TSTP Solution File: KLE015+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : KLE015+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n018.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 : Tue Apr 30 13:11:40 EDT 2024

% Result   : Theorem 4.91s 1.08s
% Output   : Refutation 4.91s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   31
%            Number of leaves      :   14
% Syntax   : Number of formulae    :  132 ( 101 unt;   0 def)
%            Number of atoms       :  203 ( 126 equ)
%            Maximal formula atoms :    8 (   1 avg)
%            Number of connectives :  110 (  39   ~;  30   |;  27   &)
%                                         (   7 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :  129 ( 118   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f27250,plain,
    $false,
    inference(subsumption_resolution,[],[f27249,f6141]) ).

fof(f6141,plain,
    zero != multiplication(multiplication(sK1,c(sK0)),c(sK1)),
    inference(superposition,[],[f40,f5778]) ).

fof(f5778,plain,
    ! [X0] : multiplication(X0,c(sK0)) = multiplication(addition(sK0,X0),c(sK0)),
    inference(forward_demodulation,[],[f5589,f104]) ).

fof(f104,plain,
    ! [X0] : addition(zero,X0) = X0,
    inference(superposition,[],[f50,f43]) ).

fof(f43,plain,
    ! [X0] : addition(X0,zero) = X0,
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] : addition(X0,zero) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).

fof(f50,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).

fof(f5589,plain,
    ! [X0] : addition(zero,multiplication(X0,c(sK0))) = multiplication(addition(sK0,X0),c(sK0)),
    inference(superposition,[],[f60,f156]) ).

fof(f156,plain,
    zero = multiplication(sK0,c(sK0)),
    inference(unit_resulting_resolution,[],[f72,f54]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( ~ complement(X1,X0)
      | zero = multiplication(X1,X0) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ( complement(X1,X0)
        | addition(X0,X1) != one
        | zero != multiplication(X1,X0)
        | zero != multiplication(X0,X1) )
      & ( ( addition(X0,X1) = one
          & zero = multiplication(X1,X0)
          & zero = multiplication(X0,X1) )
        | ~ complement(X1,X0) ) ),
    inference(flattening,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ( complement(X1,X0)
        | addition(X0,X1) != one
        | zero != multiplication(X1,X0)
        | zero != multiplication(X0,X1) )
      & ( ( addition(X0,X1) = one
          & zero = multiplication(X1,X0)
          & zero = multiplication(X0,X1) )
        | ~ complement(X1,X0) ) ),
    inference(nnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( complement(X1,X0)
    <=> ( addition(X0,X1) = one
        & zero = multiplication(X1,X0)
        & zero = multiplication(X0,X1) ) ),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ! [X3,X4] :
      ( complement(X4,X3)
    <=> ( one = addition(X3,X4)
        & zero = multiplication(X4,X3)
        & zero = multiplication(X3,X4) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_2) ).

fof(f72,plain,
    complement(sK0,c(sK0)),
    inference(unit_resulting_resolution,[],[f39,f61]) ).

fof(f61,plain,
    ! [X0] :
      ( ~ test(X0)
      | complement(X0,c(X0)) ),
    inference(equality_resolution,[],[f51]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( complement(X0,X1)
      | c(X0) != X1
      | ~ test(X0) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ( ( c(X0) = X1
          | ~ complement(X0,X1) )
        & ( complement(X0,X1)
          | c(X0) != X1 ) )
      | ~ test(X0) ),
    inference(nnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ( c(X0) = X1
      <=> complement(X0,X1) )
      | ~ test(X0) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( test(X0)
     => ( c(X0) = X1
      <=> complement(X0,X1) ) ),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X3,X4] :
      ( test(X3)
     => ( c(X3) = X4
      <=> complement(X3,X4) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_3) ).

fof(f39,plain,
    test(sK0),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    ( zero != multiplication(multiplication(addition(sK0,sK1),c(sK0)),c(sK1))
    & test(sK0)
    & test(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f26,f29]) ).

fof(f29,plain,
    ( ? [X0,X1] :
        ( zero != multiplication(multiplication(addition(X0,X1),c(X0)),c(X1))
        & test(X0)
        & test(X1) )
   => ( zero != multiplication(multiplication(addition(sK0,sK1),c(sK0)),c(sK1))
      & test(sK0)
      & test(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ? [X0,X1] :
      ( zero != multiplication(multiplication(addition(X0,X1),c(X0)),c(X1))
      & test(X0)
      & test(X1) ),
    inference(flattening,[],[f25]) ).

