%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO011-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 07:16:45 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 10 unt; 0 def)
% Number of atoms : 23 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 6 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(lower_dimension1,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('theBenchmark.p',lower_dimension1) ).
cnf(c_10,plain,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(clausify,[status(thm)],[lower_dimension1]) ).
fof(lower_dimension2,axiom,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
file('theBenchmark.p',lower_dimension2) ).
cnf(c_11,plain,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
inference(clausify,[status(thm)],[lower_dimension2]) ).
fof(lower_dimension3,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('theBenchmark.p',lower_dimension3) ).
cnf(c_12,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(clausify,[status(thm)],[lower_dimension3]) ).
fof(colinearity4,axiom,
! [VAR_0,VAR_1,VAR_2] :
( between(VAR_2,VAR_0,VAR_1)
| between(VAR_1,VAR_2,VAR_0)
| between(VAR_0,VAR_1,VAR_2)
| ~ colinear(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',colinearity4) ).
cnf(c_22,plain,
( between(C,A,B)
| between(B,C,A)
| between(A,B,C)
| ~ colinear(A,B,C) ),
inference(clausify,[status(thm)],[colinearity4]) ).
fof(prove_lower_dimension_points_not_colinear,axiom,
colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('theBenchmark.p',prove_lower_dimension_points_not_colinear) ).
cnf(c_109,plain,
colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(clausify,[status(thm)],[prove_lower_dimension_points_not_colinear]) ).
cnf(c_175,plain,
( between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
| between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
| ~ colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
inference(resolve,[status(thm)],[c_22,c_10]) ).
cnf(c_176,plain,
( between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
| ~ colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
inference(resolve,[status(thm)],[c_175,c_11]) ).
cnf(c_177,plain,
~ colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(resolve,[status(thm)],[c_176,c_12]) ).
cnf(c_174,plain,
$false,
inference(resolve,[status(thm)],[c_109,c_177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO011-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 12:36:45 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 2386882 was started by sandbox on n016,
% 0.08/0.36 % Fri Sep 25 12:36:45 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.37
% 0.13/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.37
% 0.13/0.37 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/0.37 % Length of proof is 6.
% 0.13/0.37 % Level of proof is 1.
% 0.13/0.37 % Maximum clause weight is 16.000.
% 0.13/0.37 % Given clauses 22.
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------