TSTP Solution File: KLE045+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : KLE045+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed May 31 12:15:38 EDT 2023

% Result   : Theorem 46.63s 6.23s
% Output   : CNFRefutation 47.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   42
%            Number of leaves      :   15
% Syntax   : Number of formulae    :  150 (  99 unt;   0 def)
%            Number of atoms       :  205 ( 111 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  118 (  63   ~;  45   |;   4   &)
%                                         (   2 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   2 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :  217 (; 214   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [A,B] : addition(A,B) = addition(B,A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [A] : addition(A,A) = A,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [A] : multiplication(A,one) = A,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [A] : multiplication(one,A) = A,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [A,B] :
      ( leq(A,B)
    <=> addition(A,B) = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f14,axiom,
    ! [A] : leq(addition(one,multiplication(star(A),A)),star(A)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [A,B,C] :
      ( leq(addition(multiplication(A,B),C),B)
     => leq(multiplication(star(A),C),B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ! [A,B,C] :
      ( leq(addition(multiplication(A,B),C),A)
     => leq(multiplication(C,star(B)),A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f17,conjecture,
    ! [X0,X1,X2] :
      ( leq(multiplication(X0,X2),multiplication(X2,X1))
     => leq(multiplication(star(X0),X2),multiplication(X2,star(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f18,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( leq(multiplication(X0,X2),multiplication(X2,X1))
       => leq(multiplication(star(X0),X2),multiplication(X2,star(X1))) ),
    inference(negated_conjecture,[status(cth)],[f17]) ).

fof(f19,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f20,plain,
    ! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f22,plain,
    ! [X0] : addition(X0,X0) = X0,
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f23,plain,
    ! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f24,plain,
    ! [X0] : multiplication(X0,one) = X0,
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f25,plain,
    ! [X0] : multiplication(one,X0) = X0,
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f26,plain,
    ! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f27,plain,
    ! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f30,plain,
    ! [A,B] :
      ( ( ~ leq(A,B)
        | addition(A,B) = B )
      & ( leq(A,B)
        | addition(A,B) != B ) ),
    inference(NNF_transformation,[status(esa)],[f12]) ).

fof(f31,plain,
    ( ! [A,B] :
        ( ~ leq(A,B)
        | addition(A,B) = B )
    & ! [A,B] :
        ( leq(A,B)
        | addition(A,B) != B ) ),
    inference(miniscoping,[status(esa)],[f30]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ~ leq(X0,X1)
      | addition(X0,X1) = X1 ),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( leq(X0,X1)
      | addition(X0,X1) != X1 ),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f34,plain,
    ! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
    inference(cnf_transformation,[status(esa)],[f13]) ).

fof(f35,plain,
    ! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f36,plain,
    ! [A,B,C] :
      ( ~ leq(addition(multiplication(A,B),C),B)
      | leq(multiplication(star(A),C),B) ),
    inference(pre_NNF_transformation,[status(esa)],[f15]) ).

fof(f37,plain,
    ! [X0,X1,X2] :
      ( ~ leq(addition(multiplication(X0,X1),X2),X1)
      | leq(multiplication(star(X0),X2),X1) ),
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f38,plain,
    ! [A,B,C] :
      ( ~ leq(addition(multiplication(A,B),C),A)
      | leq(multiplication(C,star(B)),A) ),
    inference(pre_NNF_transformation,[status(esa)],[f16]) ).

fof(f39,plain,
    ! [X0,X1,X2] :
      ( ~ leq(addition(multiplication(X0,X1),X2),X0)
      | leq(multiplication(X2,star(X1)),X0) ),
    inference(cnf_transformation,[status(esa)],[f38]) ).

fof(f40,plain,
    ? [X0,X1,X2] :
      ( leq(multiplication(X0,X2),multiplication(X2,X1))
      & ~ leq(multiplication(star(X0),X2),multiplication(X2,star(X1))) ),
    inference(pre_NNF_transformation,[status(esa)],[f18]) ).

fof(f41,plain,
    ( leq(multiplication(sk0_0,sk0_2),multiplication(sk0_2,sk0_1))
    & ~ leq(multiplication(star(sk0_0),sk0_2),multiplication(sk0_2,star(sk0_1))) ),
    inference(skolemization,[status(esa)],[f40]) ).

fof(f42,plain,
    leq(multiplication(sk0_0,sk0_2),multiplication(sk0_2,sk0_1)),
    inference(cnf_transformation,[status(esa)],[f41]) ).

