%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO010-3 : 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 : n015.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 16.25s 2.58s
% Output : CNFRefutation 16.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 10 unt; 0 def)
% Number of atoms : 207 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 200 ( 54 ~; 146 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 42 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(colinearity1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( colinear(VAR_0,VAR_1,VAR_2)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',colinearity1) ).
cnf(c_19,plain,
( colinear(A,B,C)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[colinearity1]) ).
fof(colinearity2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( colinear(VAR_2,VAR_0,VAR_1)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',colinearity2) ).
cnf(c_20,plain,
( colinear(C,A,B)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[colinearity2]) ).
fof(colinearity3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( colinear(VAR_1,VAR_2,VAR_0)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',colinearity3) ).
cnf(c_21,plain,
( colinear(B,C,A)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[colinearity3]) ).
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(c2_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( colinear(VAR_2,VAR_1,VAR_0)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',c2_1) ).
cnf(c_101,plain,
( colinear(C,B,A)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[c2_1]) ).
fof(c2_2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( colinear(VAR_0,VAR_2,VAR_1)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',c2_2) ).
cnf(c_102,plain,
( colinear(A,C,B)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[c2_2]) ).
fof(c2_3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( colinear(VAR_1,VAR_0,VAR_2)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',c2_3) ).
cnf(c_103,plain,
( colinear(B,A,C)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[c2_3]) ).
fof(abc_colinear,axiom,
colinear(a,b,c),
file('theBenchmark.p',abc_colinear) ).
cnf(c_104,plain,
colinear(a,b,c),
inference(clausify,[status(thm)],[abc_colinear]) ).
fof(prove_colinear_in_all_orders,axiom,
( ~ colinear(c,b,a)
| ~ colinear(c,a,b)
| ~ colinear(b,c,a)
| ~ colinear(b,a,c)
| ~ colinear(a,c,b) ),
file('theBenchmark.p',prove_colinear_in_all_orders) ).
cnf(c_105,plain,
( ~ colinear(c,b,a)
| ~ colinear(c,a,b)
| ~ colinear(b,c,a)
| ~ colinear(b,a,c)
| ~ colinear(a,c,b) ),
inference(clausify,[status(thm)],[prove_colinear_in_all_orders]) ).
cnf(c_618,plain,
( between(c,a,b)
| between(b,c,a)
| between(a,b,c) ),
inference(resolve,[status(thm)],[c_104,c_22]) ).
cnf(c_856,plain,
( colinear(a,c,b)
| between(b,c,a)
| between(a,b,c) ),
inference(resolve,[status(thm)],[c_618,c_103]) ).
cnf(c_857,plain,
( colinear(c,b,a)
| between(b,c,a)
| between(a,b,c) ),
inference(resolve,[status(thm)],[c_618,c_102]) ).
cnf(c_858,plain,
( colinear(b,a,c)
| between(b,c,a)
| between(a,b,c) ),
inference(resolve,[status(thm)],[c_618,c_101]) ).
cnf(c_884,plain,
( colinear(b,c,a)
| between(b,c,a)
| between(a,b,c) ),
inference(resolve,[status(thm)],[c_618,c_20]) ).
cnf(c_885,plain,
( colinear(c,a,b)
| between(b,c,a)
| between(a,b,c) ),
inference(resolve,[status(thm)],[c_618,c_19]) ).
cnf(c_1570,plain,
( between(b,c,a)
| between(a,b,c)
| ~ colinear(c,b,a)
| ~ colinear(c,a,b)
| ~ colinear(b,c,a)
| ~ colinear(b,a,c) ),
inference(resolve,[status(thm)],[c_105,c_856]) ).
cnf(c_1571,plain,
( between(b,c,a)
| between(a,b,c)
| between(b,c,a)
| between(a,b,c)
| ~ colinear(c,b,a)
| ~ colinear(c,a,b)
| ~ colinear(b,c,a) ),
inference(resolve,[status(thm)],[c_1570,c_858]) ).
