TSTP Solution File: KLE018+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : KLE018+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n022.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 12:15:30 EDT 2023

% Result   : Theorem 86.60s 11.32s
% Output   : CNFRefutation 87.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   42
%            Number of leaves      :   19
% Syntax   : Number of formulae    :  163 (  85 unt;   0 def)
%            Number of atoms       :  307 ( 163 equ)
%            Maximal formula atoms :    8 (   1 avg)
%            Number of connectives :  254 ( 110   ~; 102   |;  27   &)
%                                         (   9 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    9 (   7 usr;   5 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :  184 (; 178   !;   6   ?)

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

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

fof(f3,axiom,
    ! [A] : addition(A,zero) = A,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

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

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

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

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

fof(f10,axiom,
    ! [A] : multiplication(A,zero) = zero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f13,axiom,
    ! [X0] :
      ( test(X0)
    <=> ? [X1] : complement(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f14,axiom,
    ! [X0,X1] :
      ( complement(X1,X0)
    <=> ( multiplication(X0,X1) = zero
        & multiplication(X1,X0) = zero
        & addition(X0,X1) = one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [X0,X1] :
      ( test(X0)
     => ( c(X0) = X1
      <=> complement(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ! [X0] :
      ( ~ test(X0)
     => c(X0) = zero ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f17,conjecture,
    ! [X0,X1,X2] :
      ( ( test(X0)
        & test(X1)
        & test(X2) )
     => ( leq(multiplication(X0,c(X1)),X2)
       => leq(X0,addition(X1,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f18,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( test(X0)
          & test(X1)
          & test(X2) )
       => ( leq(multiplication(X0,c(X1)),X2)
         => leq(X0,addition(X1,X2)) ) ),
    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(f21,plain,
    ! [X0] : addition(X0,zero) = X0,
    inference(cnf_transformation,[status(esa)],[f3]) ).

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

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(f28,plain,
    ! [X0] : multiplication(X0,zero) = zero,
    inference(cnf_transformation,[status(esa)],[f10]) ).

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] :
      ( ( ~ test(X0)
        | ? [X1] : complement(X1,X0) )
      & ( test(X0)
        | ! [X1] : ~ complement(X1,X0) ) ),
    inference(NNF_transformation,[status(esa)],[f13]) ).

fof(f35,plain,
    ( ! [X0] :
        ( ~ test(X0)
        | ? [X1] : complement(X1,X0) )
    & ! [X0] :
        ( test(X0)
        | ! [X1] : ~ complement(X1,X0) ) ),
    inference(miniscoping,[status(esa)],[f34]) ).

fof(f36,plain,
    ( ! [X0] :
        ( ~ test(X0)
        | complement(sk0_0(X0),X0) )
    & ! [X0] :
        ( test(X0)
        | ! [X1] : ~ complement(X1,X0) ) ),
    inference(skolemization,[status(esa)],[f35]) ).

fof(f37,plain,
    ! [X0] :
      ( ~ test(X0)
      | complement(sk0_0(X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( test(X0)
      | ~ complement(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ( ~ complement(X1,X0)
        | ( multiplication(X0,X1) = zero
          & multiplication(X1,X0) = zero
          & addition(X0,X1) = one ) )
      & ( complement(X1,X0)
        | multiplication(X0,X1) != zero
        | multiplication(X1,X0) != zero
        | addition(X0,X1) != one ) ),
    inference(NNF_transformation,[status(esa)],[f14]) ).

fof(f40,plain,
    ( ! [X0,X1] :
        ( ~ complement(X1,X0)
        | ( multiplication(X0,X1) = zero
          & multiplication(X1,X0) = zero
          & addition(X0,X1) = one ) )
    & ! [X0,X1] :
        ( complement(X1,X0)
        | multiplication(X0,X1) != zero
        | multiplication(X1,X0) != zero
        | addition(X0,X1) != one ) ),
    inference(miniscoping,[status(esa)],[f39]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( ~ complement(X0,X1)
      | multiplication(X0,X1) = zero ),
    inference(cnf_transformation,[status(esa)],[f40]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( ~ complement(X0,X1)
      | addition(X1,X0) = one ),
    inference(cnf_transformation,[status(esa)],[f40]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( complement(X0,X1)
      | multiplication(X1,X0) != zero
      | multiplication(X0,X1) != zero
      | addition(X1,X0) != one ),
    inference(cnf_transformation,[status(esa)],[f40]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ~ test(X0)
      | ( c(X0) = X1
      <=> complement(X0,X1) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f15]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( ~ test(X0)
      | ( ( c(X0) != X1
          | complement(X0,X1) )
        & ( c(X0) = X1
          | ~ complement(X0,X1) ) ) ),
    inference(NNF_transformation,[status(esa)],[f45]) ).

