%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE046+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 : n005.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 07:44:11 AM UTC 2026
% Result : Theorem 244.24s 32.83s
% Output : CNFRefutation 244.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 59
% Number of leaves : 14
% Syntax : Number of formulae : 253 ( 208 unt; 0 def)
% Number of atoms : 298 ( 129 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 100 ( 55 ~; 38 |; 2 &)
% ( 1 <=>; 4 =>; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 445 ( 42 sgn 31 !; 2 ?)
% 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_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(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_unfold_left,axiom,
! [A] : leq(addition(one,multiplication(star(A),A)),star(A)),
file('theBenchmark.p',star_unfold_left) ).
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(star_induction_right,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),A)
=> leq(multiplication(C,star(B)),A) ),
file('theBenchmark.p',star_induction_right) ).
fof(goals,conjecture,
! [X0,X1] :
( leq(multiplication(star(X1),star(X0)),multiplication(star(X0),star(X1)))
=> leq(star(addition(X0,X1)),multiplication(star(X0),star(X1))) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( leq(multiplication(star(X1),star(X0)),multiplication(star(X0),star(X1)))
=> leq(star(addition(X0,X1)),multiplication(star(X0),star(X1))) ),
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_22,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(clausify,[status(thm)],[multiplicative_associativity]) ).
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_34,plain,
leq(addition(one,multiplication(star(A),A)),star(A)),
inference(clausify,[status(thm)],[star_unfold_left]) ).
cnf(c_35,plain,
( leq(multiplication(star(A),C),B)
| ~ leq(addition(multiplication(A,B),C),B) ),
inference(clausify,[status(thm)],[star_induction_left]) ).
cnf(c_36,plain,
( leq(multiplication(C,star(B)),A)
| ~ leq(addition(multiplication(A,B),C),A) ),
inference(clausify,[status(thm)],[star_induction_right]) ).
fof(nnf_17,plain,
? [X0,X1] :
( ~ leq(star(addition(X0,X1)),multiplication(star(X0),star(X1)))
& leq(multiplication(star(X1),star(X0)),multiplication(star(X0),star(X1))) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ~ leq(star(addition(sK1,sK0)),multiplication(star(sK1),star(sK0)))
& leq(multiplication(star(sK0),star(sK1)),multiplication(star(sK1),star(sK0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK1),skolemize(X1,sK0)],[nnf_17]) ).
cnf(c_37,negated_conjecture,
leq(multiplication(star(sK0),star(sK1)),multiplication(star(sK1),star(sK0))),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_38,negated_conjecture,
~ leq(star(addition(sK1,sK0)),multiplication(star(sK1),star(sK0))),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_19260,plain,
addition(addition(A,B),C) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_18,c_19]) ).
cnf(c_40,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_19,c_19260]) ).
cnf(c_19261,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_21,c_19]) ).
cnf(c_42,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_19261]) ).
cnf(c_19262,plain,
addition(addition(A,B),B) = addition(A,B),
inference(paramod,[status(thm)],[c_21,c_19]) ).
cnf(c_44,plain,
addition(A,addition(B,A)) = addition(B,A),
inference(paramod,[status(thm)],[c_18,c_19262]) ).
cnf(c_19263,plain,
addition(A,multiplication(A,B)) = multiplication(A,addition(one,B)),
inference(paramod,[status(thm)],[c_23,c_26]) ).
cnf(c_46,plain,
multiplication(A,addition(one,B)) = addition(A,multiplication(A,B)),
inference(copy,[status(thm)],[c_19263]) ).
cnf(c_19264,plain,
addition(multiplication(A,B),A) = multiplication(A,addition(B,one)),
inference(paramod,[status(thm)],[c_23,c_26]) ).
cnf(c_19265,plain,
addition(A,multiplication(A,B)) = multiplication(A,addition(B,one)),
inference(paramod,[status(thm)],[c_18,c_19264]) ).
cnf(c_47,plain,
multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)),
inference(copy,[status(thm)],[c_19265]) ).
cnf(c_19266,plain,
addition(A,multiplication(B,A)) = multiplication(addition(one,B),A),
inference(paramod,[status(thm)],[c_24,c_28]) ).
cnf(c_51,plain,
multiplication(addition(one,A),B) = addition(B,multiplication(A,B)),
inference(copy,[status(thm)],[c_19266]) ).
cnf(c_19267,plain,
addition(multiplication(A,B),B) = multiplication(addition(A,one),B),
inference(paramod,[status(thm)],[c_24,c_28]) ).
cnf(c_19268,plain,
addition(B,multiplication(A,B)) = multiplication(addition(A,one),B),
inference(paramod,[status(thm)],[c_18,c_19267]) ).
cnf(c_52,plain,
multiplication(addition(A,one),B) = addition(B,multiplication(A,B)),
inference(copy,[status(thm)],[c_19268]) ).
cnf(c_53,plain,
leq(A,A),
inference(resolve,[status(thm)],[c_32,c_21]) ).
cnf(c_19269,plain,
addition(addition(one,multiplication(A,star(A))),star(A)) = star(A),
inference(resolve,[status(thm)],[c_31,c_33]) ).
cnf(c_19270,plain,
addition(star(A),addition(one,multiplication(A,star(A)))) = star(A),
inference(paramod,[status(thm)],[c_18,c_19269]) ).
cnf(c_19271,plain,
addition(one,addition(star(A),multiplication(A,star(A)))) = star(A),
inference(paramod,[status(thm)],[c_40,c_19270]) ).
cnf(c_59,plain,
addition(one,multiplication(addition(one,A),star(A))) = star(A),
inference(paramod,[status(thm)],[c_51,c_19271]) ).
