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

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---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 : n008.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 0.17s 0.49s
% Output   : Refutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            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   :   86 (;  72   !;  14   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2803,plain,
    $false,
    inference(trivial_inequality_removal,[],[f2794]) ).

fof(f2794,plain,
    multiplication(sK1,sK0) != multiplication(sK1,sK0),
    inference(superposition,[],[f223,f2780]) ).

fof(f2780,plain,
    multiplication(sK1,sK0) = multiplication(sK1,multiplication(sK0,sK2)),
    inference(forward_demodulation,[],[f2779,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/tmp/tmp.aJTLiMcvhg/Vampire---4.8_7914',multiplicative_right_identity) ).

fof(f2779,plain,
    multiplication(sK1,multiplication(sK0,sK2)) = multiplication(sK1,multiplication(sK0,one)),
    inference(forward_demodulation,[],[f2764,f72]) ).

fof(f72,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.aJTLiMcvhg/Vampire---4.8_7914',multiplicative_associativity) ).

fof(f2764,plain,
    multiplication(sK1,multiplication(sK0,sK2)) = multiplication(multiplication(sK1,sK0),one),
    inference(superposition,[],[f358,f1501]) ).

fof(f1501,plain,
    one = addition(c(sK2),sK2),
    inference(backward_demodulation,[],[f1204,f1466]) ).

fof(f1466,plain,
    c(sK2) = sK3(sK2),
    inference(resolution,[],[f1203,f48]) ).

fof(f48,plain,
    test(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/sandbox/tmp/tmp.aJTLiMcvhg/Vampire---4.8_7914',goals) ).

fof(f1203,plain,
    ( ~ test(sK2)
    | c(sK2) = sK3(sK2) ),
    inference(resolution,[],[f1169,f62]) ).

fof(f62,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/sandbox/tmp/tmp.aJTLiMcvhg/Vampire---4.8_7914',test_3) ).

fof(f1169,plain,
    complement(sK2,sK3(sK2)),
    inference(trivial_inequality_removal,[],[f1168]) ).

fof(f1168,plain,
    ( zero != zero
    | complement(sK2,sK3(sK2)) ),
    inference(forward_demodulation,[],[f1167,f108]) ).

fof(f108,plain,
    zero = multiplication(sK3(sK2),sK2),
    inference(resolution,[],[f95,f48]) ).

fof(f95,plain,
    ! [X0] :
      ( ~ test(X0)
      | zero = multiplication(sK3(X0),X0) ),
    inference(resolution,[],[f68,f58]) ).

fof(f58,plain,
    ! [X0] :
      ( complement(sK3(X0),X0)
      | ~ test(X0) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0] :
      ( ( test(X0)
        | ! [X1] : ~ complement(X1,X0) )
      & ( complement(sK3(X0),X0)
        | ~ test(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f40,f41]) ).

fof(f41,plain,
    ! [X0] :
      ( ? [X2] : complement(X2,X0)
     => complement(sK3(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/sandbox/tmp/tmp.aJTLiMcvhg/Vampire---4.8_7914',test_1) ).

fof(f68,plain,
    ! [X0,X1] :
      ( ~ complement(X1,X0)
      | zero = multiplication(X1,X0) ),
    inference(cnf_transformation,[],[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(flattening,[],[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(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/tmp/tmp.aJTLiMcvhg/Vampire---4.8_7914',test_2) ).

fof(f1167,plain,
    ( complement(sK2,sK3(sK2))
    | zero != multiplication(sK3(sK2),sK2) ),
    inference(trivial_inequality_removal,[],[f1166]) ).

fof(f1166,plain,
    ( one != one
    | complement(sK2,sK3(sK2))
    | zero != multiplication(sK3(sK2),sK2) ),
    inference(forward_demodulation,[],[f1165,f121]) ).

fof(f121,plain,
    one = addition(sK2,sK3(sK2)),
    inference(resolution,[],[f96,f48]) ).

fof(f96,plain,
    ! [X0] :
      ( ~ test(X0)
      | one = addition(X0,sK3(X0)) ),
    inference(resolution,[],[f69,f58]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( ~ complement(X1,X0)
      | addition(X0,X1) = one ),
    inference(cnf_transformation,[],[f46]) ).

fof(f1165,plain,
    ( one != addition(sK2,sK3(sK2))
    | complement(sK2,sK3(sK2))
    | zero != multiplication(sK3(sK2),sK2) ),
    inference(forward_demodulation,[],[f1110,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/tmp/tmp.aJTLiMcvhg/Vampire---4.8_7914',additive_commutativity) ).