fof(f47,plain,
    ! [X0] :
      ( ~ test(X0)
      | ( ! [X1] :
            ( c(X0) != X1
            | complement(X0,X1) )
        & ! [X1] :
            ( c(X0) = X1
            | ~ complement(X0,X1) ) ) ),
    inference(miniscoping,[status(esa)],[f46]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( ~ test(X0)
      | c(X0) != X1
      | complement(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f47]) ).

fof(f50,plain,
    ! [X0] :
      ( test(X0)
      | c(X0) = zero ),
    inference(pre_NNF_transformation,[status(esa)],[f16]) ).

fof(f51,plain,
    ! [X0] :
      ( test(X0)
      | c(X0) = zero ),
    inference(cnf_transformation,[status(esa)],[f50]) ).

fof(f52,plain,
    ? [X0,X1,X2] :
      ( test(X0)
      & test(X1)
      & test(X2)
      & leq(multiplication(X0,c(X1)),X2)
      & ~ leq(X0,addition(X1,X2)) ),
    inference(pre_NNF_transformation,[status(esa)],[f18]) ).

fof(f53,plain,
    ( test(sk0_1)
    & test(sk0_2)
    & test(sk0_3)
    & leq(multiplication(sk0_1,c(sk0_2)),sk0_3)
    & ~ leq(sk0_1,addition(sk0_2,sk0_3)) ),
    inference(skolemization,[status(esa)],[f52]) ).

fof(f54,plain,
    test(sk0_1),
    inference(cnf_transformation,[status(esa)],[f53]) ).

fof(f55,plain,
    test(sk0_2),
    inference(cnf_transformation,[status(esa)],[f53]) ).

fof(f56,plain,
    test(sk0_3),
    inference(cnf_transformation,[status(esa)],[f53]) ).

fof(f57,plain,
    leq(multiplication(sk0_1,c(sk0_2)),sk0_3),
    inference(cnf_transformation,[status(esa)],[f53]) ).

fof(f58,plain,
    ~ leq(sk0_1,addition(sk0_2,sk0_3)),
    inference(cnf_transformation,[status(esa)],[f53]) ).

fof(f59,plain,
    ! [X0] :
      ( ~ test(X0)
      | complement(X0,c(X0)) ),
    inference(destructive_equality_resolution,[status(esa)],[f48]) ).

fof(f60,plain,
    addition(multiplication(sk0_1,c(sk0_2)),sk0_3) = sk0_3,
    inference(resolution,[status(thm)],[f32,f57]) ).

fof(f61,plain,
    addition(sk0_3,multiplication(sk0_1,c(sk0_2))) = sk0_3,
    inference(forward_demodulation,[status(thm)],[f19,f60]) ).

fof(f65,plain,
    ! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
    inference(paramodulation,[status(thm)],[f19,f20]) ).

fof(f70,plain,
    ! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
    inference(paramodulation,[status(thm)],[f22,f20]) ).

fof(f71,plain,
    ! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
    inference(paramodulation,[status(thm)],[f19,f20]) ).

fof(f72,plain,
    ! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
    inference(forward_demodulation,[status(thm)],[f20,f71]) ).

fof(f84,plain,
    ! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
    inference(paramodulation,[status(thm)],[f19,f70]) ).

fof(f118,plain,
    ! [X0] : addition(zero,X0) = X0,
    inference(paramodulation,[status(thm)],[f19,f21]) ).

fof(f162,plain,
    ! [X0] :
      ( multiplication(sk0_0(X0),X0) = zero
      | ~ test(X0) ),
    inference(resolution,[status(thm)],[f42,f37]) ).

fof(f164,plain,
    ! [X0] :
      ( addition(X0,sk0_0(X0)) = one
      | ~ test(X0) ),
    inference(resolution,[status(thm)],[f43,f37]) ).

fof(f165,plain,
    ! [X0] :
      ( addition(c(X0),X0) = one
      | ~ test(X0) ),
    inference(resolution,[status(thm)],[f43,f59]) ).

