%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO036-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 07:16:51 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 15 unt; 0 def)
% Number of atoms : 44 ( 28 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 18 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 21 ( 5 sgn 6 !; 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(b1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( between(VAR_3,VAR_1,VAR_2)
| VAR_0 != VAR_2
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',b1) ).
cnf(c_53,plain,
( between(D,B,C)
| A != C
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[b1]) ).
fof(t2,axiom,
! [VAR_0,VAR_1] : between(VAR_0,VAR_0,VAR_1),
file('theBenchmark.p',t2) ).
cnf(c_55,plain,
between(A,A,B),
inference(clausify,[status(thm)],[t2]) ).
fof(prove_axioms_points_are_distinct,axiom,
( lower_dimension_point_1 = lower_dimension_point_3
| lower_dimension_point_2 = lower_dimension_point_3
| lower_dimension_point_1 = lower_dimension_point_2 ),
file('theBenchmark.p',prove_axioms_points_are_distinct) ).
cnf(c_63,plain,
( lower_dimension_point_1 = lower_dimension_point_3
| lower_dimension_point_2 = lower_dimension_point_3
| lower_dimension_point_1 = lower_dimension_point_2 ),
inference(clausify,[status(thm)],[prove_axioms_points_are_distinct]) ).
cnf(c_209,plain,
( lower_dimension_point_1 = lower_dimension_point_3
| lower_dimension_point_2 = lower_dimension_point_3
| lower_dimension_point_2 = lower_dimension_point_1 ),
inference(copy,[status(thm)],[c_63]) ).
cnf(c_210,plain,
( lower_dimension_point_1 = lower_dimension_point_3
| lower_dimension_point_3 = lower_dimension_point_2
| lower_dimension_point_2 = lower_dimension_point_1 ),
inference(copy,[status(thm)],[c_209]) ).
cnf(c_64,plain,
( lower_dimension_point_3 = lower_dimension_point_1
| lower_dimension_point_3 = lower_dimension_point_2
| lower_dimension_point_2 = lower_dimension_point_1 ),
inference(copy,[status(thm)],[c_210]) ).
cnf(c_211,plain,
( between(C,A,B)
| A != B ),
inference(resolve,[status(thm)],[c_53,c_55]) ).
cnf(c_212,plain,
lower_dimension_point_1 != lower_dimension_point_2,
inference(resolve,[status(thm)],[c_211,c_12]) ).
cnf(c_205,plain,
lower_dimension_point_2 != lower_dimension_point_1,
inference(copy,[status(thm)],[c_212]) ).
cnf(c_213,plain,
( between(C,A,B)
| A != B ),
inference(resolve,[status(thm)],[c_53,c_55]) ).
cnf(c_206,plain,
lower_dimension_point_3 != lower_dimension_point_1,
inference(resolve,[status(thm)],[c_213,c_11]) ).
cnf(c_214,plain,
( between(C,A,B)
| A != B ),
inference(resolve,[status(thm)],[c_53,c_55]) ).
cnf(c_215,plain,
lower_dimension_point_2 != lower_dimension_point_3,
inference(resolve,[status(thm)],[c_214,c_10]) ).
cnf(c_207,plain,
lower_dimension_point_3 != lower_dimension_point_2,
inference(copy,[status(thm)],[c_215]) ).
cnf(c_216,plain,
( lower_dimension_point_3 = lower_dimension_point_1
| lower_dimension_point_3 = lower_dimension_point_2 ),
inference(resolve,[status(thm)],[c_205,c_64]) ).
cnf(c_217,plain,
lower_dimension_point_3 = lower_dimension_point_1,
inference(resolve,[status(thm)],[c_207,c_216]) ).
cnf(c_208,plain,
$false,
inference(resolve,[status(thm)],[c_206,c_217]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO036-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.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 12:35:26 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1050923 was started by sandbox2 on n008,
% 0.10/0.37 % Fri Sep 25 12:35:26 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.43
% 0.14/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.43
% 0.14/0.43 % Proof 1 at 0.03 (+ 0.00) seconds.
% 0.14/0.43 % Length of proof is 11.
% 0.14/0.43 % Level of proof is 2.
% 0.14/0.43 % Maximum clause weight is 16.000.
% 0.14/0.43 % Given clauses 42.
% 0.14/0.43
% 0.14/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------