fof(f43,plain,
    ~ leq(multiplication(star(sk0_0),sk0_2),multiplication(sk0_2,star(sk0_1))),
    inference(cnf_transformation,[status(esa)],[f41]) ).

fof(f44,plain,
    addition(multiplication(sk0_0,sk0_2),multiplication(sk0_2,sk0_1)) = multiplication(sk0_2,sk0_1),
    inference(resolution,[status(thm)],[f32,f42]) ).

fof(f49,plain,
    ~ leq(addition(multiplication(sk0_0,multiplication(sk0_2,star(sk0_1))),sk0_2),multiplication(sk0_2,star(sk0_1))),
    inference(resolution,[status(thm)],[f37,f43]) ).

fof(f50,plain,
    ! [X0,X1,X2] :
      ( ~ leq(addition(multiplication(X0,X1),X2),X1)
      | addition(multiplication(star(X0),X2),X1) = X1 ),
    inference(resolution,[status(thm)],[f37,f32]) ).

fof(f113,plain,
    ! [X0,X1] :
      ( ~ leq(multiplication(X0,X1),X1)
      | addition(multiplication(star(X0),multiplication(X0,X1)),X1) = X1 ),
    inference(paramodulation,[status(thm)],[f22,f50]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( ~ leq(addition(multiplication(X0,X1),one),X0)
      | leq(star(X1),X0) ),
    inference(paramodulation,[status(thm)],[f25,f39]) ).

fof(f234,plain,
    ~ leq(addition(sk0_2,multiplication(sk0_0,multiplication(sk0_2,star(sk0_1)))),multiplication(sk0_2,star(sk0_1))),
    inference(paramodulation,[status(thm)],[f19,f49]) ).

fof(f273,plain,
    ! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
    inference(paramodulation,[status(thm)],[f19,f20]) ).

fof(f280,plain,
    ! [X0] : addition(multiplication(sk0_0,sk0_2),addition(multiplication(sk0_2,sk0_1),X0)) = addition(multiplication(sk0_2,sk0_1),X0),
    inference(paramodulation,[status(thm)],[f44,f20]) ).

fof(f282,plain,
    ! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
    inference(paramodulation,[status(thm)],[f19,f20]) ).

fof(f283,plain,
    ! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
    inference(forward_demodulation,[status(thm)],[f20,f282]) ).

fof(f286,plain,
    ! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
    inference(paramodulation,[status(thm)],[f22,f20]) ).

fof(f307,plain,
    ! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
    inference(paramodulation,[status(thm)],[f24,f26]) ).

fof(f337,plain,
    ! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
    inference(paramodulation,[status(thm)],[f19,f27]) ).

fof(f338,plain,
    ! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
    inference(forward_demodulation,[status(thm)],[f27,f337]) ).

fof(f344,plain,
    ! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
    inference(paramodulation,[status(thm)],[f25,f27]) ).

fof(f355,plain,
    ! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),X3) = addition(multiplication(X0,X3),multiplication(X1,multiplication(X2,X3))),
    inference(paramodulation,[status(thm)],[f23,f27]) ).

fof(f389,plain,
    ! [X0] : addition(multiplication(sk0_0,sk0_2),multiplication(sk0_2,addition(sk0_1,X0))) = addition(multiplication(sk0_2,sk0_1),multiplication(sk0_2,X0)),
    inference(paramodulation,[status(thm)],[f26,f280]) ).

fof(f390,plain,
    ! [X0] : addition(multiplication(sk0_0,sk0_2),multiplication(sk0_2,addition(sk0_1,X0))) = multiplication(sk0_2,addition(sk0_1,X0)),
    inference(forward_demodulation,[status(thm)],[f26,f389]) ).

fof(f936,plain,
    ! [X0,X1] :
      ( ~ leq(addition(one,multiplication(X0,X1)),X0)
      | leq(star(X1),X0) ),
    inference(forward_demodulation,[status(thm)],[f19,f147]) ).

fof(f938,plain,
    ! [X0,X1] :
      ( ~ leq(multiplication(X0,X1),X1)
      | addition(X1,multiplication(star(X0),multiplication(X0,X1))) = X1 ),
    inference(forward_demodulation,[status(thm)],[f19,f113]) ).