fof(f25,plain,
    ? [X0,X1] :
      ( zero != multiplication(multiplication(addition(X0,X1),c(X0)),c(X1))
      & test(X0)
      & test(X1) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,plain,
    ~ ! [X0,X1] :
        ( ( test(X0)
          & test(X1) )
       => zero = multiplication(multiplication(addition(X0,X1),c(X0)),c(X1)) ),
    inference(rectify,[],[f18]) ).

fof(f18,negated_conjecture,
    ~ ! [X3,X4] :
        ( ( test(X3)
          & test(X4) )
       => zero = multiplication(multiplication(addition(X3,X4),c(X3)),c(X4)) ),
    inference(negated_conjecture,[],[f17]) ).

fof(f17,conjecture,
    ! [X3,X4] :
      ( ( test(X3)
        & test(X4) )
     => zero = multiplication(multiplication(addition(X3,X4),c(X3)),c(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

fof(f60,plain,
    ! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
    inference(cnf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).

fof(f40,plain,
    zero != multiplication(multiplication(addition(sK0,sK1),c(sK0)),c(sK1)),
    inference(cnf_transformation,[],[f30]) ).

fof(f27249,plain,
    zero = multiplication(multiplication(sK1,c(sK0)),c(sK1)),
    inference(forward_demodulation,[],[f27222,f157]) ).

fof(f157,plain,
    zero = multiplication(sK1,c(sK1)),
    inference(unit_resulting_resolution,[],[f71,f54]) ).

fof(f71,plain,
    complement(sK1,c(sK1)),
    inference(unit_resulting_resolution,[],[f38,f61]) ).

fof(f38,plain,
    test(sK1),
    inference(cnf_transformation,[],[f30]) ).

fof(f27222,plain,
    multiplication(sK1,c(sK1)) = multiplication(multiplication(sK1,c(sK0)),c(sK1)),
    inference(superposition,[],[f5783,f26912]) ).

fof(f26912,plain,
    sK1 = addition(sK1,multiplication(sK1,c(sK0))),
    inference(forward_demodulation,[],[f26911,f44]) ).

fof(f44,plain,
    ! [X0] : multiplication(X0,one) = X0,
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] : multiplication(X0,one) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).

fof(f26911,plain,
    multiplication(sK1,one) = addition(sK1,multiplication(sK1,c(sK0))),
    inference(forward_demodulation,[],[f26737,f6213]) ).

fof(f6213,plain,
    sK0 = c(c(sK0)),
    inference(forward_demodulation,[],[f6212,f6156]) ).

fof(f6156,plain,
    c(sK0) = sK2(sK0),
    inference(superposition,[],[f6148,f4323]) ).

fof(f4323,plain,
    sK2(sK0) = multiplication(sK2(sK0),c(sK0)),
    inference(forward_demodulation,[],[f4312,f44]) ).

fof(f4312,plain,
    multiplication(sK2(sK0),one) = multiplication(sK2(sK0),c(sK0)),
    inference(superposition,[],[f3596,f200]) ).

fof(f200,plain,
    one = addition(sK0,c(sK0)),
    inference(superposition,[],[f180,f50]) ).

fof(f180,plain,
    one = addition(c(sK0),sK0),
    inference(unit_resulting_resolution,[],[f72,f55]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( ~ complement(X1,X0)
      | addition(X0,X1) = one ),
    inference(cnf_transformation,[],[f37]) ).

fof(f3596,plain,
    ! [X0] : multiplication(sK2(sK0),X0) = multiplication(sK2(sK0),addition(sK0,X0)),
    inference(forward_demodulation,[],[f3473,f104]) ).

fof(f3473,plain,
    ! [X0] : multiplication(sK2(sK0),addition(sK0,X0)) = addition(zero,multiplication(sK2(sK0),X0)),
    inference(superposition,[],[f59,f159]) ).

fof(f159,plain,
    zero = multiplication(sK2(sK0),sK0),
    inference(unit_resulting_resolution,[],[f63,f54]) ).

fof(f63,plain,
    complement(sK2(sK0),sK0),
    inference(unit_resulting_resolution,[],[f39,f48]) ).

