TSTP Solution File: KRS076+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : KRS076+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% Computer : n019.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 : Wed Aug 31 17:30:44 EDT 2022

% Result   : Unsatisfiable 0.20s 0.49s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   65 (   7 unt;   0 def)
%            Number of atoms       :  246 (  29 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  293 ( 112   ~; 101   |;  61   &)
%                                         (   5 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-1 aty)
%            Number of variables   :  161 ( 134   !;  27   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f401,plain,
    $false,
    inference(resolution,[],[f400,f158]) ).

fof(f158,plain,
    cUnsatisfiable(i2003_11_14_17_19_06193),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,axiom,
    cUnsatisfiable(i2003_11_14_17_19_06193),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).

fof(f400,plain,
    ~ cUnsatisfiable(i2003_11_14_17_19_06193),
    inference(duplicate_literal_removal,[],[f399]) ).

fof(f399,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_19_06193)
    | ~ cUnsatisfiable(i2003_11_14_17_19_06193) ),
    inference(resolution,[],[f380,f154]) ).

fof(f154,plain,
    ! [X0] :
      ( cp(sK1(X0))
      | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f120,plain,
    ! [X0] :
      ( ( cUnsatisfiable(X0)
        | ! [X1] :
            ( ~ cp(X1)
            | ~ rf(X0,X1) )
        | ! [X2] :
            ( ~ rf1(X0,X2)
            | cp(X2)
            | ( rinvF1(X2,sK0(X2))
              & ! [X4] :
                  ( ~ cowlThing(X4)
                  | ~ rs(sK0(X2),X4) ) ) ) )
      & ( ( cp(sK1(X0))
          & rf(X0,sK1(X0))
          & rf1(X0,sK2(X0))
          & ~ cp(sK2(X0))
          & ! [X7] :
              ( ~ rinvF1(sK2(X0),X7)
              | ( cowlThing(sK3(X7))
                & rs(X7,sK3(X7)) ) ) )
        | ~ cUnsatisfiable(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f115,f119,f118,f117,f116]) ).

fof(f116,plain,
    ! [X2] :
      ( ? [X3] :
          ( rinvF1(X2,X3)
          & ! [X4] :
              ( ~ cowlThing(X4)
              | ~ rs(X3,X4) ) )
     => ( rinvF1(X2,sK0(X2))
        & ! [X4] :
            ( ~ cowlThing(X4)
            | ~ rs(sK0(X2),X4) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f117,plain,
    ! [X0] :
      ( ? [X5] :
          ( cp(X5)
          & rf(X0,X5) )
     => ( cp(sK1(X0))
        & rf(X0,sK1(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f118,plain,
    ! [X0] :
      ( ? [X6] :
          ( rf1(X0,X6)
          & ~ cp(X6)
          & ! [X7] :
              ( ~ rinvF1(X6,X7)
              | ? [X8] :
                  ( cowlThing(X8)
                  & rs(X7,X8) ) ) )
     => ( rf1(X0,sK2(X0))
        & ~ cp(sK2(X0))
        & ! [X7] :
            ( ~ rinvF1(sK2(X0),X7)
            | ? [X8] :
                ( cowlThing(X8)
                & rs(X7,X8) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f119,plain,
    ! [X7] :
      ( ? [X8] :
          ( cowlThing(X8)
          & rs(X7,X8) )
     => ( cowlThing(sK3(X7))
        & rs(X7,sK3(X7)) ) ),
    introduced(choice_axiom,[]) ).

fof(f115,plain,
    ! [X0] :
      ( ( cUnsatisfiable(X0)
        | ! [X1] :
            ( ~ cp(X1)
            | ~ rf(X0,X1) )
        | ! [X2] :
            ( ~ rf1(X0,X2)
            | cp(X2)
            | ? [X3] :
                ( rinvF1(X2,X3)
                & ! [X4] :
                    ( ~ cowlThing(X4)
                    | ~ rs(X3,X4) ) ) ) )
      & ( ( ? [X5] :
              ( cp(X5)
              & rf(X0,X5) )
          & ? [X6] :
              ( rf1(X0,X6)
              & ~ cp(X6)
              & ! [X7] :
                  ( ~ rinvF1(X6,X7)
                  | ? [X8] :
                      ( cowlThing(X8)
                      & rs(X7,X8) ) ) ) )
        | ~ cUnsatisfiable(X0) ) ),
    inference(rectify,[],[f114]) ).