fof(f961,plain,
    ! [X0] :
      ( ~ leq(X0,X0)
      | addition(X0,multiplication(star(one),multiplication(one,X0))) = X0 ),
    inference(paramodulation,[status(thm)],[f25,f938]) ).

fof(f962,plain,
    ! [X0] :
      ( ~ leq(X0,X0)
      | addition(X0,multiplication(star(one),X0)) = X0 ),
    inference(forward_demodulation,[status(thm)],[f25,f961]) ).

fof(f1236,plain,
    ! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
    inference(paramodulation,[status(thm)],[f19,f286]) ).

fof(f1460,plain,
    ! [X0,X1,X2,X3] : addition(X0,multiplication(addition(X1,X2),X3)) = addition(multiplication(X2,X3),addition(X0,multiplication(X1,X3))),
    inference(paramodulation,[status(thm)],[f27,f273]) ).

fof(f1466,plain,
    ! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,X1),addition(X0,X1)),
    inference(paramodulation,[status(thm)],[f1236,f273]) ).

fof(f1467,plain,
    ! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X0,X1))),
    inference(forward_demodulation,[status(thm)],[f20,f1466]) ).

fof(f1468,plain,
    ! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
    inference(forward_demodulation,[status(thm)],[f1236,f1467]) ).

fof(f1620,plain,
    ! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X0,addition(X2,X1)),
    inference(paramodulation,[status(thm)],[f273,f283]) ).

fof(f2268,plain,
    ! [X0] : addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
    inference(resolution,[status(thm)],[f34,f32]) ).

fof(f2269,plain,
    ! [X0] : addition(one,addition(multiplication(X0,star(X0)),star(X0))) = star(X0),
    inference(forward_demodulation,[status(thm)],[f20,f2268]) ).

fof(f2270,plain,
    ! [X0] : addition(one,addition(star(X0),multiplication(X0,star(X0)))) = star(X0),
    inference(forward_demodulation,[status(thm)],[f1620,f2269]) ).

fof(f2282,plain,
    ! [X0] : addition(addition(one,multiplication(star(X0),X0)),star(X0)) = star(X0),
    inference(resolution,[status(thm)],[f35,f32]) ).

fof(f2283,plain,
    ! [X0] : addition(one,addition(multiplication(star(X0),X0),star(X0))) = star(X0),
    inference(forward_demodulation,[status(thm)],[f20,f2282]) ).

fof(f2284,plain,
    ! [X0] : addition(one,addition(star(X0),multiplication(star(X0),X0))) = star(X0),
    inference(forward_demodulation,[status(thm)],[f1620,f2283]) ).

fof(f3721,plain,
    ! [X0] : addition(addition(star(X0),multiplication(X0,star(X0))),star(X0)) = addition(addition(star(X0),multiplication(X0,star(X0))),one),
    inference(paramodulation,[status(thm)],[f2270,f1236]) ).

fof(f3722,plain,
    ! [X0] : addition(star(X0),addition(multiplication(X0,star(X0)),star(X0))) = addition(addition(star(X0),multiplication(X0,star(X0))),one),
    inference(forward_demodulation,[status(thm)],[f20,f3721]) ).

fof(f3723,plain,
    ! [X0] : addition(star(X0),addition(star(X0),multiplication(X0,star(X0)))) = addition(addition(star(X0),multiplication(X0,star(X0))),one),
    inference(forward_demodulation,[status(thm)],[f1620,f3722]) ).

fof(f3724,plain,
    ! [X0] : addition(star(X0),multiplication(X0,star(X0))) = addition(addition(star(X0),multiplication(X0,star(X0))),one),
    inference(forward_demodulation,[status(thm)],[f286,f3723]) ).

fof(f3725,plain,
    ! [X0] : addition(star(X0),multiplication(X0,star(X0))) = addition(star(X0),addition(multiplication(X0,star(X0)),one)),
    inference(forward_demodulation,[status(thm)],[f20,f3724]) ).

fof(f3726,plain,
    ! [X0] : addition(star(X0),multiplication(X0,star(X0))) = addition(star(X0),addition(one,multiplication(X0,star(X0)))),
    inference(forward_demodulation,[status(thm)],[f1620,f3725]) ).

fof(f3727,plain,
    ! [X0] : addition(star(X0),multiplication(X0,star(X0))) = addition(one,addition(star(X0),multiplication(X0,star(X0)))),
    inference(forward_demodulation,[status(thm)],[f283,f3726]) ).

