%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PUZ022-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 08:23:07 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 16 unt; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 51 ( 29 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 12 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_borders,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ ocean(VAR_2)
| ~ borders(VAR_1,VAR_2)
| ~ borders(VAR_0,VAR_2)
| ~ borders(VAR_0,VAR_1)
| ~ state(VAR_1)
| ~ state(VAR_0) ),
file('theBenchmark.p',prove_borders) ).
cnf(c_1,plain,
( ~ ocean(C)
| ~ borders(B,C)
| ~ borders(A,C)
| ~ borders(A,B)
| ~ state(B)
| ~ state(A) ),
inference(clausify,[status(thm)],[prove_borders]) ).
fof(indian,axiom,
ocean(indian),
file('theBenchmark.p',indian) ).
cnf(c_4,plain,
ocean(indian),
inference(clausify,[status(thm)],[indian]) ).
cnf(c_7,plain,
( ~ borders(B,indian)
| ~ borders(A,indian)
| ~ borders(A,B)
| ~ state(B)
| ~ state(A) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
fof(indian_nt,axiom,
borders(indian,northern_territory),
file('theBenchmark.p',indian_nt) ).
cnf(c_19,plain,
borders(indian,northern_territory),
inference(clausify,[status(thm)],[indian_nt]) ).
fof(indian_wa,axiom,
borders(indian,western_australia),
file('theBenchmark.p',indian_wa) ).
cnf(c_20,plain,
borders(indian,western_australia),
inference(clausify,[status(thm)],[indian_wa]) ).
fof(wa_nt,axiom,
borders(western_australia,northern_territory),
file('theBenchmark.p',wa_nt) ).
cnf(c_29,plain,
borders(western_australia,northern_territory),
inference(clausify,[status(thm)],[wa_nt]) ).
fof(northern_territory,axiom,
state(northern_territory),
file('theBenchmark.p',northern_territory) ).
cnf(c_35,plain,
state(northern_territory),
inference(clausify,[status(thm)],[northern_territory]) ).
fof(western_australia,axiom,
state(western_australia),
file('theBenchmark.p',western_australia) ).
cnf(c_36,plain,
state(western_australia),
inference(clausify,[status(thm)],[western_australia]) ).
fof(symmetry_of_borders,axiom,
! [VAR_0,VAR_1] :
( borders(VAR_1,VAR_0)
| ~ borders(VAR_0,VAR_1) ),
file('theBenchmark.p',symmetry_of_borders) ).
cnf(c_37,plain,
( borders(B,A)
| ~ borders(A,B) ),
inference(clausify,[status(thm)],[symmetry_of_borders]) ).
cnf(c_205,plain,
( ~ borders(northern_territory,indian)
| ~ borders(western_australia,indian)
| ~ state(northern_territory)
| ~ state(western_australia) ),
inference(resolve,[status(thm)],[c_29,c_7]) ).
cnf(c_206,plain,
( ~ borders(northern_territory,indian)
| ~ borders(western_australia,indian)
| ~ state(northern_territory) ),
inference(resolve,[status(thm)],[c_36,c_205]) ).
cnf(c_116,plain,
( ~ borders(northern_territory,indian)
| ~ borders(western_australia,indian) ),
inference(resolve,[status(thm)],[c_35,c_206]) ).
cnf(c_191,plain,
borders(western_australia,indian),
inference(resolve,[status(thm)],[c_37,c_20]) ).
cnf(c_192,plain,
borders(northern_territory,indian),
inference(resolve,[status(thm)],[c_37,c_19]) ).
cnf(c_207,plain,
~ borders(northern_territory,indian),
inference(resolve,[status(thm)],[c_191,c_116]) ).
cnf(c_204,plain,
$false,
inference(resolve,[status(thm)],[c_192,c_207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ022-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 05:06:04 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 672047 was started by sandbox2 on n020,
% 0.08/0.36 % Sat Sep 26 05:06:04 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.08/0.38
% 0.08/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.38
% 0.08/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.08/0.38 % Length of proof is 13.
% 0.08/0.38 % Level of proof is 3.
% 0.08/0.38 % Maximum clause weight is 13.000.
% 0.08/0.38 % Given clauses 32.
% 0.08/0.38
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------