%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE043+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 07:44:11 AM UTC 2026
% Result : Theorem 54.85s 7.41s
% Output : CNFRefutation 54.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 14
% Syntax : Number of formulae : 185 ( 136 unt; 0 def)
% Number of atoms : 234 ( 88 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 114 ( 65 ~; 44 |; 2 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 297 ( 16 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_identity,axiom,
! [A] : addition(A,zero) = A,
file('theBenchmark.p',additive_identity) ).
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_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(addition(X1,multiplication(multiplication(X0,star(X0)),X1)),multiplication(star(X0),X1))
& leq(multiplication(star(X0),X1),addition(X1,multiplication(multiplication(X0,star(X0)),X1))) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( leq(addition(X1,multiplication(multiplication(X0,star(X0)),X1)),multiplication(star(X0),X1))
& leq(multiplication(star(X0),X1),addition(X1,multiplication(multiplication(X0,star(X0)),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_20,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
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_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(addition(X1,multiplication(multiplication(X0,star(X0)),X1)),multiplication(star(X0),X1))
| ~ leq(multiplication(star(X0),X1),addition(X1,multiplication(multiplication(X0,star(X0)),X1))) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ~ leq(addition(sK1,multiplication(multiplication(sK0,star(sK0)),sK1)),multiplication(star(sK0),sK1))
| ~ leq(multiplication(star(sK0),sK1),addition(sK1,multiplication(multiplication(sK0,star(sK0)),sK1))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[nnf_17]) ).
cnf(c_37,negated_conjecture,
( ~ leq(addition(sK1,multiplication(multiplication(sK0,star(sK0)),sK1)),multiplication(star(sK0),sK1))
| ~ leq(multiplication(star(sK0),sK1),addition(sK1,multiplication(multiplication(sK0,star(sK0)),sK1))) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_27667,negated_conjecture,
( ~ leq(addition(sK1,multiplication(multiplication(sK0,star(sK0)),sK1)),multiplication(star(sK0),sK1))
| ~ leq(multiplication(star(sK0),sK1),addition(sK1,multiplication(sK0,multiplication(star(sK0),sK1)))) ),
inference(paramod,[status(thm)],[c_22,c_37]) ).
cnf(c_38,negated_conjecture,
( ~ leq(addition(sK1,multiplication(sK0,multiplication(star(sK0),sK1))),multiplication(star(sK0),sK1))
| ~ leq(multiplication(star(sK0),sK1),addition(sK1,multiplication(sK0,multiplication(star(sK0),sK1)))) ),
inference(paramod,[status(thm)],[c_22,c_27667]) ).
cnf(c_27668,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_27668]) ).
cnf(c_27669,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_27669]) ).
cnf(c_27670,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_27670]) ).
cnf(c_27671,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_27671]) ).
cnf(c_27672,plain,
addition(multiplication(A,B),A) = multiplication(A,addition(B,one)),
inference(paramod,[status(thm)],[c_23,c_26]) ).
cnf(c_27673,plain,
addition(A,multiplication(A,B)) = multiplication(A,addition(B,one)),
inference(paramod,[status(thm)],[c_18,c_27672]) ).
cnf(c_47,plain,
multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)),
inference(copy,[status(thm)],[c_27673]) ).
cnf(c_27674,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_27674]) ).
cnf(c_27675,plain,
addition(multiplication(A,B),B) = multiplication(addition(A,one),B),
inference(paramod,[status(thm)],[c_24,c_28]) ).
cnf(c_27676,plain,
addition(B,multiplication(A,B)) = multiplication(addition(A,one),B),
inference(paramod,[status(thm)],[c_18,c_27675]) ).
cnf(c_52,plain,
multiplication(addition(A,one),B) = addition(B,multiplication(A,B)),
inference(copy,[status(thm)],[c_27676]) ).
cnf(c_53,plain,
leq(A,A),
inference(resolve,[status(thm)],[c_32,c_21]) ).
cnf(c_27677,plain,
addition(addition(one,multiplication(A,star(A))),star(A)) = star(A),
inference(resolve,[status(thm)],[c_33,c_31]) ).
cnf(c_59,plain,
addition(star(A),addition(one,multiplication(A,star(A)))) = star(A),
inference(paramod,[status(thm)],[c_18,c_27677]) ).
cnf(c_61,plain,
leq(addition(one,star(one)),star(one)),
inference(paramod,[status(thm)],[c_24,c_33]) ).
