%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE036+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 : n016.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 07:44:09 AM UTC 2026
% Result : Theorem 16.63s 2.67s
% Output : CNFRefutation 16.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 13
% Syntax : Number of formulae : 173 ( 139 unt; 0 def)
% Number of atoms : 207 ( 92 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 89 ( 55 ~; 31 |; 0 &)
% ( 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 253 ( 21 sgn 28 !; 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_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] : leq(star(X0),addition(one,multiplication(X0,star(X0)))),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] : leq(star(X0),addition(one,multiplication(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_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] : ~ leq(star(X0),addition(one,multiplication(X0,star(X0)))),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
~ leq(star(sK0),addition(one,multiplication(sK0,star(sK0)))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_17]) ).
cnf(c_37,negated_conjecture,
~ leq(star(sK0),addition(one,multiplication(sK0,star(sK0)))),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_9523,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_9523]) ).
cnf(c_9524,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_9524]) ).
cnf(c_9525,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_9525]) ).
cnf(c_9526,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_9526]) ).
cnf(c_9527,plain,
addition(multiplication(A,B),A) = multiplication(A,addition(B,one)),
inference(paramod,[status(thm)],[c_23,c_26]) ).
cnf(c_9528,plain,
addition(A,multiplication(A,B)) = multiplication(A,addition(B,one)),
inference(paramod,[status(thm)],[c_18,c_9527]) ).
cnf(c_46,plain,
multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)),
inference(copy,[status(thm)],[c_9528]) ).
cnf(c_9529,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_9529]) ).
cnf(c_52,plain,
leq(A,A),
inference(resolve,[status(thm)],[c_32,c_21]) ).
cnf(c_54,plain,
( addition(A,addition(B,C)) != C
| leq(addition(A,B),C) ),
inference(paramod,[status(thm)],[c_19,c_32]) ).
cnf(c_9530,plain,
addition(addition(one,multiplication(A,star(A))),star(A)) = star(A),
inference(resolve,[status(thm)],[c_33,c_31]) ).
cnf(c_58,plain,
addition(star(A),addition(one,multiplication(A,star(A)))) = star(A),
inference(paramod,[status(thm)],[c_18,c_9530]) ).
cnf(c_60,plain,
leq(addition(one,star(one)),star(one)),
inference(paramod,[status(thm)],[c_24,c_33]) ).
cnf(c_63,plain,
( leq(multiplication(star(B),A),C)
| ~ leq(addition(A,multiplication(B,C)),C) ),
inference(paramod,[status(thm)],[c_18,c_35]) ).
cnf(c_65,plain,
( leq(multiplication(star(A),multiplication(A,B)),B)
| ~ leq(multiplication(A,B),B) ),
inference(paramod,[status(thm)],[c_21,c_35]) ).
cnf(c_67,plain,
( leq(multiplication(star(A),B),one)
| ~ leq(addition(A,B),one) ),
inference(paramod,[status(thm)],[c_23,c_35]) ).
cnf(c_69,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_73,plain,
( leq(multiplication(A,star(C)),B)
| ~ leq(addition(A,multiplication(B,C)),B) ),
inference(paramod,[status(thm)],[c_18,c_36]) ).
cnf(c_77,plain,
( leq(multiplication(B,star(one)),A)
| ~ leq(addition(A,B),A) ),
inference(paramod,[status(thm)],[c_23,c_36]) ).
cnf(c_9531,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_80,plain,
( leq(multiplication(B,multiplication(C,star(C))),A)
| ~ leq(multiplication(addition(A,B),C),A) ),
inference(paramod,[status(thm)],[c_22,c_9531]) ).
cnf(c_95,plain,
leq(A,addition(A,B)),
inference(resolve,[status(thm)],[c_41,c_32]) ).
cnf(c_101,plain,
leq(A,addition(B,A)),
inference(paramod,[status(thm)],[c_18,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_39,c_95]) ).
cnf(c_106,plain,
leq(A,addition(B,addition(C,A))),
inference(paramod,[status(thm)],[c_19,c_101]) ).
cnf(c_9532,plain,
addition(addition(one,star(one)),star(one)) = star(one),
inference(resolve,[status(thm)],[c_60,c_31]) ).
