TSTP Solution File: KLE025+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : KLE025+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n024.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 : Fri Sep  1 17:09:06 EDT 2023

% Result   : Theorem 0.23s 0.47s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   67 (  30 unt;   0 def)
%            Number of atoms       :  158 (  88 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  143 (  52   ~;  42   |;  32   &)
%                                         (   7 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :   87 (;  73   !;  14   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1467,plain,
    $false,
    inference(trivial_inequality_removal,[],[f1459]) ).

fof(f1459,plain,
    multiplication(sK1,sK0) != multiplication(sK1,sK0),
    inference(superposition,[],[f209,f1445]) ).

fof(f1445,plain,
    multiplication(sK1,sK0) = multiplication(sK1,multiplication(sK0,sK2)),
    inference(forward_demodulation,[],[f1444,f46]) ).

fof(f46,plain,
    ! [X0] : multiplication(X0,one) = X0,
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] : multiplication(X0,one) = X0,
    file('/export/starexec/sandbox/tmp/tmp.OJaohSbceY/Vampire---4.8_3863',multiplicative_right_identity) ).

fof(f1444,plain,
    multiplication(sK1,multiplication(sK0,sK2)) = multiplication(sK1,multiplication(sK0,one)),
    inference(forward_demodulation,[],[f1430,f62]) ).

fof(f62,plain,
    ! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
    inference(cnf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
    file('/export/starexec/sandbox/tmp/tmp.OJaohSbceY/Vampire---4.8_3863',multiplicative_associativity) ).

fof(f1430,plain,
    multiplication(sK1,multiplication(sK0,sK2)) = multiplication(multiplication(sK1,sK0),one),
    inference(superposition,[],[f338,f936]) ).

fof(f936,plain,
    one = addition(c(sK2),sK2),
    inference(forward_demodulation,[],[f894,f893]) ).

fof(f893,plain,
    c(sK2) = sK3(sK2),
    inference(resolution,[],[f825,f119]) ).

fof(f119,plain,
    ! [X1] :
      ( ~ complement(sK2,X1)
      | c(sK2) = X1 ),
    inference(resolution,[],[f54,f40]) ).

fof(f40,plain,
    test(sK2),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    ( multiplication(sK1,sK0) != multiplication(multiplication(sK1,sK0),sK2)
    & zero = multiplication(multiplication(sK1,sK0),c(sK2))
    & test(sK2)
    & test(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f26,f29]) ).

fof(f29,plain,
    ( ? [X0,X1,X2] :
        ( multiplication(X1,X0) != multiplication(multiplication(X1,X0),X2)
        & zero = multiplication(multiplication(X1,X0),c(X2))
        & test(X2)
        & test(X1) )
   => ( multiplication(sK1,sK0) != multiplication(multiplication(sK1,sK0),sK2)
      & zero = multiplication(multiplication(sK1,sK0),c(sK2))
      & test(sK2)
      & test(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ? [X0,X1,X2] :
      ( multiplication(X1,X0) != multiplication(multiplication(X1,X0),X2)
      & zero = multiplication(multiplication(X1,X0),c(X2))
      & test(X2)
      & test(X1) ),
    inference(flattening,[],[f25]) ).

fof(f25,plain,
    ? [X0,X1,X2] :
      ( multiplication(X1,X0) != multiplication(multiplication(X1,X0),X2)
      & zero = multiplication(multiplication(X1,X0),c(X2))
      & test(X2)
      & test(X1) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,plain,
    ~ ! [X0,X1,X2] :
        ( ( test(X2)
          & test(X1) )
       => ( zero = multiplication(multiplication(X1,X0),c(X2))
         => multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) ) ),
    inference(rectify,[],[f18]) ).

fof(f18,negated_conjecture,
    ~ ! [X3,X4,X5] :
        ( ( test(X5)
          & test(X4) )
       => ( zero = multiplication(multiplication(X4,X3),c(X5))
         => multiplication(X4,X3) = multiplication(multiplication(X4,X3),X5) ) ),
    inference(negated_conjecture,[],[f17]) ).

