%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE051+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 07:44:12 AM UTC 2026
% Result : Theorem 0.19s 0.47s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 8 ( 8 unt; 0 def)
% Number of atoms : 8 ( 7 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 5 ( 0 sgn 3 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_idempotence,axiom,
! [A] : addition(A,A) = A,
file('theBenchmark.p',additive_idempotence) ).
fof(goals,conjecture,
! [X0] : addition(X0,X0) = X0,
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] : addition(X0,X0) = X0,
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_17,plain,
? [X0] : addition(X0,X0) != X0,
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
addition(sK0,sK0) != sK0,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_17]) ).
cnf(c_20,negated_conjecture,
addition(sK0,sK0) != sK0,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_36,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_37,plain,
$false,
inference(resolve,[status(thm)],[c_36,c_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE051+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n018.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Fri Sep 25 19:20:36 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 2627360 was started by sandbox on n018,
% 0.19/0.45 % Fri Sep 25 19:20:36 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 0.19/0.47
% 0.19/0.47 % SZS status Theorem for theBenchmark
% 0.19/0.47
% 0.19/0.47 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.19/0.47 % Length of proof is 5.
% 0.19/0.47 % Level of proof is 2.
% 0.19/0.47 % Maximum clause weight is 5.000.
% 0.19/0.47 % Given clauses 0.
% 0.19/0.47
% 0.19/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------