TSTP Solution File: KLE010+4 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : KLE010+4 : 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 : n009.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 13:11:39 EDT 2024

% Result   : Theorem 0.19s 0.49s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :   27
% Syntax   : Number of formulae    :  189 (  61 unt;   0 def)
%            Number of atoms       :  382 ( 134 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  342 ( 149   ~; 137   |;  30   &)
%                                         (  18 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :   15 (  13 usr;  11 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :  130 ( 119   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f6215,plain,
    $false,
    inference(avatar_sat_refutation,[],[f153,f162,f829,f1245,f1319,f1334,f1379,f1652,f6190,f6198]) ).

fof(f6198,plain,
    spl3_5,
    inference(avatar_contradiction_clause,[],[f6197]) ).

fof(f6197,plain,
    ( $false
    | spl3_5 ),
    inference(subsumption_resolution,[],[f6196,f98]) ).

fof(f98,plain,
    ! [X0] : leq(X0,X0),
    inference(trivial_inequality_removal,[],[f93]) ).

fof(f93,plain,
    ! [X0] :
      ( X0 != X0
      | leq(X0,X0) ),
    inference(superposition,[],[f69,f56]) ).

fof(f56,plain,
    ! [X0] : addition(X0,X0) = X0,
    inference(cnf_transformation,[],[f4]) ).

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

fof(f69,plain,
    ! [X0,X1] :
      ( addition(X0,X1) != X1
      | leq(X0,X1) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( leq(X0,X1)
      | addition(X0,X1) != X1 ),
    inference(ennf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( addition(X0,X1) = X1
     => leq(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f12]) ).

fof(f12,axiom,
    ! [X0,X1] :
      ( leq(X0,X1)
    <=> addition(X0,X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).

fof(f6196,plain,
    ( ~ leq(one,one)
    | spl3_5 ),
    inference(forward_demodulation,[],[f6195,f1154]) ).

fof(f1154,plain,
    one = addition(sK0,c(sK0)),
    inference(superposition,[],[f137,f1119]) ).

fof(f1119,plain,
    c(sK0) = sK2(sK0),
    inference(subsumption_resolution,[],[f1114,f49]) ).

fof(f49,plain,
    test(sK0),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ( ( ~ leq(addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),one)
      | ~ leq(one,addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1)))) )
    & test(sK0)
    & test(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f31,f39]) ).

fof(f39,plain,
    ( ? [X0,X1] :
        ( ( ~ leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
          | ~ leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) )
        & test(X0)
        & test(X1) )
   => ( ( ~ leq(addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),one)
        | ~ leq(one,addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1)))) )
      & test(sK0)
      & test(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ? [X0,X1] :
      ( ( ~ leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
        | ~ leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) )
      & test(X0)
      & test(X1) ),
    inference(flattening,[],[f30]) ).

fof(f30,plain,
    ? [X0,X1] :
      ( ( ~ leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
        | ~ leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) )
      & test(X0)
      & test(X1) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,plain,
    ~ ! [X0,X1] :
        ( ( test(X0)
          & test(X1) )
       => ( leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
          & leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) ) ),
    inference(rectify,[],[f20]) ).

fof(f20,negated_conjecture,
    ~ ! [X3,X4] :
        ( ( test(X3)
          & test(X4) )
       => ( leq(addition(addition(addition(addition(multiplication(X4,X3),multiplication(c(X4),X3)),multiplication(X3,X4)),multiplication(c(X3),X4)),multiplication(c(X3),c(X4))),one)
          & leq(one,addition(addition(addition(addition(multiplication(X4,X3),multiplication(c(X4),X3)),multiplication(X3,X4)),multiplication(c(X3),X4)),multiplication(c(X3),c(X4)))) ) ),
    inference(negated_conjecture,[],[f19]) ).