fof(f17,conjecture,
    ! [X3,X4,X5] :
      ( ( test(X5)
        & test(X4) )
     => ( zero = multiplication(multiplication(X4,X3),c(X5))
       => multiplication(X4,X3) = multiplication(multiplication(X4,X3),X5) ) ),
    file('/export/starexec/sandbox/tmp/tmp.OJaohSbceY/Vampire---4.8_3863',goals) ).

fof(f54,plain,
    ! [X0,X1] :
      ( ~ test(X0)
      | ~ complement(X0,X1)
      | c(X0) = X1 ),
    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/sandbox/tmp/tmp.OJaohSbceY/Vampire---4.8_3863',test_3) ).

fof(f825,plain,
    complement(sK2,sK3(sK2)),
    inference(trivial_inequality_removal,[],[f824]) ).

fof(f824,plain,
    ( zero != zero
    | complement(sK2,sK3(sK2)) ),
    inference(forward_demodulation,[],[f823,f98]) ).

fof(f98,plain,
    zero = multiplication(sK3(sK2),sK2),
    inference(resolution,[],[f84,f40]) ).

fof(f84,plain,
    ! [X0] :
      ( ~ test(X0)
      | zero = multiplication(sK3(X0),X0) ),
    inference(resolution,[],[f58,f50]) ).

fof(f50,plain,
    ! [X0] :
      ( complement(sK3(X0),X0)
      | ~ test(X0) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0] :
      ( ( test(X0)
        | ! [X1] : ~ complement(X1,X0) )
      & ( complement(sK3(X0),X0)
        | ~ test(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f32,f33]) ).

fof(f33,plain,
    ! [X0] :
      ( ? [X2] : complement(X2,X0)
     => complement(sK3(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/sandbox/tmp/tmp.OJaohSbceY/Vampire---4.8_3863',test_1) ).

fof(f58,plain,
    ! [X0,X1] :
      ( ~ complement(X1,X0)
      | zero = multiplication(X1,X0) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,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,[],[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(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/sandbox/tmp/tmp.OJaohSbceY/Vampire---4.8_3863',test_2) ).

fof(f823,plain,
    ( complement(sK2,sK3(sK2))
    | zero != multiplication(sK3(sK2),sK2) ),
    inference(trivial_inequality_removal,[],[f822]) ).

fof(f822,plain,
    ( one != one
    | complement(sK2,sK3(sK2))
    | zero != multiplication(sK3(sK2),sK2) ),
    inference(forward_demodulation,[],[f821,f107]) ).

fof(f107,plain,
    one = addition(sK2,sK3(sK2)),
    inference(resolution,[],[f85,f40]) ).

fof(f85,plain,
    ! [X0] :
      ( ~ test(X0)
      | one = addition(X0,sK3(X0)) ),
    inference(resolution,[],[f59,f50]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( ~ complement(X1,X0)
      | addition(X0,X1) = one ),
    inference(cnf_transformation,[],[f38]) ).

fof(f821,plain,
    ( one != addition(sK2,sK3(sK2))
    | complement(sK2,sK3(sK2))
    | zero != multiplication(sK3(sK2),sK2) ),
    inference(forward_demodulation,[],[f769,f52]) ).

fof(f52,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/tmp/tmp.OJaohSbceY/Vampire---4.8_3863',additive_commutativity) ).

fof(f769,plain,
    ( one != addition(sK3(sK2),sK2)
    | complement(sK2,sK3(sK2))
    | zero != multiplication(sK3(sK2),sK2) ),
    inference(trivial_inequality_removal,[],[f754]) ).

fof(f754,plain,
    ( zero != zero
    | one != addition(sK3(sK2),sK2)
    | complement(sK2,sK3(sK2))
    | zero != multiplication(sK3(sK2),sK2) ),
    inference(superposition,[],[f60,f94]) ).

fof(f94,plain,
    zero = multiplication(sK2,sK3(sK2)),
    inference(resolution,[],[f82,f40]) ).

