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

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---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 : n026.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 17:09:02 EDT 2023

% Result   : Theorem 0.23s 0.68s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   75 (  47 unt;   0 def)
%            Number of atoms       :  144 (  73 equ)
%            Maximal formula atoms :    8 (   1 avg)
%            Number of connectives :  113 (  44   ~;  26   |;  28   &)
%                                         (   8 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   97 (;  86   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f27377,plain,
    $false,
    inference(subsumption_resolution,[],[f27376,f227]) ).

fof(f227,plain,
    one = addition(sK0,c(sK0)),
    inference(superposition,[],[f185,f59]) ).

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/sandbox/tmp/tmp.ac8iraEuO6/Vampire---4.8_13843',additive_commutativity) ).

fof(f185,plain,
    one = addition(c(sK0),sK0),
    inference(unit_resulting_resolution,[],[f175,f68]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( ~ complement(X1,X0)
      | addition(X0,X1) = one ),
    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.ac8iraEuO6/Vampire---4.8_13843',test_2) ).

fof(f175,plain,
    complement(sK0,c(sK0)),
    inference(forward_demodulation,[],[f171,f54]) ).

fof(f54,plain,
    ! [X0] : multiplication(one,X0) = X0,
    inference(cnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] : multiplication(one,X0) = X0,
    file('/export/starexec/sandbox/tmp/tmp.ac8iraEuO6/Vampire---4.8_13843',multiplicative_left_identity) ).

fof(f171,plain,
    complement(sK0,multiplication(one,c(sK0))),
    inference(unit_resulting_resolution,[],[f48,f54,f60]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( ~ test(X0)
      | c(X0) != X1
      | complement(X0,X1) ),
    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.ac8iraEuO6/Vampire---4.8_13843',test_3) ).

fof(f48,plain,
    test(sK0),
    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/sandbox/tmp/tmp.ac8iraEuO6/Vampire---4.8_13843',goals) ).

fof(f27376,plain,
    one != addition(sK0,c(sK0)),
    inference(forward_demodulation,[],[f27375,f21238]) ).

fof(f21238,plain,
    ! [X2] : addition(X2,multiplication(X2,sK1)) = X2,
    inference(superposition,[],[f20754,f59]) ).

fof(f20754,plain,
    ! [X0] : addition(multiplication(X0,sK1),X0) = X0,
    inference(unit_resulting_resolution,[],[f20734,f64]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( ~ leq(X0,X1)
      | addition(X0,X1) = X1 ),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ( leq(X0,X1)
        | addition(X0,X1) != X1 )
      & ( addition(X0,X1) = X1
        | ~ leq(X0,X1) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0,X1] :
      ( leq(X0,X1)
    <=> addition(X0,X1) = X1 ),
    file('/export/starexec/sandbox/tmp/tmp.ac8iraEuO6/Vampire---4.8_13843',order) ).

fof(f20734,plain,
    ! [X126] : leq(multiplication(X126,sK1),X126),
    inference(forward_demodulation,[],[f20670,f53]) ).

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

fof(f6,axiom,
    ! [X0] : multiplication(X0,one) = X0,
    file('/export/starexec/sandbox/tmp/tmp.ac8iraEuO6/Vampire---4.8_13843',multiplicative_right_identity) ).

fof(f20670,plain,
    ! [X126] : leq(multiplication(X126,sK1),multiplication(X126,one)),
    inference(superposition,[],[f3271,f706]) ).

fof(f706,plain,
    one = addition(sK1,one),
    inference(superposition,[],[f642,f136]) ).

fof(f136,plain,
    one = addition(sK1,sK2(sK1)),
    inference(unit_resulting_resolution,[],[f74,f68]) ).

fof(f74,plain,
    complement(sK2(sK1),sK1),
    inference(unit_resulting_resolution,[],[f47,f57]) ).

fof(f57,plain,
    ! [X0] :
      ( ~ test(X0)
      | complement(sK2(X0),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/sandbox/tmp/tmp.ac8iraEuO6/Vampire---4.8_13843',test_1) ).

fof(f47,plain,
    test(sK1),
    inference(cnf_transformation,[],[f38]) ).

fof(f642,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
    inference(superposition,[],[f70,f55]) ).

fof(f55,plain,
    ! [X0] : addition(X0,X0) = X0,
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] : addition(X0,X0) = X0,
    file('/export/starexec/sandbox/tmp/tmp.ac8iraEuO6/Vampire---4.8_13843',additive_idempotence) ).

fof(f70,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/sandbox/tmp/tmp.ac8iraEuO6/Vampire---4.8_13843',additive_associativity) ).

