%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE003+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 07:44:01 AM UTC 2026
% Result : Theorem 0.09s 5.59s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 4 unt; 0 def)
% Number of atoms : 26 ( 25 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 28 ( 14 ~; 9 |; 3 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn 6 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_idempotence,axiom,
! [A] : addition(A,A) = A,
file('theBenchmark.p',additive_idempotence) ).
fof(goals,conjecture,
( ! [X0] : addition(X0,X0) = X0
<=> addition(one,one) = one ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ( ! [X0] : addition(X0,X0) = X0
<=> addition(one,one) = one ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_13,plain,
( ( addition(one,one) != one
| ? [X0] : addition(X0,X0) != X0 )
& ( addition(one,one) = one
| ! [X1] : addition(X1,X1) = X1 ) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg_sk,plain,
( ( addition(one,one) != one
| addition(sK0,sK0) != sK0 )
& ( addition(one,one) = one
| ! [X1] : addition(X1,X1) = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_13]) ).
fof(sk_goals_neg,plain,
( ( addition(one,one) != one
| addition(sK0,sK0) != sK0 )
& ! [VAR_0] :
( addition(one,one) = one
| addition(VAR_0,VAR_0) = VAR_0 ) ),
inference(cnf_transformation,[status(thm)],[sk_goals_neg_sk]) ).
cnf(c_16,negated_conjecture,
( addition(one,one) != one
| addition(sK0,sK0) != sK0 ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_25,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_30,negated_conjecture,
( addition(one,one) != one
| sK0 != sK0 ),
inference(paramod,[status(thm)],[c_25,c_16]) ).
cnf(c_31,negated_conjecture,
( one != one
| sK0 != sK0 ),
inference(paramod,[status(thm)],[c_25,c_30]) ).
cnf(c_32,negated_conjecture,
one != one,
inference(copy,[status(thm)],[c_31]) ).
cnf(c_29,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE003+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.57 % Computer : n018.cluster.edu
% 0.09/5.57 % Model : x86_64 x86_64
% 0.09/5.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.57 % Memory : 8046.5625MB
% 0.09/5.57 % OS : Linux 6.8.0-71-generic
% 0.09/5.57 % CPULimit : 300
% 0.09/5.57 % WCLimit : 300
% 0.09/5.57 % DateTime : Fri Sep 25 19:14:27 UTC 2026
% 0.09/5.57 % CPUTime :
% 0.09/5.57 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.57 % Process 2608274 was started by sandbox on n018,
% 0.09/5.57 % Fri Sep 25 19:14:27 2026
% 0.09/5.57 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/5.58
% 0.09/5.58 % From the command line: assign(max_seconds, 300).
% 0.09/5.59
% 0.09/5.59 % SZS status Theorem for theBenchmark
% 0.09/5.59
% 0.09/5.59 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/5.59 % Length of proof is 5.
% 0.09/5.59 % Level of proof is 2.
% 0.09/5.59 % Maximum clause weight is 10.000.
% 0.09/5.59 % Given clauses 0.
% 0.09/5.59
% 0.09/5.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------