Z)
& convergent_lines(Z,Y)
& convergent_lines(X,Y) )
=> ~ apart_point_and_line(intersection_point(X,Z),Y) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_14,plain,
~ distinct_points(A,A),
inference(clausify,[status(thm)],[apart1]) ).
cnf(c_22,plain,
( distinct_points(C,intersection_point(A,B))
| ~ apart_point_and_line(C,A)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[con2]) ).
cnf(c_23,plain,
( distinct_points(C,intersection_point(A,B))
| ~ apart_point_and_line(C,B)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[con2]) ).
cnf(c_24,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_27,plain,
( distinct_lines(A,B)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ceq3]) ).
fof(nnf_13,plain,
? [X,Y,Z] :
( apart_point_and_line(intersection_point(X,Z),Y)
& ~ apart_point_and_line(intersection_point(X,Y),Z)
& convergent_lines(X,Z)
& convergent_lines(Z,Y)
& convergent_lines(X,Y) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK1)
& ~ apart_point_and_line(intersection_point(sK0,sK1),sK2)
& convergent_lines(sK0,sK2)
& convergent_lines(sK2,sK1)
& convergent_lines(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X,sK0),skolemize(Y,sK1),skolemize(Z,sK2)],[nnf_13]) ).
cnf(c_28,negated_conjecture,
convergent_lines(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_30,negated_conjecture,
convergent_lines(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_31,negated_conjecture,
~ apart_point_and_line(intersection_point(sK0,sK1),sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_32,negated_conjecture,
apart_point_and_line(intersection_point(sK0,sK2),sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_34,plain,
( distinct_points(A,intersection_point(sK0,sK1))
| ~ apart_point_and_line(A,sK1) ),
inference(resolve,[status(thm)],[c_28,c_23]) ).
cnf(c_74,negated_conjecture,
( distinct_points(A,intersection_point(sK0,sK1))
| ~ apart_point_and_line(A,sK0) ),
inference(resolve,[status(thm)],[c_22,c_28]) ).
cnf(c_38,negated_conjecture,
~ apart_point_and_line(intersection_point(sK0,sK1),sK0),
inference(resolve,[status(thm)],[c_74,c_14]) ).
cnf(c_45,plain,
distinct_lines(sK0,sK2),
inference(resolve,[status(thm)],[c_30,c_27]) ).
cnf(c_75,negated_conjecture,
( distinct_points(A,intersection_point(sK0,sK2))
| ~ apart_point_and_line(A,sK2) ),
inference(resolve,[status(thm)],[c_23,c_30]) ).
cnf(c_49,negated_conjecture,
~ apart_point_and_line(intersection_point(sK0,sK2),sK2),
inference(resolve,[status(thm)],[c_75,c_14]) ).
cnf(c_76,negated_conjecture,
( distinct_points(A,intersection_point(sK0,sK2))
| ~ apart_point_and_line(A,sK0) ),
inference(resolve,[status(thm)],[c_22,c_30]) ).
cnf(c_50,negated_conjecture,
~ apart_point_and_line(intersection_point(sK0,sK2),sK0),
inference(resolve,[status(thm)],[c_76,c_14]) ).
cnf(c_71,plain,
distinct_points(intersection_point(sK0,sK2),intersection_point(sK0,sK1)),
inference(resolve,[status(thm)],[c_34,c_32]) ).
cnf(c_77,plain,
( apart_point_and_line(B,sK2)
| apart_point_and_line(B,sK0)
| apart_point_and_line(A,sK2)
| apart_point_and_line(A,sK0)
| ~ distinct_points(A,B) ),
inference(resolve,[status(thm)],[c_24,c_45]) ).
cnf(c_78,plain,
( apart_point_and_line(A,sK2)
| apart_point_and_line(A,sK0)
| apart_point_and_line(intersection_point(sK0,sK2),sK2)
| ~ distinct_points(intersection_point(sK0,sK2),A) ),
inference(resolve,[status(thm)],[c_77,c_50]) ).
cnf(c_79,plain,
( apart_point_and_line(A,sK2)
| apart_point_and_line(A,sK0)
| ~ distinct_points(intersection_point(sK0,sK2),A) ),
inference(resolve,[status(thm)],[c_78,c_49]) ).
cnf(c_80,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK2)
| ~ distinct_points(intersection_point(sK0,sK2),intersection_point(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_79,c_38]) ).
cnf(c_81,negated_conjecture,
~ distinct_points(intersection_point(sK0,sK2),intersection_point(sK0,sK1)),
inference(resolve,[status(thm)],[c_80,c_31]) ).
cnf(c_73,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_71,c_81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO198+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n018.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Fri Sep 25 13:07:12 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 2021247 was started by sandbox on n018,
% 0.10/5.38 % Fri Sep 25 13:07:12 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.39
% 0.10/5.39 % From the command line: assign(max_seconds, 300).
% 0.13/5.41
% 0.13/5.41 % SZS status Theorem for theBenchmark
% 0.13/5.41
% 0.13/5.41 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/5.41 % Length of proof is 21.
% 0.13/5.41 % Level of proof is 4.
% 0.13/5.41 % Maximum clause weight is 18.000.
% 0.13/5.41 % Given clauses 31.
% 0.13/5.41
% 0.13/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------