fof(f19,conjecture,
    ! [X3,X4] :
      ( ( test(X3)
        & test(X4) )
     => ( leq(addition(addition(addition(addition(multiplication(X4,X3),multiplication(c(X4),X3)),multiplication(X3,X4)),multiplication(c(X3),X4)),multiplication(c(X3),c(X4))),one)
        & leq(one,addition(addition(addition(addition(multiplication(X4,X3),multiplication(c(X4),X3)),multiplication(X3,X4)),multiplication(c(X3),X4)),multiplication(c(X3),c(X4)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

fof(f1114,plain,
    ( c(sK0) = sK2(sK0)
    | ~ test(sK0) ),
    inference(resolution,[],[f1074,f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( ~ complement(X0,X1)
      | c(X0) = X1
      | ~ test(X0) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ( ( c(X0) = X1
          | ~ complement(X0,X1) )
        & ( complement(X0,X1)
          | c(X0) != X1 ) )
      | ~ test(X0) ),
    inference(nnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ( c(X0) = X1
      <=> complement(X0,X1) )
      | ~ test(X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,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/sandbox/benchmark/theBenchmark.p',test_3) ).

fof(f1074,plain,
    complement(sK0,sK2(sK0)),
    inference(subsumption_resolution,[],[f1073,f137]) ).

fof(f1073,plain,
    ( one != addition(sK0,sK2(sK0))
    | complement(sK0,sK2(sK0)) ),
    inference(forward_demodulation,[],[f1072,f60]) ).

fof(f60,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/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).

fof(f1072,plain,
    ( one != addition(sK2(sK0),sK0)
    | complement(sK0,sK2(sK0)) ),
    inference(subsumption_resolution,[],[f1008,f112]) ).

fof(f112,plain,
    zero = multiplication(sK2(sK0),sK0),
    inference(resolution,[],[f87,f49]) ).

fof(f87,plain,
    ! [X0] :
      ( ~ test(X0)
      | zero = multiplication(sK2(X0),X0) ),
    inference(resolution,[],[f66,f58]) ).

fof(f58,plain,
    ! [X0] :
      ( complement(sK2(X0),X0)
      | ~ test(X0) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0] :
      ( ( test(X0)
        | ! [X1] : ~ complement(X1,X0) )
      & ( complement(sK2(X0),X0)
        | ~ test(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f42,f43]) ).

fof(f43,plain,
    ! [X0] :
      ( ? [X2] : complement(X2,X0)
     => complement(sK2(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f42,plain,
    ! [X0] :
      ( ( test(X0)
        | ! [X1] : ~ complement(X1,X0) )
      & ( ? [X2] : complement(X2,X0)
        | ~ test(X0) ) ),
    inference(rectify,[],[f41]) ).

fof(f41,plain,
    ! [X0] :
      ( ( test(X0)
        | ! [X1] : ~ complement(X1,X0) )
      & ( ? [X1] : complement(X1,X0)
        | ~ test(X0) ) ),
    inference(nnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0] :
      ( test(X0)
    <=> ? [X1] : complement(X1,X0) ),
    inference(rectify,[],[f13]) ).

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

fof(f66,plain,
    ! [X0,X1] :
      ( ~ complement(X1,X0)
      | zero = multiplication(X1,X0) ),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,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,[],[f46]) ).

fof(f46,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,[],[f27]) ).

fof(f27,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/sandbox/benchmark/theBenchmark.p',test_2) ).

fof(f1008,plain,
    ( one != addition(sK2(sK0),sK0)
    | complement(sK0,sK2(sK0))
    | zero != multiplication(sK2(sK0),sK0) ),
    inference(trivial_inequality_removal,[],[f985]) ).

fof(f985,plain,
    ( zero != zero
    | one != addition(sK2(sK0),sK0)
    | complement(sK0,sK2(sK0))
    | zero != multiplication(sK2(sK0),sK0) ),
    inference(superposition,[],[f68,f104]) ).

fof(f104,plain,
    zero = multiplication(sK0,sK2(sK0)),
    inference(resolution,[],[f85,f49]) ).

fof(f85,plain,
    ! [X0] :
      ( ~ test(X0)
      | zero = multiplication(X0,sK2(X0)) ),
    inference(resolution,[],[f65,f58]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( ~ complement(X1,X0)
      | zero = multiplication(X0,X1) ),
    inference(cnf_transformation,[],[f47]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( zero != multiplication(X1,X0)
      | addition(X0,X1) != one
      | complement(X1,X0)
      | zero != multiplication(X0,X1) ),
    inference(cnf_transformation,[],[f47]) ).

