%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE040+2 : 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 : n001.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 07:44:10 AM UTC 2026
% Result : Theorem 0.15s 0.55s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 58 ( 48 unt; 0 def)
% Number of atoms : 68 ( 39 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 25 ( 15 ~; 6 |; 2 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 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 : 91 ( 3 sgn 22 !; 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(additive_idempotence,axiom,
! [A] : addition(A,A) = A,
file('theBenchmark.p',additive_idempotence) ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A,
file('theBenchmark.p',multiplicative_right_identity) ).
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A,
file('theBenchmark.p',multiplicative_left_identity) ).
fof(right_distributivity,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('theBenchmark.p',right_distributivity) ).
fof(left_distributivity,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('theBenchmark.p',left_distributivity) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('theBenchmark.p',order) ).
fof(star_unfold_right,axiom,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
file('theBenchmark.p',star_unfold_right) ).
fof(star_induction_left,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),B)
=> leq(multiplication(star(A),C),B) ),
file('theBenchmark.p',star_induction_left) ).
fof(goals,conjecture,
! [X0] :
( leq(star(X0),multiplication(star(X0),star(X0)))
& leq(multiplication(star(X0),star(X0)),star(X0)) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] :
( leq(star(X0),multiplication(star(X0),star(X0)))
& leq(multiplication(star(X0),star(X0)),star(X0)) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_18,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_19,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_21,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_23,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_24,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_25,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_26,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_25]) ).
cnf(c_27,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_28,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_27]) ).
cnf(c_31,plain,
( addition(A,B) = B
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_32,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_33,plain,
leq(addition(one,multiplication(A,star(A))),star(A)),
inference(clausify,[status(thm)],[star_unfold_right]) ).
cnf(c_35,plain,
( leq(multiplication(star(A),C),B)
| ~ leq(addition(multiplication(A,B),C),B) ),
inference(clausify,[status(thm)],[star_induction_left]) ).
fof(nnf_17,plain,
? [X0] :
( ~ leq(star(X0),multiplication(star(X0),star(X0)))
| ~ leq(multiplication(star(X0),star(X0)),star(X0)) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ~ leq(star(sK0),multiplication(star(sK0),star(sK0)))
| ~ leq(multiplication(star(sK0),star(sK0)),star(sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_17]) ).
cnf(c_37,negated_conjecture,
( ~ leq(star(sK0),multiplication(star(sK0),star(sK0)))
| ~ leq(multiplication(star(sK0),star(sK0)),star(sK0)) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_331,plain,
addition(addition(A,B),C) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_18,c_19]) ).
cnf(c_39,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_19,c_331]) ).
cnf(c_332,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_21,c_19]) ).
cnf(c_41,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_332]) ).
cnf(c_333,plain,
addition(addition(A,B),B) = addition(A,B),
inference(paramod,[status(thm)],[c_21,c_19]) ).
cnf(c_43,plain,
addition(A,addition(B,A)) = addition(B,A),
inference(paramod,[status(thm)],[c_18,c_333]) ).
cnf(c_334,plain,
addition(A,multiplication(A,B)) = multiplication(A,addition(one,B)),
inference(paramod,[status(thm)],[c_23,c_26]) ).
cnf(c_45,plain,
multiplication(A,addition(one,B)) = addition(A,multiplication(A,B)),
inference(copy,[status(thm)],[c_334]) ).
cnf(c_335,plain,
addition(A,multiplication(B,A)) = multiplication(addition(one,B),A),
inference(paramod,[status(thm)],[c_24,c_28]) ).
cnf(c_50,plain,
multiplication(addition(one,A),B) = addition(B,multiplication(A,B)),
inference(copy,[status(thm)],[c_335]) ).
cnf(c_52,plain,
leq(A,A),
inference(resolve,[status(thm)],[c_32,c_21]) ).
cnf(c_336,plain,
addition(addition(one,multiplication(A,star(A))),star(A)) = star(A),
inference(resolve,[status(thm)],[c_31,c_33]) ).
