%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM023-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 08:16:03 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.37s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 6 unt; 0 def)
% Number of atoms : 10 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 9 ( 2 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(adding_zero,axiom,
! [VAR_0] : equalish(add(VAR_0,n0),VAR_0),
file('theBenchmark.p',adding_zero) ).
cnf(c_1,plain,
equalish(add(A,n0),A),
inference(clausify,[status(thm)],[adding_zero]) ).
fof(smaller_number,axiom,
! [VAR_0,VAR_1,VAR_2] :
( less(VAR_1,VAR_2)
| ~ equalish(add(successor(VAR_0),VAR_1),VAR_2) ),
file('theBenchmark.p',smaller_number) ).
cnf(c_8,plain,
( less(B,C)
| ~ equalish(add(successor(A),B),C) ),
inference(clausify,[status(thm)],[smaller_number]) ).
fof(prove_zero_is_less_than_all_successors,axiom,
~ less(n0,successor(a)),
file('theBenchmark.p',prove_zero_is_less_than_all_successors) ).
cnf(c_15,plain,
~ less(n0,successor(a)),
inference(clausify,[status(thm)],[prove_zero_is_less_than_all_successors]) ).
cnf(c_21,plain,
less(n0,successor(A)),
inference(resolve,[status(thm)],[c_8,c_1]) ).
cnf(c_22,plain,
$false,
inference(resolve,[status(thm)],[c_21,c_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM023-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n011.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 26 01:54:13 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 3516300 was started by sandbox2 on n011,
% 0.07/0.35 % Sat Sep 26 01:54:13 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.36
% 0.07/0.36 % From the command line: assign(max_seconds, 300).
% 0.07/0.37
% 0.07/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.07/0.37
% 0.07/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.07/0.37 % Length of proof is 5.
% 0.07/0.37 % Level of proof is 2.
% 0.07/0.37 % Maximum clause weight is 9.000.
% 0.07/0.37 % Given clauses 8.
% 0.07/0.37
% 0.07/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------