%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO200+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 : 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 07:17:26 AM UTC 2026
% Result : Theorem 0.08s 0.52s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 11 unt; 0 def)
% Number of atoms : 76 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 64 ( 21 ~; 33 |; 4 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 15 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X),
file('theBenchmark.p',apart1) ).
fof(apart4,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( distinct_points(Y,Z)
| distinct_points(X,Z) ) ),
file('theBenchmark.p',apart4) ).
fof(con1,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(X,Y))
=> ( distinct_points(Z,Y)
& distinct_points(Z,X) ) ) ),
file('theBenchmark.p',con1) ).
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(con,conjecture,
! [X,Y] :
( distinct_points(X,Y)
=> ~ distinct_lines(line_connecting(X,Y),line_connecting(Y,X)) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y] :
( distinct_points(X,Y)
=> ~ distinct_lines(line_connecting(X,Y),line_connecting(Y,X)) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_14,plain,
~ distinct_points(A,A),
inference(clausify,[status(thm)],[apart1]) ).
cnf(c_17,plain,
( distinct_points(B,C)
| distinct_points(A,C)
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[apart4]) ).
cnf(c_20,plain,
( distinct_points(C,A)
| ~ apart_point_and_line(C,line_connecting(A,B))
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[con1]) ).
cnf(c_21,plain,
( distinct_points(C,B)
| ~ apart_point_and_line(C,line_connecting(A,B))
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[con1]) ).
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]) ).
fof(nnf_13,plain,
? [X,Y] :
( distinct_lines(line_connecting(X,Y),line_connecting(Y,X))
& distinct_points(X,Y) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( distinct_lines(line_connecting(sK0,sK1),line_connecting(sK1,sK0))
& distinct_points(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_13]) ).
cnf(c_28,negated_conjecture,
distinct_points(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_29,negated_conjecture,
distinct_lines(line_connecting(sK0,sK1),line_connecting(sK1,sK0)),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_32,plain,
( distinct_points(sK1,A)
| distinct_points(sK0,A) ),
inference(resolve,[status(thm)],[c_28,c_17]) ).
cnf(c_47,negated_conjecture,
( distinct_points(A,sK1)
| ~ apart_point_and_line(A,line_connecting(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_21,c_28]) ).
cnf(c_33,negated_conjecture,
~ apart_point_and_line(sK1,line_connecting(sK0,sK1)),
inference(resolve,[status(thm)],[c_47,c_14]) ).
cnf(c_48,negated_conjecture,
( distinct_points(A,sK0)
| ~ apart_point_and_line(A,line_connecting(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_20,c_28]) ).
cnf(c_34,negated_conjecture,
~ apart_point_and_line(sK0,line_connecting(sK0,sK1)),
inference(resolve,[status(thm)],[c_48,c_14]) ).
cnf(c_35,plain,
( apart_point_and_line(B,line_connecting(sK1,sK0))
| apart_point_and_line(B,line_connecting(sK0,sK1))
| apart_point_and_line(A,line_connecting(sK1,sK0))
| apart_point_and_line(A,line_connecting(sK0,sK1))
| ~ distinct_points(A,B) ),
inference(resolve,[status(thm)],[c_29,c_24]) ).
cnf(c_39,plain,
( distinct_points(A,B)
| distinct_points(sK1,B)
| distinct_points(sK0,A) ),
inference(resolve,[status(thm)],[c_32,c_17]) ).
cnf(c_49,plain,
( distinct_points(sK1,sK0)
| distinct_points(sK0,sK0) ),
inference(factor,[status(thm)],[c_39]) ).
cnf(c_41,plain,
distinct_points(sK1,sK0),
inference(resolve,[status(thm)],[c_14,c_49]) ).
cnf(c_50,plain,
( distinct_points(A,sK0)
| ~ apart_point_and_line(A,line_connecting(sK1,sK0)) ),
inference(resolve,[status(thm)],[c_21,c_41]) ).
cnf(c_44,plain,
~ apart_point_and_line(sK0,line_connecting(sK1,sK0)),
inference(resolve,[status(thm)],[c_50,c_14]) ).
cnf(c_51,plain,
( distinct_points(A,sK1)
| ~ apart_point_and_line(A,line_connecting(sK1,sK0)) ),
inference(resolve,[status(thm)],[c_20,c_41]) ).
cnf(c_45,plain,
~ apart_point_and_line(sK1,line_connecting(sK1,sK0)),
inference(resolve,[status(thm)],[c_51,c_14]) ).
cnf(c_52,plain,
( apart_point_and_line(sK0,line_connecting(sK1,sK0))
| apart_point_and_line(sK0,line_connecting(sK0,sK1))
| apart_point_and_line(sK1,line_connecting(sK1,sK0))
| apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_35,c_41]) ).
cnf(c_53,plain,
( apart_point_and_line(sK0,line_connecting(sK1,sK0))
| apart_point_and_line(sK0,line_connecting(sK0,sK1))
| apart_point_and_line(sK1,line_connecting(sK1,sK0)) ),
inference(resolve,[status(thm)],[c_33,c_52]) ).
cnf(c_54,plain,
( apart_point_and_line(sK0,line_connecting(sK1,sK0))
| apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_45,c_53]) ).
cnf(c_55,plain,
apart_point_and_line(sK0,line_connecting(sK1,sK0)),
inference(resolve,[status(thm)],[c_34,c_54]) ).
cnf(c_46,plain,
$false,
inference(resolve,[status(thm)],[c_44,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO200+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.50 % Computer : n005.cluster.edu
% 0.08/0.50 % Model : x86_64 x86_64
% 0.08/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.50 % Memory : 8046.5625MB
% 0.08/0.50 % OS : Linux 6.8.0-71-generic
% 0.08/0.50 % CPULimit : 300
% 0.08/0.50 % WCLimit : 300
% 0.08/0.50 % DateTime : Fri Sep 25 13:05:17 UTC 2026
% 0.08/0.50 % CPUTime :
% 0.08/0.50 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.50 % Process 3542592 was started by sandbox on n005,
% 0.08/0.50 % Fri Sep 25 13:05:17 2026
% 0.08/0.50 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.51
% 0.08/0.51 % From the command line: assign(max_seconds, 300).
% 0.08/0.52
% 0.08/0.52 % SZS status Theorem for theBenchmark
% 0.08/0.52
% 0.08/0.52 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.08/0.52 % Length of proof is 21.
% 0.08/0.52 % Level of proof is 6.
% 0.08/0.52 % Maximum clause weight is 23.000.
% 0.08/0.52 % Given clauses 24.
% 0.08/0.52
% 0.08/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------