cnf(c_1572,plain,
( between(b,c,a)
| between(a,b,c)
| between(b,c,a)
| between(a,b,c)
| between(b,c,a)
| between(a,b,c)
| ~ colinear(c,b,a)
| ~ colinear(c,a,b) ),
inference(resolve,[status(thm)],[c_1571,c_884]) ).
cnf(c_1573,plain,
( between(b,c,a)
| between(a,b,c)
| between(b,c,a)
| between(a,b,c)
| between(b,c,a)
| between(a,b,c)
| between(b,c,a)
| between(a,b,c)
| ~ colinear(c,b,a) ),
inference(resolve,[status(thm)],[c_1572,c_885]) ).
cnf(c_1574,plain,
( between(b,c,a)
| between(a,b,c)
| between(b,c,a)
| between(a,b,c)
| between(b,c,a)
| between(a,b,c)
| between(b,c,a)
| between(a,b,c)
| between(b,c,a)
| between(a,b,c) ),
inference(resolve,[status(thm)],[c_1573,c_857]) ).
cnf(c_1575,plain,
( between(b,c,a)
| between(a,b,c)
| between(b,c,a)
| between(a,b,c)
| between(b,c,a)
| between(a,b,c)
| between(b,c,a)
| between(b,c,a)
| between(a,b,c) ),
inference(copy,[status(thm)],[c_1574]) ).
cnf(c_1576,plain,
( between(b,c,a)
| between(a,b,c)
| between(b,c,a)
| between(a,b,c)
| between(b,c,a)
| between(a,b,c)
| between(b,c,a)
| between(a,b,c) ),
inference(copy,[status(thm)],[c_1575]) ).
cnf(c_1577,plain,
( between(b,c,a)
| between(a,b,c)
| between(b,c,a)
| between(a,b,c)
| between(b,c,a)
| between(b,c,a)
| between(a,b,c) ),
inference(copy,[status(thm)],[c_1576]) ).
cnf(c_1578,plain,
( between(b,c,a)
| between(a,b,c)
| between(b,c,a)
| between(a,b,c)
| between(b,c,a)
| between(a,b,c) ),
inference(copy,[status(thm)],[c_1577]) ).
cnf(c_1579,plain,
( between(b,c,a)
| between(a,b,c)
| between(b,c,a)
| between(b,c,a)
| between(a,b,c) ),
inference(copy,[status(thm)],[c_1578]) ).
cnf(c_1580,plain,
( between(b,c,a)
| between(a,b,c)
| between(b,c,a)
| between(a,b,c) ),
inference(copy,[status(thm)],[c_1579]) ).
cnf(c_1581,plain,
( between(b,c,a)
| between(b,c,a)
| between(a,b,c) ),
inference(copy,[status(thm)],[c_1580]) ).
cnf(c_1131,plain,
( between(b,c,a)
| between(a,b,c) ),
inference(copy,[status(thm)],[c_1581]) ).
cnf(c_1145,plain,
( colinear(c,b,a)
| between(a,b,c) ),
inference(resolve,[status(thm)],[c_1131,c_103]) ).
cnf(c_1146,plain,
( colinear(b,a,c)
| between(a,b,c) ),
inference(resolve,[status(thm)],[c_1131,c_102]) ).
cnf(c_1147,plain,
( colinear(a,c,b)
| between(a,b,c) ),
inference(resolve,[status(thm)],[c_1131,c_101]) ).
cnf(c_1174,plain,
( colinear(c,a,b)
| between(a,b,c) ),
inference(resolve,[status(thm)],[c_1131,c_21]) ).
cnf(c_1175,plain,
( colinear(b,c,a)
| between(a,b,c) ),
inference(resolve,[status(thm)],[c_1131,c_19]) ).
cnf(c_1582,plain,
( between(a,b,c)
| ~ colinear(c,b,a)
| ~ colinear(c,a,b)
| ~ colinear(b,c,a)
| ~ colinear(b,a,c) ),
inference(resolve,[status(thm)],[c_105,c_1147]) ).