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_68,plain,
( leq(multiplication(star(A),B),one)
| ~ leq(addition(A,B),one) ),
inference(paramod,[status(thm)],[c_23,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_78,plain,
( leq(multiplication(B,star(one)),A)
| ~ leq(addition(A,B),A) ),
inference(paramod,[status(thm)],[c_23,c_36]) ).
cnf(c_27678,plain,
( leq(multiplication(multiplication(B,C),star(C)),A)
| ~ leq(multiplication(addition(A,B),C),A) ),
inference(paramod,[status(thm)],[c_28,c_36]) ).
cnf(c_81,plain,
( leq(multiplication(B,multiplication(C,star(C))),A)
| ~ leq(multiplication(addition(A,B),C),A) ),
inference(paramod,[status(thm)],[c_22,c_27678]) ).
cnf(c_87,plain,
( leq(multiplication(star(B),addition(A,D)),C)
| ~ leq(addition(A,addition(multiplication(B,C),D)),C) ),
inference(paramod,[status(thm)],[c_40,c_35]) ).
cnf(c_95,plain,
leq(A,addition(A,B)),
inference(resolve,[status(thm)],[c_42,c_32]) ).
cnf(c_101,plain,
leq(A,addition(B,A)),
inference(paramod,[status(thm)],[c_18,c_95]) ).
cnf(c_103,plain,
leq(multiplication(A,B),multiplication(A,addition(B,C))),
inference(paramod,[status(thm)],[c_26,c_95]) ).
cnf(c_104,plain,
leq(multiplication(A,B),multiplication(addition(A,C),B)),
inference(paramod,[status(thm)],[c_28,c_95]) ).
cnf(c_105,plain,
leq(A,addition(B,addition(A,C))),
inference(paramod,[status(thm)],[c_40,c_95]) ).
cnf(c_106,plain,
leq(A,addition(B,addition(C,A))),
inference(paramod,[status(thm)],[c_19,c_101]) ).
cnf(c_108,plain,
leq(multiplication(A,B),multiplication(addition(C,A),B)),
inference(paramod,[status(thm)],[c_28,c_101]) ).
cnf(c_27679,plain,
addition(addition(one,star(one)),star(one)) = star(one),
inference(resolve,[status(thm)],[c_61,c_31]) ).
cnf(c_27680,plain,
addition(star(one),addition(one,star(one))) = star(one),
inference(paramod,[status(thm)],[c_18,c_27679]) ).
cnf(c_119,plain,
addition(one,star(one)) = star(one),
inference(paramod,[status(thm)],[c_44,c_27680]) ).
cnf(c_27681,plain,
addition(multiplication(A,B),addition(A,multiplication(A,C))) = multiplication(A,addition(B,addition(one,C))),
inference(paramod,[status(thm)],[c_46,c_26]) ).
cnf(c_27682,plain,
addition(A,addition(multiplication(A,B),multiplication(A,C))) = multiplication(A,addition(B,addition(one,C))),
inference(paramod,[status(thm)],[c_40,c_27681]) ).
cnf(c_27683,plain,
addition(A,multiplication(A,addition(B,C))) = multiplication(A,addition(B,addition(one,C))),
inference(paramod,[status(thm)],[c_26,c_27682]) ).
cnf(c_179,plain,
multiplication(A,addition(B,addition(one,C))) = addition(A,multiplication(A,addition(B,C))),
inference(copy,[status(thm)],[c_27683]) ).
cnf(c_191,plain,
addition(A,multiplication(A,addition(one,B))) = addition(A,multiplication(A,B)),
inference(paramod,[status(thm)],[c_46,c_42]) ).
cnf(c_27684,plain,
multiplication(A,addition(B,one)) = addition(A,multiplication(A,addition(B,one))),
inference(paramod,[status(thm)],[c_44,c_46]) ).
cnf(c_195,plain,
addition(A,multiplication(A,addition(B,one))) = multiplication(A,addition(B,one)),
inference(copy,[status(thm)],[c_27684]) ).
cnf(c_214,plain,
leq(A,multiplication(addition(one,B),A)),
inference(paramod,[status(thm)],[c_24,c_104]) ).