cnf(c_19272,plain,
addition(addition(one,multiplication(star(A),A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_31,c_34]) ).
cnf(c_19273,plain,
addition(star(A),addition(one,multiplication(star(A),A))) = star(A),
inference(paramod,[status(thm)],[c_18,c_19272]) ).
cnf(c_19274,plain,
addition(one,addition(star(A),multiplication(star(A),A))) = star(A),
inference(paramod,[status(thm)],[c_40,c_19273]) ).
cnf(c_63,plain,
addition(one,multiplication(star(A),addition(one,A))) = star(A),
inference(paramod,[status(thm)],[c_46,c_19274]) ).
cnf(c_64,plain,
( leq(multiplication(star(B),A),C)
| ~ leq(addition(A,multiplication(B,C)),C) ),
inference(paramod,[status(thm)],[c_18,c_35]) ).
cnf(c_66,plain,
( leq(multiplication(star(A),multiplication(A,B)),B)
| ~ leq(multiplication(A,B),B) ),
inference(paramod,[status(thm)],[c_21,c_35]) ).
cnf(c_70,plain,
( leq(multiplication(star(A),multiplication(A,C)),B)
| ~ leq(multiplication(A,addition(B,C)),B) ),
inference(paramod,[status(thm)],[c_26,c_35]) ).
cnf(c_74,plain,
( leq(multiplication(A,star(C)),B)
| ~ leq(addition(A,multiplication(B,C)),B) ),
inference(paramod,[status(thm)],[c_18,c_36]) ).
cnf(c_19275,negated_conjecture,
addition(multiplication(star(sK0),star(sK1)),multiplication(star(sK1),star(sK0))) = multiplication(star(sK1),star(sK0)),
inference(resolve,[status(thm)],[c_31,c_37]) ).
cnf(c_84,negated_conjecture,
addition(multiplication(star(sK1),star(sK0)),multiplication(star(sK0),star(sK1))) = multiplication(star(sK1),star(sK0)),
inference(paramod,[status(thm)],[c_18,c_19275]) ).
cnf(c_112,plain,
leq(A,addition(A,B)),
inference(resolve,[status(thm)],[c_32,c_42]) ).
cnf(c_19276,plain,
addition(addition(A,B),addition(B,C)) = addition(A,addition(B,C)),
inference(paramod,[status(thm)],[c_42,c_19]) ).
cnf(c_19277,plain,
addition(B,addition(addition(A,B),C)) = addition(A,addition(B,C)),
inference(paramod,[status(thm)],[c_40,c_19276]) ).
cnf(c_114,plain,
addition(A,addition(B,addition(A,C))) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_19,c_19277]) ).
cnf(c_118,plain,
leq(A,addition(B,A)),
inference(paramod,[status(thm)],[c_18,c_112]) ).
cnf(c_119,plain,
leq(addition(A,B),addition(A,addition(B,C))),
inference(paramod,[status(thm)],[c_19,c_112]) ).
cnf(c_120,plain,
leq(multiplication(A,B),multiplication(A,addition(B,C))),
inference(paramod,[status(thm)],[c_26,c_112]) ).
cnf(c_121,plain,
leq(multiplication(A,B),multiplication(addition(A,C),B)),
inference(paramod,[status(thm)],[c_28,c_112]) ).
cnf(c_122,plain,
leq(A,addition(B,addition(C,A))),
inference(paramod,[status(thm)],[c_19,c_118]) ).
cnf(c_146,plain,
leq(A,multiplication(addition(one,B),A)),
inference(paramod,[status(thm)],[c_24,c_121]) ).
cnf(c_148,plain,
addition(A,multiplication(addition(one,B),A)) = multiplication(addition(one,B),A),
inference(resolve,[status(thm)],[c_31,c_146]) ).
cnf(c_153,plain,
leq(A,addition(B,addition(A,C))),
inference(paramod,[status(thm)],[c_18,c_122]) ).
cnf(c_155,plain,
leq(multiplication(A,B),addition(C,multiplication(A,addition(D,B)))),
inference(paramod,[status(thm)],[c_26,c_122]) ).
cnf(c_202,plain,
leq(A,addition(B,multiplication(A,addition(one,C)))),
inference(paramod,[status(thm)],[c_46,c_153]) ).
cnf(c_260,plain,
leq(A,addition(B,multiplication(addition(one,C),A))),
inference(paramod,[status(thm)],[c_51,c_153]) ).
cnf(c_19278,plain,
multiplication(A,addition(one,A)) = multiplication(addition(one,A),A),
inference(paramod,[status(thm)],[c_51,c_46]) ).
cnf(c_263,plain,
multiplication(addition(one,A),A) = multiplication(A,addition(one,A)),
inference(copy,[status(thm)],[c_19278]) ).
cnf(c_352,plain,
leq(addition(A,B),addition(B,A)),
inference(paramod,[status(thm)],[c_44,c_119]) ).
cnf(c_362,plain,
leq(addition(A,addition(B,C)),addition(B,addition(C,A))),
inference(paramod,[status(thm)],[c_19,c_352]) ).
cnf(c_532,plain,
( leq(multiplication(star(A),A),B)
| ~ leq(multiplication(A,addition(one,B)),B) ),
inference(paramod,[status(thm)],[c_46,c_64]) ).
cnf(c_536,plain,
( leq(multiplication(star(A),B),B)
| ~ leq(multiplication(addition(one,A),B),B) ),
inference(paramod,[status(thm)],[c_51,c_64]) ).
