TSTP Solution File: NUN054+2 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : NUN054+2 : TPTP v8.1.0. Released v7.3.0.
% 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 : n018.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 18:08:00 EDT 2022

% Result   : Theorem 0.20s 0.53s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   72 (  26 unt;   0 def)
%            Number of atoms       :  233 (  60 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  250 (  89   ~;  60   |;  90   &)
%                                         (   2 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   1 con; 0-2 aty)
%            Number of variables   :  187 ( 129   !;  58   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f842,plain,
    $false,
    inference(subsumption_resolution,[],[f841,f104]) ).

fof(f104,plain,
    r1(sK4),
    inference(equality_resolution,[],[f68]) ).

fof(f68,plain,
    ! [X1] :
      ( r1(X1)
      | sK4 != X1 ),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X1] :
      ( ( r1(X1)
        & sK4 = X1 )
      | ( ~ r1(X1)
        & sK4 != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f1,f32]) ).

fof(f32,plain,
    ( ? [X0] :
      ! [X1] :
        ( ( r1(X1)
          & X0 = X1 )
        | ( ~ r1(X1)
          & X0 != X1 ) )
   => ! [X1] :
        ( ( r1(X1)
          & sK4 = X1 )
        | ( ~ r1(X1)
          & sK4 != X1 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f1,axiom,
    ? [X0] :
    ! [X1] :
      ( ( r1(X1)
        & X0 = X1 )
      | ( ~ r1(X1)
        & X0 != X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).

fof(f841,plain,
    ~ r1(sK4),
    inference(resolution,[],[f838,f203]) ).

fof(f203,plain,
    ! [X0] : r3(X0,sK19(sK4),sK19(X0)),
    inference(superposition,[],[f151,f188]) ).

fof(f188,plain,
    ! [X2] : sK11(X2,sK4) = sK19(X2),
    inference(resolution,[],[f185,f95]) ).

fof(f95,plain,
    ! [X2,X0] :
      ( ~ r2(X0,X2)
      | sK19(X0) = X2 ),
    inference(cnf_transformation,[],[f57]) ).

fof(f57,plain,
    ! [X0,X2] :
      ( ( sK19(X0) != X2
        & ~ r2(X0,X2) )
      | ( sK19(X0) = X2
        & r2(X0,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f21,f56]) ).

fof(f56,plain,
    ! [X0] :
      ( ? [X1] :
        ! [X2] :
          ( ( X1 != X2
            & ~ r2(X0,X2) )
          | ( X1 = X2
            & r2(X0,X2) ) )
     => ! [X2] :
          ( ( sK19(X0) != X2
            & ~ r2(X0,X2) )
          | ( sK19(X0) = X2
            & r2(X0,X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,plain,
    ! [X0] :
    ? [X1] :
    ! [X2] :
      ( ( X1 != X2
        & ~ r2(X0,X2) )
      | ( X1 = X2
        & r2(X0,X2) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X2] :
    ? [X3] :
    ! [X4] :
      ( ( X3 = X4
        & r2(X2,X4) )
      | ( X3 != X4
        & ~ r2(X2,X4) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

fof(f185,plain,
    ! [X0] : r2(X0,sK11(X0,sK4)),
    inference(superposition,[],[f82,f179]) ).

fof(f179,plain,
    ! [X0] : sK14(X0,sK4) = X0,
    inference(superposition,[],[f171,f170]) ).

fof(f170,plain,
    ! [X0] : sK18(sK4,X0) = X0,
    inference(resolution,[],[f90,f124]) ).

fof(f124,plain,
    ! [X0] : r3(X0,sK4,X0),
    inference(backward_demodulation,[],[f118,f120]) ).

fof(f120,plain,
    ! [X0] : sK7(X0) = sK4,
    inference(resolution,[],[f67,f74]) ).

fof(f74,plain,
    ! [X0] : r1(sK7(X0)),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0] :
      ( sK6(X0) = X0
      & r3(X0,sK7(X0),sK6(X0))
      & r1(sK7(X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f18,f37,f36]) ).