fof(f114,plain,
    ! [X0] :
      ( ( cUnsatisfiable(X0)
        | ! [X1] :
            ( ~ cp(X1)
            | ~ rf(X0,X1) )
        | ! [X2] :
            ( ~ rf1(X0,X2)
            | cp(X2)
            | ? [X3] :
                ( rinvF1(X2,X3)
                & ! [X4] :
                    ( ~ cowlThing(X4)
                    | ~ rs(X3,X4) ) ) ) )
      & ( ( ? [X1] :
              ( cp(X1)
              & rf(X0,X1) )
          & ? [X2] :
              ( rf1(X0,X2)
              & ~ cp(X2)
              & ! [X3] :
                  ( ~ rinvF1(X2,X3)
                  | ? [X4] :
                      ( cowlThing(X4)
                      & rs(X3,X4) ) ) ) )
        | ~ cUnsatisfiable(X0) ) ),
    inference(flattening,[],[f113]) ).

fof(f113,plain,
    ! [X0] :
      ( ( cUnsatisfiable(X0)
        | ! [X1] :
            ( ~ cp(X1)
            | ~ rf(X0,X1) )
        | ! [X2] :
            ( ~ rf1(X0,X2)
            | cp(X2)
            | ? [X3] :
                ( rinvF1(X2,X3)
                & ! [X4] :
                    ( ~ cowlThing(X4)
                    | ~ rs(X3,X4) ) ) ) )
      & ( ( ? [X1] :
              ( cp(X1)
              & rf(X0,X1) )
          & ? [X2] :
              ( rf1(X0,X2)
              & ~ cp(X2)
              & ! [X3] :
                  ( ~ rinvF1(X2,X3)
                  | ? [X4] :
                      ( cowlThing(X4)
                      & rs(X3,X4) ) ) ) )
        | ~ cUnsatisfiable(X0) ) ),
    inference(nnf_transformation,[],[f93]) ).

fof(f93,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ? [X1] :
            ( cp(X1)
            & rf(X0,X1) )
        & ? [X2] :
            ( rf1(X0,X2)
            & ~ cp(X2)
            & ! [X3] :
                ( ~ rinvF1(X2,X3)
                | ? [X4] :
                    ( cowlThing(X4)
                    & rs(X3,X4) ) ) ) ) ),
    inference(ennf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X0] :
      ( ( ? [X1] :
            ( cp(X1)
            & rf(X0,X1) )
        & ? [X2] :
            ( ! [X3] :
                ( rinvF1(X2,X3)
               => ? [X4] :
                    ( cowlThing(X4)
                    & rs(X3,X4) ) )
            & rf1(X0,X2)
            & ~ cp(X2) ) )
    <=> cUnsatisfiable(X0) ),
    inference(rectify,[],[f21]) ).

fof(f21,axiom,
    ! [X3] :
      ( cUnsatisfiable(X3)
    <=> ( ? [X4] :
            ( rf(X3,X4)
            & cp(X4) )
        & ? [X4] :
            ( ! [X5] :
                ( rinvF1(X4,X5)
               => ? [X6] :
                    ( cowlThing(X6)
                    & rs(X5,X6) ) )
            & rf1(X3,X4)
            & ~ cp(X4) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

fof(f380,plain,
    ( ~ cp(sK1(i2003_11_14_17_19_06193))
    | ~ cUnsatisfiable(i2003_11_14_17_19_06193) ),
    inference(superposition,[],[f151,f370]) ).

fof(f370,plain,
    sK1(i2003_11_14_17_19_06193) = sK2(i2003_11_14_17_19_06193),
    inference(backward_demodulation,[],[f310,f367]) ).

fof(f367,plain,
    sK1(i2003_11_14_17_19_06193) = sK3(i2003_11_14_17_19_06193),
    inference(resolution,[],[f360,f158]) ).

fof(f360,plain,
    ! [X0] :
      ( ~ cUnsatisfiable(X0)
      | sK3(X0) = sK1(X0) ),
    inference(duplicate_literal_removal,[],[f357]) ).

fof(f357,plain,
    ! [X0] :
      ( ~ cUnsatisfiable(X0)
      | sK3(X0) = sK1(X0)
      | ~ cUnsatisfiable(X0) ),
    inference(resolution,[],[f356,f153]) ).

fof(f153,plain,
    ! [X0] :
      ( rf(X0,sK1(X0))
      | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f356,plain,
    ! [X0,X1] :
      ( ~ rf(X0,X1)
      | sK3(X0) = X1
      | ~ cUnsatisfiable(X0) ),
    inference(duplicate_literal_removal,[],[f353]) ).

fof(f353,plain,
    ! [X0,X1] :
      ( ~ cUnsatisfiable(X0)
      | ~ rf(X0,X1)
      | sK3(X0) = X1
      | ~ cUnsatisfiable(X0) ),
    inference(resolution,[],[f285,f152]) ).