fof(f3728,plain,
    ! [X0] : addition(star(X0),multiplication(X0,star(X0))) = star(X0),
    inference(forward_demodulation,[status(thm)],[f2270,f3727]) ).

fof(f3729,plain,
    ! [X0] : addition(one,star(X0)) = addition(one,addition(star(X0),multiplication(X0,star(X0)))),
    inference(paramodulation,[status(thm)],[f2270,f286]) ).

fof(f3730,plain,
    ! [X0] : addition(one,star(X0)) = star(X0),
    inference(forward_demodulation,[status(thm)],[f2270,f3729]) ).

fof(f3737,plain,
    ! [X0,X1] : addition(star(X0),addition(one,X1)) = addition(X1,star(X0)),
    inference(paramodulation,[status(thm)],[f3730,f1468]) ).

fof(f3738,plain,
    ! [X0,X1] : addition(one,addition(star(X0),X1)) = addition(X1,star(X0)),
    inference(forward_demodulation,[status(thm)],[f283,f3737]) ).

fof(f3741,plain,
    ! [X0,X1] : addition(one,addition(X0,star(X1))) = addition(X0,star(X1)),
    inference(paramodulation,[status(thm)],[f3730,f283]) ).

fof(f5204,plain,
    ! [X0] : addition(multiplication(star(X0),X0),star(X0)) = star(X0),
    inference(forward_demodulation,[status(thm)],[f3738,f2284]) ).

fof(f5205,plain,
    ! [X0] : addition(star(X0),multiplication(star(X0),X0)) = star(X0),
    inference(forward_demodulation,[status(thm)],[f19,f5204]) ).

fof(f5658,plain,
    ! [X0,X1] : multiplication(X0,star(X1)) = addition(X0,multiplication(X0,star(X1))),
    inference(paramodulation,[status(thm)],[f3730,f307]) ).

fof(f5677,plain,
    ! [X0] : multiplication(star(X0),addition(one,X0)) = star(X0),
    inference(paramodulation,[status(thm)],[f5205,f307]) ).

fof(f7239,plain,
    ! [X0] : multiplication(star(star(X0)),star(X0)) = star(star(X0)),
    inference(paramodulation,[status(thm)],[f3730,f5677]) ).

fof(f7379,plain,
    ! [X0,X1] : multiplication(star(X0),X1) = addition(X1,multiplication(star(X0),X1)),
    inference(paramodulation,[status(thm)],[f3730,f344]) ).

fof(f7398,plain,
    ! [X0] : multiplication(addition(one,X0),star(X0)) = star(X0),
    inference(paramodulation,[status(thm)],[f3728,f344]) ).

fof(f7404,plain,
    ! [X0] : multiplication(addition(one,star(X0)),addition(one,X0)) = addition(addition(one,X0),star(X0)),
    inference(paramodulation,[status(thm)],[f5677,f344]) ).

fof(f7405,plain,
    ! [X0] : multiplication(star(X0),addition(one,X0)) = addition(addition(one,X0),star(X0)),
    inference(forward_demodulation,[status(thm)],[f3730,f7404]) ).

fof(f7406,plain,
    ! [X0] : star(X0) = addition(addition(one,X0),star(X0)),
    inference(forward_demodulation,[status(thm)],[f5677,f7405]) ).

fof(f7407,plain,
    ! [X0] : star(X0) = addition(one,addition(X0,star(X0))),
    inference(forward_demodulation,[status(thm)],[f20,f7406]) ).

fof(f7408,plain,
    ! [X0] : star(X0) = addition(X0,star(X0)),
    inference(forward_demodulation,[status(thm)],[f3741,f7407]) ).

fof(f7599,plain,
    addition(multiplication(sk0_0,sk0_2),multiplication(sk0_2,star(sk0_1))) = multiplication(sk0_2,addition(sk0_1,star(sk0_1))),
    inference(paramodulation,[status(thm)],[f7408,f390]) ).

fof(f7600,plain,
    addition(multiplication(sk0_0,sk0_2),multiplication(sk0_2,star(sk0_1))) = multiplication(sk0_2,star(sk0_1)),
    inference(forward_demodulation,[status(thm)],[f7408,f7599]) ).

fof(f7699,plain,
    ! [X0] : multiplication(star(X0),star(star(X0))) = star(star(X0)),
    inference(paramodulation,[status(thm)],[f3730,f7398]) ).

