TSTP Solution File: KLE010+3 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : KLE010+3 : 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 : n032.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 05:36:17 EDT 2023

% Result   : Theorem 0.15s 0.42s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   89 (  61 unt;   0 def)
%            Number of atoms       :  156 (  90 equ)
%            Maximal formula atoms :    8 (   1 avg)
%            Number of connectives :  102 (  35   ~;  26   |;  27   &)
%                                         (   7 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   19 (  19 usr;  15 con; 0-2 aty)
%            Number of variables   :   87 (;  76   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4442,plain,
    $false,
    inference(subsumption_resolution,[],[f4441,f83]) ).

fof(f83,plain,
    one != sF13,
    inference(definition_folding,[],[f48,f82,f81,f73,f78,f80,f79,f78,f77,f76,f75,f74,f73,f72]) ).

fof(f72,plain,
    multiplication(sK1,sK0) = sF3,
    introduced(function_definition,[]) ).

fof(f74,plain,
    multiplication(sF4,sK0) = sF5,
    introduced(function_definition,[]) ).

fof(f75,plain,
    addition(sF3,sF5) = sF6,
    introduced(function_definition,[]) ).

fof(f76,plain,
    multiplication(sK0,sK1) = sF7,
    introduced(function_definition,[]) ).

fof(f77,plain,
    addition(sF6,sF7) = sF8,
    introduced(function_definition,[]) ).

fof(f79,plain,
    multiplication(sF9,sK1) = sF10,
    introduced(function_definition,[]) ).

fof(f80,plain,
    addition(sF8,sF10) = sF11,
    introduced(function_definition,[]) ).

fof(f78,plain,
    c(sK0) = sF9,
    introduced(function_definition,[]) ).

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

fof(f81,plain,
    multiplication(sF9,sF4) = sF12,
    introduced(function_definition,[]) ).

fof(f82,plain,
    addition(sF11,sF12) = sF13,
    introduced(function_definition,[]) ).

fof(f48,plain,
    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,[],[f38]) ).

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

fof(f37,plain,
    ( ? [X0,X1] :
        ( 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) )
   => ( 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(f30,plain,
    ? [X0,X1] :
      ( 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,[],[f29]) ).

fof(f29,plain,
    ? [X0,X1] :
      ( 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) )
       => 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) )
       => 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) )
     => 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/sandbox2/tmp/tmp.65gTqaqk5t/Vampire---4.8_25529',goals) ).

fof(f4441,plain,
    one = sF13,
    inference(forward_demodulation,[],[f4440,f105]) ).

fof(f105,plain,
    one = addition(sF9,sK0),
    inference(resolution,[],[f65,f87]) ).

fof(f87,plain,
    complement(sK0,sF9),
    inference(subsumption_resolution,[],[f85,f47]) ).

fof(f47,plain,
    test(sK0),
    inference(cnf_transformation,[],[f38]) ).

fof(f85,plain,
    ( complement(sK0,sF9)
    | ~ test(sK0) ),
    inference(superposition,[],[f71,f78]) ).

fof(f71,plain,
    ! [X0] :
      ( complement(X0,c(X0))
      | ~ test(X0) ),
    inference(equality_resolution,[],[f59]) ).

fof(f59,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.65gTqaqk5t/Vampire---4.8_25529',test_3) ).

fof(f65,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.65gTqaqk5t/Vampire---4.8_25529',test_2) ).

fof(f4440,plain,
    sF13 = addition(sF9,sK0),
    inference(backward_demodulation,[],[f3558,f4433]) ).

fof(f4433,plain,
    sK0 = sF8,
    inference(forward_demodulation,[],[f4423,f1792]) ).

fof(f1792,plain,
    sK0 = addition(sK0,sF7),
    inference(forward_demodulation,[],[f1791,f52]) ).

fof(f52,plain,
    ! [X0] : multiplication(X0,one) = X0,
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] : multiplication(X0,one) = X0,
    file('/export/starexec/sandbox2/tmp/tmp.65gTqaqk5t/Vampire---4.8_25529',multiplicative_right_identity) ).

