%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE138+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 : n019.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 07:44:22 AM UTC 2026
% Result : Theorem 0.17s 10.69s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 17 unt; 0 def)
% Number of atoms : 17 ( 16 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 12 ( 1 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('theBenchmark.p',additive_commutativity) ).
fof(additive_identity,axiom,
! [A] : addition(A,zero) = A,
file('theBenchmark.p',additive_identity) ).
fof(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero,
file('theBenchmark.p',left_annihilation) ).
fof(infty_unfold1,axiom,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
file('theBenchmark.p',infty_unfold1) ).
fof(goals,conjecture,
strong_iteration(zero) = one,
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
strong_iteration(zero) != one,
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_20,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_22,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_31,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
cnf(c_38,plain,
strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
inference(clausify,[status(thm)],[infty_unfold1]) ).
cnf(c_92,plain,
strong_iteration(A) = addition(one,multiplication(A,strong_iteration(A))),
inference(paramod,[status(thm)],[c_20,c_38]) ).
cnf(c_39,plain,
addition(one,multiplication(A,strong_iteration(A))) = strong_iteration(A),
inference(copy,[status(thm)],[c_92]) ).
cnf(c_45,negated_conjecture,
strong_iteration(zero) != one,
inference(clausify,[status(thm)],[goals_neg]) ).
cnf(c_93,plain,
addition(one,zero) = strong_iteration(zero),
inference(paramod,[status(thm)],[c_31,c_39]) ).
cnf(c_94,plain,
one = strong_iteration(zero),
inference(paramod,[status(thm)],[c_22,c_93]) ).
cnf(c_95,plain,
strong_iteration(zero) = one,
inference(copy,[status(thm)],[c_94]) ).
cnf(c_91,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_45,c_95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE138+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/10.65 % Computer : n019.cluster.edu
% 0.17/10.65 % Model : x86_64 x86_64
% 0.17/10.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/10.65 % Memory : 8046.5625MB
% 0.17/10.65 % OS : Linux 6.8.0-71-generic
% 0.17/10.66 % CPULimit : 300
% 0.17/10.66 % WCLimit : 300
% 0.17/10.66 % DateTime : Fri Sep 25 19:26:15 UTC 2026
% 0.17/10.66 % CPUTime :
% 0.17/10.66 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/10.66 % Process 3466291 was started by sandbox on n019,
% 0.17/10.66 % Fri Sep 25 19:26:15 2026
% 0.17/10.66 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/10.67
% 0.17/10.67 % From the command line: assign(max_seconds, 300).
% 0.17/10.69
% 0.17/10.69 % SZS status Theorem for theBenchmark
% 0.17/10.69
% 0.17/10.69 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.17/10.69 % Length of proof is 12.
% 0.17/10.69 % Level of proof is 3.
% 0.17/10.69 % Maximum clause weight is 29.000.
% 0.17/10.69 % Given clauses 15.
% 0.17/10.69
% 0.17/10.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------