fof(f48,plain,
    ! [X0] :
      ( ~ test(X0)
      | complement(sK2(X0),X0) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0] :
      ( ( test(X0)
        | ! [X1] : ~ complement(X1,X0) )
      & ( complement(sK2(X0),X0)
        | ~ test(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f32,f33]) ).

fof(f33,plain,
    ! [X0] :
      ( ? [X2] : complement(X2,X0)
     => complement(sK2(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f32,plain,
    ! [X0] :
      ( ( test(X0)
        | ! [X1] : ~ complement(X1,X0) )
      & ( ? [X2] : complement(X2,X0)
        | ~ test(X0) ) ),
    inference(rectify,[],[f31]) ).

fof(f31,plain,
    ! [X0] :
      ( ( test(X0)
        | ! [X1] : ~ complement(X1,X0) )
      & ( ? [X1] : complement(X1,X0)
        | ~ test(X0) ) ),
    inference(nnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0] :
      ( test(X0)
    <=> ? [X1] : complement(X1,X0) ),
    inference(rectify,[],[f13]) ).

fof(f13,axiom,
    ! [X3] :
      ( test(X3)
    <=> ? [X4] : complement(X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_1) ).

fof(f59,plain,
    ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
    inference(cnf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).

fof(f6148,plain,
    c(sK0) = multiplication(sK2(sK0),c(sK0)),
    inference(forward_demodulation,[],[f6133,f45]) ).

fof(f45,plain,
    ! [X0] : multiplication(one,X0) = X0,
    inference(cnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] : multiplication(one,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).

fof(f6133,plain,
    multiplication(sK2(sK0),c(sK0)) = multiplication(one,c(sK0)),
    inference(superposition,[],[f5778,f183]) ).

fof(f183,plain,
    one = addition(sK0,sK2(sK0)),
    inference(unit_resulting_resolution,[],[f63,f55]) ).

fof(f6212,plain,
    sK0 = c(sK2(sK0)),
    inference(subsumption_resolution,[],[f6177,f82]) ).

fof(f82,plain,
    test(c(sK0)),
    inference(unit_resulting_resolution,[],[f72,f49]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( ~ complement(X1,X0)
      | test(X0) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f6177,plain,
    ( ~ test(c(sK0))
    | sK0 = c(sK2(sK0)) ),
    inference(superposition,[],[f244,f6156]) ).

fof(f244,plain,
    ( ~ test(sK2(sK0))
    | sK0 = c(sK2(sK0)) ),
    inference(resolution,[],[f52,f63]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( ~ complement(X0,X1)
      | c(X0) = X1
      | ~ test(X0) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f26737,plain,
    multiplication(sK1,one) = addition(sK1,multiplication(sK1,c(c(c(sK0))))),
    inference(superposition,[],[f15789,f580]) ).

fof(f580,plain,
    one = addition(c(c(c(sK0))),one),
    inference(superposition,[],[f519,f179]) ).

fof(f179,plain,
    one = addition(c(c(c(sK0))),c(c(sK0))),
    inference(unit_resulting_resolution,[],[f98,f55]) ).

fof(f98,plain,
    complement(c(c(sK0)),c(c(c(sK0)))),
    inference(unit_resulting_resolution,[],[f96,f61]) ).

fof(f96,plain,
    test(c(c(sK0))),
    inference(unit_resulting_resolution,[],[f84,f49]) ).

fof(f84,plain,
    complement(c(sK0),c(c(sK0))),
    inference(unit_resulting_resolution,[],[f82,f61]) ).

fof(f519,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
    inference(superposition,[],[f57,f46]) ).

fof(f46,plain,
    ! [X0] : addition(X0,X0) = X0,
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] : addition(X0,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).

fof(f57,plain,
    ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X2,X1,X0] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).

fof(f15789,plain,
    ! [X0] : multiplication(sK1,addition(X0,one)) = addition(sK1,multiplication(sK1,X0)),
    inference(forward_demodulation,[],[f15788,f519]) ).

fof(f15788,plain,
    ! [X0] : multiplication(sK1,addition(X0,one)) = addition(sK1,addition(sK1,multiplication(sK1,X0))),
    inference(forward_demodulation,[],[f15659,f3423]) ).

fof(f3423,plain,
    ! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
    inference(superposition,[],[f59,f44]) ).

fof(f15659,plain,
    ! [X0] : multiplication(sK1,addition(X0,one)) = addition(sK1,multiplication(sK1,addition(one,X0))),
    inference(superposition,[],[f3892,f15561]) ).