cnf(c_337,plain,
addition(star(A),addition(one,multiplication(A,star(A)))) = star(A),
inference(paramod,[status(thm)],[c_18,c_336]) ).
cnf(c_338,plain,
addition(one,addition(star(A),multiplication(A,star(A)))) = star(A),
inference(paramod,[status(thm)],[c_39,c_337]) ).
cnf(c_58,plain,
addition(one,multiplication(addition(one,A),star(A))) = star(A),
inference(paramod,[status(thm)],[c_50,c_338]) ).
cnf(c_94,plain,
leq(A,addition(A,B)),
inference(resolve,[status(thm)],[c_32,c_41]) ).
cnf(c_137,plain,
leq(A,multiplication(A,addition(one,B))),
inference(paramod,[status(thm)],[c_45,c_94]) ).
cnf(c_230,plain,
addition(A,multiplication(addition(one,B),A)) = addition(A,multiplication(B,A)),
inference(paramod,[status(thm)],[c_50,c_41]) ).
cnf(c_339,plain,
addition(multiplication(addition(one,A),star(A)),star(A)) = addition(one,multiplication(addition(one,A),star(A))),
inference(paramod,[status(thm)],[c_58,c_43]) ).
cnf(c_340,plain,
addition(star(A),multiplication(addition(one,A),star(A))) = addition(one,multiplication(addition(one,A),star(A))),
inference(paramod,[status(thm)],[c_18,c_339]) ).
cnf(c_341,plain,
addition(star(A),multiplication(A,star(A))) = addition(one,multiplication(addition(one,A),star(A))),
inference(paramod,[status(thm)],[c_230,c_340]) ).
cnf(c_342,plain,
multiplication(addition(one,A),star(A)) = addition(one,multiplication(addition(one,A),star(A))),
inference(paramod,[status(thm)],[c_50,c_341]) ).
cnf(c_312,plain,
multiplication(addition(one,A),star(A)) = star(A),
inference(paramod,[status(thm)],[c_58,c_342]) ).
cnf(c_318,plain,
leq(A,multiplication(A,star(B))),
inference(paramod,[status(thm)],[c_58,c_137]) ).
cnf(c_327,negated_conjecture,
~ leq(multiplication(star(sK0),star(sK0)),star(sK0)),
inference(resolve,[status(thm)],[c_318,c_37]) ).
cnf(c_343,negated_conjecture,
~ leq(addition(multiplication(sK0,star(sK0)),star(sK0)),star(sK0)),
inference(resolve,[status(thm)],[c_35,c_327]) ).
cnf(c_344,negated_conjecture,
~ leq(addition(star(sK0),multiplication(sK0,star(sK0))),star(sK0)),
inference(paramod,[status(thm)],[c_18,c_343]) ).
cnf(c_345,negated_conjecture,
~ leq(multiplication(addition(one,sK0),star(sK0)),star(sK0)),
inference(paramod,[status(thm)],[c_50,c_344]) ).
cnf(c_346,negated_conjecture,
~ leq(star(sK0),star(sK0)),
inference(paramod,[status(thm)],[c_312,c_345]) ).
cnf(c_330,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_52,c_346]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE040+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n001.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Fri Sep 25 19:22:40 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.42 % Process 4020098 was started by sandbox on n001,
% 0.15/0.42 % Fri Sep 25 19:22:40 2026
% 0.15/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.43
% 0.15/0.43 % From the command line: assign(max_seconds, 300).
% 0.15/0.55
% 0.15/0.55 % SZS status Theorem for theBenchmark
% 0.15/0.55
% 0.15/0.55 % Proof 1 at 0.07 (+ 0.03) seconds.
% 0.15/0.55 % Length of proof is 39.
% 0.15/0.55 % Level of proof is 7.
% 0.15/0.55 % Maximum clause weight is 22.000.
% 0.15/0.55 % Given clauses 70.
% 0.15/0.55
% 0.15/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------