fof(f166,plain,
    ! [X0] :
      ( addition(X0,c(X0)) = one
      | ~ test(X0) ),
    inference(forward_demodulation,[status(thm)],[f19,f165]) ).

fof(f207,plain,
    ! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
    inference(paramodulation,[status(thm)],[f25,f27]) ).

fof(f239,plain,
    ! [X0,X1] :
      ( multiplication(X0,X1) != zero
      | multiplication(X1,X0) != zero
      | addition(X0,X1) != one
      | test(X0) ),
    inference(resolution,[status(thm)],[f44,f38]) ).

fof(f242,plain,
    ! [X0] : addition(sk0_3,addition(multiplication(sk0_1,c(sk0_2)),X0)) = addition(sk0_3,X0),
    inference(paramodulation,[status(thm)],[f61,f20]) ).

fof(f249,plain,
    ! [X0] : addition(sk0_3,addition(multiplication(sk0_1,c(sk0_2)),X0)) = addition(sk0_3,addition(X0,multiplication(sk0_1,c(sk0_2)))),
    inference(paramodulation,[status(thm)],[f84,f242]) ).

fof(f250,plain,
    ! [X0] : addition(sk0_3,X0) = addition(sk0_3,addition(X0,multiplication(sk0_1,c(sk0_2)))),
    inference(forward_demodulation,[status(thm)],[f242,f249]) ).

fof(f268,plain,
    ! [X0] : addition(sk0_3,multiplication(sk0_1,X0)) = addition(sk0_3,multiplication(sk0_1,addition(X0,c(sk0_2)))),
    inference(paramodulation,[status(thm)],[f26,f250]) ).

fof(f274,plain,
    ! [X0] : addition(addition(X0,multiplication(sk0_1,c(sk0_2))),addition(sk0_3,X0)) = addition(addition(X0,multiplication(sk0_1,c(sk0_2))),sk0_3),
    inference(paramodulation,[status(thm)],[f250,f84]) ).

fof(f275,plain,
    ! [X0] : addition(X0,addition(multiplication(sk0_1,c(sk0_2)),addition(sk0_3,X0))) = addition(addition(X0,multiplication(sk0_1,c(sk0_2))),sk0_3),
    inference(forward_demodulation,[status(thm)],[f20,f274]) ).

fof(f276,plain,
    ! [X0] : addition(X0,addition(multiplication(sk0_1,c(sk0_2)),addition(sk0_3,X0))) = addition(X0,addition(multiplication(sk0_1,c(sk0_2)),sk0_3)),
    inference(forward_demodulation,[status(thm)],[f20,f275]) ).

fof(f277,plain,
    ! [X0] : addition(X0,addition(multiplication(sk0_1,c(sk0_2)),addition(sk0_3,X0))) = addition(X0,addition(sk0_3,multiplication(sk0_1,c(sk0_2)))),
    inference(forward_demodulation,[status(thm)],[f19,f276]) ).

fof(f278,plain,
    ! [X0] : addition(X0,addition(multiplication(sk0_1,c(sk0_2)),addition(sk0_3,X0))) = addition(X0,sk0_3),
    inference(forward_demodulation,[status(thm)],[f61,f277]) ).

fof(f281,plain,
    ! [X0,X1] : addition(sk0_3,addition(addition(X0,multiplication(sk0_1,c(sk0_2))),X1)) = addition(addition(sk0_3,X0),X1),
    inference(paramodulation,[status(thm)],[f250,f20]) ).

fof(f282,plain,
    ! [X0,X1] : addition(sk0_3,addition(X0,addition(multiplication(sk0_1,c(sk0_2)),X1))) = addition(addition(sk0_3,X0),X1),
    inference(forward_demodulation,[status(thm)],[f20,f281]) ).

fof(f283,plain,
    ! [X0,X1] : addition(sk0_3,addition(X0,addition(multiplication(sk0_1,c(sk0_2)),X1))) = addition(sk0_3,addition(X0,X1)),
    inference(forward_demodulation,[status(thm)],[f20,f282]) ).

fof(f628,plain,
    ! [X0,X1] : addition(sk0_3,addition(addition(multiplication(sk0_1,c(sk0_2)),X0),X1)) = addition(sk0_3,addition(X1,X0)),
    inference(paramodulation,[status(thm)],[f19,f283]) ).

fof(f629,plain,
    ! [X0,X1] : addition(sk0_3,addition(multiplication(sk0_1,c(sk0_2)),addition(X0,X1))) = addition(sk0_3,addition(X1,X0)),
    inference(forward_demodulation,[status(thm)],[f20,f628]) ).