fof(f137,plain,
    one = addition(sK0,sK2(sK0)),
    inference(resolution,[],[f89,f49]) ).

fof(f89,plain,
    ! [X0] :
      ( ~ test(X0)
      | one = addition(X0,sK2(X0)) ),
    inference(resolution,[],[f67,f58]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( ~ complement(X1,X0)
      | addition(X0,X1) = one ),
    inference(cnf_transformation,[],[f47]) ).

fof(f6195,plain,
    ( ~ leq(addition(sK0,c(sK0)),one)
    | spl3_5 ),
    inference(forward_demodulation,[],[f6194,f54]) ).

fof(f54,plain,
    ! [X0] : multiplication(X0,one) = X0,
    inference(cnf_transformation,[],[f6]) ).

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

fof(f6194,plain,
    ( ~ leq(addition(sK0,multiplication(c(sK0),one)),one)
    | spl3_5 ),
    inference(forward_demodulation,[],[f6193,f1200]) ).

fof(f1200,plain,
    one = addition(sK1,c(sK1)),
    inference(superposition,[],[f138,f1132]) ).

fof(f1132,plain,
    c(sK1) = sK2(sK1),
    inference(subsumption_resolution,[],[f1127,f48]) ).

fof(f48,plain,
    test(sK1),
    inference(cnf_transformation,[],[f40]) ).

fof(f1127,plain,
    ( c(sK1) = sK2(sK1)
    | ~ test(sK1) ),
    inference(resolution,[],[f1105,f62]) ).

fof(f1105,plain,
    complement(sK1,sK2(sK1)),
    inference(subsumption_resolution,[],[f1104,f138]) ).

fof(f1104,plain,
    ( one != addition(sK1,sK2(sK1))
    | complement(sK1,sK2(sK1)) ),
    inference(forward_demodulation,[],[f1103,f60]) ).

fof(f1103,plain,
    ( one != addition(sK2(sK1),sK1)
    | complement(sK1,sK2(sK1)) ),
    inference(subsumption_resolution,[],[f1004,f113]) ).

fof(f113,plain,
    zero = multiplication(sK2(sK1),sK1),
    inference(resolution,[],[f87,f48]) ).

fof(f1004,plain,
    ( one != addition(sK2(sK1),sK1)
    | complement(sK1,sK2(sK1))
    | zero != multiplication(sK2(sK1),sK1) ),
    inference(trivial_inequality_removal,[],[f995]) ).

fof(f995,plain,
    ( zero != zero
    | one != addition(sK2(sK1),sK1)
    | complement(sK1,sK2(sK1))
    | zero != multiplication(sK2(sK1),sK1) ),
    inference(superposition,[],[f68,f105]) ).

fof(f105,plain,
    zero = multiplication(sK1,sK2(sK1)),
    inference(resolution,[],[f85,f48]) ).

fof(f138,plain,
    one = addition(sK1,sK2(sK1)),
    inference(resolution,[],[f89,f48]) ).

fof(f6193,plain,
    ( ~ leq(addition(sK0,multiplication(c(sK0),addition(sK1,c(sK1)))),one)
    | spl3_5 ),
    inference(forward_demodulation,[],[f6192,f72]) ).

fof(f72,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/sandbox/benchmark/theBenchmark.p',right_distributivity) ).

fof(f6192,plain,
    ( ~ leq(addition(sK0,addition(multiplication(c(sK0),sK1),multiplication(c(sK0),c(sK1)))),one)
    | spl3_5 ),
    inference(forward_demodulation,[],[f6191,f60]) ).

fof(f6191,plain,
    ( ~ leq(addition(sK0,addition(multiplication(c(sK0),c(sK1)),multiplication(c(sK0),sK1))),one)
    | spl3_5 ),
    inference(forward_demodulation,[],[f6109,f126]) ).

fof(f126,plain,
    ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
    inference(superposition,[],[f70,f60]) ).

fof(f70,plain,
    ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,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/sandbox/benchmark/theBenchmark.p',additive_associativity) ).

fof(f6109,plain,
    ( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),sK0)),one)
    | spl3_5 ),
    inference(superposition,[],[f1300,f5949]) ).

