%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV006-1 : 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 : 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 09:06:38 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 11 unt; 0 def)
% Number of atoms : 27 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 13 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 14 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(less_than_successor,axiom,
! [VAR_0] : less_than(VAR_0,successor(VAR_0)),
file('theBenchmark.p',less_than_successor) ).
cnf(c_6,plain,
less_than(A,successor(A)),
inference(clausify,[status(thm)],[less_than_successor]) ).
fof(transitivity_of_less_than,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ less_than(VAR_2,VAR_1)
| ~ less_than(VAR_0,VAR_2)
| less_than(VAR_0,VAR_1) ),
file('theBenchmark.p',transitivity_of_less_than) ).
cnf(c_7,plain,
( ~ less_than(C,B)
| ~ less_than(A,C)
| less_than(A,B) ),
inference(clausify,[status(thm)],[transitivity_of_less_than]) ).
fof(x_not_less_than_x,axiom,
! [VAR_0] : ~ less_than(VAR_0,VAR_0),
file('theBenchmark.p',x_not_less_than_x) ).
cnf(c_9,plain,
~ less_than(A,A),
inference(clausify,[status(thm)],[x_not_less_than_x]) ).
fof(clause_3,axiom,
less_than(i,n),
file('theBenchmark.p',clause_3) ).
cnf(c_15,plain,
less_than(i,n),
inference(clausify,[status(thm)],[clause_3]) ).
fof(clause_5,axiom,
less_than(a(i),a(m)),
file('theBenchmark.p',clause_5) ).
cnf(c_17,plain,
less_than(a(i),a(m)),
inference(clausify,[status(thm)],[clause_5]) ).
fof(clause_6,axiom,
! [VAR_0] :
( ~ less_than(a(VAR_0),a(m))
| ~ less_than(VAR_0,successor(n))
| less_than(VAR_0,i) ),
file('theBenchmark.p',clause_6) ).
cnf(c_18,plain,
( ~ less_than(a(A),a(m))
| ~ less_than(A,successor(n))
| less_than(A,i) ),
inference(clausify,[status(thm)],[clause_6]) ).
cnf(c_23,plain,
( ~ less_than(A,B)
| less_than(A,successor(B)) ),
inference(resolve,[status(thm)],[c_7,c_6]) ).
cnf(c_102,plain,
( ~ less_than(i,successor(n))
| less_than(i,i) ),
inference(resolve,[status(thm)],[c_18,c_17]) ).
cnf(c_87,plain,
~ less_than(i,successor(n)),
inference(resolve,[status(thm)],[c_9,c_102]) ).
cnf(c_103,plain,
less_than(i,successor(n)),
inference(resolve,[status(thm)],[c_23,c_15]) ).
cnf(c_101,plain,
$false,
inference(resolve,[status(thm)],[c_87,c_103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 13:05:36 UTC 2026
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 1641444 was started by sandbox2 on n020,
% 0.13/0.36 % Sat Sep 26 13:05:36 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.37
% 0.13/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.37
% 0.13/0.37 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/0.37 % Length of proof is 9.
% 0.13/0.37 % Level of proof is 2.
% 0.13/0.37 % Maximum clause weight is 22.000.
% 0.13/0.37 % Given clauses 23.
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------