fof(f630,plain,
    ! [X0,X1] : addition(sk0_3,addition(X0,X1)) = addition(sk0_3,addition(X1,X0)),
    inference(forward_demodulation,[status(thm)],[f242,f629]) ).

fof(f694,plain,
    ! [X0,X1,X2] : addition(sk0_3,addition(X0,addition(X1,X2))) = addition(sk0_3,addition(X2,addition(X0,X1))),
    inference(paramodulation,[status(thm)],[f20,f630]) ).

fof(f907,plain,
    ! [X0,X1] : addition(sk0_3,addition(X0,X1)) = addition(sk0_3,addition(X1,addition(sk0_3,X0))),
    inference(paramodulation,[status(thm)],[f70,f694]) ).

fof(f1378,plain,
    ! [X0,X1] : addition(addition(X0,addition(sk0_3,X1)),addition(multiplication(sk0_1,c(sk0_2)),addition(sk0_3,addition(X1,X0)))) = addition(addition(X0,addition(sk0_3,X1)),sk0_3),
    inference(paramodulation,[status(thm)],[f907,f278]) ).

fof(f1379,plain,
    ! [X0,X1] : addition(X0,addition(addition(sk0_3,X1),addition(multiplication(sk0_1,c(sk0_2)),addition(sk0_3,addition(X1,X0))))) = addition(addition(X0,addition(sk0_3,X1)),sk0_3),
    inference(forward_demodulation,[status(thm)],[f20,f1378]) ).

fof(f1380,plain,
    ! [X0,X1] : addition(X0,addition(sk0_3,addition(X1,addition(multiplication(sk0_1,c(sk0_2)),addition(sk0_3,addition(X1,X0)))))) = addition(addition(X0,addition(sk0_3,X1)),sk0_3),
    inference(forward_demodulation,[status(thm)],[f20,f1379]) ).

fof(f1381,plain,
    ! [X0,X1] : addition(X0,addition(sk0_3,addition(X1,addition(sk0_3,addition(X1,X0))))) = addition(addition(X0,addition(sk0_3,X1)),sk0_3),
    inference(forward_demodulation,[status(thm)],[f283,f1380]) ).

fof(f1382,plain,
    ! [X0,X1] : addition(X0,addition(sk0_3,addition(addition(X1,X0),X1))) = addition(addition(X0,addition(sk0_3,X1)),sk0_3),
    inference(forward_demodulation,[status(thm)],[f907,f1381]) ).

fof(f1383,plain,
    ! [X0,X1] : addition(X0,addition(sk0_3,addition(X1,addition(X1,X0)))) = addition(addition(X0,addition(sk0_3,X1)),sk0_3),
    inference(forward_demodulation,[status(thm)],[f630,f1382]) ).

fof(f1384,plain,
    ! [X0,X1] : addition(X0,addition(sk0_3,addition(X1,X0))) = addition(addition(X0,addition(sk0_3,X1)),sk0_3),
    inference(forward_demodulation,[status(thm)],[f70,f1383]) ).

fof(f1385,plain,
    ! [X0,X1] : addition(X0,addition(sk0_3,addition(X1,X0))) = addition(X0,addition(addition(sk0_3,X1),sk0_3)),
    inference(forward_demodulation,[status(thm)],[f20,f1384]) ).

fof(f1386,plain,
    ! [X0,X1] : addition(X0,addition(sk0_3,addition(X1,X0))) = addition(X0,addition(sk0_3,addition(X1,sk0_3))),
    inference(forward_demodulation,[status(thm)],[f20,f1385]) ).

fof(f1387,plain,
    ! [X0,X1] : addition(X0,addition(sk0_3,addition(X1,X0))) = addition(X0,addition(sk0_3,X1)),
    inference(forward_demodulation,[status(thm)],[f84,f1386]) ).

fof(f1472,plain,
    ! [X0,X1] : addition(X0,addition(sk0_3,addition(X0,X1))) = addition(X0,addition(sk0_3,X1)),
    inference(paramodulation,[status(thm)],[f630,f1387]) ).

fof(f2769,plain,
    addition(sk0_3,c(sk0_3)) = one,
    inference(resolution,[status(thm)],[f166,f56]) ).

fof(f2770,plain,
    addition(sk0_2,c(sk0_2)) = one,
    inference(resolution,[status(thm)],[f166,f55]) ).

