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

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%------------------------------------------------------------------------------
% File     : Vampire---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 : n006.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 0.22s 0.43s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   47 (  29 unt;   0 def)
%            Number of atoms       :  106 (  66 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   85 (  26   ~;  16   |;  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   :   55 (;  46   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f312,plain,
    $false,
    inference(trivial_inequality_removal,[],[f310]) ).

fof(f310,plain,
    sF4 != sF4,
    inference(backward_demodulation,[],[f65,f309]) ).

fof(f309,plain,
    sF4 = sF5,
    inference(forward_demodulation,[],[f308,f64]) ).

fof(f64,plain,
    multiplication(sF4,sK2) = sF5,
    introduced(function_definition,[]) ).

fof(f308,plain,
    sF4 = multiplication(sF4,sK2),
    inference(forward_demodulation,[],[f304,f45]) ).

fof(f45,plain,
    ! [X0] : multiplication(X0,one) = X0,
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] : multiplication(X0,one) = X0,
    file('/export/starexec/sandbox/tmp/tmp.rB0tfLrDlH/Vampire---4.8_13037',multiplicative_right_identity) ).

fof(f304,plain,
    multiplication(sF4,sK2) = multiplication(sF4,one),
    inference(superposition,[],[f89,f96]) ).

fof(f96,plain,
    one = addition(sK2,sF6),
    inference(forward_demodulation,[],[f93,f51]) ).

fof(f51,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.rB0tfLrDlH/Vampire---4.8_13037',additive_commutativity) ).

fof(f93,plain,
    one = addition(sF6,sK2),
    inference(resolution,[],[f76,f56]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( addition(X0,X1) = one
      | ~ complement(X1,X0) ),
    inference(cnf_transformation,[],[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(flattening,[],[f36]) ).

fof(f36,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.rB0tfLrDlH/Vampire---4.8_13037',test_2) ).

fof(f76,plain,
    complement(sK2,sF6),
    inference(forward_demodulation,[],[f73,f66]) ).

fof(f66,plain,
    c(sK2) = sF6,
    introduced(function_definition,[]) ).

fof(f73,plain,
    complement(sK2,c(sK2)),
    inference(resolution,[],[f39,f62]) ).

fof(f62,plain,
    ! [X0] :
      ( complement(X0,c(X0))
      | ~ test(X0) ),
    inference(equality_resolution,[],[f52]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( complement(X0,X1)
      | c(X0) != X1
      | ~ test(X0) ),
    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.rB0tfLrDlH/Vampire---4.8_13037',test_3) ).

fof(f39,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.rB0tfLrDlH/Vampire---4.8_13037',goals) ).

fof(f89,plain,
    ! [X2] : multiplication(sF4,addition(X2,sF6)) = multiplication(sF4,X2),
    inference(forward_demodulation,[],[f82,f44]) ).

fof(f44,plain,
    ! [X0] : addition(X0,zero) = X0,
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] : addition(X0,zero) = X0,
    file('/export/starexec/sandbox/tmp/tmp.rB0tfLrDlH/Vampire---4.8_13037',additive_identity) ).

fof(f82,plain,
    ! [X2] : multiplication(sF4,addition(X2,sF6)) = addition(multiplication(sF4,X2),zero),
    inference(superposition,[],[f60,f69]) ).

fof(f69,plain,
    zero = multiplication(sF4,sF6),
    inference(backward_demodulation,[],[f67,f68]) ).

fof(f68,plain,
    zero = sF7,
    inference(definition_folding,[],[f40,f67,f66,f63]) ).

fof(f63,plain,
    multiplication(sK1,sK0) = sF4,
    introduced(function_definition,[]) ).

fof(f40,plain,
    zero = multiplication(multiplication(sK1,sK0),c(sK2)),
    inference(cnf_transformation,[],[f30]) ).

fof(f67,plain,
    multiplication(sF4,sF6) = sF7,
    introduced(function_definition,[]) ).

fof(f60,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.rB0tfLrDlH/Vampire---4.8_13037',right_distributivity) ).

fof(f65,plain,
    sF4 != sF5,
    inference(definition_folding,[],[f41,f64,f63,f63]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : KLE025+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.14  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.35  % Computer : n006.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Aug 29 12:14:06 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  This is a FOF_THM_RFO_SEQ problem
% 0.14/0.35  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.rB0tfLrDlH/Vampire---4.8_13037
% 0.14/0.36  % (13148)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.41  % (13149)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_1169 on Vampire---4 for (1169ds/0Mi)
% 0.22/0.41  % (13150)lrs-11_28_aac=none:afr=on:anc=none:bs=on:drc=off:fde=unused:gs=on:nm=2:nwc=1.3:sp=frequency:stl=188_1092 on Vampire---4 for (1092ds/0Mi)
% 0.22/0.41  % (13152)lrs+3_20_av=off:bd=preordered:drc=off:fsd=off:fsr=off:fde=unused:irw=on:lcm=reverse:sos=theory:stl=315_961 on Vampire---4 for (961ds/0Mi)
% 0.22/0.41  % (13151)ott-4_11_av=off:bd=preordered:bce=on:drc=off:flr=on:fsr=off:lma=on:nwc=2.0:sp=occurrence:tgt=ground:urr=ec_only_1010 on Vampire---4 for (1010ds/0Mi)
% 0.22/0.41  % (13153)ott+1003_4:1_av=off:cond=on:drc=off:fsd=off:fsr=off:fde=none:gsp=on:nm=2:nwc=1.5:sos=all:sp=reverse_arity:tgt=full_871 on Vampire---4 for (871ds/0Mi)
% 0.22/0.42  % (13154)lrs-11_32_av=off:bd=off:bs=on:bsr=on:drc=off:flr=on:fsd=off:fsr=off:fde=none:gsp=on:irw=on:lcm=predicate:nm=4:sp=scramble:stl=125_825 on Vampire---4 for (825ds/0Mi)
% 0.22/0.42  % (13153)First to succeed.
% 0.22/0.43  % (13153)Refutation found. Thanks to Tanya!
% 0.22/0.43  % SZS status Theorem for Vampire---4
% 0.22/0.43  % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.43  % (13153)------------------------------
% 0.22/0.43  % (13153)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.43  % (13153)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.43  % (13153)Termination reason: Refutation
% 0.22/0.43  
% 0.22/0.43  % (13153)Memory used [KB]: 1151
% 0.22/0.43  % (13153)Time elapsed: 0.013 s
% 0.22/0.43  % (13153)------------------------------
% 0.22/0.43  % (13153)------------------------------
% 0.22/0.43  % (13148)Success in time 0.071 s
% 0.22/0.43  % Vampire---4.8 exiting
%------------------------------------------------------------------------------