cnf(c_538,plain,
( leq(multiplication(star(A),B),B)
| ~ leq(multiplication(addition(A,one),B),B) ),
inference(paramod,[status(thm)],[c_52,c_64]) ).
cnf(c_546,plain,
( leq(multiplication(A,star(B)),A)
| ~ leq(multiplication(A,addition(one,B)),A) ),
inference(paramod,[status(thm)],[c_46,c_74]) ).
cnf(c_552,plain,
( leq(multiplication(B,star(B)),A)
| ~ leq(multiplication(addition(A,one),B),A) ),
inference(paramod,[status(thm)],[c_52,c_74]) ).
cnf(c_19279,plain,
( leq(multiplication(star(addition(B,one)),addition(B,one)),A)
| ~ leq(addition(addition(one,A),multiplication(B,addition(one,A))),A) ),
inference(paramod,[status(thm)],[c_52,c_532]) ).
cnf(c_728,plain,
( leq(multiplication(star(addition(A,one)),addition(A,one)),B)
| ~ leq(multiplication(addition(one,A),addition(one,B)),B) ),
inference(paramod,[status(thm)],[c_51,c_19279]) ).
cnf(c_19280,plain,
( leq(multiplication(addition(B,one),star(addition(B,one))),A)
| ~ leq(addition(addition(A,one),multiplication(addition(A,one),B)),A) ),
inference(paramod,[status(thm)],[c_47,c_552]) ).
cnf(c_756,plain,
( leq(multiplication(addition(B,one),star(addition(B,one))),A)
| ~ leq(multiplication(addition(A,one),addition(one,B)),A) ),
inference(paramod,[status(thm)],[c_46,c_19280]) ).
cnf(c_836,plain,
leq(A,multiplication(addition(B,A),addition(one,C))),
inference(paramod,[status(thm)],[c_28,c_202]) ).
cnf(c_840,plain,
leq(A,multiplication(addition(A,B),addition(one,C))),
inference(paramod,[status(thm)],[c_18,c_836]) ).
cnf(c_898,plain,
leq(A,multiplication(addition(one,B),addition(C,A))),
inference(paramod,[status(thm)],[c_26,c_260]) ).
cnf(c_904,plain,
leq(A,multiplication(addition(one,B),addition(A,C))),
inference(paramod,[status(thm)],[c_18,c_898]) ).
cnf(c_19281,plain,
addition(one,star(A)) = addition(one,multiplication(addition(one,A),star(A))),
inference(paramod,[status(thm)],[c_59,c_42]) ).
cnf(c_1570,plain,
addition(one,star(A)) = star(A),
inference(paramod,[status(thm)],[c_59,c_19281]) ).
cnf(c_19282,plain,
addition(multiplication(addition(one,A),star(A)),star(A)) = addition(one,multiplication(addition(one,A),star(A))),
inference(paramod,[status(thm)],[c_59,c_44]) ).
cnf(c_19283,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_19282]) ).
cnf(c_19284,plain,
multiplication(addition(one,A),star(A)) = addition(one,multiplication(addition(one,A),star(A))),
inference(paramod,[status(thm)],[c_148,c_19283]) ).
cnf(c_1581,plain,
multiplication(addition(one,A),star(A)) = star(A),
inference(paramod,[status(thm)],[c_59,c_19284]) ).
cnf(c_1582,plain,
addition(one,multiplication(addition(A,one),star(addition(A,one)))) = star(addition(A,one)),
inference(paramod,[status(thm)],[c_44,c_59]) ).
cnf(c_19285,plain,
multiplication(star(A),B) = addition(B,multiplication(multiplication(addition(one,A),star(A)),B)),
inference(paramod,[status(thm)],[c_59,c_51]) ).
cnf(c_19286,plain,
multiplication(star(A),B) = addition(B,multiplication(star(A),B)),
inference(paramod,[status(thm)],[c_1581,c_19285]) ).
cnf(c_1584,plain,
addition(A,multiplication(star(B),A)) = multiplication(star(B),A),
inference(copy,[status(thm)],[c_19286]) ).
cnf(c_19287,plain,
( leq(multiplication(star(addition(one,A)),one),star(A))
| ~ leq(star(A),star(A)) ),
inference(paramod,[status(thm)],[c_59,c_64]) ).
cnf(c_19288,plain,
( leq(star(addition(one,A)),star(A))
| ~ leq(star(A),star(A)) ),
inference(paramod,[status(thm)],[c_23,c_19287]) ).
cnf(c_1592,plain,
leq(star(addition(one,A)),star(A)),
inference(resolve,[status(thm)],[c_53,c_19288]) ).
cnf(c_1603,plain,
leq(A,multiplication(addition(B,A),star(C))),
inference(paramod,[status(thm)],[c_59,c_836]) ).
cnf(c_1605,plain,
leq(A,multiplication(addition(A,B),star(C))),
inference(paramod,[status(thm)],[c_59,c_840]) ).
cnf(c_1609,plain,
leq(A,multiplication(star(B),addition(A,C))),
inference(paramod,[status(thm)],[c_59,c_904]) ).
cnf(c_19289,plain,
addition(A,star(B)) = addition(one,addition(A,multiplication(addition(one,B),star(B)))),
inference(paramod,[status(thm)],[c_59,c_40]) ).
cnf(c_19290,plain,
addition(A,star(B)) = addition(one,addition(A,star(B))),
inference(paramod,[status(thm)],[c_1581,c_19289]) ).
cnf(c_1616,plain,
addition(one,addition(A,star(B))) = addition(A,star(B)),
inference(copy,[status(thm)],[c_19290]) ).