fof(f5949,plain,
    ! [X0] : addition(X0,multiplication(X0,sK1)) = X0,
    inference(forward_demodulation,[],[f5857,f54]) ).

fof(f5857,plain,
    ! [X0] : multiplication(X0,one) = addition(X0,multiplication(X0,sK1)),
    inference(superposition,[],[f285,f1638]) ).

fof(f1638,plain,
    one = addition(one,sK1),
    inference(superposition,[],[f1607,f60]) ).

fof(f1607,plain,
    one = addition(sK1,one),
    inference(superposition,[],[f119,f138]) ).

fof(f119,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
    inference(superposition,[],[f70,f56]) ).

fof(f285,plain,
    ! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
    inference(superposition,[],[f72,f54]) ).

fof(f1300,plain,
    ( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(sK0,multiplication(sK0,sK1)))),one)
    | spl3_5 ),
    inference(forward_demodulation,[],[f1299,f55]) ).

fof(f55,plain,
    ! [X0] : multiplication(one,X0) = X0,
    inference(cnf_transformation,[],[f7]) ).

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

fof(f1299,plain,
    ( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(one,sK0),multiplication(sK0,sK1)))),one)
    | spl3_5 ),
    inference(forward_demodulation,[],[f1298,f60]) ).

fof(f1298,plain,
    ( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(one,sK0)))),one)
    | spl3_5 ),
    inference(forward_demodulation,[],[f1240,f1200]) ).

fof(f1240,plain,
    ( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)))),one)
    | spl3_5 ),
    inference(avatar_component_clause,[],[f1238]) ).

fof(f1238,plain,
    ( spl3_5
  <=> leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)))),one) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

fof(f6190,plain,
    spl3_6,
    inference(avatar_contradiction_clause,[],[f6189]) ).

fof(f6189,plain,
    ( $false
    | spl3_6 ),
    inference(subsumption_resolution,[],[f6188,f98]) ).

fof(f6188,plain,
    ( ~ leq(one,one)
    | spl3_6 ),
    inference(forward_demodulation,[],[f6187,f1154]) ).

fof(f6187,plain,
    ( ~ leq(one,addition(sK0,c(sK0)))
    | spl3_6 ),
    inference(forward_demodulation,[],[f6186,f54]) ).

fof(f6186,plain,
    ( ~ leq(one,addition(sK0,multiplication(c(sK0),one)))
    | spl3_6 ),
    inference(forward_demodulation,[],[f6185,f1200]) ).

fof(f6185,plain,
    ( ~ leq(one,addition(sK0,multiplication(c(sK0),addition(sK1,c(sK1)))))
    | spl3_6 ),
    inference(forward_demodulation,[],[f6184,f72]) ).

fof(f6184,plain,
    ( ~ leq(one,addition(sK0,addition(multiplication(c(sK0),sK1),multiplication(c(sK0),c(sK1)))))
    | spl3_6 ),
    inference(forward_demodulation,[],[f6183,f60]) ).

fof(f6183,plain,
    ( ~ leq(one,addition(sK0,addition(multiplication(c(sK0),c(sK1)),multiplication(c(sK0),sK1))))
    | spl3_6 ),
    inference(forward_demodulation,[],[f6108,f126]) ).

fof(f6108,plain,
    ( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),sK0)))
    | spl3_6 ),
    inference(superposition,[],[f1337,f5949]) ).

fof(f1337,plain,
    ( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(sK0,multiplication(sK0,sK1)))))
    | spl3_6 ),
    inference(forward_demodulation,[],[f1336,f55]) ).

fof(f1336,plain,
    ( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(one,sK0),multiplication(sK0,sK1)))))
    | spl3_6 ),
    inference(forward_demodulation,[],[f1335,f60]) ).

fof(f1335,plain,
    ( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(one,sK0)))))
    | spl3_6 ),
    inference(forward_demodulation,[],[f1244,f1200]) ).

fof(f1244,plain,
    ( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)))))
    | spl3_6 ),
    inference(avatar_component_clause,[],[f1242]) ).

fof(f1242,plain,
    ( spl3_6
  <=> leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).

fof(f1652,plain,
    spl3_3,
    inference(avatar_contradiction_clause,[],[f1651]) ).