cnf(c_9533,plain,
addition(star(one),addition(one,star(one))) = star(one),
inference(paramod,[status(thm)],[c_18,c_9532]) ).
cnf(c_119,plain,
addition(one,star(one)) = star(one),
inference(paramod,[status(thm)],[c_43,c_9533]) ).
cnf(c_9534,plain,
addition(multiplication(A,B),addition(A,multiplication(A,C))) = multiplication(A,addition(B,addition(one,C))),
inference(paramod,[status(thm)],[c_45,c_26]) ).
cnf(c_9535,plain,
addition(A,addition(multiplication(A,B),multiplication(A,C))) = multiplication(A,addition(B,addition(one,C))),
inference(paramod,[status(thm)],[c_39,c_9534]) ).
cnf(c_9536,plain,
addition(A,multiplication(A,addition(B,C))) = multiplication(A,addition(B,addition(one,C))),
inference(paramod,[status(thm)],[c_26,c_9535]) ).
cnf(c_179,plain,
multiplication(A,addition(B,addition(one,C))) = addition(A,multiplication(A,addition(B,C))),
inference(copy,[status(thm)],[c_9536]) ).
cnf(c_191,plain,
addition(A,multiplication(A,addition(one,B))) = addition(A,multiplication(A,B)),
inference(paramod,[status(thm)],[c_45,c_41]) ).
cnf(c_9537,plain,
multiplication(A,addition(B,one)) = addition(A,multiplication(A,addition(B,one))),
inference(paramod,[status(thm)],[c_43,c_45]) ).
cnf(c_195,plain,
addition(A,multiplication(A,addition(B,one))) = multiplication(A,addition(B,one)),
inference(copy,[status(thm)],[c_9537]) ).
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_370,plain,
( leq(multiplication(star(A),A),one)
| ~ leq(A,one) ),
inference(paramod,[status(thm)],[c_21,c_67]) ).
cnf(c_9538,plain,
leq(multiplication(star(one),one),one),
inference(resolve,[status(thm)],[c_370,c_52]) ).
cnf(c_382,plain,
leq(star(one),one),
inference(paramod,[status(thm)],[c_23,c_9538]) ).
cnf(c_9539,plain,
addition(star(one),one) = one,
inference(resolve,[status(thm)],[c_382,c_31]) ).
cnf(c_9540,plain,
addition(one,star(one)) = one,
inference(paramod,[status(thm)],[c_18,c_9539]) ).
cnf(c_385,plain,
star(one) = one,
inference(paramod,[status(thm)],[c_119,c_9540]) ).
cnf(c_9541,plain,
( leq(multiplication(B,one),A)
| ~ leq(addition(A,B),A) ),
inference(paramod,[status(thm)],[c_385,c_77]) ).
cnf(c_389,plain,
( leq(B,A)
| ~ leq(addition(A,B),A) ),
inference(paramod,[status(thm)],[c_23,c_9541]) ).
cnf(c_9542,negated_conjecture,
~ leq(addition(addition(one,multiplication(sK0,star(sK0))),star(sK0)),addition(one,multiplication(sK0,star(sK0)))),
inference(resolve,[status(thm)],[c_389,c_37]) ).
cnf(c_9543,negated_conjecture,
~ leq(addition(star(sK0),addition(one,multiplication(sK0,star(sK0)))),addition(one,multiplication(sK0,star(sK0)))),
inference(paramod,[status(thm)],[c_18,c_9542]) ).
cnf(c_9544,negated_conjecture,
~ leq(addition(one,addition(star(sK0),multiplication(sK0,star(sK0)))),addition(one,multiplication(sK0,star(sK0)))),
inference(paramod,[status(thm)],[c_39,c_9543]) ).
cnf(c_416,negated_conjecture,
~ leq(addition(one,multiplication(addition(one,sK0),star(sK0))),addition(one,multiplication(sK0,star(sK0)))),
inference(paramod,[status(thm)],[c_50,c_9544]) ).
cnf(c_423,plain,
( leq(multiplication(A,B),A)
| ~ leq(multiplication(A,addition(one,B)),A) ),
inference(paramod,[status(thm)],[c_45,c_389]) ).