cnf(c_19291,plain,
addition(star(addition(one,A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_31,c_1592]) ).
cnf(c_1629,plain,
addition(star(A),star(addition(one,A))) = star(A),
inference(paramod,[status(thm)],[c_18,c_19291]) ).
cnf(c_1639,plain,
addition(A,multiplication(addition(B,A),star(C))) = multiplication(addition(B,A),star(C)),
inference(resolve,[status(thm)],[c_31,c_1603]) ).
cnf(c_1647,plain,
multiplication(addition(A,one),star(addition(A,one))) = star(addition(A,one)),
inference(paramod,[status(thm)],[c_1639,c_1582]) ).
cnf(c_1649,plain,
( leq(star(addition(B,one)),A)
| ~ leq(multiplication(addition(A,one),addition(one,B)),A) ),
inference(paramod,[status(thm)],[c_1647,c_756]) ).
cnf(c_1661,plain,
leq(one,multiplication(star(A),star(B))),
inference(paramod,[status(thm)],[c_1570,c_1605]) ).
cnf(c_1664,plain,
addition(one,multiplication(star(A),star(B))) = multiplication(star(A),star(B)),
inference(resolve,[status(thm)],[c_31,c_1661]) ).
cnf(c_1673,plain,
addition(A,multiplication(star(B),addition(A,C))) = multiplication(star(B),addition(A,C)),
inference(resolve,[status(thm)],[c_31,c_1609]) ).
cnf(c_1683,plain,
multiplication(star(A),addition(one,A)) = star(A),
inference(paramod,[status(thm)],[c_1673,c_63]) ).
cnf(c_19292,plain,
multiplication(star(A),B) = multiplication(addition(one,A),multiplication(star(A),B)),
inference(paramod,[status(thm)],[c_1581,c_22]) ).
cnf(c_1692,plain,
multiplication(addition(one,A),multiplication(star(A),B)) = multiplication(star(A),B),
inference(copy,[status(thm)],[c_19292]) ).
cnf(c_19293,plain,
multiplication(addition(one,A),addition(one,star(A))) = addition(addition(one,A),star(A)),
inference(paramod,[status(thm)],[c_1581,c_46]) ).
cnf(c_19294,plain,
multiplication(addition(one,A),star(A)) = addition(addition(one,A),star(A)),
inference(paramod,[status(thm)],[c_1570,c_19293]) ).
cnf(c_19295,plain,
star(A) = addition(addition(one,A),star(A)),
inference(paramod,[status(thm)],[c_1581,c_19294]) ).
cnf(c_19296,plain,
star(A) = addition(one,addition(A,star(A))),
inference(paramod,[status(thm)],[c_19,c_19295]) ).
cnf(c_19297,plain,
star(A) = addition(A,star(A)),
inference(paramod,[status(thm)],[c_1616,c_19296]) ).
cnf(c_1699,plain,
addition(A,star(A)) = star(A),
inference(copy,[status(thm)],[c_19297]) ).
cnf(c_19298,plain,
( leq(multiplication(star(A),star(A)),star(A))
| ~ leq(star(A),star(A)) ),
inference(paramod,[status(thm)],[c_1581,c_536]) ).
cnf(c_1702,plain,
leq(multiplication(star(A),star(A)),star(A)),
inference(resolve,[status(thm)],[c_53,c_19298]) ).
cnf(c_19299,plain,
( leq(multiplication(star(addition(one,A)),multiplication(addition(one,A),star(A))),star(A))
| ~ leq(star(A),star(A)) ),
inference(paramod,[status(thm)],[c_1581,c_66]) ).
cnf(c_19300,plain,
( leq(multiplication(star(addition(one,A)),star(A)),star(A))
| ~ leq(star(A),star(A)) ),
inference(paramod,[status(thm)],[c_1581,c_19299]) ).
cnf(c_1708,plain,
leq(multiplication(star(addition(one,A)),star(A)),star(A)),
inference(resolve,[status(thm)],[c_53,c_19300]) ).
cnf(c_1726,plain,
leq(multiplication(A,B),multiplication(A,star(B))),
inference(paramod,[status(thm)],[c_1699,c_120]) ).
cnf(c_1756,plain,
leq(addition(star(A),addition(B,A)),addition(B,star(A))),
inference(paramod,[status(thm)],[c_1699,c_362]) ).
cnf(c_1769,plain,
leq(multiplication(star(star(A)),multiplication(star(A),star(A))),star(A)),
inference(resolve,[status(thm)],[c_66,c_1702]) ).
cnf(c_19301,plain,
addition(multiplication(star(A),star(A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_31,c_1702]) ).
cnf(c_19302,plain,
addition(star(A),multiplication(star(A),star(A))) = star(A),
inference(paramod,[status(thm)],[c_18,c_19301]) ).
cnf(c_19303,plain,
multiplication(star(A),addition(one,star(A))) = star(A),
inference(paramod,[status(thm)],[c_46,c_19302]) ).
cnf(c_1770,plain,
multiplication(star(A),star(A)) = star(A),
inference(paramod,[status(thm)],[c_1570,c_19303]) ).
cnf(c_1771,plain,
leq(multiplication(star(star(A)),star(A)),star(A)),
inference(paramod,[status(thm)],[c_1770,c_1769]) ).
cnf(c_19304,plain,
leq(multiplication(addition(one,star(A)),A),multiplication(star(A),addition(one,star(A)))),
inference(paramod,[status(thm)],[c_263,c_1726]) ).
cnf(c_19305,plain,
leq(multiplication(star(A),A),multiplication(star(A),addition(one,star(A)))),
inference(paramod,[status(thm)],[c_1570,c_19304]) ).