fof(f8347,plain,
    ! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,star(X2)))) = addition(X1,multiplication(X0,star(X2))),
    inference(paramodulation,[status(thm)],[f5658,f283]) ).

fof(f8453,plain,
    ! [X0] :
      ( ~ leq(X0,X0)
      | multiplication(star(one),X0) = X0 ),
    inference(backward_demodulation,[status(thm)],[f7379,f962]) ).

fof(f8664,plain,
    ! [X0] :
      ( multiplication(star(one),X0) = X0
      | addition(X0,X0) != X0 ),
    inference(resolution,[status(thm)],[f8453,f33]) ).

fof(f8665,plain,
    ! [X0] :
      ( multiplication(star(one),X0) = X0
      | X0 != X0 ),
    inference(forward_demodulation,[status(thm)],[f22,f8664]) ).

fof(f8666,plain,
    ! [X0] : multiplication(star(one),X0) = X0,
    inference(trivial_equality_resolution,[status(esa)],[f8665]) ).

fof(f8701,plain,
    ! [X0,X1] :
      ( ~ leq(addition(multiplication(one,X0),X1),X0)
      | leq(X1,X0) ),
    inference(paramodulation,[status(thm)],[f8666,f37]) ).

fof(f8702,plain,
    ! [X0,X1] :
      ( ~ leq(addition(X0,X1),X0)
      | leq(X1,X0) ),
    inference(forward_demodulation,[status(thm)],[f25,f8701]) ).

fof(f9831,plain,
    ~ leq(addition(multiplication(sk0_2,star(sk0_1)),addition(sk0_2,multiplication(sk0_0,multiplication(sk0_2,star(sk0_1))))),multiplication(sk0_2,star(sk0_1))),
    inference(resolution,[status(thm)],[f8702,f234]) ).

fof(f9832,plain,
    ~ leq(addition(sk0_2,addition(multiplication(sk0_2,star(sk0_1)),multiplication(sk0_0,multiplication(sk0_2,star(sk0_1))))),multiplication(sk0_2,star(sk0_1))),
    inference(forward_demodulation,[status(thm)],[f283,f9831]) ).

fof(f9833,plain,
    ~ leq(addition(sk0_2,multiplication(addition(sk0_2,multiplication(sk0_0,sk0_2)),star(sk0_1))),multiplication(sk0_2,star(sk0_1))),
    inference(forward_demodulation,[status(thm)],[f355,f9832]) ).

fof(f9874,plain,
    ! [X0,X1] :
      ( ~ leq(addition(X0,X1),X0)
      | addition(X1,X0) = X0 ),
    inference(resolution,[status(thm)],[f8702,f32]) ).

fof(f9970,plain,
    ! [X0,X1] :
      ( ~ leq(multiplication(star(X0),X1),X1)
      | addition(multiplication(star(X0),X1),X1) = X1 ),
    inference(paramodulation,[status(thm)],[f7379,f9874]) ).

fof(f9971,plain,
    ! [X0,X1] :
      ( ~ leq(multiplication(star(X0),X1),X1)
      | addition(X1,multiplication(star(X0),X1)) = X1 ),
    inference(forward_demodulation,[status(thm)],[f19,f9970]) ).

fof(f9972,plain,
    ! [X0,X1] :
      ( ~ leq(multiplication(star(X0),X1),X1)
      | multiplication(star(X0),X1) = X1 ),
    inference(forward_demodulation,[status(thm)],[f7379,f9971]) ).

fof(f10779,plain,
    ( spl0_252
  <=> leq(multiplication(sk0_2,star(sk0_1)),multiplication(sk0_2,star(sk0_1))) ),
    introduced(split_symbol_definition) ).

fof(f10780,plain,
    ( leq(multiplication(sk0_2,star(sk0_1)),multiplication(sk0_2,star(sk0_1)))
    | ~ spl0_252 ),
    inference(component_clause,[status(thm)],[f10779]) ).

fof(f10781,plain,
    ( ~ leq(multiplication(sk0_2,star(sk0_1)),multiplication(sk0_2,star(sk0_1)))
    | spl0_252 ),
    inference(component_clause,[status(thm)],[f10779]) ).

fof(f11767,plain,
    ( addition(multiplication(sk0_2,star(sk0_1)),multiplication(sk0_2,star(sk0_1))) != multiplication(sk0_2,star(sk0_1))
    | spl0_252 ),
    inference(resolution,[status(thm)],[f10781,f33]) ).