cnf(c_246,plain,
addition(A,multiplication(addition(one,B),A)) = multiplication(addition(one,B),A),
inference(resolve,[status(thm)],[c_214,c_31]) ).
cnf(c_304,plain,
multiplication(addition(one,multiplication(A,B)),C) = addition(C,multiplication(A,multiplication(B,C))),
inference(paramod,[status(thm)],[c_22,c_51]) ).
cnf(c_324,plain,
leq(addition(A,multiplication(B,A)),multiplication(addition(one,B),addition(A,C))),
inference(paramod,[status(thm)],[c_51,c_103]) ).
cnf(c_370,plain,
( leq(multiplication(star(A),A),one)
| ~ leq(A,one) ),
inference(paramod,[status(thm)],[c_21,c_68]) ).
cnf(c_27685,plain,
leq(multiplication(star(one),one),one),
inference(resolve,[status(thm)],[c_370,c_53]) ).
cnf(c_382,plain,
leq(star(one),one),
inference(paramod,[status(thm)],[c_23,c_27685]) ).
cnf(c_27686,plain,
addition(star(one),one) = one,
inference(resolve,[status(thm)],[c_382,c_31]) ).
cnf(c_27687,plain,
addition(one,star(one)) = one,
inference(paramod,[status(thm)],[c_18,c_27686]) ).
cnf(c_385,plain,
star(one) = one,
inference(paramod,[status(thm)],[c_119,c_27687]) ).
cnf(c_27688,plain,
( leq(multiplication(B,one),A)
| ~ leq(addition(A,B),A) ),
inference(paramod,[status(thm)],[c_385,c_78]) ).
cnf(c_389,plain,
( leq(B,A)
| ~ leq(addition(A,B),A) ),
inference(paramod,[status(thm)],[c_23,c_27688]) ).
cnf(c_422,plain,
( leq(multiplication(A,B),A)
| ~ leq(multiplication(A,addition(one,B)),A) ),
inference(paramod,[status(thm)],[c_46,c_389]) ).
cnf(c_593,plain,
leq(A,addition(B,multiplication(A,addition(one,C)))),
inference(paramod,[status(thm)],[c_46,c_105]) ).
cnf(c_690,plain,
( leq(multiplication(A,star(B)),A)
| ~ leq(multiplication(A,addition(one,B)),A) ),
inference(paramod,[status(thm)],[c_46,c_74]) ).
cnf(c_725,plain,
leq(multiplication(addition(one,multiplication(A,star(A))),B),multiplication(star(A),B)),
inference(paramod,[status(thm)],[c_59,c_108]) ).
cnf(c_735,plain,
leq(one,star(A)),
inference(paramod,[status(thm)],[c_59,c_105]) ).
cnf(c_737,plain,
leq(multiplication(A,star(A)),star(A)),
inference(paramod,[status(thm)],[c_59,c_106]) ).
cnf(c_740,plain,
addition(one,star(A)) = star(A),
inference(resolve,[status(thm)],[c_735,c_31]) ).
cnf(c_27689,plain,
addition(multiplication(A,star(A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_737,c_31]) ).
cnf(c_744,plain,
addition(star(A),multiplication(A,star(A))) = star(A),
inference(paramod,[status(thm)],[c_18,c_27689]) ).
cnf(c_27690,plain,
star(A) = addition(star(A),one),
inference(paramod,[status(thm)],[c_740,c_18]) ).
cnf(c_749,plain,
addition(star(A),one) = star(A),
inference(copy,[status(thm)],[c_27690]) ).
cnf(c_27691,plain,
addition(multiplication(A,one),multiplication(A,star(B))) = multiplication(A,star(B)),
inference(paramod,[status(thm)],[c_740,c_26]) ).
cnf(c_751,plain,
addition(A,multiplication(A,star(B))) = multiplication(A,star(B)),
inference(paramod,[status(thm)],[c_23,c_27691]) ).
cnf(c_27692,plain,
addition(multiplication(one,A),multiplication(star(B),A)) = multiplication(star(B),A),
inference(paramod,[status(thm)],[c_740,c_28]) ).
cnf(c_752,plain,
addition(A,multiplication(star(B),A)) = multiplication(star(B),A),
inference(paramod,[status(thm)],[c_24,c_27692]) ).
