%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE146+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 : n004.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 07:44:24 AM UTC 2026
% Result : Theorem 0.19s 0.49s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 21 unt; 0 def)
% Number of atoms : 25 ( 17 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 6 ~; 1 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 11 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('theBenchmark.p',additive_commutativity) ).
fof(additive_associativity,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('theBenchmark.p',additive_associativity) ).
fof(idempotence,axiom,
! [A] : addition(A,A) = A,
file('theBenchmark.p',idempotence) ).
fof(infty_unfold1,axiom,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
file('theBenchmark.p',infty_unfold1) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('theBenchmark.p',order) ).
fof(goals,conjecture,
! [X0] : leq(one,strong_iteration(X0)),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] : leq(one,strong_iteration(X0)),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_20,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_21,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_23,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[idempotence]) ).
cnf(c_38,plain,
strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
inference(clausify,[status(thm)],[infty_unfold1]) ).
cnf(c_132,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_132]) ).
cnf(c_44,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
fof(nnf_19,plain,
? [X0] : ~ leq(one,strong_iteration(X0)),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
~ leq(one,strong_iteration(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_19]) ).
cnf(c_45,negated_conjecture,
~ leq(one,strong_iteration(sK0)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_133,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_23,c_21]) ).
cnf(c_49,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_133]) ).
cnf(c_112,negated_conjecture,
addition(one,strong_iteration(sK0)) != strong_iteration(sK0),
inference(resolve,[status(thm)],[c_44,c_45]) ).
cnf(c_134,plain,
addition(one,strong_iteration(A)) = addition(one,multiplication(A,strong_iteration(A))),
inference(paramod,[status(thm)],[c_39,c_49]) ).
cnf(c_130,plain,
addition(one,strong_iteration(A)) = strong_iteration(A),
inference(paramod,[status(thm)],[c_39,c_134]) ).
cnf(c_131,plain,
$false,
inference(resolve,[status(thm)],[c_130,c_112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE146+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n004.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 19:26:51 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 3880278 was started by sandbox on n004,
% 0.19/0.45 % Fri Sep 25 19:26:51 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).
% 0.19/0.49
% 0.19/0.49 % SZS status Theorem for theBenchmark
% 0.19/0.49
% 0.19/0.49 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.19/0.49 % Length of proof is 17.
% 0.19/0.49 % Level of proof is 4.
% 0.19/0.49 % Maximum clause weight is 11.000.
% 0.19/0.49 % Given clauses 27.
% 0.19/0.49
% 0.19/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------