fof(f1110,plain,
    ( one != addition(sK3(sK2),sK2)
    | complement(sK2,sK3(sK2))
    | zero != multiplication(sK3(sK2),sK2) ),
    inference(trivial_inequality_removal,[],[f1095]) ).

fof(f1095,plain,
    ( zero != zero
    | one != addition(sK3(sK2),sK2)
    | complement(sK2,sK3(sK2))
    | zero != multiplication(sK3(sK2),sK2) ),
    inference(superposition,[],[f70,f105]) ).

fof(f105,plain,
    zero = multiplication(sK2,sK3(sK2)),
    inference(resolution,[],[f93,f48]) ).

fof(f93,plain,
    ! [X0] :
      ( ~ test(X0)
      | zero = multiplication(X0,sK3(X0)) ),
    inference(resolution,[],[f67,f58]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( ~ complement(X1,X0)
      | zero = multiplication(X0,X1) ),
    inference(cnf_transformation,[],[f46]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( zero != multiplication(X1,X0)
      | addition(X0,X1) != one
      | complement(X1,X0)
      | zero != multiplication(X0,X1) ),
    inference(cnf_transformation,[],[f46]) ).

fof(f1204,plain,
    one = addition(sK3(sK2),sK2),
    inference(resolution,[],[f1169,f69]) ).

fof(f358,plain,
    ! [X6] : multiplication(multiplication(sK1,sK0),addition(c(sK2),X6)) = multiplication(sK1,multiplication(sK0,X6)),
    inference(forward_demodulation,[],[f357,f72]) ).

fof(f357,plain,
    ! [X6] : multiplication(multiplication(sK1,sK0),addition(c(sK2),X6)) = multiplication(multiplication(sK1,sK0),X6),
    inference(forward_demodulation,[],[f304,f76]) ).

fof(f76,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/tmp/tmp.aJTLiMcvhg/Vampire---4.8_7914',additive_identity) ).

fof(f304,plain,
    ! [X6] : multiplication(multiplication(sK1,sK0),addition(c(sK2),X6)) = addition(zero,multiplication(multiplication(sK1,sK0),X6)),
    inference(superposition,[],[f73,f49]) ).

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

fof(f73,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.aJTLiMcvhg/Vampire---4.8_7914',right_distributivity) ).

fof(f223,plain,
    multiplication(sK1,sK0) != multiplication(sK1,multiplication(sK0,sK2)),
    inference(superposition,[],[f50,f72]) ).

fof(f50,plain,
    multiplication(sK1,sK0) != multiplication(multiplication(sK1,sK0),sK2),
    inference(cnf_transformation,[],[f38]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : KLE025+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.13/0.35  % Computer : n008.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Wed Aug 30 17:48:02 EDT 2023
% 0.13/0.35  % CPUTime    : 
% 0.17/0.41  % (8041)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.42  % (8044)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.17/0.42  % (8046)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.17/0.42  % (8043)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.17/0.42  % (8048)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)
% 0.17/0.42  % (8045)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)
% 0.17/0.42  % (8050)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)
% 0.17/0.42  % (8052)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)
% 0.17/0.42  TRYING [1]
% 0.17/0.42  TRYING [2]
% 0.17/0.42  TRYING [3]
% 0.17/0.42  TRYING [1]
% 0.17/0.42  TRYING [2]
% 0.17/0.43  TRYING [4]
% 0.17/0.43  TRYING [3]
% 0.17/0.46  TRYING [5]
% 0.17/0.47  TRYING [4]
% 0.17/0.49  % (8050)First to succeed.
% 0.17/0.49  % (8050)Refutation found. Thanks to Tanya!
% 0.17/0.49  % SZS status Theorem for Vampire---4
% 0.17/0.49  % SZS output start Proof for Vampire---4
% See solution above
% 0.17/0.50  % (8050)------------------------------
% 0.17/0.50  % (8050)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.17/0.50  % (8050)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.17/0.50  % (8050)Termination reason: Refutation
% 0.17/0.50  
% 0.17/0.50  % (8050)Memory used [KB]: 2814
% 0.17/0.50  % (8050)Time elapsed: 0.076 s
% 0.17/0.50  % (8050)------------------------------
% 0.17/0.50  % (8050)------------------------------
% 0.17/0.50  % (8041)Success in time 0.137 s
% 0.17/0.50  % Vampire---4.8 exiting
%------------------------------------------------------------------------------