%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE151+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 : n006.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 07:44:25 AM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 34 ( 30 unt; 0 def)
% Number of atoms : 38 ( 20 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 11 ~; 2 |; 0 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 20 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('theBenchmark.p',additive_commutativity) ).
fof(idempotence,axiom,
! [A] : addition(A,A) = A,
file('theBenchmark.p',idempotence) ).
fof(multiplicative_associativity,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('theBenchmark.p',multiplicative_associativity) ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A,
file('theBenchmark.p',multiplicative_right_identity) ).
fof(distributivity1,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('theBenchmark.p',distributivity1) ).
fof(infty_unfold1,axiom,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
file('theBenchmark.p',infty_unfold1) ).
fof(infty_coinduction,axiom,
! [A,B,C] :
( leq(C,addition(multiplication(A,C),B))
=> leq(C,multiplication(strong_iteration(A),B)) ),
file('theBenchmark.p',infty_coinduction) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('theBenchmark.p',order) ).
fof(goals,conjecture,
! [X0,X1] : leq(multiplication(X0,strong_iteration(multiplication(X1,X0))),multiplication(strong_iteration(multiplication(X0,X1)),X0)),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] : leq(multiplication(X0,strong_iteration(multiplication(X1,X0))),multiplication(strong_iteration(multiplication(X0,X1)),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_23,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[idempotence]) ).
cnf(c_24,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(clausify,[status(thm)],[multiplicative_associativity]) ).
cnf(c_25,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_27,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[distributivity1]) ).
cnf(c_28,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_27]) ).
cnf(c_38,plain,
strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
inference(clausify,[status(thm)],[infty_unfold1]) ).
cnf(c_115,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_115]) ).
cnf(c_40,plain,
( leq(A,multiplication(strong_iteration(B),C))
| ~ leq(A,addition(multiplication(B,A),C)) ),
inference(clausify,[status(thm)],[infty_coinduction]) ).
cnf(c_44,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
fof(nnf_19,plain,
? [X0,X1] : ~ leq(multiplication(X0,strong_iteration(multiplication(X1,X0))),multiplication(strong_iteration(multiplication(X0,X1)),X0)),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
~ leq(multiplication(sK0,strong_iteration(multiplication(sK1,sK0))),multiplication(strong_iteration(multiplication(sK0,sK1)),sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[nnf_19]) ).
cnf(c_45,negated_conjecture,
~ leq(multiplication(sK0,strong_iteration(multiplication(sK1,sK0))),multiplication(strong_iteration(multiplication(sK0,sK1)),sK0)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_116,plain,
addition(A,multiplication(A,B)) = multiplication(A,addition(one,B)),
inference(paramod,[status(thm)],[c_25,c_28]) ).
cnf(c_53,plain,
multiplication(A,addition(one,B)) = addition(A,multiplication(A,B)),
inference(copy,[status(thm)],[c_116]) ).
cnf(c_87,plain,
addition(one,multiplication(A,multiplication(B,strong_iteration(multiplication(A,B))))) = strong_iteration(multiplication(A,B)),
inference(paramod,[status(thm)],[c_24,c_39]) ).
cnf(c_102,plain,
leq(A,A),
inference(resolve,[status(thm)],[c_44,c_23]) ).
cnf(c_117,negated_conjecture,
~ leq(multiplication(sK0,strong_iteration(multiplication(sK1,sK0))),addition(multiplication(multiplication(sK0,sK1),multiplication(sK0,strong_iteration(multiplication(sK1,sK0)))),sK0)),
inference(resolve,[status(thm)],[c_40,c_45]) ).
cnf(c_118,negated_conjecture,
~ leq(multiplication(sK0,strong_iteration(multiplication(sK1,sK0))),addition(multiplication(sK0,multiplication(sK1,multiplication(sK0,strong_iteration(multiplication(sK1,sK0))))),sK0)),
inference(paramod,[status(thm)],[c_24,c_117]) ).
cnf(c_119,negated_conjecture,
~ leq(multiplication(sK0,strong_iteration(multiplication(sK1,sK0))),addition(sK0,multiplication(sK0,multiplication(sK1,multiplication(sK0,strong_iteration(multiplication(sK1,sK0))))))),
inference(paramod,[status(thm)],[c_20,c_118]) ).
cnf(c_120,negated_conjecture,
~ leq(multiplication(sK0,strong_iteration(multiplication(sK1,sK0))),multiplication(sK0,addition(one,multiplication(sK1,multiplication(sK0,strong_iteration(multiplication(sK1,sK0))))))),
inference(paramod,[status(thm)],[c_53,c_119]) ).
cnf(c_113,negated_conjecture,
~ leq(multiplication(sK0,strong_iteration(multiplication(sK1,sK0))),multiplication(sK0,strong_iteration(multiplication(sK1,sK0)))),
inference(paramod,[status(thm)],[c_87,c_120]) ).
cnf(c_114,plain,
$false,
inference(resolve,[status(thm)],[c_113,c_102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE151+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.37 % Computer : n006.cluster.edu
% 0.06/0.37 % Model : x86_64 x86_64
% 0.06/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.37 % Memory : 8046.5625MB
% 0.06/0.37 % OS : Linux 6.8.0-71-generic
% 0.06/0.37 % CPULimit : 300
% 0.06/0.37 % WCLimit : 300
% 0.06/0.37 % DateTime : Fri Sep 25 19:27:25 UTC 2026
% 0.06/0.38 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 3550272 was started by sandbox on n006,
% 0.11/0.38 % Fri Sep 25 19:27:25 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 0.11/0.45
% 0.11/0.45 % SZS status Theorem for theBenchmark
% 0.11/0.45
% 0.11/0.45 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.11/0.45 % Length of proof is 25.
% 0.11/0.45 % Level of proof is 5.
% 0.11/0.45 % Maximum clause weight is 15.000.
% 0.11/0.45 % Given clauses 20.
% 0.11/0.45
% 0.11/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------