cnf(c_594,plain,
leq(A,addition(B,multiplication(A,addition(one,C)))),
inference(paramod,[status(thm)],[c_45,c_105]) ).
cnf(c_691,plain,
( leq(multiplication(A,star(B)),A)
| ~ leq(multiplication(A,addition(one,B)),A) ),
inference(paramod,[status(thm)],[c_45,c_73]) ).
cnf(c_736,plain,
leq(one,star(A)),
inference(paramod,[status(thm)],[c_58,c_105]) ).
cnf(c_738,plain,
leq(multiplication(A,star(A)),star(A)),
inference(paramod,[status(thm)],[c_58,c_106]) ).
cnf(c_741,plain,
addition(one,star(A)) = star(A),
inference(resolve,[status(thm)],[c_736,c_31]) ).
cnf(c_9545,plain,
addition(multiplication(A,star(A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_738,c_31]) ).
cnf(c_745,plain,
addition(star(A),multiplication(A,star(A))) = star(A),
inference(paramod,[status(thm)],[c_18,c_9545]) ).
cnf(c_9546,plain,
star(A) = addition(star(A),one),
inference(paramod,[status(thm)],[c_741,c_18]) ).
cnf(c_750,plain,
addition(star(A),one) = star(A),
inference(copy,[status(thm)],[c_9546]) ).
cnf(c_9547,plain,
addition(multiplication(A,one),multiplication(A,star(B))) = multiplication(A,star(B)),
inference(paramod,[status(thm)],[c_741,c_26]) ).
cnf(c_752,plain,
addition(A,multiplication(A,star(B))) = multiplication(A,star(B)),
inference(paramod,[status(thm)],[c_23,c_9547]) ).
cnf(c_9548,plain,
addition(multiplication(one,A),multiplication(star(B),A)) = multiplication(star(B),A),
inference(paramod,[status(thm)],[c_741,c_28]) ).
cnf(c_753,plain,
addition(A,multiplication(star(B),A)) = multiplication(star(B),A),
inference(paramod,[status(thm)],[c_24,c_9548]) ).
cnf(c_763,plain,
leq(one,addition(A,star(B))),
inference(paramod,[status(thm)],[c_741,c_105]) ).
cnf(c_784,plain,
leq(one,addition(star(A),B)),
inference(paramod,[status(thm)],[c_18,c_763]) ).
cnf(c_787,plain,
leq(one,multiplication(star(A),addition(one,B))),
inference(paramod,[status(thm)],[c_45,c_784]) ).
cnf(c_789,plain,
leq(one,multiplication(addition(one,A),star(B))),
inference(paramod,[status(thm)],[c_50,c_784]) ).
cnf(c_796,plain,
addition(one,multiplication(star(A),addition(one,B))) = multiplication(star(A),addition(one,B)),
inference(resolve,[status(thm)],[c_787,c_31]) ).
cnf(c_811,plain,
addition(one,multiplication(addition(one,A),star(B))) = multiplication(addition(one,A),star(B)),
inference(resolve,[status(thm)],[c_789,c_31]) ).
cnf(c_815,negated_conjecture,
~ leq(multiplication(addition(one,sK0),star(sK0)),addition(one,multiplication(sK0,star(sK0)))),
inference(paramod,[status(thm)],[c_811,c_416]) ).
cnf(c_9549,plain,
~ leq(addition(addition(one,sK0),multiplication(addition(one,multiplication(sK0,star(sK0))),sK0)),addition(one,multiplication(sK0,star(sK0)))),
inference(resolve,[status(thm)],[c_73,c_815]) ).
cnf(c_9550,plain,
~ leq(addition(one,addition(sK0,multiplication(addition(one,multiplication(sK0,star(sK0))),sK0))),addition(one,multiplication(sK0,star(sK0)))),
inference(paramod,[status(thm)],[c_19,c_9549]) ).
cnf(c_846,plain,
~ leq(addition(one,multiplication(addition(one,multiplication(sK0,star(sK0))),sK0)),addition(one,multiplication(sK0,star(sK0)))),
inference(paramod,[status(thm)],[c_246,c_9550]) ).
cnf(c_9551,plain,
~ leq(addition(one,addition(sK0,multiplication(multiplication(sK0,star(sK0)),sK0))),addition(one,multiplication(sK0,star(sK0)))),
inference(paramod,[status(thm)],[c_50,c_846]) ).