fof(f15561,plain,
    ! [X0] : addition(X0,one) = addition(sK1,addition(one,X0)),
    inference(forward_demodulation,[],[f15475,f566]) ).

fof(f566,plain,
    ! [X0,X1] : addition(X1,X0) = addition(X0,addition(X1,X0)),
    inference(superposition,[],[f519,f50]) ).

fof(f15475,plain,
    ! [X0] : addition(sK1,addition(one,X0)) = addition(one,addition(X0,one)),
    inference(superposition,[],[f547,f13153]) ).

fof(f13153,plain,
    ! [X0] : addition(one,X0) = addition(c(sK1),addition(X0,one)),
    inference(superposition,[],[f11919,f57]) ).

fof(f11919,plain,
    ! [X0] : addition(one,X0) = addition(addition(c(sK1),X0),one),
    inference(forward_demodulation,[],[f11791,f1247]) ).

fof(f1247,plain,
    ! [X0] : addition(one,X0) = addition(addition(c(sK1),X0),addition(one,X0)),
    inference(superposition,[],[f566,f547]) ).

fof(f11791,plain,
    ! [X0] : addition(addition(c(sK1),X0),one) = addition(addition(c(sK1),X0),addition(one,X0)),
    inference(superposition,[],[f11787,f632]) ).

fof(f632,plain,
    ! [X0] : addition(one,X0) = addition(one,addition(c(sK1),X0)),
    inference(superposition,[],[f57,f619]) ).

fof(f619,plain,
    one = addition(one,c(sK1)),
    inference(superposition,[],[f583,f50]) ).

fof(f583,plain,
    one = addition(c(sK1),one),
    inference(superposition,[],[f519,f208]) ).

fof(f208,plain,
    one = addition(c(sK1),c(c(sK1))),
    inference(superposition,[],[f176,f50]) ).

fof(f176,plain,
    one = addition(c(c(sK1)),c(sK1)),
    inference(unit_resulting_resolution,[],[f78,f55]) ).

fof(f78,plain,
    complement(c(sK1),c(c(sK1))),
    inference(unit_resulting_resolution,[],[f76,f61]) ).

fof(f76,plain,
    test(c(sK1)),
    inference(unit_resulting_resolution,[],[f71,f49]) ).

fof(f11787,plain,
    ! [X0] : addition(X0,one) = addition(X0,addition(one,X0)),
    inference(forward_demodulation,[],[f11786,f616]) ).

fof(f616,plain,
    ! [X0] : addition(one,X0) = addition(one,addition(sK0,X0)),
    inference(superposition,[],[f57,f603]) ).

fof(f603,plain,
    one = addition(one,sK0),
    inference(superposition,[],[f591,f50]) ).

fof(f591,plain,
    one = addition(sK0,one),
    inference(superposition,[],[f519,f183]) ).

fof(f11786,plain,
    ! [X0] : addition(X0,one) = addition(X0,addition(one,addition(sK0,X0))),
    inference(forward_demodulation,[],[f11703,f551]) ).

fof(f551,plain,
    ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
    inference(superposition,[],[f57,f50]) ).

fof(f11703,plain,
    ! [X0] : addition(X0,one) = addition(X0,addition(sK0,addition(X0,one))),
    inference(superposition,[],[f5179,f57]) ).

fof(f5179,plain,
    ! [X0] : addition(X0,one) = addition(addition(X0,sK0),addition(X0,one)),
    inference(superposition,[],[f847,f50]) ).

fof(f847,plain,
    ! [X0] : addition(one,X0) = addition(addition(X0,sK0),addition(one,X0)),
    inference(superposition,[],[f566,f707]) ).

fof(f707,plain,
    ! [X0] : addition(one,X0) = addition(one,addition(X0,sK0)),
    inference(superposition,[],[f616,f50]) ).

fof(f547,plain,
    ! [X0] : addition(one,X0) = addition(sK1,addition(c(sK1),X0)),
    inference(superposition,[],[f57,f204]) ).

fof(f204,plain,
    one = addition(sK1,c(sK1)),
    inference(superposition,[],[f181,f50]) ).

fof(f181,plain,
    one = addition(c(sK1),sK1),
    inference(unit_resulting_resolution,[],[f71,f55]) ).