cnf(c_27693,plain,
( leq(multiplication(star(addition(C,one)),multiplication(addition(C,one),B)),A)
| ~ leq(addition(addition(A,B),multiplication(C,addition(A,B))),A) ),
inference(paramod,[status(thm)],[c_52,c_70]) ).
cnf(c_887,plain,
( leq(multiplication(star(addition(A,one)),multiplication(addition(A,one),C)),B)
| ~ leq(multiplication(addition(one,A),addition(B,C)),B) ),
inference(paramod,[status(thm)],[c_51,c_27693]) ).
cnf(c_27694,plain,
( leq(multiplication(star(A),multiplication(A,one)),star(B))
| ~ leq(multiplication(A,star(B)),star(B)) ),
inference(paramod,[status(thm)],[c_749,c_70]) ).
cnf(c_893,plain,
( leq(multiplication(star(A),A),star(B))
| ~ leq(multiplication(A,star(B)),star(B)) ),
inference(paramod,[status(thm)],[c_23,c_27694]) ).
cnf(c_1014,plain,
leq(addition(A,multiplication(B,A)),multiplication(addition(one,B),A)),
inference(paramod,[status(thm)],[c_20,c_324]) ).
cnf(c_1027,plain,
leq(addition(A,multiplication(B,multiplication(C,A))),multiplication(addition(one,multiplication(B,C)),A)),
inference(paramod,[status(thm)],[c_22,c_1014]) ).
cnf(c_27695,plain,
( leq(multiplication(one,multiplication(B,star(B))),star(A))
| ~ leq(multiplication(star(A),B),star(A)) ),
inference(paramod,[status(thm)],[c_749,c_81]) ).
cnf(c_1178,plain,
( leq(multiplication(B,star(B)),star(A))
| ~ leq(multiplication(star(A),B),star(A)) ),
inference(paramod,[status(thm)],[c_24,c_27695]) ).
cnf(c_1907,plain,
leq(A,addition(B,multiplication(A,star(C)))),
inference(paramod,[status(thm)],[c_740,c_593]) ).
cnf(c_2289,plain,
leq(multiplication(star(A),A),star(A)),
inference(resolve,[status(thm)],[c_893,c_737]) ).
cnf(c_2294,plain,
leq(multiplication(star(addition(one,A)),star(A)),star(addition(one,A))),
inference(resolve,[status(thm)],[c_2289,c_690]) ).
cnf(c_2513,plain,
multiplication(addition(one,A),star(A)) = star(A),
inference(paramod,[status(thm)],[c_744,c_51]) ).
cnf(c_27696,plain,
( leq(multiplication(star(A),star(A)),star(A))
| ~ leq(star(A),star(A)) ),
inference(paramod,[status(thm)],[c_744,c_64]) ).
cnf(c_2523,plain,
leq(multiplication(star(A),star(A)),star(A)),
inference(resolve,[status(thm)],[c_53,c_27696]) ).
cnf(c_2545,plain,
leq(A,star(A)),
inference(paramod,[status(thm)],[c_744,c_1907]) ).
cnf(c_2554,plain,
addition(A,star(A)) = star(A),
inference(resolve,[status(thm)],[c_2545,c_31]) ).
cnf(c_2673,plain,
leq(multiplication(star(A),star(star(A))),star(A)),
inference(resolve,[status(thm)],[c_2523,c_1178]) ).
cnf(c_27697,plain,
addition(multiplication(star(A),star(A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_2523,c_31]) ).
cnf(c_27698,plain,
addition(star(A),multiplication(star(A),star(A))) = star(A),
inference(paramod,[status(thm)],[c_18,c_27697]) ).
cnf(c_2677,plain,
multiplication(star(A),star(A)) = star(A),
inference(paramod,[status(thm)],[c_751,c_27698]) ).
cnf(c_2893,plain,
multiplication(star(A),star(star(A))) = star(star(A)),
inference(paramod,[status(thm)],[c_740,c_2513]) ).
cnf(c_27699,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_2513,c_66]) ).
cnf(c_27700,plain,
( leq(multiplication(star(addition(one,A)),star(A)),star(A))
| ~ leq(star(A),star(A)) ),
inference(paramod,[status(thm)],[c_2513,c_27699]) ).