cnf(c_19306,plain,
leq(multiplication(star(A),A),multiplication(star(A),star(A))),
inference(paramod,[status(thm)],[c_1570,c_19305]) ).
cnf(c_1775,plain,
leq(multiplication(star(A),A),star(A)),
inference(paramod,[status(thm)],[c_1770,c_19306]) ).
cnf(c_1777,plain,
leq(multiplication(star(addition(one,A)),star(A)),star(addition(one,A))),
inference(resolve,[status(thm)],[c_546,c_1775]) ).
cnf(c_19307,plain,
multiplication(star(A),B) = multiplication(star(A),multiplication(star(A),B)),
inference(paramod,[status(thm)],[c_1770,c_22]) ).
cnf(c_1819,plain,
multiplication(star(A),multiplication(star(A),B)) = multiplication(star(A),B),
inference(copy,[status(thm)],[c_19307]) ).
cnf(c_1827,plain,
( leq(multiplication(A,star(star(B))),star(B))
| ~ leq(addition(A,star(B)),star(B)) ),
inference(paramod,[status(thm)],[c_1770,c_74]) ).
cnf(c_19308,plain,
multiplication(star(A),B) = multiplication(star(A),multiplication(addition(one,A),B)),
inference(paramod,[status(thm)],[c_1683,c_22]) ).
cnf(c_1864,plain,
multiplication(star(A),multiplication(addition(one,A),B)) = multiplication(star(A),B),
inference(copy,[status(thm)],[c_19308]) ).
cnf(c_1872,plain,
multiplication(star(addition(A,one)),addition(A,one)) = star(addition(A,one)),
inference(paramod,[status(thm)],[c_44,c_1683]) ).
cnf(c_1881,plain,
multiplication(star(star(A)),star(A)) = star(star(A)),
inference(paramod,[status(thm)],[c_1570,c_1683]) ).
cnf(c_1883,plain,
( leq(star(addition(A,one)),B)
| ~ leq(multiplication(addition(one,A),addition(one,B)),B) ),
inference(paramod,[status(thm)],[c_1872,c_728]) ).
cnf(c_1884,plain,
leq(star(star(A)),star(A)),
inference(paramod,[status(thm)],[c_1881,c_1771]) ).
cnf(c_19309,plain,
addition(star(star(A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_31,c_1884]) ).
cnf(c_19310,plain,
addition(star(A),star(star(A))) = star(A),
inference(paramod,[status(thm)],[c_18,c_19309]) ).
cnf(c_1885,plain,
star(star(A)) = star(A),
inference(paramod,[status(thm)],[c_1699,c_19310]) ).
cnf(c_1890,plain,
( leq(multiplication(A,star(B)),star(B))
| ~ leq(addition(A,star(B)),star(B)) ),
inference(paramod,[status(thm)],[c_1885,c_1827]) ).
cnf(c_19311,plain,
addition(addition(star(A),addition(B,A)),addition(B,star(A))) = addition(B,star(A)),
inference(resolve,[status(thm)],[c_31,c_1756]) ).
cnf(c_19312,plain,
addition(B,addition(addition(star(A),addition(B,A)),star(A))) = addition(B,star(A)),
inference(paramod,[status(thm)],[c_40,c_19311]) ).
cnf(c_19313,plain,
addition(B,addition(star(A),addition(star(A),addition(B,A)))) = addition(B,star(A)),
inference(paramod,[status(thm)],[c_18,c_19312]) ).
cnf(c_19314,plain,
addition(B,addition(star(A),addition(B,A))) = addition(B,star(A)),
inference(paramod,[status(thm)],[c_42,c_19313]) ).
cnf(c_2359,plain,
addition(star(A),addition(B,A)) = addition(B,star(A)),
inference(paramod,[status(thm)],[c_114,c_19314]) ).
cnf(c_2570,plain,
addition(star(A),addition(B,A)) = addition(star(A),B),
inference(paramod,[status(thm)],[c_2359,c_18]) ).
cnf(c_19315,plain,
addition(star(addition(A,B)),addition(A,B)) = addition(A,star(addition(A,B))),
inference(paramod,[status(thm)],[c_42,c_2359]) ).
cnf(c_19316,plain,
addition(addition(A,B),star(addition(A,B))) = addition(A,star(addition(A,B))),
inference(paramod,[status(thm)],[c_18,c_19315]) ).
cnf(c_19317,plain,
star(addition(A,B)) = addition(A,star(addition(A,B))),
inference(paramod,[status(thm)],[c_1699,c_19316]) ).
cnf(c_2576,plain,
addition(A,star(addition(A,B))) = star(addition(A,B)),
inference(copy,[status(thm)],[c_19317]) ).
cnf(c_3173,plain,
( leq(star(addition(B,one)),A)
| ~ leq(multiplication(addition(A,one),addition(B,one)),A) ),
inference(paramod,[status(thm)],[c_18,c_1649]) ).
cnf(c_19318,plain,
addition(multiplication(star(addition(one,A)),star(A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_31,c_1708]) ).
cnf(c_19319,plain,
addition(star(A),multiplication(star(addition(one,A)),star(A))) = star(A),
inference(paramod,[status(thm)],[c_18,c_19318]) ).
cnf(c_3204,plain,
multiplication(star(addition(one,A)),star(A)) = star(A),
inference(paramod,[status(thm)],[c_1584,c_19319]) ).
cnf(c_3206,plain,
leq(star(A),star(addition(one,A))),
inference(paramod,[status(thm)],[c_3204,c_1777]) ).
