%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO205+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 : n011.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 07:17:28 AM UTC 2026
% Result : Theorem 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 47 ( 18 unt; 0 def)
% Number of atoms : 108 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 104 ( 43 ~; 43 |; 9 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 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 : 64 ( 0 sgn 26 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X),
file('theBenchmark.p',apart1) ).
fof(apart2,axiom,
! [X] : ~ distinct_lines(X,X),
file('theBenchmark.p',apart2) ).
fof(apart5,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(Y,Z)
| distinct_lines(X,Z) ) ),
file('theBenchmark.p',apart5) ).
fof(apart6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('theBenchmark.p',apart6) ).
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(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] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ),
file('theBenchmark.p',ceq3) ).
fof(con,conjecture,
! [X,Y,Z] :
( ( ~ distinct_lines(Y,Z)
& convergent_lines(X,Y) )
=> ( ~ distinct_points(intersection_point(X,Y),intersection_point(X,Z))
& convergent_lines(X,Z) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( ~ distinct_lines(Y,Z)
& convergent_lines(X,Y) )
=> ( ~ distinct_points(intersection_point(X,Y),intersection_point(X,Z))
& convergent_lines(X,Z) ) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_14,plain,
~ distinct_points(A,A),
inference(clausify,[status(thm)],[apart1]) ).
cnf(c_15,plain,
~ distinct_lines(A,A),
inference(clausify,[status(thm)],[apart2]) ).
cnf(c_18,plain,
( distinct_lines(B,C)
| distinct_lines(A,C)
| ~ distinct_lines(A,B) ),
inference(clausify,[status(thm)],[apart5]) ).
cnf(c_19,plain,
( convergent_lines(B,C)
| convergent_lines(A,C)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[apart6]) ).
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_26,plain,
( apart_point_and_line(A,C)
| distinct_lines(B,C)
| ~ apart_point_and_line(A,B) ),
inference(clausify,[status(thm)],[ceq2]) ).
cnf(c_27,plain,
( distinct_lines(A,B)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ceq3]) ).
fof(nnf_13,plain,
? [X,Y,Z] :
( ( distinct_points(intersection_point(X,Y),intersection_point(X,Z))
| ~ convergent_lines(X,Z) )
& ~ distinct_lines(Y,Z)
& convergent_lines(X,Y) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ( distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
| ~ convergent_lines(sK0,sK2) )
& ~ distinct_lines(sK1,sK2)
& 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_29,negated_conjecture,
~ distinct_lines(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_30,negated_conjecture,
( distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
| ~ convergent_lines(sK0,sK2) ),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_34,plain,
( convergent_lines(sK1,A)
| convergent_lines(sK0,A) ),
inference(resolve,[status(thm)],[c_28,c_19]) ).
cnf(c_65,negated_conjecture,
( distinct_points(A,intersection_point(sK0,sK1))
| ~ apart_point_and_line(A,sK1) ),
inference(resolve,[status(thm)],[c_23,c_28]) ).
cnf(c_35,negated_conjecture,
~ apart_point_and_line(intersection_point(sK0,sK1),sK1),
inference(resolve,[status(thm)],[c_65,c_14]) ).
cnf(c_66,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_36,negated_conjecture,
~ apart_point_and_line(intersection_point(sK0,sK1),sK0),
inference(resolve,[status(thm)],[c_66,c_14]) ).
cnf(c_37,negated_conjecture,
~ convergent_lines(sK1,sK2),
inference(resolve,[status(thm)],[c_27,c_29]) ).
cnf(c_67,plain,
( distinct_lines(B,A)
| ~ distinct_lines(A,B) ),
inference(resolve,[status(thm)],[c_18,c_15]) ).
cnf(c_38,negated_conjecture,
~ distinct_lines(sK2,sK1),
inference(resolve,[status(thm)],[c_67,c_29]) ).
cnf(c_68,plain,
( apart_point_and_line(A,sK1)
| ~ apart_point_and_line(A,sK2) ),
inference(resolve,[status(thm)],[c_26,c_38]) ).
cnf(c_42,plain,
~ apart_point_and_line(intersection_point(sK0,sK1),sK2),
inference(resolve,[status(thm)],[c_68,c_35]) ).
cnf(c_43,plain,
convergent_lines(sK0,sK2),
inference(resolve,[status(thm)],[c_34,c_37]) ).
cnf(c_48,negated_conjecture,
distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2)),
inference(resolve,[status(thm)],[c_43,c_30]) ).
cnf(c_50,plain,
distinct_lines(sK0,sK2),
inference(resolve,[status(thm)],[c_43,c_27]) ).
cnf(c_69,plain,
( distinct_points(A,intersection_point(sK0,sK2))
| ~ apart_point_and_line(A,sK2) ),
inference(resolve,[status(thm)],[c_23,c_43]) ).
cnf(c_54,plain,
~ apart_point_and_line(intersection_point(sK0,sK2),sK2),
inference(resolve,[status(thm)],[c_69,c_14]) ).
cnf(c_70,plain,
( distinct_points(A,intersection_point(sK0,sK2))
| ~ apart_point_and_line(A,sK0) ),
inference(resolve,[status(thm)],[c_22,c_43]) ).
cnf(c_55,plain,
~ apart_point_and_line(intersection_point(sK0,sK2),sK0),
inference(resolve,[status(thm)],[c_70,c_14]) ).
cnf(c_71,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_50]) ).
cnf(c_72,plain,
( apart_point_and_line(A,sK2)
| apart_point_and_line(A,sK0)
| apart_point_and_line(intersection_point(sK0,sK1),sK2)
| ~ distinct_points(intersection_point(sK0,sK1),A) ),
inference(resolve,[status(thm)],[c_71,c_36]) ).
cnf(c_73,plain,
( apart_point_and_line(A,sK2)
| apart_point_and_line(A,sK0)
| ~ distinct_points(intersection_point(sK0,sK1),A) ),
inference(resolve,[status(thm)],[c_72,c_42]) ).
cnf(c_74,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK2)
| ~ distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2)) ),
inference(resolve,[status(thm)],[c_73,c_55]) ).
cnf(c_75,plain,
~ distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2)),
inference(resolve,[status(thm)],[c_74,c_54]) ).
cnf(c_64,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_48,c_75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO205+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n011.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 13:05:30 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 2080049 was started by sandbox2 on n011,
% 0.18/0.44 % Fri Sep 25 13:05:30 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.18/0.47
% 0.18/0.47 % SZS status Theorem for theBenchmark
% 0.18/0.47
% 0.18/0.47 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.18/0.47 % Length of proof is 33.
% 0.18/0.47 % Level of proof is 5.
% 0.18/0.47 % Maximum clause weight is 18.000.
% 0.18/0.47 % Given clauses 31.
% 0.18/0.47
% 0.18/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------