cnf(c_2895,plain,
leq(multiplication(star(addition(one,A)),star(A)),star(A)),
inference(resolve,[status(thm)],[c_53,c_27700]) ).
cnf(c_2927,plain,
leq(star(star(A)),star(A)),
inference(paramod,[status(thm)],[c_2893,c_2673]) ).
cnf(c_27701,plain,
addition(star(star(A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_2927,c_31]) ).
cnf(c_27702,plain,
addition(star(A),star(star(A))) = star(A),
inference(paramod,[status(thm)],[c_18,c_27701]) ).
cnf(c_3650,plain,
star(star(A)) = star(A),
inference(paramod,[status(thm)],[c_2554,c_27702]) ).
cnf(c_27703,plain,
( leq(multiplication(A,addition(one,B)),A)
| ~ leq(addition(A,multiplication(A,addition(one,B))),A) ),
inference(paramod,[status(thm)],[c_179,c_422]) ).
cnf(c_7715,plain,
( leq(multiplication(A,addition(one,B)),A)
| ~ leq(addition(A,multiplication(A,B)),A) ),
inference(paramod,[status(thm)],[c_191,c_27703]) ).
cnf(c_27704,plain,
( leq(multiplication(A,addition(one,addition(B,one))),A)
| ~ leq(addition(A,addition(A,multiplication(A,B))),A) ),
inference(paramod,[status(thm)],[c_47,c_7715]) ).
cnf(c_27705,plain,
( leq(multiplication(A,addition(one,addition(B,one))),A)
| ~ leq(addition(A,multiplication(A,B)),A) ),
inference(paramod,[status(thm)],[c_42,c_27704]) ).
cnf(c_8082,plain,
( leq(multiplication(A,addition(B,one)),A)
| ~ leq(addition(A,multiplication(A,B)),A) ),
inference(paramod,[status(thm)],[c_44,c_27705]) ).
cnf(c_8268,plain,
( leq(multiplication(A,addition(B,one)),A)
| ~ leq(multiplication(A,addition(one,B)),A) ),
inference(paramod,[status(thm)],[c_46,c_8082]) ).
cnf(c_8288,plain,
leq(multiplication(star(addition(one,A)),addition(A,one)),star(addition(one,A))),
inference(resolve,[status(thm)],[c_8268,c_2289]) ).
cnf(c_27706,plain,
leq(multiplication(star(star(addition(one,A))),star(addition(one,A))),star(A)),
inference(resolve,[status(thm)],[c_2895,c_893]) ).
cnf(c_27707,plain,
leq(multiplication(star(addition(one,A)),star(addition(one,A))),star(A)),
inference(paramod,[status(thm)],[c_3650,c_27706]) ).
cnf(c_8478,plain,
leq(star(addition(one,A)),star(A)),
inference(paramod,[status(thm)],[c_2677,c_27707]) ).
cnf(c_27708,plain,
addition(multiplication(star(addition(one,A)),star(A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_2895,c_31]) ).
cnf(c_27709,plain,
addition(star(A),multiplication(star(addition(one,A)),star(A))) = star(A),
inference(paramod,[status(thm)],[c_18,c_27708]) ).
cnf(c_8479,plain,
multiplication(star(addition(one,A)),star(A)) = star(A),
inference(paramod,[status(thm)],[c_752,c_27709]) ).
cnf(c_8485,plain,
leq(star(A),star(addition(one,A))),
inference(paramod,[status(thm)],[c_8479,c_2294]) ).
cnf(c_27710,plain,
addition(star(addition(one,A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_8478,c_31]) ).
cnf(c_8486,plain,
addition(star(A),star(addition(one,A))) = star(A),
inference(paramod,[status(thm)],[c_18,c_27710]) ).
cnf(c_27711,plain,
addition(star(A),star(addition(one,A))) = star(addition(one,A)),
inference(resolve,[status(thm)],[c_8485,c_31]) ).
cnf(c_27712,plain,
star(A) = star(addition(one,A)),
inference(paramod,[status(thm)],[c_8486,c_27711]) ).
cnf(c_8789,plain,
star(addition(one,A)) = star(A),
inference(copy,[status(thm)],[c_27712]) ).
