%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO186+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 07:17:20 AM UTC 2026
% Result : Theorem 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 11 unt; 0 def)
% Number of atoms : 75 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 78 ( 31 ~; 26 |; 15 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 18 !; 4 ?)
% 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,U,V] :
( ( ~ apart_point_and_line(X,V)
& ~ apart_point_and_line(X,U)
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> ~ distinct_points(X,intersection_point(U,V)) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y,U,V] :
( ( ~ apart_point_and_line(X,V)
& ~ apart_point_and_line(X,U)
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> ~ distinct_points(X,intersection_point(U,V)) ),
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,U,V] :
( distinct_points(X,intersection_point(U,V))
& ~ apart_point_and_line(X,V)
& ~ apart_point_and_line(X,U)
& convergent_lines(U,V)
& distinct_points(X,Y) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( distinct_points(sK2,intersection_point(sK0,sK1))
& ~ apart_point_and_line(sK2,sK1)
& ~ apart_point_and_line(sK2,sK0)
& convergent_lines(sK0,sK1)
& distinct_points(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK0,sK1]),skolemize(X,sK2),skolemize(Y,sK3),skolemize(U,sK0),skolemize(V,sK1)],[nnf_13]) ).
cnf(c_29,negated_conjecture,
convergent_lines(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_30,negated_conjecture,
~ apart_point_and_line(sK2,sK0),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_31,negated_conjecture,
~ apart_point_and_line(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_32,negated_conjecture,
distinct_points(sK2,intersection_point(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_36,plain,
distinct_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_29,c_27]) ).
cnf(c_49,negated_conjecture,
( distinct_points(A,intersection_point(sK0,sK1))
| ~ apart_point_and_line(A,sK1) ),
inference(resolve,[status(thm)],[c_23,c_29]) ).
cnf(c_40,negated_conjecture,
~ apart_point_and_line(intersection_point(sK0,sK1),sK1),
inference(resolve,[status(thm)],[c_49,c_14]) ).
cnf(c_50,negated_conjecture,
( distinct_points(A,intersection_point(sK0,sK1))
| ~ apart_point_and_line(A,sK0) ),
inference(resolve,[status(thm)],[c_22,c_29]) ).
cnf(c_41,negated_conjecture,
~ apart_point_and_line(intersection_point(sK0,sK1),sK0),
inference(resolve,[status(thm)],[c_50,c_14]) ).
cnf(c_51,negated_conjecture,
( apart_point_and_line(intersection_point(sK0,sK1),B)
| apart_point_and_line(intersection_point(sK0,sK1),A)
| apart_point_and_line(sK2,B)
| apart_point_and_line(sK2,A)
| ~ distinct_lines(A,B) ),
inference(resolve,[status(thm)],[c_24,c_32]) ).
cnf(c_52,negated_conjecture,
( apart_point_and_line(intersection_point(sK0,sK1),A)
| apart_point_and_line(intersection_point(sK0,sK1),sK0)
| apart_point_and_line(sK2,A)
| ~ distinct_lines(sK0,A) ),
inference(resolve,[status(thm)],[c_51,c_30]) ).
cnf(c_53,negated_conjecture,
( apart_point_and_line(intersection_point(sK0,sK1),sK1)
| apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ distinct_lines(sK0,sK1) ),
inference(resolve,[status(thm)],[c_52,c_31]) ).
cnf(c_54,negated_conjecture,
( apart_point_and_line(intersection_point(sK0,sK1),sK1)
| ~ distinct_lines(sK0,sK1) ),
inference(resolve,[status(thm)],[c_53,c_41]) ).
cnf(c_55,negated_conjecture,
~ distinct_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_54,c_40]) ).
cnf(c_48,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_36,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO186+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.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 13:05:20 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.36 % Process 2017295 was started by sandbox2 on n018,
% 0.14/0.36 % Fri Sep 25 13:05:20 2026
% 0.14/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.38
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38
% 0.14/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.38 % Length of proof is 18.
% 0.14/0.38 % Level of proof is 3.
% 0.14/0.38 % Maximum clause weight is 23.000.
% 0.14/0.38 % Given clauses 24.
% 0.14/0.38
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------