fof(f2771,plain,
    addition(sk0_1,c(sk0_1)) = one,
    inference(resolution,[status(thm)],[f166,f54]) ).

fof(f2772,plain,
    ! [X0] :
      ( addition(X0,c(X0)) = one
      | c(X0) = zero ),
    inference(resolution,[status(thm)],[f166,f51]) ).

fof(f2775,plain,
    addition(sk0_3,addition(sk0_3,one)) = addition(sk0_3,addition(sk0_3,c(sk0_3))),
    inference(paramodulation,[status(thm)],[f2769,f1472]) ).

fof(f2776,plain,
    addition(sk0_3,addition(one,sk0_3)) = addition(sk0_3,addition(sk0_3,c(sk0_3))),
    inference(forward_demodulation,[status(thm)],[f630,f2775]) ).

fof(f2777,plain,
    addition(sk0_3,one) = addition(sk0_3,addition(sk0_3,c(sk0_3))),
    inference(forward_demodulation,[status(thm)],[f84,f2776]) ).

fof(f2778,plain,
    addition(one,sk0_3) = addition(sk0_3,addition(sk0_3,c(sk0_3))),
    inference(forward_demodulation,[status(thm)],[f19,f2777]) ).

fof(f2779,plain,
    addition(one,sk0_3) = addition(sk0_3,c(sk0_3)),
    inference(forward_demodulation,[status(thm)],[f70,f2778]) ).

fof(f2780,plain,
    addition(one,sk0_3) = one,
    inference(forward_demodulation,[status(thm)],[f2769,f2779]) ).

fof(f3209,plain,
    ! [X0] : addition(one,addition(sk0_3,X0)) = addition(X0,one),
    inference(paramodulation,[status(thm)],[f2780,f65]) ).

fof(f3306,plain,
    addition(sk0_1,one) = addition(sk0_1,c(sk0_1)),
    inference(paramodulation,[status(thm)],[f2771,f70]) ).

fof(f3307,plain,
    addition(one,sk0_1) = addition(sk0_1,c(sk0_1)),
    inference(forward_demodulation,[status(thm)],[f19,f3306]) ).

fof(f3308,plain,
    addition(one,sk0_1) = one,
    inference(forward_demodulation,[status(thm)],[f2771,f3307]) ).

fof(f3476,plain,
    ! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(X0,addition(X2,X1)),
    inference(paramodulation,[status(thm)],[f19,f72]) ).

fof(f3477,plain,
    ! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X0,addition(X2,X1)),
    inference(forward_demodulation,[status(thm)],[f20,f3476]) ).

fof(f5389,plain,
    ( spl0_2
  <=> c(sk0_2) = zero ),
    introduced(split_symbol_definition) ).

fof(f5390,plain,
    ( c(sk0_2) = zero
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f5389]) ).

fof(f5481,plain,
    ( spl0_13
  <=> multiplication(c(sk0_2),zero) = zero ),
    introduced(split_symbol_definition) ).

fof(f5483,plain,
    ( multiplication(c(sk0_2),zero) != zero
    | spl0_13 ),
    inference(component_clause,[status(thm)],[f5481]) ).

fof(f5641,plain,
    ( spl0_38
  <=> addition(sk0_3,multiplication(sk0_1,sk0_2)) = addition(sk0_3,multiplication(sk0_1,one)) ),
    introduced(split_symbol_definition) ).

fof(f5642,plain,
    ( addition(sk0_3,multiplication(sk0_1,sk0_2)) = addition(sk0_3,multiplication(sk0_1,one))
    | ~ spl0_38 ),
    inference(component_clause,[status(thm)],[f5641]) ).

fof(f5644,plain,
    ( addition(sk0_3,multiplication(sk0_1,sk0_2)) = addition(sk0_3,multiplication(sk0_1,one))
    | c(sk0_2) = zero ),
    inference(paramodulation,[status(thm)],[f2772,f268]) ).

fof(f5645,plain,
    ( spl0_38
    | spl0_2 ),
    inference(split_clause,[status(thm)],[f5644,f5641,f5389]) ).

fof(f5907,plain,
    addition(sk0_2,sk0_0(sk0_2)) = one,
    inference(resolution,[status(thm)],[f164,f55]) ).

fof(f7159,plain,
    ( addition(sk0_2,zero) = one
    | ~ spl0_2 ),
    inference(backward_demodulation,[status(thm)],[f5390,f2770]) ).