cnf(c_1583,plain,
( between(a,b,c)
| between(a,b,c)
| ~ colinear(c,b,a)
| ~ colinear(c,a,b)
| ~ colinear(b,c,a) ),
inference(resolve,[status(thm)],[c_1582,c_1146]) ).
cnf(c_1584,plain,
( between(a,b,c)
| between(a,b,c)
| between(a,b,c)
| ~ colinear(c,b,a)
| ~ colinear(c,a,b) ),
inference(resolve,[status(thm)],[c_1583,c_1175]) ).
cnf(c_1585,plain,
( between(a,b,c)
| between(a,b,c)
| between(a,b,c)
| between(a,b,c)
| ~ colinear(c,b,a) ),
inference(resolve,[status(thm)],[c_1584,c_1174]) ).
cnf(c_1586,plain,
( between(a,b,c)
| between(a,b,c)
| between(a,b,c)
| between(a,b,c)
| between(a,b,c) ),
inference(resolve,[status(thm)],[c_1585,c_1145]) ).
cnf(c_1587,plain,
( between(a,b,c)
| between(a,b,c)
| between(a,b,c)
| between(a,b,c) ),
inference(copy,[status(thm)],[c_1586]) ).
cnf(c_1588,plain,
( between(a,b,c)
| between(a,b,c)
| between(a,b,c) ),
inference(copy,[status(thm)],[c_1587]) ).
cnf(c_1589,plain,
( between(a,b,c)
| between(a,b,c) ),
inference(copy,[status(thm)],[c_1588]) ).
cnf(c_1441,plain,
between(a,b,c),
inference(copy,[status(thm)],[c_1589]) ).
cnf(c_1455,plain,
colinear(b,a,c),
inference(resolve,[status(thm)],[c_1441,c_103]) ).
cnf(c_1456,plain,
colinear(a,c,b),
inference(resolve,[status(thm)],[c_1441,c_102]) ).
cnf(c_1457,plain,
colinear(c,b,a),
inference(resolve,[status(thm)],[c_1441,c_101]) ).
cnf(c_1485,plain,
colinear(b,c,a),
inference(resolve,[status(thm)],[c_1441,c_21]) ).
cnf(c_1486,plain,
colinear(c,a,b),
inference(resolve,[status(thm)],[c_1441,c_20]) ).
cnf(c_1590,plain,
( ~ colinear(c,b,a)
| ~ colinear(c,a,b)
| ~ colinear(b,c,a)
| ~ colinear(b,a,c) ),
inference(resolve,[status(thm)],[c_1456,c_105]) ).
cnf(c_1591,plain,
( ~ colinear(c,b,a)
| ~ colinear(c,a,b)
| ~ colinear(b,c,a) ),
inference(resolve,[status(thm)],[c_1455,c_1590]) ).
cnf(c_1592,plain,
( ~ colinear(c,b,a)
| ~ colinear(c,a,b) ),
inference(resolve,[status(thm)],[c_1485,c_1591]) ).
cnf(c_1593,plain,
~ colinear(c,b,a),
inference(resolve,[status(thm)],[c_1486,c_1592]) ).
cnf(c_1569,plain,
$false,
inference(resolve,[status(thm)],[c_1457,c_1593]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO010-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n015.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 25 12:34:13 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.12/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.36 % Process 1351484 was started by sandbox2 on n015,
% 0.12/0.36 % Fri Sep 25 12:34:13 2026
% 0.12/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 16.25/2.58
% 16.25/2.58 % SZS status Unsatisfiable for theBenchmark
% 16.25/2.58
% 16.25/2.58 % Proof 1 at 2.01 (+ 0.10) seconds.
% 16.25/2.58 % Length of proof is 28.
% 16.25/2.58 % Level of proof is 7.
% 16.25/2.58 % Maximum clause weight is 25.000.
% 16.25/2.58 % Given clauses 169.
% 16.25/2.58
% 16.25/2.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------