cnf(c_19320,plain,
addition(star(A),star(addition(one,A))) = star(addition(one,A)),
inference(resolve,[status(thm)],[c_31,c_3206]) ).
cnf(c_19321,plain,
star(A) = star(addition(one,A)),
inference(paramod,[status(thm)],[c_1629,c_19320]) ).
cnf(c_3207,plain,
star(addition(one,A)) = star(A),
inference(copy,[status(thm)],[c_19321]) ).
cnf(c_3251,plain,
star(addition(A,one)) = star(A),
inference(paramod,[status(thm)],[c_18,c_3207]) ).
cnf(c_3252,plain,
star(addition(A,addition(one,B))) = star(addition(A,B)),
inference(paramod,[status(thm)],[c_40,c_3207]) ).
cnf(c_3311,plain,
( leq(star(B),A)
| ~ leq(multiplication(addition(A,one),addition(B,one)),A) ),
inference(paramod,[status(thm)],[c_3251,c_3173]) ).
cnf(c_3357,plain,
( leq(star(A),B)
| ~ leq(multiplication(addition(one,A),addition(one,B)),B) ),
inference(paramod,[status(thm)],[c_3251,c_1883]) ).
cnf(c_3484,plain,
( leq(star(A),B)
| ~ leq(multiplication(addition(A,one),addition(one,B)),B) ),
inference(paramod,[status(thm)],[c_18,c_3357]) ).
cnf(c_3508,plain,
( leq(star(A),star(B))
| ~ leq(multiplication(addition(A,one),star(B)),star(B)) ),
inference(paramod,[status(thm)],[c_1570,c_3484]) ).
cnf(c_3985,plain,
leq(multiplication(star(A),A),addition(B,star(A))),
inference(paramod,[status(thm)],[c_1683,c_155]) ).
cnf(c_3989,plain,
leq(multiplication(star(A),A),addition(star(A),B)),
inference(paramod,[status(thm)],[c_18,c_3985]) ).
cnf(c_3992,plain,
leq(multiplication(star(A),A),multiplication(star(A),addition(one,B))),
inference(paramod,[status(thm)],[c_46,c_3989]) ).
cnf(c_4036,plain,
leq(multiplication(star(A),A),multiplication(star(A),star(B))),
inference(paramod,[status(thm)],[c_1570,c_3992]) ).
cnf(c_19322,plain,
addition(multiplication(star(A),A),multiplication(star(A),star(B))) = multiplication(star(A),star(B)),
inference(resolve,[status(thm)],[c_31,c_4036]) ).
cnf(c_4037,plain,
multiplication(star(A),addition(A,star(B))) = multiplication(star(A),star(B)),
inference(paramod,[status(thm)],[c_26,c_19322]) ).
cnf(c_19323,plain,
( leq(multiplication(A,star(addition(A,B))),star(addition(A,B)))
| ~ leq(star(addition(A,B)),star(addition(A,B))) ),
inference(paramod,[status(thm)],[c_2576,c_1890]) ).
cnf(c_5904,plain,
leq(multiplication(A,star(addition(A,B))),star(addition(A,B))),
inference(resolve,[status(thm)],[c_53,c_19323]) ).
cnf(c_19324,plain,
leq(star(A),star(addition(addition(A,one),B))),
inference(resolve,[status(thm)],[c_3508,c_5904]) ).
cnf(c_19325,plain,
leq(star(A),star(addition(A,addition(one,B)))),
inference(paramod,[status(thm)],[c_19,c_19324]) ).
cnf(c_7732,plain,
leq(star(A),star(addition(A,B))),
inference(paramod,[status(thm)],[c_3252,c_19325]) ).
cnf(c_19326,plain,
leq(multiplication(star(A),star(addition(addition(A,one),B))),star(addition(addition(A,one),B))),
inference(resolve,[status(thm)],[c_538,c_5904]) ).
cnf(c_19327,plain,
leq(multiplication(star(A),star(addition(A,addition(one,B)))),star(addition(addition(A,one),B))),
inference(paramod,[status(thm)],[c_19,c_19326]) ).
cnf(c_19328,plain,
leq(multiplication(star(A),star(addition(A,B))),star(addition(addition(A,one),B))),
inference(paramod,[status(thm)],[c_3252,c_19327]) ).
cnf(c_19329,plain,
leq(multiplication(star(A),star(addition(A,B))),star(addition(A,addition(one,B)))),
inference(paramod,[status(thm)],[c_19,c_19328]) ).
cnf(c_7735,plain,
leq(multiplication(star(A),star(addition(A,B))),star(addition(A,B))),
inference(paramod,[status(thm)],[c_3252,c_19329]) ).
cnf(c_7759,plain,
leq(star(A),star(addition(B,A))),
inference(paramod,[status(thm)],[c_18,c_7732]) ).
cnf(c_7761,plain,
leq(star(multiplication(A,B)),star(multiplication(A,addition(B,C)))),
inference(paramod,[status(thm)],[c_26,c_7732]) ).
cnf(c_7769,plain,
leq(star(A),star(multiplication(star(B),A))),
inference(paramod,[status(thm)],[c_1584,c_7732]) ).
cnf(c_7770,plain,
addition(star(A),star(addition(B,A))) = star(addition(B,A)),
inference(resolve,[status(thm)],[c_31,c_7759]) ).
cnf(c_7775,plain,
leq(star(addition(A,B)),star(addition(star(B),A))),
inference(paramod,[status(thm)],[c_2570,c_7759]) ).