fof(f36,plain,
    ! [X0] :
      ( ? [X1] :
          ( X0 = X1
          & ? [X2] :
              ( r3(X0,X2,X1)
              & r1(X2) ) )
     => ( sK6(X0) = X0
        & ? [X2] :
            ( r3(X0,X2,sK6(X0))
            & r1(X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f37,plain,
    ! [X0] :
      ( ? [X2] :
          ( r3(X0,X2,sK6(X0))
          & r1(X2) )
     => ( r3(X0,sK7(X0),sK6(X0))
        & r1(sK7(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ! [X0] :
    ? [X1] :
      ( X0 = X1
      & ? [X2] :
          ( r3(X0,X2,X1)
          & r1(X2) ) ),
    inference(rectify,[],[f8]) ).

fof(f8,axiom,
    ! [X29] :
    ? [X30] :
      ( X29 = X30
      & ? [X31] :
          ( r3(X29,X31,X30)
          & r1(X31) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4a) ).

fof(f67,plain,
    ! [X1] :
      ( ~ r1(X1)
      | sK4 = X1 ),
    inference(cnf_transformation,[],[f33]) ).

fof(f118,plain,
    ! [X0] : r3(X0,sK7(X0),X0),
    inference(forward_demodulation,[],[f75,f76]) ).

fof(f76,plain,
    ! [X0] : sK6(X0) = X0,
    inference(cnf_transformation,[],[f38]) ).

fof(f75,plain,
    ! [X0] : r3(X0,sK7(X0),sK6(X0)),
    inference(cnf_transformation,[],[f38]) ).

fof(f90,plain,
    ! [X3,X0,X1] :
      ( ~ r3(X1,X0,X3)
      | sK18(X0,X1) = X3 ),
    inference(cnf_transformation,[],[f55]) ).

fof(f55,plain,
    ! [X0,X1,X3] :
      ( ( r3(X1,X0,X3)
        & sK18(X0,X1) = X3 )
      | ( sK18(X0,X1) != X3
        & ~ r3(X1,X0,X3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f17,f54]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( ? [X2] :
        ! [X3] :
          ( ( r3(X1,X0,X3)
            & X2 = X3 )
          | ( X2 != X3
            & ~ r3(X1,X0,X3) ) )
     => ! [X3] :
          ( ( r3(X1,X0,X3)
            & sK18(X0,X1) = X3 )
          | ( sK18(X0,X1) != X3
            & ~ r3(X1,X0,X3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f17,plain,
    ! [X0,X1] :
    ? [X2] :
    ! [X3] :
      ( ( r3(X1,X0,X3)
        & X2 = X3 )
      | ( X2 != X3
        & ~ r3(X1,X0,X3) ) ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X6,X5] :
    ? [X7] :
    ! [X8] :
      ( ( ~ r3(X5,X6,X8)
        & X7 != X8 )
      | ( X7 = X8
        & r3(X5,X6,X8) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).

fof(f171,plain,
    ! [X2,X1] : sK18(X1,X2) = sK14(X2,X1),
    inference(resolution,[],[f90,f81]) ).

fof(f81,plain,
    ! [X0,X1] : r3(X0,X1,sK14(X0,X1)),
    inference(cnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( sK12(X0,X1) = sK11(X0,X1)
      & r3(X0,sK13(X0,X1),sK12(X0,X1))
      & r2(X1,sK13(X0,X1))
      & r2(sK14(X0,X1),sK11(X0,X1))
      & r3(X0,X1,sK14(X0,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14])],[f44,f48,f47,f46,f45]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( X2 = X3
              & ? [X4] :
                  ( r3(X0,X4,X3)
                  & r2(X1,X4) ) )
          & ? [X5] :
              ( r2(X5,X2)
              & r3(X0,X1,X5) ) )
     => ( ? [X3] :
            ( sK11(X0,X1) = X3
            & ? [X4] :
                ( r3(X0,X4,X3)
                & r2(X1,X4) ) )
        & ? [X5] :
            ( r2(X5,sK11(X0,X1))
            & r3(X0,X1,X5) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( sK11(X0,X1) = X3
          & ? [X4] :
              ( r3(X0,X4,X3)
              & r2(X1,X4) ) )
     => ( sK12(X0,X1) = sK11(X0,X1)
        & ? [X4] :
            ( r3(X0,X4,sK12(X0,X1))
            & r2(X1,X4) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( r3(X0,X4,sK12(X0,X1))
          & r2(X1,X4) )
     => ( r3(X0,sK13(X0,X1),sK12(X0,X1))
        & r2(X1,sK13(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( r2(X5,sK11(X0,X1))
          & r3(X0,X1,X5) )
     => ( r2(sK14(X0,X1),sK11(X0,X1))
        & r3(X0,X1,sK14(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f44,plain,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X3] :
          ( X2 = X3
          & ? [X4] :
              ( r3(X0,X4,X3)
              & r2(X1,X4) ) )
      & ? [X5] :
          ( r2(X5,X2)
          & r3(X0,X1,X5) ) ),
    inference(rectify,[],[f15]) ).

