%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO009-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 07:16:44 AM UTC 2026
% Result : Unsatisfiable 32.67s 9.56s
% Output : CNFRefutation 32.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 39 ( 26 unt; 0 def)
% Number of atoms : 63 ( 7 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 56 ( 32 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-4 aty)
% Number of variables : 50 ( 9 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(segment_construction1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : between(VAR_0,VAR_1,extension(VAR_0,VAR_1,VAR_2,VAR_3)),
file('theBenchmark.p',segment_construction1) ).
cnf(c_4,plain,
between(A,B,extension(A,B,C,D)),
inference(clausify,[status(thm)],[segment_construction1]) ).
fof(t1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( between(VAR_2,VAR_1,VAR_0)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',t1) ).
cnf(c_55,plain,
( between(C,B,A)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[t1]) ).
fof(b5,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( between(VAR_1,VAR_2,VAR_3)
| ~ between(VAR_0,VAR_2,VAR_3)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',b5) ).
cnf(c_59,plain,
( between(B,C,D)
| ~ between(A,C,D)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[b5]) ).
fof(e3_1,axiom,
! [VAR_0,VAR_1] : VAR_0 != extension(VAR_1,VAR_0,lower_dimension_point_1,lower_dimension_point_2),
file('theBenchmark.p',e3_1) ).
cnf(c_70,plain,
A != extension(B,A,lower_dimension_point_1,lower_dimension_point_2),
inference(clausify,[status(thm)],[e3_1]) ).
cnf(c_71,plain,
extension(A,B,lower_dimension_point_1,lower_dimension_point_2) != B,
inference(copy,[status(thm)],[c_70]) ).
fof(t7,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( between(VAR_3,VAR_0,VAR_1)
| between(VAR_0,VAR_3,VAR_1)
| VAR_1 = VAR_2
| ~ between(VAR_3,VAR_1,VAR_2)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',t7) ).
cnf(c_92,plain,
( between(D,A,B)
| between(A,D,B)
| B = C
| ~ between(D,B,C)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[t7]) ).
fof(c_between_a_and_e,axiom,
between(a,c,e),
file('theBenchmark.p',c_between_a_and_e) ).
cnf(c_93,plain,
between(a,c,e),
inference(clausify,[status(thm)],[c_between_a_and_e]) ).
fof(d_between_a_and_e,axiom,
between(a,d,e),
file('theBenchmark.p',d_between_a_and_e) ).
cnf(c_94,plain,
between(a,d,e),
inference(clausify,[status(thm)],[d_between_a_and_e]) ).
fof(c_not_between_a_and_d,axiom,
~ between(a,c,d),
file('theBenchmark.p',c_not_between_a_and_d) ).
cnf(c_95,plain,
~ between(a,c,d),
inference(clausify,[status(thm)],[c_not_between_a_and_d]) ).
fof(prove_d_between_a_and_c,axiom,
~ between(a,d,c),
file('theBenchmark.p',prove_d_between_a_and_c) ).
cnf(c_96,plain,
~ between(a,d,c),
inference(clausify,[status(thm)],[prove_d_between_a_and_c]) ).
cnf(c_439,plain,
( between(c,e,A)
| ~ between(a,e,A) ),
inference(resolve,[status(thm)],[c_93,c_59]) ).
cnf(c_442,plain,
between(e,c,a),
inference(resolve,[status(thm)],[c_93,c_55]) ).
cnf(c_473,plain,
( between(d,e,A)
| ~ between(a,e,A) ),
inference(resolve,[status(thm)],[c_94,c_59]) ).
cnf(c_476,plain,
between(e,d,a),
inference(resolve,[status(thm)],[c_94,c_55]) ).
cnf(c_500,plain,
~ between(d,c,a),
inference(resolve,[status(thm)],[c_55,c_95]) ).
cnf(c_512,plain,
~ between(c,d,a),
inference(resolve,[status(thm)],[c_55,c_96]) ).
cnf(c_1586,plain,
( between(A,c,a)
| ~ between(e,A,c) ),
inference(resolve,[status(thm)],[c_59,c_442]) ).
cnf(c_936,plain,
~ between(e,d,c),
inference(resolve,[status(thm)],[c_1586,c_500]) ).
cnf(c_1587,plain,
( between(A,d,a)
| ~ between(e,A,d) ),
inference(resolve,[status(thm)],[c_59,c_476]) ).
cnf(c_1050,plain,
~ between(e,c,d),
inference(resolve,[status(thm)],[c_1587,c_512]) ).
cnf(c_1116,plain,
between(c,e,extension(a,e,A,B)),
inference(resolve,[status(thm)],[c_439,c_4]) ).
cnf(c_1148,plain,
~ between(c,d,e),
inference(resolve,[status(thm)],[c_55,c_936]) ).
cnf(c_1174,plain,
between(d,e,extension(a,e,A,B)),
inference(resolve,[status(thm)],[c_473,c_4]) ).
cnf(c_1224,plain,
~ between(d,c,e),
inference(resolve,[status(thm)],[c_55,c_1050]) ).
cnf(c_1588,plain,
( between(c,A,e)
| between(A,c,e)
| e = extension(a,e,B,C)
| ~ between(A,e,extension(a,e,B,C)) ),
inference(resolve,[status(thm)],[c_92,c_1116]) ).
cnf(c_1589,plain,
B != extension(A,B,lower_dimension_point_1,lower_dimension_point_2),
inference(copy,[status(thm)],[c_71]) ).
cnf(c_1590,plain,
( between(c,A,e)
| between(A,c,e)
| ~ between(A,e,extension(a,e,lower_dimension_point_1,lower_dimension_point_2)) ),
inference(resolve,[status(thm)],[c_1588,c_1589]) ).
cnf(c_1591,plain,
( between(c,d,e)
| ~ between(d,e,extension(a,e,lower_dimension_point_1,lower_dimension_point_2)) ),
inference(resolve,[status(thm)],[c_1590,c_1224]) ).
cnf(c_1592,plain,
~ between(d,e,extension(a,e,lower_dimension_point_1,lower_dimension_point_2)),
inference(resolve,[status(thm)],[c_1591,c_1148]) ).
cnf(c_1585,plain,
$false,
inference(resolve,[status(thm)],[c_1174,c_1592]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO009-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.39 % Computer : n009.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Fri Sep 25 12:31:19 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.39 % Process 1603980 was started by sandbox2 on n009,
% 0.11/5.39 % Fri Sep 25 12:31:19 2026
% 0.11/5.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/5.41
% 0.16/5.41 % From the command line: assign(max_seconds, 300).
% 32.67/9.56
% 32.67/9.56 % SZS status Unsatisfiable for theBenchmark
% 32.67/9.56
% 32.67/9.56 % Proof 1 at 4.00 (+ 0.15) seconds.
% 32.67/9.56 % Length of proof is 23.
% 32.67/9.56 % Level of proof is 4.
% 32.67/9.56 % Maximum clause weight is 19.000.
% 32.67/9.56 % Given clauses 244.
% 32.67/9.56
% 32.67/9.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------