fof(f7160,plain,
    ( sk0_2 = one
    | ~ spl0_2 ),
    inference(forward_demodulation,[status(thm)],[f21,f7159]) ).

fof(f7221,plain,
    ( addition(sk0_3,multiplication(sk0_1,sk0_2)) = addition(sk0_3,sk0_1)
    | ~ spl0_38 ),
    inference(forward_demodulation,[status(thm)],[f24,f5642]) ).

fof(f7222,plain,
    ( addition(sk0_3,multiplication(sk0_1,sk0_2)) = addition(sk0_1,sk0_3)
    | ~ spl0_38 ),
    inference(forward_demodulation,[status(thm)],[f19,f7221]) ).

fof(f7280,plain,
    ( spl0_71
  <=> test(one) ),
    introduced(split_symbol_definition) ).

fof(f7281,plain,
    ( test(one)
    | ~ spl0_71 ),
    inference(component_clause,[status(thm)],[f7280]) ).

fof(f7282,plain,
    ( ~ test(one)
    | spl0_71 ),
    inference(component_clause,[status(thm)],[f7280]) ).

fof(f8903,plain,
    ! [X0] : multiplication(one,X0) = addition(X0,multiplication(sk0_1,X0)),
    inference(paramodulation,[status(thm)],[f3308,f207]) ).

fof(f8904,plain,
    ! [X0] : X0 = addition(X0,multiplication(sk0_1,X0)),
    inference(forward_demodulation,[status(thm)],[f25,f8903]) ).

fof(f9893,plain,
    ! [X0,X1] : addition(X0,addition(X1,multiplication(sk0_1,X0))) = addition(X1,X0),
    inference(paramodulation,[status(thm)],[f8904,f72]) ).

fof(f28898,plain,
    ! [X0] : X0 = addition(X0,zero),
    inference(paramodulation,[status(thm)],[f118,f19]) ).

fof(f29805,plain,
    addition(sk0_1,addition(sk0_2,sk0_3)) != addition(sk0_2,sk0_3),
    inference(resolution,[status(thm)],[f58,f33]) ).

fof(f33366,plain,
    ! [X0] :
      ( multiplication(one,X0) != zero
      | multiplication(X0,one) != zero
      | addition(one,X0) != one
      | spl0_71 ),
    inference(resolution,[status(thm)],[f7282,f239]) ).

fof(f33367,plain,
    ! [X0] :
      ( X0 != zero
      | multiplication(X0,one) != zero
      | addition(one,X0) != one
      | spl0_71 ),
    inference(forward_demodulation,[status(thm)],[f25,f33366]) ).

fof(f33368,plain,
    ! [X0] :
      ( X0 != zero
      | X0 != zero
      | addition(one,X0) != one
      | spl0_71 ),
    inference(forward_demodulation,[status(thm)],[f24,f33367]) ).

fof(f33369,plain,
    ! [X0] :
      ( X0 != zero
      | addition(one,X0) != one
      | spl0_71 ),
    inference(duplicate_literals_removal,[status(esa)],[f33368]) ).

fof(f33370,plain,
    ( addition(one,zero) != one
    | spl0_71 ),
    inference(destructive_equality_resolution,[status(esa)],[f33369]) ).

fof(f33371,plain,
    ( $false
    | spl0_71 ),
    inference(forward_subsumption_resolution,[status(thm)],[f33370,f28898]) ).

fof(f33372,plain,
    spl0_71,
    inference(contradiction_clause,[status(thm)],[f33371]) ).

fof(f33455,plain,
    ( multiplication(sk0_0(one),one) = zero
    | ~ spl0_71 ),
    inference(resolution,[status(thm)],[f7281,f162]) ).

fof(f33456,plain,
    ( sk0_0(one) = zero
    | ~ spl0_71 ),
    inference(forward_demodulation,[status(thm)],[f24,f33455]) ).

fof(f62488,plain,
    ( addition(sk0_2,addition(sk0_1,sk0_3)) = addition(sk0_3,sk0_2)
    | ~ spl0_38 ),
    inference(paramodulation,[status(thm)],[f7222,f9893]) ).

fof(f62489,plain,
    ( addition(sk0_1,addition(sk0_3,sk0_2)) = addition(sk0_3,sk0_2)
    | ~ spl0_38 ),
    inference(forward_demodulation,[status(thm)],[f65,f62488]) ).