fof(f152,plain,
    ! [X0] :
      ( rf1(X0,sK2(X0))
      | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f285,plain,
    ! [X2,X0,X1] :
      ( ~ rf(X0,X1)
      | ~ rf1(X0,sK2(X2))
      | sK3(X0) = X1
      | ~ cUnsatisfiable(X2) ),
    inference(resolution,[],[f241,f159]) ).

fof(f159,plain,
    ! [X0,X1] :
      ( rinvF1(X0,X1)
      | ~ rf1(X1,X0) ),
    inference(cnf_transformation,[],[f123]) ).

fof(f123,plain,
    ! [X0,X1] :
      ( ( rf1(X1,X0)
        | ~ rinvF1(X0,X1) )
      & ( rinvF1(X0,X1)
        | ~ rf1(X1,X0) ) ),
    inference(rectify,[],[f122]) ).

fof(f122,plain,
    ! [X1,X0] :
      ( ( rf1(X0,X1)
        | ~ rinvF1(X1,X0) )
      & ( rinvF1(X1,X0)
        | ~ rf1(X0,X1) ) ),
    inference(nnf_transformation,[],[f53]) ).

fof(f53,plain,
    ! [X1,X0] :
      ( rf1(X0,X1)
    <=> rinvF1(X1,X0) ),
    inference(rectify,[],[f25]) ).

fof(f25,axiom,
    ! [X4,X3] :
      ( rinvF1(X3,X4)
    <=> rf1(X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).

fof(f241,plain,
    ! [X10,X8,X9] :
      ( ~ rinvF1(sK2(X8),X9)
      | ~ rf(X9,X10)
      | ~ cUnsatisfiable(X8)
      | sK3(X9) = X10 ),
    inference(resolution,[],[f149,f198]) ).

fof(f198,plain,
    ! [X6,X7,X5] :
      ( ~ rs(X5,X7)
      | ~ rf(X5,X6)
      | X6 = X7 ),
    inference(resolution,[],[f132,f167]) ).

fof(f167,plain,
    ! [X0,X1] :
      ( rf(X1,X0)
      | ~ rs(X1,X0) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( rf(X1,X0)
      | ~ rs(X1,X0) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( rs(X1,X0)
     => rf(X1,X0) ),
    inference(rectify,[],[f30]) ).

fof(f30,axiom,
    ! [X4,X3] :
      ( rs(X3,X4)
     => rf(X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).

fof(f132,plain,
    ! [X2,X0,X1] :
      ( ~ rf(X2,X1)
      | ~ rf(X2,X0)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f100]) ).

fof(f100,plain,
    ! [X0,X1,X2] :
      ( X0 = X1
      | ~ rf(X2,X0)
      | ~ rf(X2,X1) ),
    inference(rectify,[],[f66]) ).

fof(f66,plain,
    ! [X1,X2,X0] :
      ( X1 = X2
      | ~ rf(X0,X1)
      | ~ rf(X0,X2) ),
    inference(flattening,[],[f65]) ).

fof(f65,plain,
    ! [X0,X2,X1] :
      ( X1 = X2
      | ~ rf(X0,X1)
      | ~ rf(X0,X2) ),
    inference(ennf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X0,X2,X1] :
      ( ( rf(X0,X1)
        & rf(X0,X2) )
     => X1 = X2 ),
    inference(rectify,[],[f22]) ).

fof(f22,axiom,
    ! [X3,X4,X5] :
      ( ( rf(X3,X4)
        & rf(X3,X5) )
     => X4 = X5 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).

fof(f149,plain,
    ! [X0,X7] :
      ( rs(X7,sK3(X7))
      | ~ cUnsatisfiable(X0)
      | ~ rinvF1(sK2(X0),X7) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f310,plain,
    sK2(i2003_11_14_17_19_06193) = sK3(i2003_11_14_17_19_06193),
    inference(resolution,[],[f309,f158]) ).

fof(f309,plain,
    ! [X0] :
      ( ~ cUnsatisfiable(X0)
      | sK2(X0) = sK3(X0) ),
    inference(duplicate_literal_removal,[],[f306]) ).

fof(f306,plain,
    ! [X0] :
      ( ~ cUnsatisfiable(X0)
      | sK2(X0) = sK3(X0)
      | ~ cUnsatisfiable(X0) ),
    inference(resolution,[],[f305,f152]) ).

fof(f305,plain,
    ! [X0,X1] :
      ( ~ rf1(X0,sK2(X1))
      | ~ cUnsatisfiable(X1)
      | sK2(X1) = sK3(X0) ),
    inference(resolution,[],[f304,f159]) ).