cnf(c_9552,plain,
~ leq(addition(one,addition(sK0,multiplication(sK0,multiplication(star(sK0),sK0)))),addition(one,multiplication(sK0,star(sK0)))),
inference(paramod,[status(thm)],[c_22,c_9551]) ).
cnf(c_849,plain,
~ leq(addition(one,multiplication(sK0,addition(one,multiplication(star(sK0),sK0)))),addition(one,multiplication(sK0,star(sK0)))),
inference(paramod,[status(thm)],[c_45,c_9552]) ).
cnf(c_9553,plain,
addition(one,addition(multiplication(sK0,addition(one,multiplication(star(sK0),sK0))),addition(one,multiplication(sK0,star(sK0))))) != addition(one,multiplication(sK0,star(sK0))),
inference(resolve,[status(thm)],[c_54,c_849]) ).
cnf(c_9554,plain,
addition(one,addition(addition(one,multiplication(sK0,star(sK0))),multiplication(sK0,addition(one,multiplication(star(sK0),sK0))))) != addition(one,multiplication(sK0,star(sK0))),
inference(paramod,[status(thm)],[c_18,c_9553]) ).
cnf(c_9555,plain,
addition(one,addition(one,addition(multiplication(sK0,star(sK0)),multiplication(sK0,addition(one,multiplication(star(sK0),sK0)))))) != addition(one,multiplication(sK0,star(sK0))),
inference(paramod,[status(thm)],[c_19,c_9554]) ).
cnf(c_9556,plain,
addition(one,addition(one,multiplication(sK0,addition(star(sK0),addition(one,multiplication(star(sK0),sK0)))))) != addition(one,multiplication(sK0,star(sK0))),
inference(paramod,[status(thm)],[c_26,c_9555]) ).
cnf(c_9557,plain,
addition(one,addition(one,multiplication(sK0,addition(one,addition(star(sK0),multiplication(star(sK0),sK0)))))) != addition(one,multiplication(sK0,star(sK0))),
inference(paramod,[status(thm)],[c_39,c_9556]) ).
cnf(c_9558,plain,
addition(one,addition(one,multiplication(sK0,addition(one,multiplication(star(sK0),addition(one,sK0)))))) != addition(one,multiplication(sK0,star(sK0))),
inference(paramod,[status(thm)],[c_45,c_9557]) ).
cnf(c_9559,plain,
addition(one,addition(one,multiplication(sK0,multiplication(star(sK0),addition(one,sK0))))) != addition(one,multiplication(sK0,star(sK0))),
inference(paramod,[status(thm)],[c_796,c_9558]) ).
cnf(c_851,plain,
addition(one,multiplication(sK0,multiplication(star(sK0),addition(one,sK0)))) != addition(one,multiplication(sK0,star(sK0))),
inference(paramod,[status(thm)],[c_41,c_9559]) ).
cnf(c_9560,plain,
( leq(multiplication(star(A),multiplication(A,one)),star(B))
| ~ leq(multiplication(A,star(B)),star(B)) ),
inference(paramod,[status(thm)],[c_750,c_69]) ).
cnf(c_902,plain,
( leq(multiplication(star(A),A),star(B))
| ~ leq(multiplication(A,star(B)),star(B)) ),
inference(paramod,[status(thm)],[c_23,c_9560]) ).
cnf(c_9561,plain,
( leq(multiplication(one,multiplication(B,star(B))),star(A))
| ~ leq(multiplication(star(A),B),star(A)) ),
inference(paramod,[status(thm)],[c_750,c_80]) ).
cnf(c_1187,plain,
( leq(multiplication(B,star(B)),star(A))
| ~ leq(multiplication(star(A),B),star(A)) ),
inference(paramod,[status(thm)],[c_24,c_9561]) ).
cnf(c_1916,plain,
leq(A,addition(B,multiplication(A,star(C)))),
inference(paramod,[status(thm)],[c_741,c_594]) ).
cnf(c_2300,plain,
leq(multiplication(star(A),A),star(A)),
inference(resolve,[status(thm)],[c_902,c_738]) ).