cnf(c_7938,plain,
addition(star(A),star(multiplication(star(B),A))) = star(multiplication(star(B),A)),
inference(resolve,[status(thm)],[c_31,c_7769]) ).
cnf(c_7962,plain,
leq(star(addition(A,B)),star(addition(A,star(B)))),
inference(paramod,[status(thm)],[c_18,c_7775]) ).
cnf(c_19330,plain,
leq(star(addition(star(A),B)),star(addition(star(addition(B,A)),star(A)))),
inference(paramod,[status(thm)],[c_2570,c_7775]) ).
cnf(c_19331,plain,
leq(star(addition(star(A),B)),star(addition(star(A),star(addition(B,A))))),
inference(paramod,[status(thm)],[c_18,c_19330]) ).
cnf(c_19332,plain,
leq(star(addition(star(A),B)),star(star(addition(B,A)))),
inference(paramod,[status(thm)],[c_7770,c_19331]) ).
cnf(c_7977,plain,
leq(star(addition(star(A),B)),star(addition(B,A))),
inference(paramod,[status(thm)],[c_1885,c_19332]) ).
cnf(c_8001,plain,
addition(star(addition(A,B)),star(addition(A,star(B)))) = star(addition(A,star(B))),
inference(resolve,[status(thm)],[c_31,c_7962]) ).
cnf(c_8756,plain,
leq(star(addition(A,star(B))),star(addition(A,B))),
inference(paramod,[status(thm)],[c_18,c_7977]) ).
cnf(c_19333,plain,
addition(star(addition(A,star(B))),star(addition(A,B))) = star(addition(A,B)),
inference(resolve,[status(thm)],[c_31,c_8756]) ).
cnf(c_19334,plain,
addition(star(addition(A,B)),star(addition(A,star(B)))) = star(addition(A,B)),
inference(paramod,[status(thm)],[c_18,c_19333]) ).
cnf(c_8785,plain,
star(addition(A,star(B))) = star(addition(A,B)),
inference(paramod,[status(thm)],[c_8001,c_19334]) ).
cnf(c_10959,plain,
leq(star(multiplication(A,B)),star(multiplication(A,star(B)))),
inference(paramod,[status(thm)],[c_1699,c_7761]) ).
cnf(c_19335,plain,
( leq(multiplication(star(addition(one,C)),multiplication(addition(one,C),B)),A)
| ~ leq(addition(addition(A,B),multiplication(C,addition(A,B))),A) ),
inference(paramod,[status(thm)],[c_51,c_70]) ).
cnf(c_19336,plain,
( leq(multiplication(star(addition(one,C)),multiplication(addition(one,C),B)),A)
| ~ leq(multiplication(addition(one,C),addition(A,B)),A) ),
inference(paramod,[status(thm)],[c_51,c_19335]) ).
cnf(c_19337,plain,
( leq(multiplication(star(C),multiplication(addition(one,C),B)),A)
| ~ leq(multiplication(addition(one,C),addition(A,B)),A) ),
inference(paramod,[status(thm)],[c_3207,c_19336]) ).
cnf(c_13454,plain,
( leq(multiplication(star(A),C),B)
| ~ leq(multiplication(addition(one,A),addition(B,C)),B) ),
inference(paramod,[status(thm)],[c_1864,c_19337]) ).
cnf(c_13463,plain,
( leq(multiplication(star(A),C),B)
| ~ leq(multiplication(addition(A,one),addition(B,C)),B) ),
inference(paramod,[status(thm)],[c_18,c_13454]) ).
cnf(c_13524,plain,
( leq(multiplication(star(A),B),C)
| ~ leq(multiplication(addition(A,one),addition(B,C)),C) ),
inference(paramod,[status(thm)],[c_18,c_13463]) ).
cnf(c_19338,plain,
addition(multiplication(star(A),star(addition(A,B))),star(addition(A,B))) = star(addition(A,B)),
inference(resolve,[status(thm)],[c_31,c_7735]) ).
cnf(c_19339,plain,
addition(star(addition(A,B)),multiplication(star(A),star(addition(A,B)))) = star(addition(A,B)),
inference(paramod,[status(thm)],[c_18,c_19338]) ).
cnf(c_16260,plain,
multiplication(star(A),star(addition(A,B))) = star(addition(A,B)),
inference(paramod,[status(thm)],[c_1584,c_19339]) ).
cnf(c_19340,plain,
leq(star(multiplication(star(A),addition(A,B))),star(star(addition(A,B)))),
inference(paramod,[status(thm)],[c_16260,c_10959]) ).
cnf(c_17750,plain,
leq(star(multiplication(star(A),addition(A,B))),star(addition(A,B))),
inference(paramod,[status(thm)],[c_1885,c_19340]) ).
cnf(c_19341,plain,
addition(star(multiplication(star(A),addition(A,B))),star(addition(A,B))) = star(addition(A,B)),
inference(resolve,[status(thm)],[c_31,c_17750]) ).
cnf(c_19342,plain,
addition(star(addition(A,B)),star(multiplication(star(A),addition(A,B)))) = star(addition(A,B)),
inference(paramod,[status(thm)],[c_18,c_19341]) ).
cnf(c_18379,plain,
star(multiplication(star(A),addition(A,B))) = star(addition(A,B)),
inference(paramod,[status(thm)],[c_7938,c_19342]) ).
cnf(c_19343,plain,
star(multiplication(star(A),addition(A,star(B)))) = star(addition(A,B)),
inference(paramod,[status(thm)],[c_8785,c_18379]) ).
cnf(c_18463,plain,
star(multiplication(star(A),star(B))) = star(addition(A,B)),
inference(paramod,[status(thm)],[c_4037,c_19343]) ).
