%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO200+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 0.04s 15.35s
% Output : CNFRefutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 12 unt; 0 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 59 ( 21 ~; 28 |; 3 &)
% ( 1 <=>; 6 =>; 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 18 !; 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(ci1,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('theBenchmark.p',ci1) ).
fof(ci2,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
file('theBenchmark.p',ci2) ).
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(ax2,axiom,
! [X,Y] :
( equal_lines(X,Y)
<=> ~ distinct_lines(X,Y) ),
file('theBenchmark.p',ax2) ).
fof(con,conjecture,
! [X,Y] :
( distinct_points(X,Y)
=> equal_lines(line_connecting(X,Y),line_connecting(Y,X)) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y] :
( distinct_points(X,Y)
=> equal_lines(line_connecting(X,Y),line_connecting(Y,X)) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_39,plain,
( distinct_lines(A,B)
| equal_lines(A,B) ),
inference(clausify,[status(thm)],[ax2]) ).
fof(nnf_36,plain,
? [X,Y] :
( ~ equal_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,
( ~ equal_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_36]) ).
cnf(c_40,negated_conjecture,
~ equal_lines(line_connecting(sK0,sK1),line_connecting(sK1,sK0)),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_48,negated_conjecture,
distinct_points(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_72,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_75,plain,
( ~ apart_point_and_line(B,line_connecting(A,B))
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[ci2]) ).
cnf(c_76,plain,
( ~ apart_point_and_line(A,line_connecting(A,B))
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[ci1]) ).
cnf(c_79,plain,
( distinct_points(B,C)
| distinct_points(A,C)
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[apart4]) ).
cnf(c_82,plain,
~ distinct_points(A,A),
inference(clausify,[status(thm)],[apart1]) ).
cnf(c_83,negated_conjecture,
distinct_lines(line_connecting(sK0,sK1),line_connecting(sK1,sK0)),
inference(resolve,[status(thm)],[c_39,c_40]) ).
cnf(c_87,plain,
( apart_point_and_line(sK1,B)
| apart_point_and_line(sK1,A)
| apart_point_and_line(sK0,B)
| apart_point_and_line(sK0,A)
| ~ distinct_lines(A,B) ),
inference(resolve,[status(thm)],[c_72,c_48]) ).
cnf(c_88,plain,
~ apart_point_and_line(sK1,line_connecting(sK0,sK1)),
inference(resolve,[status(thm)],[c_75,c_48]) ).
cnf(c_89,plain,
~ apart_point_and_line(sK0,line_connecting(sK0,sK1)),
inference(resolve,[status(thm)],[c_76,c_48]) ).
cnf(c_91,plain,
( distinct_points(sK1,A)
| distinct_points(sK0,A) ),
inference(resolve,[status(thm)],[c_79,c_48]) ).
cnf(c_110,plain,
( distinct_points(A,B)
| distinct_points(sK1,B)
| distinct_points(sK0,A) ),
inference(resolve,[status(thm)],[c_91,c_79]) ).
cnf(c_126,plain,
( distinct_points(sK1,sK0)
| distinct_points(sK0,sK0) ),
inference(factor,[status(thm)],[c_110]) ).
cnf(c_115,plain,
distinct_points(sK1,sK0),
inference(resolve,[status(thm)],[c_82,c_126]) ).
cnf(c_116,plain,
~ apart_point_and_line(sK1,line_connecting(sK1,sK0)),
inference(resolve,[status(thm)],[c_115,c_76]) ).
cnf(c_117,plain,
~ apart_point_and_line(sK0,line_connecting(sK1,sK0)),
inference(resolve,[status(thm)],[c_115,c_75]) ).
cnf(c_127,negated_conjecture,
( apart_point_and_line(sK1,line_connecting(sK1,sK0))
| apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,line_connecting(sK1,sK0))
| apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_87,c_83]) ).
cnf(c_128,negated_conjecture,
( apart_point_and_line(sK1,line_connecting(sK1,sK0))
| apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,line_connecting(sK1,sK0)) ),
inference(resolve,[status(thm)],[c_89,c_127]) ).
cnf(c_129,negated_conjecture,
( apart_point_and_line(sK1,line_connecting(sK1,sK0))
| apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_117,c_128]) ).
cnf(c_130,negated_conjecture,
apart_point_and_line(sK1,line_connecting(sK1,sK0)),
inference(resolve,[status(thm)],[c_88,c_129]) ).
cnf(c_125,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_116,c_130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO200+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/15.33 % Computer : n012.cluster.edu
% 0.04/15.33 % Model : x86_64 x86_64
% 0.04/15.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/15.33 % Memory : 8046.5625MB
% 0.04/15.33 % OS : Linux 6.8.0-71-generic
% 0.04/15.33 % CPULimit : 300
% 0.04/15.33 % WCLimit : 300
% 0.04/15.33 % DateTime : Fri Sep 25 13:05:08 UTC 2026
% 0.04/15.33 % CPUTime :
% 0.04/15.33 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/15.33 % Process 2161146 was started by sandbox on n012,
% 0.04/15.33 % Fri Sep 25 13:05:08 2026
% 0.04/15.33 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.04/15.34
% 0.04/15.34 % From the command line: assign(max_seconds, 300).
% 0.04/15.35
% 0.04/15.35 % SZS status Theorem for theBenchmark
% 0.04/15.35
% 0.04/15.35 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.04/15.35 % Length of proof is 25.
% 0.04/15.35 % Level of proof is 6.
% 0.04/15.35 % Maximum clause weight is 18.000.
% 0.04/15.35 % Given clauses 44.
% 0.04/15.35
% 0.04/15.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------