%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE001+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 : n016.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 07:44:01 AM UTC 2026
% Result : Theorem 0.16s 15.67s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 5 unt; 0 def)
% Number of atoms : 17 ( 4 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 5 ~; 1 |; 2 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 9 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_idempotence,axiom,
! [A] : addition(A,A) = A,
file('theBenchmark.p',additive_idempotence) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('theBenchmark.p',order) ).
fof(goals,conjecture,
! [X0,X1,X2] :
( leq(X0,X1)
=> leq(addition(X0,X2),addition(X0,X2)) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( leq(X0,X1)
=> leq(addition(X0,X2),addition(X0,X2)) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_17,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_26,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
fof(nnf_13,plain,
? [X0,X1,X2] :
( ~ leq(addition(X0,X2),addition(X0,X2))
& leq(X0,X1) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ~ leq(addition(sK0,sK1),addition(sK0,sK1))
& leq(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK1]),skolemize(X0,sK0),skolemize(X1,sK2),skolemize(X2,sK1)],[nnf_13]) ).
cnf(c_28,negated_conjecture,
~ leq(addition(sK0,sK1),addition(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_35,plain,
leq(A,A),
inference(resolve,[status(thm)],[c_26,c_17]) ).
cnf(c_36,plain,
$false,
inference(resolve,[status(thm)],[c_35,c_28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE001+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.16/15.64 % CPULimit : 300
% 0.16/15.64 % WCLimit : 300
% 0.16/15.64 % DateTime : Fri Sep 25 19:11:53 UTC 2026
% 0.16/15.65 % CPUTime :
% 0.16/15.65 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/15.65 % Process 976386 was started by sandbox on n013,
% 0.16/15.65 % Fri Sep 25 19:11:53 2026
% 0.16/15.65 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/15.66
% 0.16/15.66 % From the command line: assign(max_seconds, 300).
% 0.16/15.67
% 0.16/15.67 % SZS status Theorem for theBenchmark
% 0.16/15.67
% 0.16/15.67 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/15.67 % Length of proof is 8.
% 0.16/15.67 % Level of proof is 3.
% 0.16/15.67 % Maximum clause weight is 8.000.
% 0.16/15.67 % Given clauses 13.
% 0.16/15.67
% 0.16/15.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------