fof(f82,plain,
    ! [X0] :
      ( ~ test(X0)
      | zero = multiplication(X0,sK3(X0)) ),
    inference(resolution,[],[f57,f50]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( ~ complement(X1,X0)
      | zero = multiplication(X0,X1) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( zero != multiplication(X1,X0)
      | addition(X0,X1) != one
      | complement(X1,X0)
      | zero != multiplication(X0,X1) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f894,plain,
    one = addition(sK3(sK2),sK2),
    inference(resolution,[],[f825,f59]) ).

fof(f338,plain,
    ! [X6] : multiplication(multiplication(sK1,sK0),addition(c(sK2),X6)) = multiplication(sK1,multiplication(sK0,X6)),
    inference(forward_demodulation,[],[f337,f62]) ).

fof(f337,plain,
    ! [X6] : multiplication(multiplication(sK1,sK0),addition(c(sK2),X6)) = multiplication(multiplication(sK1,sK0),X6),
    inference(forward_demodulation,[],[f286,f65]) ).

fof(f65,plain,
    ! [X0] : addition(zero,X0) = X0,
    inference(superposition,[],[f52,f45]) ).

fof(f45,plain,
    ! [X0] : addition(X0,zero) = X0,
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] : addition(X0,zero) = X0,
    file('/export/starexec/sandbox/tmp/tmp.OJaohSbceY/Vampire---4.8_3863',additive_identity) ).

fof(f286,plain,
    ! [X6] : multiplication(multiplication(sK1,sK0),addition(c(sK2),X6)) = addition(zero,multiplication(multiplication(sK1,sK0),X6)),
    inference(superposition,[],[f63,f41]) ).

fof(f41,plain,
    zero = multiplication(multiplication(sK1,sK0),c(sK2)),
    inference(cnf_transformation,[],[f30]) ).

fof(f63,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/tmp/tmp.OJaohSbceY/Vampire---4.8_3863',right_distributivity) ).

fof(f209,plain,
    multiplication(sK1,sK0) != multiplication(sK1,multiplication(sK0,sK2)),
    inference(superposition,[],[f42,f62]) ).

fof(f42,plain,
    multiplication(sK1,sK0) != multiplication(multiplication(sK1,sK0),sK2),
    inference(cnf_transformation,[],[f30]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : KLE025+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.15  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36  % Computer : n024.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   : Wed Aug 30 17:46:22 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.23/0.42  % (4110)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.43  % (4156)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.23/0.43  % (4157)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.23/0.43  % (4159)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.23/0.43  % (4158)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 Vampire---4 for (569ds/0Mi)
% 0.23/0.43  % (4161)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 Vampire---4 for (522ds/0Mi)
% 0.23/0.43  % (4162)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 Vampire---4 for (497ds/0Mi)
% 0.23/0.43  % (4160)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 Vampire---4 for (531ds/0Mi)
% 0.23/0.43  TRYING [1]
% 0.23/0.43  TRYING [2]
% 0.23/0.43  TRYING [3]
% 0.23/0.43  TRYING [1]
% 0.23/0.43  TRYING [2]
% 0.23/0.44  TRYING [4]
% 0.23/0.45  TRYING [3]
% 0.23/0.47  % (4161)First to succeed.
% 0.23/0.47  TRYING [5]
% 0.23/0.47  % (4161)Refutation found. Thanks to Tanya!
% 0.23/0.47  % SZS status Theorem for Vampire---4
% 0.23/0.47  % SZS output start Proof for Vampire---4
% See solution above
% 0.23/0.47  % (4161)------------------------------
% 0.23/0.47  % (4161)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.47  % (4161)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.47  % (4161)Termination reason: Refutation
% 0.23/0.47  
% 0.23/0.47  % (4161)Memory used [KB]: 1918
% 0.23/0.47  % (4161)Time elapsed: 0.042 s
% 0.23/0.47  % (4161)------------------------------
% 0.23/0.47  % (4161)------------------------------
% 0.23/0.47  % (4110)Success in time 0.103 s
% 0.23/0.47  % Vampire---4.8 exiting
%------------------------------------------------------------------------------