fof(f1791,plain,
    multiplication(sK0,one) = addition(sK0,sF7),
    inference(forward_demodulation,[],[f1715,f659]) ).

fof(f659,plain,
    one = addition(one,sK1),
    inference(superposition,[],[f614,f58]) ).

fof(f58,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.65gTqaqk5t/Vampire---4.8_25529',additive_commutativity) ).

fof(f614,plain,
    one = addition(sK1,one),
    inference(superposition,[],[f124,f560]) ).

fof(f560,plain,
    one = addition(sK1,sK2(sK1)),
    inference(resolution,[],[f107,f46]) ).

fof(f46,plain,
    test(sK1),
    inference(cnf_transformation,[],[f38]) ).

fof(f107,plain,
    ! [X1] :
      ( ~ test(X1)
      | one = addition(X1,sK2(X1)) ),
    inference(resolution,[],[f65,f56]) ).

fof(f56,plain,
    ! [X0] :
      ( complement(sK2(X0),X0)
      | ~ test(X0) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0] :
      ( ( test(X0)
        | ! [X1] : ~ complement(X1,X0) )
      & ( complement(sK2(X0),X0)
        | ~ test(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f40,f41]) ).

fof(f41,plain,
    ! [X0] :
      ( ? [X2] : complement(X2,X0)
     => complement(sK2(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f40,plain,
    ! [X0] :
      ( ( test(X0)
        | ! [X1] : ~ complement(X1,X0) )
      & ( ? [X2] : complement(X2,X0)
        | ~ test(X0) ) ),
    inference(rectify,[],[f39]) ).

fof(f39,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/sandbox2/tmp/tmp.65gTqaqk5t/Vampire---4.8_25529',test_1) ).

fof(f124,plain,
    ! [X2,X3] : addition(X2,X3) = addition(X2,addition(X2,X3)),
    inference(superposition,[],[f67,f54]) ).

fof(f54,plain,
    ! [X0] : addition(X0,X0) = X0,
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] : addition(X0,X0) = X0,
    file('/export/starexec/sandbox2/tmp/tmp.65gTqaqk5t/Vampire---4.8_25529',additive_idempotence) ).

fof(f67,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/sandbox2/tmp/tmp.65gTqaqk5t/Vampire---4.8_25529',additive_associativity) ).

fof(f1715,plain,
    multiplication(sK0,addition(one,sK1)) = addition(sK0,sF7),
    inference(superposition,[],[f192,f76]) ).

fof(f192,plain,
    ! [X2,X3] : multiplication(X2,addition(one,X3)) = addition(X2,multiplication(X2,X3)),
    inference(superposition,[],[f69,f52]) ).

fof(f69,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.65gTqaqk5t/Vampire---4.8_25529',right_distributivity) ).

fof(f4423,plain,
    sF8 = addition(sK0,sF7),
    inference(backward_demodulation,[],[f77,f4414]) ).

fof(f4414,plain,
    sK0 = sF6,
    inference(backward_demodulation,[],[f75,f4391]) ).

fof(f4391,plain,
    sK0 = addition(sF3,sF5),
    inference(forward_demodulation,[],[f4390,f53]) ).

fof(f53,plain,
    ! [X0] : multiplication(one,X0) = X0,
    inference(cnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] : multiplication(one,X0) = X0,
    file('/export/starexec/sandbox2/tmp/tmp.65gTqaqk5t/Vampire---4.8_25529',multiplicative_left_identity) ).

fof(f4390,plain,
    addition(sF3,sF5) = multiplication(one,sK0),
    inference(forward_demodulation,[],[f4370,f113]) ).

fof(f113,plain,
    one = addition(sK1,sF4),
    inference(superposition,[],[f106,f58]) ).

fof(f106,plain,
    one = addition(sF4,sK1),
    inference(resolution,[],[f65,f86]) ).