fof(f1651,plain,
    ( $false
    | spl3_3 ),
    inference(subsumption_resolution,[],[f1649,f156]) ).

fof(f156,plain,
    ( ~ leq(sK1,one)
    | spl3_3 ),
    inference(avatar_component_clause,[],[f155]) ).

fof(f155,plain,
    ( spl3_3
  <=> leq(sK1,one) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

fof(f1649,plain,
    leq(sK1,one),
    inference(trivial_inequality_removal,[],[f1646]) ).

fof(f1646,plain,
    ( one != one
    | leq(sK1,one) ),
    inference(superposition,[],[f69,f1607]) ).

fof(f1379,plain,
    ( spl3_7
    | ~ spl3_9 ),
    inference(avatar_contradiction_clause,[],[f1378]) ).

fof(f1378,plain,
    ( $false
    | spl3_7
    | ~ spl3_9 ),
    inference(subsumption_resolution,[],[f1375,f97]) ).

fof(f97,plain,
    ! [X0] : leq(zero,X0),
    inference(trivial_inequality_removal,[],[f96]) ).

fof(f96,plain,
    ! [X0] :
      ( X0 != X0
      | leq(zero,X0) ),
    inference(superposition,[],[f69,f77]) ).

fof(f77,plain,
    ! [X0] : addition(zero,X0) = X0,
    inference(superposition,[],[f60,f53]) ).

fof(f53,plain,
    ! [X0] : addition(X0,zero) = X0,
    inference(cnf_transformation,[],[f3]) ).

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

fof(f1375,plain,
    ( ~ leq(zero,one)
    | spl3_7
    | ~ spl3_9 ),
    inference(superposition,[],[f1313,f1374]) ).

fof(f1374,plain,
    ( zero = c(one)
    | ~ spl3_9 ),
    inference(subsumption_resolution,[],[f1369,f1353]) ).

fof(f1353,plain,
    test(one),
    inference(equality_resolution,[],[f1351]) ).

fof(f1351,plain,
    ! [X0] :
      ( one != X0
      | test(X0) ),
    inference(resolution,[],[f1034,f59]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( ~ complement(X1,X0)
      | test(X0) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f1034,plain,
    ! [X0] :
      ( complement(zero,X0)
      | one != X0 ),
    inference(forward_demodulation,[],[f1033,f53]) ).

fof(f1033,plain,
    ! [X0] :
      ( addition(X0,zero) != one
      | complement(zero,X0) ),
    inference(subsumption_resolution,[],[f1016,f51]) ).

fof(f51,plain,
    ! [X0] : zero = multiplication(X0,zero),
    inference(cnf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0] : zero = multiplication(X0,zero),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).

fof(f1016,plain,
    ! [X0] :
      ( addition(X0,zero) != one
      | complement(zero,X0)
      | zero != multiplication(X0,zero) ),
    inference(trivial_inequality_removal,[],[f969]) ).

fof(f969,plain,
    ! [X0] :
      ( zero != zero
      | addition(X0,zero) != one
      | complement(zero,X0)
      | zero != multiplication(X0,zero) ),
    inference(superposition,[],[f68,f52]) ).

fof(f52,plain,
    ! [X0] : zero = multiplication(zero,X0),
    inference(cnf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0] : zero = multiplication(zero,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).

fof(f1369,plain,
    ( zero = c(one)
    | ~ test(one)
    | ~ spl3_9 ),
    inference(resolution,[],[f1368,f62]) ).

fof(f1368,plain,
    ( complement(one,zero)
    | ~ spl3_9 ),
    inference(subsumption_resolution,[],[f1367,f1330]) ).

fof(f1330,plain,
    ( test(zero)
    | ~ spl3_9 ),
    inference(avatar_component_clause,[],[f1328]) ).

fof(f1328,plain,
    ( spl3_9
  <=> test(zero) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).

fof(f1367,plain,
    ( complement(one,zero)
    | ~ test(zero)
    | ~ spl3_9 ),
    inference(superposition,[],[f58,f1362]) ).

fof(f1362,plain,
    ( one = sK2(zero)
    | ~ spl3_9 ),
    inference(superposition,[],[f1344,f77]) ).