cnf(c_2305,plain,
leq(multiplication(star(addition(one,A)),star(A)),star(addition(one,A))),
inference(resolve,[status(thm)],[c_2300,c_691]) ).
cnf(c_2524,plain,
multiplication(addition(one,A),star(A)) = star(A),
inference(paramod,[status(thm)],[c_745,c_50]) ).
cnf(c_9562,plain,
( leq(multiplication(star(A),star(A)),star(A))
| ~ leq(star(A),star(A)) ),
inference(paramod,[status(thm)],[c_745,c_63]) ).
cnf(c_2534,plain,
leq(multiplication(star(A),star(A)),star(A)),
inference(resolve,[status(thm)],[c_52,c_9562]) ).
cnf(c_2556,plain,
leq(A,star(A)),
inference(paramod,[status(thm)],[c_745,c_1916]) ).
cnf(c_2566,plain,
addition(A,star(A)) = star(A),
inference(resolve,[status(thm)],[c_2556,c_31]) ).
cnf(c_2685,plain,
leq(multiplication(star(A),star(star(A))),star(A)),
inference(resolve,[status(thm)],[c_2534,c_1187]) ).
cnf(c_9563,plain,
addition(multiplication(star(A),star(A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_2534,c_31]) ).
cnf(c_9564,plain,
addition(star(A),multiplication(star(A),star(A))) = star(A),
inference(paramod,[status(thm)],[c_18,c_9563]) ).
cnf(c_2689,plain,
multiplication(star(A),star(A)) = star(A),
inference(paramod,[status(thm)],[c_752,c_9564]) ).
cnf(c_2905,plain,
multiplication(star(A),star(star(A))) = star(star(A)),
inference(paramod,[status(thm)],[c_741,c_2524]) ).
cnf(c_9565,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_2524,c_65]) ).
cnf(c_9566,plain,
( leq(multiplication(star(addition(one,A)),star(A)),star(A))
| ~ leq(star(A),star(A)) ),
inference(paramod,[status(thm)],[c_2524,c_9565]) ).
cnf(c_2907,plain,
leq(multiplication(star(addition(one,A)),star(A)),star(A)),
inference(resolve,[status(thm)],[c_52,c_9566]) ).
cnf(c_2939,plain,
leq(star(star(A)),star(A)),
inference(paramod,[status(thm)],[c_2905,c_2685]) ).
cnf(c_9567,plain,
addition(star(star(A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_2939,c_31]) ).
cnf(c_9568,plain,
addition(star(A),star(star(A))) = star(A),
inference(paramod,[status(thm)],[c_18,c_9567]) ).
cnf(c_3662,plain,
star(star(A)) = star(A),
inference(paramod,[status(thm)],[c_2566,c_9568]) ).
cnf(c_9569,plain,
( leq(multiplication(A,addition(one,B)),A)
| ~ leq(addition(A,multiplication(A,addition(one,B))),A) ),
inference(paramod,[status(thm)],[c_179,c_423]) ).
cnf(c_7733,plain,
( leq(multiplication(A,addition(one,B)),A)
| ~ leq(addition(A,multiplication(A,B)),A) ),
inference(paramod,[status(thm)],[c_191,c_9569]) ).
cnf(c_9570,plain,
( leq(multiplication(A,addition(one,addition(B,one))),A)
| ~ leq(addition(A,addition(A,multiplication(A,B))),A) ),
inference(paramod,[status(thm)],[c_46,c_7733]) ).
cnf(c_9571,plain,
( leq(multiplication(A,addition(one,addition(B,one))),A)
| ~ leq(addition(A,multiplication(A,B)),A) ),
inference(paramod,[status(thm)],[c_41,c_9570]) ).
cnf(c_8101,plain,
( leq(multiplication(A,addition(B,one)),A)
| ~ leq(addition(A,multiplication(A,B)),A) ),
inference(paramod,[status(thm)],[c_43,c_9571]) ).
cnf(c_8287,plain,
( leq(multiplication(A,addition(B,one)),A)
| ~ leq(multiplication(A,addition(one,B)),A) ),
inference(paramod,[status(thm)],[c_45,c_8101]) ).