fof(f304,plain,
    ! [X0,X1] :
      ( ~ rinvF1(sK2(X0),X1)
      | sK3(X1) = sK2(X0)
      | ~ cUnsatisfiable(X0) ),
    inference(factoring,[],[f265]) ).

fof(f265,plain,
    ! [X3,X4,X5] :
      ( ~ rinvF1(sK2(X5),X4)
      | ~ rinvF1(X3,X4)
      | sK3(X4) = X3
      | ~ cUnsatisfiable(X5) ),
    inference(resolution,[],[f231,f149]) ).

fof(f231,plain,
    ! [X6,X7,X5] :
      ( ~ rs(X5,X6)
      | ~ rinvF1(X7,X5)
      | X6 = X7 ),
    inference(resolution,[],[f204,f160]) ).

fof(f160,plain,
    ! [X0,X1] :
      ( rf1(X1,X0)
      | ~ rinvF1(X0,X1) ),
    inference(cnf_transformation,[],[f123]) ).

fof(f204,plain,
    ! [X2,X3,X4] :
      ( ~ rs(X2,X4)
      | ~ rf1(X2,X3)
      | X3 = X4 ),
    inference(resolution,[],[f162,f173]) ).

fof(f173,plain,
    ! [X0,X1] :
      ( rf1(X1,X0)
      | ~ rs(X1,X0) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( rf1(X1,X0)
      | ~ rs(X1,X0) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( rs(X1,X0)
     => rf1(X1,X0) ),
    inference(rectify,[],[f29]) ).

fof(f29,axiom,
    ! [X4,X3] :
      ( rs(X3,X4)
     => rf1(X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).

fof(f162,plain,
    ! [X2,X0,X1] :
      ( ~ rf1(X0,X1)
      | ~ rf1(X0,X2)
      | X1 = X2 ),
    inference(cnf_transformation,[],[f125]) ).

fof(f125,plain,
    ! [X0,X1,X2] :
      ( ~ rf1(X0,X1)
      | ~ rf1(X0,X2)
      | X1 = X2 ),
    inference(rectify,[],[f82]) ).

fof(f82,plain,
    ! [X1,X2,X0] :
      ( ~ rf1(X1,X2)
      | ~ rf1(X1,X0)
      | X0 = X2 ),
    inference(flattening,[],[f81]) ).

fof(f81,plain,
    ! [X1,X0,X2] :
      ( X0 = X2
      | ~ rf1(X1,X2)
      | ~ rf1(X1,X0) ),
    inference(ennf_transformation,[],[f43]) ).

fof(f43,plain,
    ! [X1,X0,X2] :
      ( ( rf1(X1,X2)
        & rf1(X1,X0) )
     => X0 = X2 ),
    inference(rectify,[],[f23]) ).

fof(f23,axiom,
    ! [X5,X3,X4] :
      ( ( rf1(X3,X4)
        & rf1(X3,X5) )
     => X4 = X5 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).

fof(f151,plain,
    ! [X0] :
      ( ~ cp(sK2(X0))
      | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[],[f120]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : KRS076+1 : TPTP v8.1.0. Released v3.1.0.
% 0.12/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n019.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % 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   : Tue Aug 30 00:35:20 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.48  % (31885)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.48  % (31893)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.49  % (31893)First to succeed.
% 0.20/0.49  % (31885)Refutation not found, incomplete strategy% (31885)------------------------------
% 0.20/0.49  % (31885)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49  % (31885)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49  % (31885)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.49  
% 0.20/0.49  % (31885)Memory used [KB]: 5500
% 0.20/0.49  % (31885)Time elapsed: 0.078 s
% 0.20/0.49  % (31885)Instructions burned: 3 (million)
% 0.20/0.49  % (31885)------------------------------
% 0.20/0.49  % (31885)------------------------------
% 0.20/0.49  % (31893)Refutation found. Thanks to Tanya!
% 0.20/0.49  % SZS status Unsatisfiable for theBenchmark
% 0.20/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.49  % (31893)------------------------------
% 0.20/0.49  % (31893)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49  % (31893)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49  % (31893)Termination reason: Refutation
% 0.20/0.49  
% 0.20/0.49  % (31893)Memory used [KB]: 1151
% 0.20/0.49  % (31893)Time elapsed: 0.076 s
% 0.20/0.49  % (31893)Instructions burned: 13 (million)
% 0.20/0.49  % (31893)------------------------------
% 0.20/0.49  % (31893)------------------------------
% 0.20/0.49  % (31880)Success in time 0.135 s
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