fof(f1344,plain,
    ( one = addition(zero,sK2(zero))
    | ~ spl3_9 ),
    inference(resolution,[],[f1330,f89]) ).

fof(f1313,plain,
    ( ~ leq(c(one),one)
    | spl3_7 ),
    inference(avatar_component_clause,[],[f1312]) ).

fof(f1312,plain,
    ( spl3_7
  <=> leq(c(one),one) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).

fof(f1334,plain,
    ( spl3_9
    | spl3_10 ),
    inference(avatar_split_clause,[],[f1325,f1332,f1328]) ).

fof(f1332,plain,
    ( spl3_10
  <=> ! [X0] : one != X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).

fof(f1325,plain,
    ! [X0] :
      ( one != X0
      | test(zero) ),
    inference(resolution,[],[f1019,f59]) ).

fof(f1019,plain,
    ! [X0] :
      ( complement(X0,zero)
      | one != X0 ),
    inference(forward_demodulation,[],[f1018,f77]) ).

fof(f1018,plain,
    ! [X0] :
      ( one != addition(zero,X0)
      | complement(X0,zero) ),
    inference(subsumption_resolution,[],[f1017,f52]) ).

fof(f1017,plain,
    ! [X0] :
      ( one != addition(zero,X0)
      | complement(X0,zero)
      | zero != multiplication(zero,X0) ),
    inference(trivial_inequality_removal,[],[f959]) ).

fof(f959,plain,
    ! [X0] :
      ( zero != zero
      | one != addition(zero,X0)
      | complement(X0,zero)
      | zero != multiplication(zero,X0) ),
    inference(superposition,[],[f68,f51]) ).

fof(f1319,plain,
    ( spl3_7
    | ~ spl3_8 ),
    inference(avatar_split_clause,[],[f1262,f1316,f1312]) ).

fof(f1316,plain,
    ( spl3_8
  <=> one = sK0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).

fof(f1262,plain,
    ( one != sK0
    | leq(c(one),one) ),
    inference(inner_rewriting,[],[f1256]) ).

fof(f1256,plain,
    ( one != sK0
    | leq(c(sK0),sK0) ),
    inference(superposition,[],[f69,f1248]) ).

fof(f1248,plain,
    one = addition(c(sK0),sK0),
    inference(forward_demodulation,[],[f1115,f1119]) ).

fof(f1115,plain,
    one = addition(sK2(sK0),sK0),
    inference(resolution,[],[f1074,f67]) ).

fof(f1245,plain,
    ( ~ spl3_5
    | ~ spl3_6 ),
    inference(avatar_split_clause,[],[f1197,f1242,f1238]) ).

fof(f1197,plain,
    ( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)))))
    | ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)))),one) ),
    inference(forward_demodulation,[],[f1196,f73]) ).

fof(f73,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/sandbox/benchmark/theBenchmark.p',left_distributivity) ).

fof(f1196,plain,
    ( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0))))))
    | ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)))),one) ),
    inference(forward_demodulation,[],[f1195,f60]) ).

fof(f1195,plain,
    ( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)))))
    | ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)))),one) ),
    inference(forward_demodulation,[],[f1194,f60]) ).

fof(f1194,plain,
    ( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1))))
    | ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)))),one) ),
    inference(forward_demodulation,[],[f1193,f60]) ).

fof(f1193,plain,
    ( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)))),one)
    | ~ leq(one,addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1)))) ),
    inference(forward_demodulation,[],[f1192,f73]) ).

fof(f1192,plain,
    ( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0))))),one)
    | ~ leq(one,addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1)))) ),
    inference(forward_demodulation,[],[f1191,f60]) ).

fof(f1191,plain,
    ( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)))),one)
    | ~ leq(one,addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1)))) ),
    inference(forward_demodulation,[],[f1190,f60]) ).

fof(f1190,plain,
    ( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1))),one)
    | ~ leq(one,addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1)))) ),
    inference(forward_demodulation,[],[f50,f60]) ).

fof(f50,plain,
    ( ~ leq(addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),one)
    | ~ leq(one,addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1)))) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f829,plain,
    spl3_1,
    inference(avatar_contradiction_clause,[],[f828]) ).