cnf(c_8307,plain,
leq(multiplication(star(addition(one,A)),addition(A,one)),star(addition(one,A))),
inference(resolve,[status(thm)],[c_8287,c_2300]) ).
cnf(c_9572,plain,
leq(multiplication(star(star(addition(one,A))),star(addition(one,A))),star(A)),
inference(resolve,[status(thm)],[c_2907,c_902]) ).
cnf(c_9573,plain,
leq(multiplication(star(addition(one,A)),star(addition(one,A))),star(A)),
inference(paramod,[status(thm)],[c_3662,c_9572]) ).
cnf(c_8497,plain,
leq(star(addition(one,A)),star(A)),
inference(paramod,[status(thm)],[c_2689,c_9573]) ).
cnf(c_9574,plain,
addition(multiplication(star(addition(one,A)),star(A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_2907,c_31]) ).
cnf(c_9575,plain,
addition(star(A),multiplication(star(addition(one,A)),star(A))) = star(A),
inference(paramod,[status(thm)],[c_18,c_9574]) ).
cnf(c_8498,plain,
multiplication(star(addition(one,A)),star(A)) = star(A),
inference(paramod,[status(thm)],[c_753,c_9575]) ).
cnf(c_8504,plain,
leq(star(A),star(addition(one,A))),
inference(paramod,[status(thm)],[c_8498,c_2305]) ).
cnf(c_9576,plain,
addition(star(addition(one,A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_8497,c_31]) ).
cnf(c_8505,plain,
addition(star(A),star(addition(one,A))) = star(A),
inference(paramod,[status(thm)],[c_18,c_9576]) ).
cnf(c_9577,plain,
addition(star(A),star(addition(one,A))) = star(addition(one,A)),
inference(resolve,[status(thm)],[c_8504,c_31]) ).
cnf(c_9578,plain,
star(A) = star(addition(one,A)),
inference(paramod,[status(thm)],[c_8505,c_9577]) ).
cnf(c_8809,plain,
star(addition(one,A)) = star(A),
inference(copy,[status(thm)],[c_9578]) ).
cnf(c_9579,plain,
leq(multiplication(star(A),addition(A,one)),star(addition(one,A))),
inference(paramod,[status(thm)],[c_8809,c_8307]) ).
cnf(c_8821,plain,
leq(multiplication(star(A),addition(A,one)),star(A)),
inference(paramod,[status(thm)],[c_8809,c_9579]) ).
cnf(c_9580,plain,
addition(multiplication(star(A),addition(A,one)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_8821,c_31]) ).
cnf(c_9581,plain,
addition(star(A),multiplication(star(A),addition(A,one))) = star(A),
inference(paramod,[status(thm)],[c_18,c_9580]) ).
cnf(c_9472,plain,
multiplication(star(A),addition(A,one)) = star(A),
inference(paramod,[status(thm)],[c_195,c_9581]) ).
cnf(c_9484,plain,
multiplication(star(A),addition(one,A)) = star(A),
inference(paramod,[status(thm)],[c_18,c_9472]) ).
cnf(c_9582,plain,
addition(one,multiplication(sK0,star(sK0))) != addition(one,multiplication(sK0,star(sK0))),
inference(paramod,[status(thm)],[c_9484,c_851]) ).
cnf(c_9522,plain,
$false,
inference(copy,[status(thm)],[c_9582]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE036+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.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 19:21:29 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3083287 was started by sandbox on n016,
% 0.09/0.37 % Fri Sep 25 19:21:29 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 16.63/2.67
% 16.63/2.67 % Assigning unary symbol star kb_weight 0 and highest precedence (8).
% 16.63/2.67
% 16.63/2.67 % given #500 (W,wt=29): 6016 leq(one,addition(multiplication(star(A),star(B)),C)). [para(741(a,1),2037(a,2,1,1))].
% 16.63/2.67
% 16.63/2.67 % SZS status Theorem for theBenchmark
% 16.63/2.67
% 16.63/2.67 % Proof 1 at 1.72 (+ 0.51) seconds.
% 16.63/2.67 % Length of proof is 110.
% 16.63/2.67 % Level of proof is 18.
% 16.63/2.67 % Maximum clause weight is 47.000.
% 16.63/2.67 % Given clauses 560.
% 16.63/2.67
% 16.63/2.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------