fof(f62490,plain,
    ( addition(sk0_1,addition(sk0_2,sk0_3)) = addition(sk0_3,sk0_2)
    | ~ spl0_38 ),
    inference(forward_demodulation,[status(thm)],[f3477,f62489]) ).

fof(f62491,plain,
    ( addition(sk0_1,addition(sk0_2,sk0_3)) = addition(sk0_2,sk0_3)
    | ~ spl0_38 ),
    inference(forward_demodulation,[status(thm)],[f19,f62490]) ).

fof(f62492,plain,
    ( $false
    | ~ spl0_38 ),
    inference(forward_subsumption_resolution,[status(thm)],[f62491,f29805]) ).

fof(f62493,plain,
    ~ spl0_38,
    inference(contradiction_clause,[status(thm)],[f62492]) ).

fof(f62517,plain,
    ( addition(sk0_2,sk0_0(one)) = one
    | ~ spl0_2 ),
    inference(backward_demodulation,[status(thm)],[f7160,f5907]) ).

fof(f62518,plain,
    ( addition(sk0_2,zero) = one
    | ~ spl0_71
    | ~ spl0_2 ),
    inference(forward_demodulation,[status(thm)],[f33456,f62517]) ).

fof(f62519,plain,
    ( sk0_2 = one
    | ~ spl0_71
    | ~ spl0_2 ),
    inference(forward_demodulation,[status(thm)],[f28898,f62518]) ).

fof(f62619,plain,
    ( zero != zero
    | spl0_13 ),
    inference(forward_demodulation,[status(thm)],[f28,f5483]) ).

fof(f62620,plain,
    ( $false
    | spl0_13 ),
    inference(trivial_equality_resolution,[status(esa)],[f62619]) ).

fof(f62621,plain,
    spl0_13,
    inference(contradiction_clause,[status(thm)],[f62620]) ).

fof(f62863,plain,
    ( addition(sk0_1,addition(sk0_2,sk0_3)) != addition(one,sk0_3)
    | ~ spl0_71
    | ~ spl0_2 ),
    inference(backward_demodulation,[status(thm)],[f62519,f29805]) ).

fof(f62864,plain,
    ( addition(sk0_1,addition(one,sk0_3)) != addition(one,sk0_3)
    | ~ spl0_71
    | ~ spl0_2 ),
    inference(forward_demodulation,[status(thm)],[f62519,f62863]) ).

fof(f62865,plain,
    ( addition(one,addition(sk0_3,sk0_1)) != addition(one,sk0_3)
    | ~ spl0_71
    | ~ spl0_2 ),
    inference(forward_demodulation,[status(thm)],[f65,f62864]) ).

fof(f62866,plain,
    ( addition(sk0_1,one) != addition(one,sk0_3)
    | ~ spl0_71
    | ~ spl0_2 ),
    inference(forward_demodulation,[status(thm)],[f3209,f62865]) ).

fof(f62867,plain,
    ( addition(one,sk0_1) != addition(one,sk0_3)
    | ~ spl0_71
    | ~ spl0_2 ),
    inference(forward_demodulation,[status(thm)],[f19,f62866]) ).

fof(f62868,plain,
    ( one != addition(one,sk0_3)
    | ~ spl0_71
    | ~ spl0_2 ),
    inference(forward_demodulation,[status(thm)],[f3308,f62867]) ).

fof(f62869,plain,
    ( one != one
    | ~ spl0_71
    | ~ spl0_2 ),
    inference(forward_demodulation,[status(thm)],[f2780,f62868]) ).

fof(f62870,plain,
    ( $false
    | ~ spl0_71
    | ~ spl0_2 ),
    inference(trivial_equality_resolution,[status(esa)],[f62869]) ).

fof(f62871,plain,
    ( ~ spl0_71
    | ~ spl0_2 ),
    inference(contradiction_clause,[status(thm)],[f62870]) ).

fof(f62872,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f5645,f33372,f62493,f62621,f62871]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : KLE018+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n022.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Tue May 30 11:45:42 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.5.1
% 86.60/11.32  % Refutation found
% 86.60/11.32  % SZS status Theorem for theBenchmark: Theorem is valid
% 86.60/11.32  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 87.94/11.52  % Elapsed time: 11.155812 seconds
% 87.94/11.52  % CPU time: 87.929061 seconds
% 87.94/11.52  % Memory used: 574.859 MB
%------------------------------------------------------------------------------