fof(f3892,plain,
    ! [X0] : multiplication(sK1,addition(sK1,X0)) = addition(sK1,multiplication(sK1,X0)),
    inference(forward_demodulation,[],[f3878,f3423]) ).

fof(f3878,plain,
    ! [X0] : multiplication(sK1,addition(sK1,X0)) = multiplication(sK1,addition(one,X0)),
    inference(superposition,[],[f3582,f1179]) ).

fof(f1179,plain,
    ! [X0] : addition(one,X0) = addition(sK2(sK1),addition(sK1,X0)),
    inference(superposition,[],[f57,f1166]) ).

fof(f1166,plain,
    one = addition(sK2(sK1),sK1),
    inference(forward_demodulation,[],[f1147,f609]) ).

fof(f609,plain,
    one = addition(one,sK1),
    inference(superposition,[],[f593,f50]) ).

fof(f593,plain,
    one = addition(sK1,one),
    inference(superposition,[],[f519,f182]) ).

fof(f182,plain,
    one = addition(sK1,sK2(sK1)),
    inference(unit_resulting_resolution,[],[f62,f55]) ).

fof(f62,plain,
    complement(sK2(sK1),sK1),
    inference(unit_resulting_resolution,[],[f38,f48]) ).

fof(f1147,plain,
    addition(sK2(sK1),sK1) = addition(one,sK1),
    inference(superposition,[],[f546,f566]) ).

fof(f546,plain,
    ! [X0] : addition(one,X0) = addition(sK1,addition(sK2(sK1),X0)),
    inference(superposition,[],[f57,f182]) ).

fof(f3582,plain,
    ! [X0] : multiplication(sK1,X0) = multiplication(sK1,addition(sK2(sK1),X0)),
    inference(forward_demodulation,[],[f3459,f104]) ).

fof(f3459,plain,
    ! [X0] : multiplication(sK1,addition(sK2(sK1),X0)) = addition(zero,multiplication(sK1,X0)),
    inference(superposition,[],[f59,f134]) ).

fof(f134,plain,
    zero = multiplication(sK1,sK2(sK1)),
    inference(unit_resulting_resolution,[],[f62,f53]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( ~ complement(X1,X0)
      | zero = multiplication(X0,X1) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f5783,plain,
    ! [X0] : multiplication(X0,c(sK1)) = multiplication(addition(sK1,X0),c(sK1)),
    inference(forward_demodulation,[],[f5603,f104]) ).

fof(f5603,plain,
    ! [X0] : addition(zero,multiplication(X0,c(sK1))) = multiplication(addition(sK1,X0),c(sK1)),
    inference(superposition,[],[f60,f157]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : KLE015+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n018.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Tue Apr 30 05:17:13 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (24736)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38  % (24737)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.39  TRYING [1]
% 0.22/0.39  TRYING [2]
% 0.22/0.39  % (24739)WARNING: value z3 for option sas not known
% 0.22/0.39  % (24739)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.39  % (24738)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.39  % (24740)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.39  % (24741)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.22/0.39  % (24743)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.39  % (24742)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.22/0.40  TRYING [1]
% 0.22/0.40  TRYING [2]
% 0.22/0.40  TRYING [3]
% 0.22/0.40  TRYING [3]
% 0.22/0.41  TRYING [4]
% 0.22/0.44  TRYING [5]
% 0.22/0.46  TRYING [4]
% 1.25/0.53  TRYING [6]
% 1.37/0.57  TRYING [5]
% 2.30/0.74  TRYING [7]
% 2.94/0.77  TRYING [6]
% 4.91/1.07  % (24743)First to succeed.
% 4.91/1.08  % (24743)Refutation found. Thanks to Tanya!
% 4.91/1.08  % SZS status Theorem for theBenchmark
% 4.91/1.08  % SZS output start Proof for theBenchmark
% See solution above
% 4.91/1.08  % (24743)------------------------------
% 4.91/1.08  % (24743)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 4.91/1.08  % (24743)Termination reason: Refutation
% 4.91/1.08  
% 4.91/1.08  % (24743)Memory used [KB]: 5997
% 4.91/1.08  % (24743)Time elapsed: 0.683 s
% 4.91/1.08  % (24743)Instructions burned: 1409 (million)
% 4.91/1.08  % (24743)------------------------------
% 4.91/1.08  % (24743)------------------------------
% 4.91/1.08  % (24736)Success in time 0.711 s
%------------------------------------------------------------------------------