TSTP Solution File: KLE025+2 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : KLE025+2 : 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 : n020.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 : Thu Aug 31 05:36:25 EDT 2023

% Result   : Theorem 0.23s 0.45s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   46 (  27 unt;   0 def)
%            Number of atoms       :  106 (  65 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   86 (  26   ~;  17   |;  29   &)
%                                         (   5 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   9 con; 0-2 aty)
%            Number of variables   :   56 (;  47   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f562,plain,
    $false,
    inference(subsumption_resolution,[],[f555,f75]) ).

fof(f75,plain,
    sF4 != sF5,
    inference(definition_folding,[],[f49,f74,f73,f73]) ).

fof(f73,plain,
    multiplication(sK1,sK0) = sF4,
    introduced(function_definition,[]) ).

fof(f74,plain,
    multiplication(sF4,sK2) = sF5,
    introduced(function_definition,[]) ).

fof(f49,plain,
    multiplication(sK1,sK0) != multiplication(multiplication(sK1,sK0),sK2),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,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])],[f30,f37]) ).

fof(f37,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(f30,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,[],[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) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,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,[],[f20]) ).

fof(f20,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,[],[f19]) ).

fof(f19,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/sandbox2/tmp/tmp.3d8Ca14Svo/Vampire---4.8_2801',goals) ).

fof(f555,plain,
    sF4 = sF5,
    inference(backward_demodulation,[],[f74,f549]) ).

fof(f549,plain,
    sF4 = multiplication(sF4,sK2),
    inference(forward_demodulation,[],[f539,f53]) ).

fof(f53,plain,
    ! [X0] : multiplication(X0,one) = X0,
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] : multiplication(X0,one) = X0,
    file('/export/starexec/sandbox2/tmp/tmp.3d8Ca14Svo/Vampire---4.8_2801',multiplicative_right_identity) ).

fof(f539,plain,
    multiplication(sF4,sK2) = multiplication(sF4,one),
    inference(superposition,[],[f236,f98]) ).

fof(f98,plain,
    one = addition(sF6,sK2),
    inference(resolution,[],[f66,f81]) ).

fof(f81,plain,
    complement(sK2,sF6),
    inference(subsumption_resolution,[],[f80,f47]) ).

fof(f47,plain,
    test(sK2),
    inference(cnf_transformation,[],[f38]) ).

fof(f80,plain,
    ( complement(sK2,sF6)
    | ~ test(sK2) ),
    inference(superposition,[],[f72,f76]) ).

fof(f76,plain,
    c(sK2) = sF6,
    introduced(function_definition,[]) ).

fof(f72,plain,
    ! [X0] :
      ( complement(X0,c(X0))
      | ~ test(X0) ),
    inference(equality_resolution,[],[f60]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( complement(X0,X1)
      | c(X0) != X1
      | ~ test(X0) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( ( ( c(X0) = X1
          | ~ complement(X0,X1) )
        & ( complement(X0,X1)
          | c(X0) != X1 ) )
      | ~ test(X0) ),
    inference(nnf_transformation,[],[f32]) ).

fof(f32,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/sandbox2/tmp/tmp.3d8Ca14Svo/Vampire---4.8_2801',test_3) ).

fof(f66,plain,
    ! [X0,X1] :
      ( ~ complement(X1,X0)
      | addition(X0,X1) = one ),
    inference(cnf_transformation,[],[f45]) ).

fof(f45,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,[],[f44]) ).

fof(f44,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/sandbox2/tmp/tmp.3d8Ca14Svo/Vampire---4.8_2801',test_2) ).

fof(f236,plain,
    ! [X20] : multiplication(sF4,addition(sF6,X20)) = multiplication(sF4,X20),
    inference(forward_demodulation,[],[f198,f82]) ).

fof(f82,plain,
    ! [X0] : addition(zero,X0) = X0,
    inference(superposition,[],[f59,f52]) ).

fof(f52,plain,
    ! [X0] : addition(X0,zero) = X0,
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] : addition(X0,zero) = X0,
    file('/export/starexec/sandbox2/tmp/tmp.3d8Ca14Svo/Vampire---4.8_2801',additive_identity) ).

fof(f59,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/tmp/tmp.3d8Ca14Svo/Vampire---4.8_2801',additive_commutativity) ).

fof(f198,plain,
    ! [X20] : multiplication(sF4,addition(sF6,X20)) = addition(zero,multiplication(sF4,X20)),
    inference(superposition,[],[f70,f79]) ).

fof(f79,plain,
    zero = multiplication(sF4,sF6),
    inference(forward_demodulation,[],[f77,f78]) ).

fof(f78,plain,
    zero = sF7,
    inference(definition_folding,[],[f48,f77,f76,f73]) ).

fof(f48,plain,
    zero = multiplication(multiplication(sK1,sK0),c(sK2)),
    inference(cnf_transformation,[],[f38]) ).

fof(f77,plain,
    multiplication(sF4,sF6) = sF7,
    introduced(function_definition,[]) ).

fof(f70,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/tmp/tmp.3d8Ca14Svo/Vampire---4.8_2801',right_distributivity) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem    : KLE025+2 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.15  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.37  % Computer : n020.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit   : 300
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Tue Aug 29 11:23:29 EDT 2023
% 0.15/0.37  % CPUTime    : 
% 0.15/0.37  This is a FOF_THM_RFO_SEQ problem
% 0.15/0.37  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.3d8Ca14Svo/Vampire---4.8_2801
% 0.15/0.38  % (3002)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.44  % (3005)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_730 on Vampire---4 for (730ds/0Mi)
% 0.23/0.44  % (3008)lrs-3_8_anc=none:bce=on:cond=on:drc=off:flr=on:fsd=off:fsr=off:fde=unused:gsp=on:gs=on:gsaa=full_model:lcm=predicate:lma=on:nm=16:sos=all:sp=weighted_frequency:tgt=ground:urr=ec_only:stl=188_482 on Vampire---4 for (482ds/0Mi)
% 0.23/0.44  % (3009)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_424 on Vampire---4 for (424ds/0Mi)
% 0.23/0.44  % (3006)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_680 on Vampire---4 for (680ds/0Mi)
% 0.23/0.44  % (3010)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.23/0.44  % (3011)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_386 on Vampire---4 for (386ds/0Mi)
% 0.23/0.44  % (3007)dis-11_4:1_aac=none:add=off:afr=on:anc=none:bd=preordered:bs=on:bsr=on:drc=off:fsr=off:fde=none:gsp=on:irw=on:lcm=reverse:lma=on:nm=0:nwc=1.7:nicw=on:sas=z3:sims=off:sos=all:sac=on:sp=weighted_frequency:tgt=full_602 on Vampire---4 for (602ds/0Mi)
% 0.23/0.45  % (3010)First to succeed.
% 0.23/0.45  % (3010)Refutation found. Thanks to Tanya!
% 0.23/0.45  % SZS status Theorem for Vampire---4
% 0.23/0.45  % SZS output start Proof for Vampire---4
% See solution above
% 0.23/0.46  % (3010)------------------------------
% 0.23/0.46  % (3010)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.46  % (3010)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.46  % (3010)Termination reason: Refutation
% 0.23/0.46  
% 0.23/0.46  % (3010)Memory used [KB]: 5756
% 0.23/0.46  % (3010)Time elapsed: 0.017 s
% 0.23/0.46  % (3010)------------------------------
% 0.23/0.46  % (3010)------------------------------
% 0.23/0.46  % (3002)Success in time 0.076 s
% 0.23/0.46  % Vampire---4.8 exiting
%------------------------------------------------------------------------------