%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV005-1 : 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 : n003.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 09:06:38 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 10 unt; 0 def)
% Number of atoms : 23 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 18 ( 9 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 3 ( 0 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause_1,axiom,
~ less_than(n,k),
file('theBenchmark.p',clause_1) ).
cnf(c_13,plain,
~ less_than(n,k),
inference(clausify,[status(thm)],[clause_1]) ).
fof(clause_2,axiom,
~ less_than(k,l),
file('theBenchmark.p',clause_2) ).
cnf(c_14,plain,
~ less_than(k,l),
inference(clausify,[status(thm)],[clause_2]) ).
fof(clause_5,axiom,
less_than(one,l),
file('theBenchmark.p',clause_5) ).
cnf(c_17,plain,
less_than(one,l),
inference(clausify,[status(thm)],[clause_5]) ).
fof(clause_6,axiom,
less_than(a(k),a(predecessor(l))),
file('theBenchmark.p',clause_6) ).
cnf(c_18,plain,
less_than(a(k),a(predecessor(l))),
inference(clausify,[status(thm)],[clause_6]) ).
fof(clause_8,axiom,
! [VAR_0] :
( ~ less_than(a(VAR_0),a(predecessor(l)))
| ~ less_than(one,l)
| less_than(n,VAR_0)
| less_than(VAR_0,l) ),
file('theBenchmark.p',clause_8) ).
cnf(c_20,plain,
( ~ less_than(a(A),a(predecessor(l)))
| ~ less_than(one,l)
| less_than(n,A)
| less_than(A,l) ),
inference(clausify,[status(thm)],[clause_8]) ).
cnf(c_21,plain,
( ~ less_than(a(A),a(predecessor(l)))
| less_than(n,A)
| less_than(A,l) ),
inference(resolve,[status(thm)],[c_17,c_20]) ).
cnf(c_100,plain,
( less_than(n,k)
| less_than(k,l) ),
inference(resolve,[status(thm)],[c_21,c_18]) ).
cnf(c_101,plain,
less_than(n,k),
inference(resolve,[status(thm)],[c_14,c_100]) ).
cnf(c_99,plain,
$false,
inference(resolve,[status(thm)],[c_13,c_101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV005-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n003.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 13:06:27 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 2950431 was started by sandbox2 on n003,
% 0.18/0.44 % Sat Sep 26 13:06:27 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.18/0.47
% 0.18/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.47
% 0.18/0.47 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.18/0.47 % Length of proof is 7.
% 0.18/0.47 % Level of proof is 2.
% 0.18/0.47 % Maximum clause weight is 27.000.
% 0.18/0.47 % Given clauses 20.
% 0.18/0.47
% 0.18/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------