fof(f11768,plain,
    ( multiplication(addition(sk0_2,sk0_2),star(sk0_1)) != multiplication(sk0_2,star(sk0_1))
    | spl0_252 ),
    inference(forward_demodulation,[status(thm)],[f27,f11767]) ).

fof(f11769,plain,
    ( multiplication(sk0_2,star(sk0_1)) != multiplication(sk0_2,star(sk0_1))
    | spl0_252 ),
    inference(forward_demodulation,[status(thm)],[f22,f11768]) ).

fof(f11770,plain,
    ( $false
    | spl0_252 ),
    inference(trivial_equality_resolution,[status(esa)],[f11769]) ).

fof(f11771,plain,
    spl0_252,
    inference(contradiction_clause,[status(thm)],[f11770]) ).

fof(f12139,plain,
    ! [X0,X1] :
      ( multiplication(star(X0),X1) = X1
      | ~ leq(addition(multiplication(X0,X1),X1),X1) ),
    inference(resolution,[status(thm)],[f9972,f37]) ).

fof(f12140,plain,
    ! [X0,X1] :
      ( multiplication(star(X0),X1) = X1
      | ~ leq(addition(X1,multiplication(X0,X1)),X1) ),
    inference(forward_demodulation,[status(thm)],[f19,f12139]) ).

fof(f12260,plain,
    ! [X0] :
      ( multiplication(star(X0),X0) = X0
      | ~ leq(multiplication(X0,addition(one,X0)),X0) ),
    inference(paramodulation,[status(thm)],[f307,f12140]) ).

fof(f12902,plain,
    ! [X0] :
      ( multiplication(star(star(X0)),star(X0)) = star(X0)
      | ~ leq(addition(multiplication(X0,star(X0)),addition(one,star(X0))),star(X0)) ),
    inference(resolution,[status(thm)],[f12260,f37]) ).

fof(f12903,plain,
    ! [X0] :
      ( star(star(X0)) = star(X0)
      | ~ leq(addition(multiplication(X0,star(X0)),addition(one,star(X0))),star(X0)) ),
    inference(forward_demodulation,[status(thm)],[f7239,f12902]) ).

fof(f12904,plain,
    ! [X0] :
      ( star(star(X0)) = star(X0)
      | ~ leq(addition(star(X0),addition(one,multiplication(X0,star(X0)))),star(X0)) ),
    inference(forward_demodulation,[status(thm)],[f1468,f12903]) ).

fof(f12905,plain,
    ! [X0] :
      ( star(star(X0)) = star(X0)
      | ~ leq(addition(one,addition(star(X0),multiplication(X0,star(X0)))),star(X0)) ),
    inference(forward_demodulation,[status(thm)],[f283,f12904]) ).

fof(f12906,plain,
    ! [X0] :
      ( star(star(X0)) = star(X0)
      | ~ leq(addition(multiplication(X0,star(X0)),star(X0)),star(X0)) ),
    inference(forward_demodulation,[status(thm)],[f3738,f12905]) ).

fof(f12907,plain,
    ! [X0] :
      ( star(star(X0)) = star(X0)
      | ~ leq(addition(star(X0),multiplication(X0,star(X0))),star(X0)) ),
    inference(forward_demodulation,[status(thm)],[f19,f12906]) ).

fof(f12908,plain,
    ! [X0] :
      ( star(star(X0)) = star(X0)
      | ~ leq(star(X0),star(X0)) ),
    inference(forward_demodulation,[status(thm)],[f3728,f12907]) ).

fof(f13042,plain,
    ! [X0] :
      ( star(star(X0)) = star(X0)
      | ~ leq(addition(one,multiplication(star(X0),X0)),star(X0)) ),
    inference(resolution,[status(thm)],[f12908,f936]) ).

fof(f13043,plain,
    ! [X0] : star(star(X0)) = star(X0),
    inference(forward_subsumption_resolution,[status(thm)],[f13042,f35]) ).

fof(f13084,plain,
    ! [X0] : multiplication(star(X0),star(star(X0))) = star(X0),
    inference(backward_demodulation,[status(thm)],[f13043,f7699]) ).

fof(f13085,plain,
    ! [X0] : multiplication(star(X0),star(X0)) = star(X0),
    inference(forward_demodulation,[status(thm)],[f13043,f13084]) ).

