%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO008-3 : 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 : 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 07:16:44 AM UTC 2026
% Result : Unsatisfiable 8.18s 1.68s
% Output : CNFRefutation 8.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 15 unt; 0 def)
% Number of atoms : 52 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 50 ( 27 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 35 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(b8,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( between(VAR_0,VAR_3,VAR_2)
| ~ between(VAR_1,VAR_3,VAR_2)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',b8) ).
cnf(c_62,plain,
( between(A,D,C)
| ~ between(B,D,C)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[b8]) ).
fof(b9,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( between(VAR_0,VAR_1,VAR_3)
| ~ between(VAR_0,VAR_2,VAR_3)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',b9) ).
cnf(c_63,plain,
( between(A,B,D)
| ~ between(A,C,D)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[b9]) ).
fof(t9,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( between(VAR_0,VAR_3,VAR_1)
| between(VAR_0,VAR_1,VAR_3)
| ~ between(VAR_0,VAR_3,VAR_2)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',t9) ).
cnf(c_93,plain,
( between(A,D,B)
| between(A,B,D)
| ~ between(A,D,C)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[t9]) ).
fof(c_between_a_and_e,axiom,
between(a,c,e),
file('theBenchmark.p',c_between_a_and_e) ).
cnf(c_95,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_96,plain,
between(a,d,e),
inference(clausify,[status(thm)],[d_between_a_and_e]) ).
fof(b_between_c_and_d,axiom,
between(c,b,d),
file('theBenchmark.p',b_between_c_and_d) ).
cnf(c_97,plain,
between(c,b,d),
inference(clausify,[status(thm)],[b_between_c_and_d]) ).
fof(prove_betweenness,axiom,
~ between(a,b,e),
file('theBenchmark.p',prove_betweenness) ).
cnf(c_98,plain,
~ between(a,b,e),
inference(clausify,[status(thm)],[prove_betweenness]) ).
cnf(c_478,plain,
between(d,b,c),
inference(resolve,[status(thm)],[c_97,c_55]) ).
cnf(c_1120,plain,
( between(a,A,e)
| ~ between(a,A,d) ),
inference(resolve,[status(thm)],[c_63,c_96]) ).
cnf(c_502,plain,
~ between(a,b,d),
inference(resolve,[status(thm)],[c_1120,c_98]) ).
cnf(c_1121,plain,
( between(a,A,e)
| ~ between(a,A,c) ),
inference(resolve,[status(thm)],[c_63,c_95]) ).
cnf(c_503,plain,
~ between(a,b,c),
inference(resolve,[status(thm)],[c_1121,c_98]) ).
cnf(c_1122,plain,
( between(A,b,d)
| ~ between(A,c,d) ),
inference(resolve,[status(thm)],[c_62,c_97]) ).
cnf(c_827,plain,
~ between(a,c,d),
inference(resolve,[status(thm)],[c_1122,c_502]) ).
cnf(c_1123,plain,
( between(A,b,c)
| ~ between(A,d,c) ),
inference(resolve,[status(thm)],[c_62,c_478]) ).
cnf(c_877,plain,
~ between(a,d,c),
inference(resolve,[status(thm)],[c_1123,c_503]) ).
cnf(c_1124,plain,
( between(a,d,A)
| between(a,A,d)
| ~ between(a,A,e) ),
inference(resolve,[status(thm)],[c_93,c_96]) ).
cnf(c_1125,plain,
( between(a,d,c)
| ~ between(a,c,e) ),
inference(resolve,[status(thm)],[c_1124,c_827]) ).
cnf(c_1126,plain,
~ between(a,c,e),
inference(resolve,[status(thm)],[c_1125,c_877]) ).
cnf(c_1119,plain,
$false,
inference(resolve,[status(thm)],[c_95,c_1126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO008-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.56 % Computer : n016.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.56 % CPULimit : 300
% 0.09/0.56 % WCLimit : 300
% 0.09/0.56 % DateTime : Fri Sep 25 12:36:16 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.57 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.57 % Process 2384898 was started by sandbox2 on n016,
% 0.09/0.57 % Fri Sep 25 12:36:16 2026
% 0.09/0.57 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.58
% 0.09/0.58 % From the command line: assign(max_seconds, 300).
% 8.18/1.68
% 8.18/1.68 % SZS status Unsatisfiable for theBenchmark
% 8.18/1.68
% 8.18/1.68 % Proof 1 at 1.01 (+ 0.05) seconds.
% 8.18/1.68 % Length of proof is 14.
% 8.18/1.68 % Level of proof is 3.
% 8.18/1.68 % Maximum clause weight is 18.000.
% 8.18/1.68 % Given clauses 164.
% 8.18/1.68
% 8.18/1.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------