cnf(c_27713,plain,
leq(multiplication(star(A),addition(A,one)),star(addition(one,A))),
inference(paramod,[status(thm)],[c_8789,c_8288]) ).
cnf(c_8801,plain,
leq(multiplication(star(A),addition(A,one)),star(A)),
inference(paramod,[status(thm)],[c_8789,c_27713]) ).
cnf(c_8898,plain,
star(addition(A,one)) = star(A),
inference(paramod,[status(thm)],[c_18,c_8789]) ).
cnf(c_9020,plain,
( leq(multiplication(star(A),multiplication(addition(A,one),C)),B)
| ~ leq(multiplication(addition(one,A),addition(B,C)),B) ),
inference(paramod,[status(thm)],[c_8898,c_887]) ).
cnf(c_27714,plain,
addition(multiplication(star(A),addition(A,one)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_8801,c_31]) ).
cnf(c_27715,plain,
addition(star(A),multiplication(star(A),addition(A,one))) = star(A),
inference(paramod,[status(thm)],[c_18,c_27714]) ).
cnf(c_9452,plain,
multiplication(star(A),addition(A,one)) = star(A),
inference(paramod,[status(thm)],[c_195,c_27715]) ).
cnf(c_27716,plain,
multiplication(star(A),B) = multiplication(star(A),multiplication(addition(A,one),B)),
inference(paramod,[status(thm)],[c_9452,c_22]) ).
cnf(c_9466,plain,
multiplication(star(A),multiplication(addition(A,one),B)) = multiplication(star(A),B),
inference(copy,[status(thm)],[c_27716]) ).
cnf(c_9502,plain,
( leq(multiplication(star(A),C),B)
| ~ leq(multiplication(addition(one,A),addition(B,C)),B) ),
inference(paramod,[status(thm)],[c_9466,c_9020]) ).
cnf(c_27717,plain,
( leq(multiplication(star(star(A)),C),B)
| ~ leq(multiplication(star(A),addition(B,C)),B) ),
inference(paramod,[status(thm)],[c_740,c_9502]) ).
cnf(c_17077,plain,
( leq(multiplication(star(A),C),B)
| ~ leq(multiplication(star(A),addition(B,C)),B) ),
inference(paramod,[status(thm)],[c_3650,c_27717]) ).
cnf(c_17359,plain,
( leq(multiplication(star(A),B),C)
| ~ leq(multiplication(star(A),addition(B,C)),C) ),
inference(paramod,[status(thm)],[c_18,c_17077]) ).
cnf(c_27718,plain,
( ~ leq(multiplication(addition(one,multiplication(sK0,star(sK0))),sK1),multiplication(star(sK0),sK1))
| ~ leq(multiplication(star(sK0),sK1),addition(sK1,multiplication(sK0,multiplication(star(sK0),sK1)))) ),
inference(paramod,[status(thm)],[c_304,c_38]) ).
cnf(c_27502,plain,
~ leq(multiplication(star(sK0),sK1),addition(sK1,multiplication(sK0,multiplication(star(sK0),sK1)))),
inference(resolve,[status(thm)],[c_725,c_27718]) ).
cnf(c_27603,plain,
~ leq(multiplication(star(sK0),sK1),multiplication(addition(one,multiplication(sK0,star(sK0))),sK1)),
inference(paramod,[status(thm)],[c_304,c_27502]) ).
cnf(c_27719,plain,
~ leq(multiplication(star(sK0),addition(sK1,multiplication(addition(one,multiplication(sK0,star(sK0))),sK1))),multiplication(addition(one,multiplication(sK0,star(sK0))),sK1)),
inference(resolve,[status(thm)],[c_17359,c_27603]) ).
cnf(c_27605,plain,
~ leq(multiplication(star(sK0),multiplication(addition(one,multiplication(sK0,star(sK0))),sK1)),multiplication(addition(one,multiplication(sK0,star(sK0))),sK1)),
inference(paramod,[status(thm)],[c_246,c_27719]) ).
cnf(c_27720,plain,
~ leq(multiplication(star(sK0),addition(sK1,multiplication(multiplication(sK0,star(sK0)),sK1))),multiplication(addition(one,multiplication(sK0,star(sK0))),sK1)),
inference(paramod,[status(thm)],[c_51,c_27605]) ).