fof(f13163,plain,
    ! [X0,X1,X2] :
      ( ~ leq(addition(multiplication(X0,star(X1)),X2),X0)
      | leq(multiplication(X2,star(X1)),X0) ),
    inference(paramodulation,[status(thm)],[f13043,f39]) ).

fof(f25359,plain,
    ! [X0,X1,X2] : addition(X0,multiplication(addition(X0,X1),star(X2))) = addition(multiplication(X1,star(X2)),multiplication(X0,star(X2))),
    inference(paramodulation,[status(thm)],[f5658,f1460]) ).

fof(f25360,plain,
    ! [X0,X1,X2] : addition(X0,multiplication(addition(X0,X1),star(X2))) = multiplication(addition(X1,X0),star(X2)),
    inference(forward_demodulation,[status(thm)],[f27,f25359]) ).

fof(f41974,plain,
    ~ leq(multiplication(addition(multiplication(sk0_0,sk0_2),sk0_2),star(sk0_1)),multiplication(sk0_2,star(sk0_1))),
    inference(backward_demodulation,[status(thm)],[f25360,f9833]) ).

fof(f41975,plain,
    ~ leq(multiplication(addition(sk0_2,multiplication(sk0_0,sk0_2)),star(sk0_1)),multiplication(sk0_2,star(sk0_1))),
    inference(forward_demodulation,[status(thm)],[f338,f41974]) ).

fof(f45898,plain,
    ~ leq(addition(multiplication(multiplication(sk0_2,star(sk0_1)),star(sk0_1)),addition(sk0_2,multiplication(sk0_0,sk0_2))),multiplication(sk0_2,star(sk0_1))),
    inference(resolution,[status(thm)],[f41975,f13163]) ).

fof(f45899,plain,
    ~ leq(addition(multiplication(sk0_0,sk0_2),addition(sk0_2,multiplication(multiplication(sk0_2,star(sk0_1)),star(sk0_1)))),multiplication(sk0_2,star(sk0_1))),
    inference(forward_demodulation,[status(thm)],[f1468,f45898]) ).

fof(f45900,plain,
    ~ leq(addition(sk0_2,addition(multiplication(sk0_0,sk0_2),multiplication(multiplication(sk0_2,star(sk0_1)),star(sk0_1)))),multiplication(sk0_2,star(sk0_1))),
    inference(forward_demodulation,[status(thm)],[f283,f45899]) ).

fof(f45901,plain,
    ~ leq(addition(sk0_2,addition(multiplication(sk0_0,sk0_2),multiplication(sk0_2,multiplication(star(sk0_1),star(sk0_1))))),multiplication(sk0_2,star(sk0_1))),
    inference(forward_demodulation,[status(thm)],[f23,f45900]) ).

fof(f45902,plain,
    ~ leq(addition(sk0_2,addition(multiplication(sk0_0,sk0_2),multiplication(sk0_2,star(sk0_1)))),multiplication(sk0_2,star(sk0_1))),
    inference(forward_demodulation,[status(thm)],[f13085,f45901]) ).

fof(f45903,plain,
    ~ leq(addition(multiplication(sk0_0,sk0_2),multiplication(sk0_2,star(sk0_1))),multiplication(sk0_2,star(sk0_1))),
    inference(forward_demodulation,[status(thm)],[f8347,f45902]) ).

fof(f45904,plain,
    ~ leq(multiplication(sk0_2,star(sk0_1)),multiplication(sk0_2,star(sk0_1))),
    inference(forward_demodulation,[status(thm)],[f7600,f45903]) ).

fof(f45905,plain,
    ( $false
    | ~ spl0_252 ),
    inference(forward_subsumption_resolution,[status(thm)],[f45904,f10780]) ).

fof(f45906,plain,
    ~ spl0_252,
    inference(contradiction_clause,[status(thm)],[f45905]) ).

fof(f45907,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f11771,f45906]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : KLE045+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n006.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Tue May 30 11:42:47 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  % Drodi V3.5.1
% 46.63/6.23  % Refutation found
% 46.63/6.23  % SZS status Theorem for theBenchmark: Theorem is valid
% 46.63/6.23  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 48.20/6.39  % Elapsed time: 6.039019 seconds
% 48.20/6.39  % CPU time: 47.535809 seconds
% 48.20/6.39  % Memory used: 587.448 MB
%------------------------------------------------------------------------------