fof(f15,plain,
    ! [X1,X0] :
    ? [X2] :
      ( ? [X3] :
          ( X2 = X3
          & ? [X4] :
              ( r3(X1,X4,X3)
              & r2(X0,X4) ) )
      & ? [X5] :
          ( r2(X5,X2)
          & r3(X1,X0,X5) ) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X14,X13] :
    ? [X15] :
      ( ? [X16] :
          ( X15 = X16
          & ? [X17] :
              ( r3(X13,X17,X16)
              & r2(X14,X17) ) )
      & ? [X18] :
          ( r3(X13,X14,X18)
          & r2(X18,X15) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1a) ).

fof(f82,plain,
    ! [X0,X1] : r2(sK14(X0,X1),sK11(X0,X1)),
    inference(cnf_transformation,[],[f49]) ).

fof(f151,plain,
    ! [X0,X1] : r3(X0,sK19(X1),sK11(X0,X1)),
    inference(backward_demodulation,[],[f102,f144]) ).

fof(f144,plain,
    ! [X3,X4] : sK19(X3) = sK13(X4,X3),
    inference(resolution,[],[f95,f83]) ).

fof(f83,plain,
    ! [X0,X1] : r2(X1,sK13(X0,X1)),
    inference(cnf_transformation,[],[f49]) ).

fof(f102,plain,
    ! [X0,X1] : r3(X0,sK13(X0,X1),sK11(X0,X1)),
    inference(definition_unfolding,[],[f84,f85]) ).

fof(f85,plain,
    ! [X0,X1] : sK12(X0,X1) = sK11(X0,X1),
    inference(cnf_transformation,[],[f49]) ).

fof(f84,plain,
    ! [X0,X1] : r3(X0,sK13(X0,X1),sK12(X0,X1)),
    inference(cnf_transformation,[],[f49]) ).

fof(f838,plain,
    ! [X0] :
      ( ~ r3(X0,sK19(sK4),sK19(sK4))
      | ~ r1(X0) ),
    inference(resolution,[],[f208,f131]) ).

fof(f131,plain,
    sP20(sK19(sK4)),
    inference(resolution,[],[f130,f111]) ).

fof(f111,plain,
    ! [X0] : r2(X0,sK19(X0)),
    inference(equality_resolution,[],[f96]) ).

fof(f96,plain,
    ! [X2,X0] :
      ( sK19(X0) != X2
      | r2(X0,X2) ),
    inference(cnf_transformation,[],[f57]) ).

fof(f130,plain,
    ! [X0] :
      ( ~ r2(sK4,X0)
      | sP20(X0) ),
    inference(resolution,[],[f114,f104]) ).

fof(f114,plain,
    ! [X2,X1] :
      ( ~ r1(X2)
      | sP20(X1)
      | ~ r2(X2,X1) ),
    inference(cnf_transformation,[],[f114_D]) ).

fof(f114_D,plain,
    ! [X1] :
      ( ! [X2] :
          ( ~ r1(X2)
          | ~ r2(X2,X1) )
    <=> ~ sP20(X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP20])]) ).

fof(f208,plain,
    ! [X0,X1] :
      ( ~ sP20(X1)
      | ~ r3(X0,sK19(sK4),X1)
      | ~ r1(X0) ),
    inference(resolution,[],[f117,f139]) ).

fof(f139,plain,
    sP21(sK19(sK4)),
    inference(resolution,[],[f134,f111]) ).

fof(f134,plain,
    ! [X0] :
      ( ~ r2(sK4,X0)
      | sP21(X0) ),
    inference(resolution,[],[f116,f104]) ).

fof(f116,plain,
    ! [X3,X5] :
      ( ~ r1(X5)
      | sP21(X3)
      | ~ r2(X5,X3) ),
    inference(cnf_transformation,[],[f116_D]) ).

fof(f116_D,plain,
    ! [X3] :
      ( ! [X5] :
          ( ~ r1(X5)
          | ~ r2(X5,X3) )
    <=> ~ sP21(X3) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP21])]) ).