fof(f828,plain,
    ( $false
    | spl3_1 ),
    inference(subsumption_resolution,[],[f827,f147]) ).

fof(f147,plain,
    ( ~ leq(sK0,one)
    | spl3_1 ),
    inference(avatar_component_clause,[],[f146]) ).

fof(f146,plain,
    ( spl3_1
  <=> leq(sK0,one) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f827,plain,
    leq(sK0,one),
    inference(trivial_inequality_removal,[],[f824]) ).

fof(f824,plain,
    ( one != one
    | leq(sK0,one) ),
    inference(superposition,[],[f69,f817]) ).

fof(f817,plain,
    one = addition(sK0,one),
    inference(forward_demodulation,[],[f811,f56]) ).

fof(f811,plain,
    addition(one,one) = addition(sK0,one),
    inference(superposition,[],[f165,f170]) ).

fof(f170,plain,
    one = addition(one,sK2(sK0)),
    inference(forward_demodulation,[],[f164,f137]) ).

fof(f164,plain,
    addition(sK0,sK2(sK0)) = addition(one,sK2(sK0)),
    inference(superposition,[],[f139,f56]) ).

fof(f139,plain,
    ! [X0] : addition(sK0,addition(sK2(sK0),X0)) = addition(one,X0),
    inference(superposition,[],[f70,f137]) ).

fof(f165,plain,
    ! [X0] : addition(one,X0) = addition(sK0,addition(X0,sK2(sK0))),
    inference(superposition,[],[f139,f60]) ).

fof(f162,plain,
    ( spl3_3
    | ~ spl3_4 ),
    inference(avatar_split_clause,[],[f144,f159,f155]) ).

fof(f159,plain,
    ( spl3_4
  <=> one = sK2(sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

fof(f144,plain,
    ( one != sK2(sK1)
    | leq(sK1,one) ),
    inference(inner_rewriting,[],[f143]) ).

fof(f143,plain,
    ( one != sK2(sK1)
    | leq(sK1,sK2(sK1)) ),
    inference(superposition,[],[f69,f138]) ).

fof(f153,plain,
    ( spl3_1
    | ~ spl3_2 ),
    inference(avatar_split_clause,[],[f141,f150,f146]) ).

fof(f150,plain,
    ( spl3_2
  <=> one = sK2(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f141,plain,
    ( one != sK2(sK0)
    | leq(sK0,one) ),
    inference(inner_rewriting,[],[f140]) ).

fof(f140,plain,
    ( one != sK2(sK0)
    | leq(sK0,sK2(sK0)) ),
    inference(superposition,[],[f69,f137]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem    : KLE010+4 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n009.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 Apr 30 04:57:11 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.34  % (27469)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36  % (27474)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)
% 0.13/0.36  % (27472)WARNING: value z3 for option sas not known
% 0.13/0.36  % (27470)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.36  % (27471)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.36  % (27472)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)
% 0.13/0.36  % (27473)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36  % (27475)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)
% 0.13/0.36  % (27476)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)
% 0.13/0.37  TRYING [1]
% 0.13/0.37  TRYING [2]
% 0.13/0.37  TRYING [3]
% 0.13/0.37  TRYING [1]
% 0.13/0.37  TRYING [2]
% 0.13/0.38  TRYING [4]
% 0.19/0.39  TRYING [3]
% 0.19/0.41  TRYING [5]
% 0.19/0.43  TRYING [4]
% 0.19/0.49  % (27472)First to succeed.
% 0.19/0.49  % (27472)Refutation found. Thanks to Tanya!
% 0.19/0.49  % SZS status Theorem for theBenchmark
% 0.19/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.49  % (27472)------------------------------
% 0.19/0.49  % (27472)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.19/0.49  % (27472)Termination reason: Refutation
% 0.19/0.49  
% 0.19/0.49  % (27472)Memory used [KB]: 2474
% 0.19/0.49  % (27472)Time elapsed: 0.128 s
% 0.19/0.49  % (27472)Instructions burned: 280 (million)
% 0.19/0.49  % (27472)------------------------------
% 0.19/0.49  % (27472)------------------------------
% 0.19/0.49  % (27469)Success in time 0.144 s
%------------------------------------------------------------------------------