cnf(c_18522,plain,
star(multiplication(star(A),star(B))) = star(addition(B,A)),
inference(paramod,[status(thm)],[c_18,c_18463]) ).
cnf(c_19171,plain,
~ leq(star(multiplication(star(sK0),star(sK1))),multiplication(star(sK1),star(sK0))),
inference(paramod,[status(thm)],[c_18522,c_38]) ).
cnf(c_19344,plain,
~ leq(multiplication(addition(multiplication(star(sK1),star(sK0)),one),addition(multiplication(star(sK0),star(sK1)),one)),multiplication(star(sK1),star(sK0))),
inference(resolve,[status(thm)],[c_3311,c_19171]) ).
cnf(c_19345,plain,
~ leq(multiplication(addition(one,multiplication(star(sK1),star(sK0))),addition(multiplication(star(sK0),star(sK1)),one)),multiplication(star(sK1),star(sK0))),
inference(paramod,[status(thm)],[c_18,c_19344]) ).
cnf(c_19346,plain,
~ leq(multiplication(multiplication(star(sK1),star(sK0)),addition(multiplication(star(sK0),star(sK1)),one)),multiplication(star(sK1),star(sK0))),
inference(paramod,[status(thm)],[c_1664,c_19345]) ).
cnf(c_19347,plain,
~ leq(multiplication(multiplication(star(sK1),star(sK0)),addition(one,multiplication(star(sK0),star(sK1)))),multiplication(star(sK1),star(sK0))),
inference(paramod,[status(thm)],[c_18,c_19346]) ).
cnf(c_19348,plain,
~ leq(multiplication(multiplication(star(sK1),star(sK0)),multiplication(star(sK0),star(sK1))),multiplication(star(sK1),star(sK0))),
inference(paramod,[status(thm)],[c_1664,c_19347]) ).
cnf(c_19349,plain,
~ leq(multiplication(star(sK1),multiplication(star(sK0),multiplication(star(sK0),star(sK1)))),multiplication(star(sK1),star(sK0))),
inference(paramod,[status(thm)],[c_22,c_19348]) ).
cnf(c_19253,plain,
~ leq(multiplication(star(sK1),multiplication(star(sK0),star(sK1))),multiplication(star(sK1),star(sK0))),
inference(paramod,[status(thm)],[c_1819,c_19349]) ).
cnf(c_19350,plain,
~ leq(multiplication(addition(sK1,one),addition(multiplication(star(sK0),star(sK1)),multiplication(star(sK1),star(sK0)))),multiplication(star(sK1),star(sK0))),
inference(resolve,[status(thm)],[c_13524,c_19253]) ).
cnf(c_19351,plain,
~ leq(multiplication(addition(one,sK1),addition(multiplication(star(sK0),star(sK1)),multiplication(star(sK1),star(sK0)))),multiplication(star(sK1),star(sK0))),
inference(paramod,[status(thm)],[c_18,c_19350]) ).
cnf(c_19352,plain,
~ leq(multiplication(addition(one,sK1),addition(multiplication(star(sK1),star(sK0)),multiplication(star(sK0),star(sK1)))),multiplication(star(sK1),star(sK0))),
inference(paramod,[status(thm)],[c_18,c_19351]) ).
cnf(c_19353,plain,
~ leq(multiplication(addition(one,sK1),multiplication(star(sK1),star(sK0))),multiplication(star(sK1),star(sK0))),
inference(paramod,[status(thm)],[c_84,c_19352]) ).
cnf(c_19354,plain,
~ leq(multiplication(star(sK1),star(sK0)),multiplication(star(sK1),star(sK0))),
inference(paramod,[status(thm)],[c_1692,c_19353]) ).
cnf(c_19259,plain,
$false,
inference(resolve,[status(thm)],[c_53,c_19354]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE046+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 19:18:02 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 4136308 was started by sandbox on n005,
% 0.10/0.37 % Fri Sep 25 19:18:02 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 244.24/32.83
% 244.24/32.83 % given #500 (W,wt=29): 2709 -leq(addition(star(A),B),one) | leq(multiplication(addition(B,A),star(A)),one). [para(2570(a,1),79(a,1)),rewrite([1885(7)])].
% 244.24/32.83
% 244.24/32.83 % given #1000 (T,wt=29): 6173 leq(addition(A,B),star(addition(A,star(B)))). [para(18(a,1),5992(a,2,1))].
% 244.24/32.83
% 244.24/32.83 % given #1500 (T,wt=31): 9959 leq(multiplication(star(addition(A,B)),B),star(addition(B,A))). [para(18(a,1),5905(a,1,1,1))].
% 244.24/32.83
% 244.24/32.83 % given #2000 (T,wt=32): 6392 leq(multiplication(A,star(A)),star(multiplication(addition(one,B),star(A)))). [para(51(a,2),5953(a,2,1))].
% 244.24/32.83
% 244.24/32.83 % given #2500 (W,wt=32): 17449 leq(addition(A,B),addition(B,multiplication(star(A),addition(one,C)))). [para(46(a,2),14463(a,2,2))].
% 244.24/32.83
% 244.24/32.83 % SZS status Theorem for theBenchmark
% 244.24/32.83
% 244.24/32.83 % Proof 1 at 5.52 (+ 2.24) seconds.
% 244.24/32.83 % Length of proof is 155.
% 244.24/32.83 % Level of proof is 29.
% 244.24/32.83 % Maximum clause weight is 41.000.
% 244.24/32.83 % Given clauses 2566.
% 244.24/32.83
% 244.24/32.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------