cnf(c_27661,plain,
~ leq(multiplication(star(sK0),addition(sK1,multiplication(sK0,multiplication(star(sK0),sK1)))),multiplication(addition(one,multiplication(sK0,star(sK0))),sK1)),
inference(paramod,[status(thm)],[c_22,c_27720]) ).
cnf(c_27721,plain,
~ leq(addition(sK1,addition(multiplication(sK0,multiplication(addition(one,multiplication(sK0,star(sK0))),sK1)),multiplication(sK0,multiplication(star(sK0),sK1)))),multiplication(addition(one,multiplication(sK0,star(sK0))),sK1)),
inference(resolve,[status(thm)],[c_87,c_27661]) ).
cnf(c_27722,plain,
~ leq(addition(sK1,addition(multiplication(sK0,multiplication(star(sK0),sK1)),multiplication(sK0,multiplication(addition(one,multiplication(sK0,star(sK0))),sK1)))),multiplication(addition(one,multiplication(sK0,star(sK0))),sK1)),
inference(paramod,[status(thm)],[c_18,c_27721]) ).
cnf(c_27723,plain,
~ leq(addition(sK1,multiplication(sK0,addition(multiplication(star(sK0),sK1),multiplication(addition(one,multiplication(sK0,star(sK0))),sK1)))),multiplication(addition(one,multiplication(sK0,star(sK0))),sK1)),
inference(paramod,[status(thm)],[c_26,c_27722]) ).
cnf(c_27724,plain,
~ leq(addition(sK1,multiplication(sK0,multiplication(addition(star(sK0),addition(one,multiplication(sK0,star(sK0)))),sK1))),multiplication(addition(one,multiplication(sK0,star(sK0))),sK1)),
inference(paramod,[status(thm)],[c_28,c_27723]) ).
cnf(c_27725,plain,
~ leq(addition(sK1,multiplication(sK0,multiplication(addition(one,addition(star(sK0),multiplication(sK0,star(sK0)))),sK1))),multiplication(addition(one,multiplication(sK0,star(sK0))),sK1)),
inference(paramod,[status(thm)],[c_40,c_27724]) ).
cnf(c_27726,plain,
~ leq(addition(sK1,multiplication(sK0,multiplication(addition(one,multiplication(addition(one,sK0),star(sK0))),sK1))),multiplication(addition(one,multiplication(sK0,star(sK0))),sK1)),
inference(paramod,[status(thm)],[c_51,c_27725]) ).
cnf(c_27727,plain,
~ leq(addition(sK1,multiplication(sK0,multiplication(addition(one,star(sK0)),sK1))),multiplication(addition(one,multiplication(sK0,star(sK0))),sK1)),
inference(paramod,[status(thm)],[c_2513,c_27726]) ).
cnf(c_27728,plain,
~ leq(addition(sK1,multiplication(sK0,multiplication(star(sK0),sK1))),multiplication(addition(one,multiplication(sK0,star(sK0))),sK1)),
inference(paramod,[status(thm)],[c_740,c_27727]) ).
cnf(c_27666,plain,
$false,
inference(resolve,[status(thm)],[c_1027,c_27728]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE043+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 19:17:10 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3538948 was started by sandbox2 on n006,
% 0.09/0.36 % Fri Sep 25 19:17:10 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 54.85/7.41
% 54.85/7.41 % Assigning unary symbol star kb_weight 0 and highest precedence (9).
% 54.85/7.41
% 54.85/7.41 % given #500 (W,wt=29): 6024 leq(one,multiplication(addition(star(A),B),star(C))). [para(28(a,1),6004(a,2))].
% 54.85/7.41
% 54.85/7.41 % given #1000 (T,wt=29): 23560 -leq(star(A),addition(one,A)) | leq(multiplication(A,star(A)),addition(A,one)). [para(18(a,1),23559(a,2))].
% 54.85/7.41
% 54.85/7.41 % SZS status Theorem for theBenchmark
% 54.85/7.41
% 54.85/7.41 % Proof 1 at 5.58 (+ 1.43) seconds.
% 54.85/7.41 % Length of proof is 120.
% 54.85/7.41 % Level of proof is 23.
% 54.85/7.41 % Maximum clause weight is 61.000.
% 54.85/7.41 % Given clauses 1195.
% 54.85/7.41
% 54.85/7.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------