%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO202+1 : 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 : n005.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 07:17:27 AM UTC 2026
% Result : Theorem 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 13 unt; 0 def)
% Number of atoms : 75 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 69 ( 26 ~; 25 |; 11 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 20 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart3,axiom,
! [X] : ~ convergent_lines(X,X),
file('theBenchmark.p',apart3) ).
fof(ci1,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('theBenchmark.p',ci1) ).
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(ceq3,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('theBenchmark.p',ceq3) ).
fof(con,conjecture,
! [X,Y,Z] :
( ( convergent_lines(line_connecting(X,Y),line_connecting(X,Z))
& distinct_points(X,Z)
& distinct_points(X,Y) )
=> ~ distinct_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( convergent_lines(line_connecting(X,Y),line_connecting(X,Z))
& distinct_points(X,Z)
& distinct_points(X,Y) )
=> ~ distinct_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_18,plain,
~ convergent_lines(A,A),
inference(clausify,[status(thm)],[apart3]) ).
cnf(c_22,plain,
( ~ apart_point_and_line(A,line_connecting(A,B))
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[ci1]) ).
cnf(c_24,plain,
( ~ apart_point_and_line(intersection_point(A,B),A)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ci3]) ).
cnf(c_25,plain,
( ~ apart_point_and_line(intersection_point(A,B),B)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ci4]) ).
cnf(c_26,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_29,plain,
( convergent_lines(A,C)
| distinct_lines(B,C)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ceq3]) ).
fof(nnf_15,plain,
? [X,Y,Z] :
( distinct_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X)
& convergent_lines(line_connecting(X,Y),line_connecting(X,Z))
& distinct_points(X,Z)
& distinct_points(X,Y) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( distinct_points(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),sK0)
& convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
& distinct_points(sK0,sK2)
& distinct_points(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X,sK0),skolemize(Y,sK1),skolemize(Z,sK2)],[nnf_15]) ).
cnf(c_30,negated_conjecture,
distinct_points(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_31,negated_conjecture,
distinct_points(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_32,negated_conjecture,
convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_33,negated_conjecture,
distinct_points(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),sK0),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_35,plain,
~ apart_point_and_line(sK0,line_connecting(sK0,sK1)),
inference(resolve,[status(thm)],[c_30,c_22]) ).
cnf(c_38,plain,
~ apart_point_and_line(sK0,line_connecting(sK0,sK2)),
inference(resolve,[status(thm)],[c_31,c_22]) ).
cnf(c_40,plain,
( convergent_lines(line_connecting(sK0,sK1),A)
| distinct_lines(line_connecting(sK0,sK2),A) ),
inference(resolve,[status(thm)],[c_32,c_29]) ).
cnf(c_41,plain,
~ apart_point_and_line(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),line_connecting(sK0,sK2)),
inference(resolve,[status(thm)],[c_32,c_25]) ).
cnf(c_42,plain,
~ apart_point_and_line(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),line_connecting(sK0,sK1)),
inference(resolve,[status(thm)],[c_32,c_24]) ).
cnf(c_95,negated_conjecture,
( apart_point_and_line(sK0,B)
| apart_point_and_line(sK0,A)
| apart_point_and_line(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),B)
| apart_point_and_line(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),A)
| ~ distinct_lines(A,B) ),
inference(resolve,[status(thm)],[c_26,c_33]) ).
cnf(c_96,negated_conjecture,
( apart_point_and_line(sK0,A)
| apart_point_and_line(sK0,line_connecting(sK0,sK2))
| apart_point_and_line(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),A)
| ~ distinct_lines(line_connecting(sK0,sK2),A) ),
inference(resolve,[status(thm)],[c_95,c_41]) ).
cnf(c_97,negated_conjecture,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,line_connecting(sK0,sK2))
| ~ distinct_lines(line_connecting(sK0,sK2),line_connecting(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_96,c_42]) ).
cnf(c_98,negated_conjecture,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ distinct_lines(line_connecting(sK0,sK2),line_connecting(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_97,c_38]) ).
cnf(c_54,negated_conjecture,
~ distinct_lines(line_connecting(sK0,sK2),line_connecting(sK0,sK1)),
inference(resolve,[status(thm)],[c_98,c_35]) ).
cnf(c_99,plain,
distinct_lines(line_connecting(sK0,sK2),line_connecting(sK0,sK1)),
inference(resolve,[status(thm)],[c_40,c_18]) ).
cnf(c_94,plain,
$false,
inference(resolve,[status(thm)],[c_54,c_99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO202+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n005.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 13:05:02 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3541419 was started by sandbox on n005,
% 0.10/0.37 % Fri Sep 25 13:05:02 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.39
% 0.10/0.39 % SZS status Theorem for theBenchmark
% 0.10/0.39
% 0.10/0.39 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.10/0.39 % Length of proof is 24.
% 0.10/0.39 % Level of proof is 4.
% 0.10/0.39 % Maximum clause weight is 26.000.
% 0.10/0.39 % Given clauses 32.
% 0.10/0.39
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------