fof(f86,plain,
    complement(sK1,sF4),
    inference(subsumption_resolution,[],[f84,f46]) ).

fof(f84,plain,
    ( complement(sK1,sF4)
    | ~ test(sK1) ),
    inference(superposition,[],[f71,f73]) ).

fof(f4370,plain,
    addition(sF3,sF5) = multiplication(addition(sK1,sF4),sK0),
    inference(superposition,[],[f307,f74]) ).

fof(f307,plain,
    ! [X20] : multiplication(addition(sK1,X20),sK0) = addition(sF3,multiplication(X20,sK0)),
    inference(superposition,[],[f70,f72]) ).

fof(f70,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/tmp/tmp.65gTqaqk5t/Vampire---4.8_25529',left_distributivity) ).

fof(f3558,plain,
    sF13 = addition(sF9,sF8),
    inference(forward_demodulation,[],[f3557,f82]) ).

fof(f3557,plain,
    addition(sF11,sF12) = addition(sF9,sF8),
    inference(forward_demodulation,[],[f3550,f58]) ).

fof(f3550,plain,
    addition(sF11,sF12) = addition(sF8,sF9),
    inference(superposition,[],[f134,f3538]) ).

fof(f3538,plain,
    sF9 = addition(sF10,sF12),
    inference(forward_demodulation,[],[f3537,f52]) ).

fof(f3537,plain,
    multiplication(sF9,one) = addition(sF10,sF12),
    inference(forward_demodulation,[],[f3519,f113]) ).

fof(f3519,plain,
    multiplication(sF9,addition(sK1,sF4)) = addition(sF10,sF12),
    inference(superposition,[],[f205,f81]) ).

fof(f205,plain,
    ! [X22] : multiplication(sF9,addition(sK1,X22)) = addition(sF10,multiplication(sF9,X22)),
    inference(superposition,[],[f69,f79]) ).

fof(f134,plain,
    ! [X21] : addition(sF8,addition(sF10,X21)) = addition(sF11,X21),
    inference(superposition,[],[f67,f80]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10  % Problem    : KLE010+3 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.11  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.11/0.30  % Computer : n032.cluster.edu
% 0.11/0.30  % Model    : x86_64 x86_64
% 0.11/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30  % Memory   : 8042.1875MB
% 0.11/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30  % CPULimit   : 300
% 0.11/0.30  % WCLimit    : 300
% 0.11/0.30  % DateTime   : Tue Aug 29 12:35:31 EDT 2023
% 0.11/0.30  % CPUTime    : 
% 0.11/0.30  This is a FOF_THM_RFO_SEQ problem
% 0.11/0.31  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.65gTqaqk5t/Vampire---4.8_25529
% 0.11/0.31  % (25715)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.35  % (25722)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)
% 0.15/0.35  % (25720)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)
% 0.15/0.35  % (25717)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)
% 0.15/0.35  % (25721)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.15/0.35  % (25716)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)
% 0.15/0.36  % (25719)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)
% 0.15/0.36  % (25718)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)
% 0.15/0.42  % (25721)First to succeed.
% 0.15/0.42  % (25721)Refutation found. Thanks to Tanya!
% 0.15/0.42  % SZS status Theorem for Vampire---4
% 0.15/0.42  % SZS output start Proof for Vampire---4
% See solution above
% 0.15/0.42  % (25721)------------------------------
% 0.15/0.42  % (25721)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.15/0.42  % (25721)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.15/0.42  % (25721)Termination reason: Refutation
% 0.15/0.42  
% 0.15/0.42  % (25721)Memory used [KB]: 7547
% 0.15/0.42  % (25721)Time elapsed: 0.066 s
% 0.15/0.42  % (25721)------------------------------
% 0.15/0.42  % (25721)------------------------------
% 0.15/0.42  % (25715)Success in time 0.112 s
% 0.15/0.42  % Vampire---4.8 exiting
%------------------------------------------------------------------------------