fof(f3271,plain,
    ! [X21,X22,X23] : leq(multiplication(X21,X22),multiplication(X21,addition(X22,X23))),
    inference(superposition,[],[f681,f72]) ).

fof(f72,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.ac8iraEuO6/Vampire---4.8_13843',right_distributivity) ).

fof(f681,plain,
    ! [X0,X1] : leq(X0,addition(X0,X1)),
    inference(unit_resulting_resolution,[],[f642,f65]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( addition(X0,X1) != X1
      | leq(X0,X1) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f27375,plain,
    one != addition(addition(sK0,multiplication(sK0,sK1)),c(sK0)),
    inference(forward_demodulation,[],[f27374,f54]) ).

fof(f27374,plain,
    one != addition(addition(multiplication(one,sK0),multiplication(sK0,sK1)),c(sK0)),
    inference(forward_demodulation,[],[f27373,f59]) ).

fof(f27373,plain,
    one != addition(addition(multiplication(sK0,sK1),multiplication(one,sK0)),c(sK0)),
    inference(forward_demodulation,[],[f27372,f239]) ).

fof(f239,plain,
    one = addition(sK1,c(sK1)),
    inference(superposition,[],[f206,f59]) ).

fof(f206,plain,
    one = addition(c(sK1),sK1),
    inference(unit_resulting_resolution,[],[f176,f68]) ).

fof(f176,plain,
    complement(sK1,c(sK1)),
    inference(forward_demodulation,[],[f170,f54]) ).

fof(f170,plain,
    complement(sK1,multiplication(one,c(sK1))),
    inference(unit_resulting_resolution,[],[f47,f54,f60]) ).

fof(f27372,plain,
    one != addition(addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)),c(sK0)),
    inference(forward_demodulation,[],[f27371,f73]) ).

fof(f73,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/sandbox/tmp/tmp.ac8iraEuO6/Vampire---4.8_13843',left_distributivity) ).

fof(f27371,plain,
    one != addition(addition(multiplication(sK0,sK1),addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0))),c(sK0)),
    inference(forward_demodulation,[],[f27370,f59]) ).

fof(f27370,plain,
    one != addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),c(sK0)),
    inference(forward_demodulation,[],[f27369,f53]) ).

fof(f27369,plain,
    one != addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),one)),
    inference(forward_demodulation,[],[f27368,f239]) ).

fof(f27368,plain,
    one != addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),addition(sK1,c(sK1)))),
    inference(forward_demodulation,[],[f27271,f72]) ).

fof(f27271,plain,
    one != addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),addition(multiplication(c(sK0),sK1),multiplication(c(sK0),c(sK1)))),
    inference(superposition,[],[f49,f70]) ).

fof(f49,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]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : KLE010+3 : 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
% 0.16/0.37  % Computer : n026.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Wed Aug 30 18:05:51 EDT 2023
% 0.16/0.37  % CPUTime    : 
% 0.23/0.43  % (14197)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.44  % (14218)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.23/0.44  % (14219)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.23/0.44  % (14221)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.23/0.44  % (14220)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)
% 0.23/0.44  % (14222)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)
% 0.23/0.44  % (14223)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)
% 0.23/0.44  % (14224)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)
% 0.23/0.44  TRYING [1]
% 0.23/0.44  TRYING [2]
% 0.23/0.44  TRYING [3]
% 0.23/0.44  TRYING [1]
% 0.23/0.45  TRYING [2]
% 0.23/0.45  TRYING [4]
% 0.23/0.46  TRYING [3]
% 0.23/0.49  TRYING [5]
% 0.23/0.50  TRYING [4]
% 0.23/0.58  TRYING [6]
% 0.23/0.62  TRYING [5]
% 0.23/0.68  % (14224)First to succeed.
% 0.23/0.68  % (14224)Refutation found. Thanks to Tanya!
% 0.23/0.68  % SZS status Theorem for Vampire---4
% 0.23/0.68  % SZS output start Proof for Vampire---4
% See solution above
% 0.23/0.68  % (14224)------------------------------
% 0.23/0.68  % (14224)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.68  % (14224)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.68  % (14224)Termination reason: Refutation
% 0.23/0.68  
% 0.23/0.68  % (14224)Memory used [KB]: 6396
% 0.23/0.68  % (14224)Time elapsed: 0.242 s
% 0.23/0.68  % (14224)------------------------------
% 0.23/0.68  % (14224)------------------------------
% 0.23/0.68  % (14197)Success in time 0.285 s
% 0.23/0.68  % Vampire---4.8 exiting
%------------------------------------------------------------------------------