fof(f117,plain,
    ! [X3,X1,X4] :
      ( ~ sP21(X3)
      | ~ r1(X4)
      | ~ sP20(X1)
      | ~ r3(X4,X3,X1) ),
    inference(general_splitting,[],[f115,f116_D]) ).

fof(f115,plain,
    ! [X3,X1,X4,X5] :
      ( ~ r3(X4,X3,X1)
      | ~ r1(X4)
      | ~ r1(X5)
      | ~ r2(X5,X3)
      | ~ sP20(X1) ),
    inference(general_splitting,[],[f113,f114_D]) ).

fof(f113,plain,
    ! [X2,X3,X1,X4,X5] :
      ( ~ r2(X2,X1)
      | ~ r1(X2)
      | ~ r3(X4,X3,X1)
      | ~ r1(X4)
      | ~ r1(X5)
      | ~ r2(X5,X3) ),
    inference(equality_resolution,[],[f99]) ).

fof(f99,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ r2(X2,X1)
      | ~ r1(X2)
      | X0 != X1
      | ~ r3(X4,X3,X0)
      | ~ r1(X4)
      | ~ r1(X5)
      | ~ r2(X5,X3) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f59,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ~ r2(X2,X1)
              | ~ r1(X2) )
          | X0 != X1 )
      | ! [X3] :
          ( ! [X4] :
              ( ~ r3(X4,X3,X0)
              | ~ r1(X4) )
          | ! [X5] :
              ( ~ r1(X5)
              | ~ r2(X5,X3) ) ) ),
    inference(rectify,[],[f25]) ).

fof(f25,plain,
    ! [X0] :
      ( ! [X4] :
          ( ! [X5] :
              ( ~ r2(X5,X4)
              | ~ r1(X5) )
          | X0 != X4 )
      | ! [X1] :
          ( ! [X3] :
              ( ~ r3(X3,X1,X0)
              | ~ r1(X3) )
          | ! [X2] :
              ( ~ r1(X2)
              | ~ r2(X2,X1) ) ) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,plain,
    ~ ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( r1(X2)
                & r2(X2,X1) )
            & ? [X3] :
                ( r1(X3)
                & r3(X3,X1,X0) ) )
        & ? [X4] :
            ( X0 = X4
            & ? [X5] :
                ( r1(X5)
                & r2(X5,X4) ) ) ),
    inference(rectify,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ? [X38] :
        ( ? [X21] :
            ( ? [X16] :
                ( r1(X16)
                & r2(X16,X21) )
            & ? [X15] :
                ( r3(X15,X21,X38)
                & r1(X15) ) )
        & ? [X22] :
            ( X22 = X38
            & ? [X24] :
                ( r2(X24,X22)
                & r1(X24) ) ) ),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ? [X38] :
      ( ? [X21] :
          ( ? [X16] :
              ( r1(X16)
              & r2(X16,X21) )
          & ? [X15] :
              ( r3(X15,X21,X38)
              & r1(X15) ) )
      & ? [X22] :
          ( X22 = X38
          & ? [X24] :
              ( r2(X24,X22)
              & r1(X24) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zeroplusoneeqone) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13  % Problem    : NUN054+2 : TPTP v8.1.0. Released v7.3.0.
% 0.06/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.34  % Computer : n018.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % 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 30 09:45:10 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.20/0.49  % (15201)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.20/0.49  % (15193)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.52  % (15193)First to succeed.
% 0.20/0.52  % (15195)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.20/0.52  % (15201)Also succeeded, but the first one will report.
% 0.20/0.53  % (15193)Refutation found. Thanks to Tanya!
% 0.20/0.53  % SZS status Theorem for theBenchmark
% 0.20/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.53  % (15193)------------------------------
% 0.20/0.53  % (15193)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (15193)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (15193)Termination reason: Refutation
% 0.20/0.53  
% 0.20/0.53  % (15193)Memory used [KB]: 5884
% 0.20/0.53  % (15193)Time elapsed: 0.099 s
% 0.20/0.53  % (15193)Instructions burned: 29 (million)
% 0.20/0.53  % (15193)------------------------------
% 0.20/0.53  % (15193)------------------------------
% 0.20/0.53  % (15171)Success in time 0.172 s
%------------------------------------------------------------------------------