TSTP Solution File: NUN062+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : NUN062+1 : TPTP v8.1.0. Bugfixed v7.4.0.
% 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 : n029.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 18:08:02 EDT 2022

% Result   : Theorem 0.20s 0.53s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   42 (  11 unt;   0 def)
%            Number of atoms       :  130 (   0 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  137 (  49   ~;  37   |;  45   &)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-2 aty)
%            Number of variables   :  124 (  87   !;  37   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f215,plain,
    $false,
    inference(resolution,[],[f211,f176]) ).

fof(f176,plain,
    ! [X2] : id(sK14(X2),X2),
    inference(resolution,[],[f165,f121]) ).

fof(f121,plain,
    ! [X0,X1] :
      ( ~ id(X0,X1)
      | id(X1,X0) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( id(X1,X0)
      | ~ id(X0,X1) ),
    inference(rectify,[],[f21]) ).

fof(f21,plain,
    ! [X1,X0] :
      ( id(X0,X1)
      | ~ id(X1,X0) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X15,X14] :
      ( id(X15,X14)
      | ~ id(X14,X15) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).

fof(f165,plain,
    ! [X0] : id(X0,sK14(X0)),
    inference(resolution,[],[f146,f136]) ).

fof(f136,plain,
    ! [X0] : id(X0,X0),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0] : id(X0,X0),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X13] : id(X13,X13),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).

fof(f146,plain,
    ! [X0,X1] :
      ( ~ id(sK19(sK13,X0),X1)
      | id(X0,sK14(X0)) ),
    inference(resolution,[],[f129,f123]) ).

fof(f123,plain,
    ! [X2,X1,X4] :
      ( ~ r3(sK13,X2,X4)
      | ~ id(X4,X1)
      | id(X2,sK14(X2)) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X1,X2] :
      ( ( id(X2,sK14(X2))
        & r1(sK14(X2)) )
      | ! [X4] :
          ( ~ r3(sK13,X2,X4)
          | ~ id(X4,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14])],[f65,f67,f66]) ).

fof(f66,plain,
    ( ? [X0] :
      ! [X1,X2] :
        ( ? [X3] :
            ( id(X2,X3)
            & r1(X3) )
        | ! [X4] :
            ( ~ r3(X0,X2,X4)
            | ~ id(X4,X1) ) )
   => ! [X2,X1] :
        ( ? [X3] :
            ( id(X2,X3)
            & r1(X3) )
        | ! [X4] :
            ( ~ r3(sK13,X2,X4)
            | ~ id(X4,X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f67,plain,
    ! [X2] :
      ( ? [X3] :
          ( id(X2,X3)
          & r1(X3) )
     => ( id(X2,sK14(X2))
        & r1(sK14(X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f65,plain,
    ? [X0] :
    ! [X1,X2] :
      ( ? [X3] :
          ( id(X2,X3)
          & r1(X3) )
      | ! [X4] :
          ( ~ r3(X0,X2,X4)
          | ~ id(X4,X1) ) ),
    inference(rectify,[],[f39]) ).

fof(f39,plain,
    ? [X0] :
    ! [X2,X1] :
      ( ? [X4] :
          ( id(X1,X4)
          & r1(X4) )
      | ! [X3] :
          ( ~ r3(X0,X1,X3)
          | ~ id(X3,X2) ) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f34,plain,
    ~ ! [X0] :
      ? [X2,X1] :
        ( ? [X3] :
            ( r3(X0,X1,X3)
            & id(X3,X2) )
        & ! [X4] :
            ( ~ r1(X4)
            | ~ id(X1,X4) ) ),
    inference(rectify,[],[f20]) ).

fof(f20,negated_conjecture,
    ~ ! [X37] :
      ? [X62,X45] :
        ( ? [X46] :
            ( id(X46,X45)
            & r3(X37,X62,X46) )
        & ! [X39] :
            ( ~ r1(X39)
            | ~ id(X62,X39) ) ),
    inference(negated_conjecture,[],[f19]) ).

fof(f19,conjecture,
    ! [X37] :
    ? [X62,X45] :
      ( ? [X46] :
          ( id(X46,X45)
          & r3(X37,X62,X46) )
      & ! [X39] :
          ( ~ r1(X39)
          | ~ id(X62,X39) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',infiniteNumbersid) ).

fof(f129,plain,
    ! [X0,X1] : r3(X0,X1,sK19(X0,X1)),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( r3(X0,sK18(X0,X1),sK17(X0,X1))
      & r2(X1,sK18(X0,X1))
      & id(sK17(X0,X1),sK16(X0,X1))
      & r3(X0,X1,sK19(X0,X1))
      & r2(sK19(X0,X1),sK16(X0,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17,sK18,sK19])],[f25,f74,f73,f72,f71]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( r3(X0,X4,X3)
                  & r2(X1,X4) )
              & id(X3,X2) )
          & ? [X5] :
              ( r3(X0,X1,X5)
              & r2(X5,X2) ) )
     => ( ? [X3] :
            ( ? [X4] :
                ( r3(X0,X4,X3)
                & r2(X1,X4) )
            & id(X3,sK16(X0,X1)) )
        & ? [X5] :
            ( r3(X0,X1,X5)
            & r2(X5,sK16(X0,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ? [X4] :
              ( r3(X0,X4,X3)
              & r2(X1,X4) )
          & id(X3,sK16(X0,X1)) )
     => ( ? [X4] :
            ( r3(X0,X4,sK17(X0,X1))
            & r2(X1,X4) )
        & id(sK17(X0,X1),sK16(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( r3(X0,X4,sK17(X0,X1))
          & r2(X1,X4) )
     => ( r3(X0,sK18(X0,X1),sK17(X0,X1))
        & r2(X1,sK18(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( r3(X0,X1,X5)
          & r2(X5,sK16(X0,X1)) )
     => ( r3(X0,X1,sK19(X0,X1))
        & r2(sK19(X0,X1),sK16(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f25,plain,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X3] :
          ( ? [X4] :
              ( r3(X0,X4,X3)
              & r2(X1,X4) )
          & id(X3,X2) )
      & ? [X5] :
          ( r3(X0,X1,X5)
          & r2(X5,X2) ) ),
    inference(rectify,[],[f12]) ).

fof(f12,axiom,
    ! [X37,X38] :
    ? [X39] :
      ( ? [X40] :
          ( ? [X41] :
              ( r3(X37,X41,X40)
              & r2(X38,X41) )
          & id(X40,X39) )
      & ? [X42] :
          ( r3(X37,X38,X42)
          & r2(X42,X39) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1a) ).

fof(f211,plain,
    ! [X2,X0,X1] : ~ id(X0,sK18(X1,X2)),
    inference(subsumption_resolution,[],[f209,f179]) ).

fof(f179,plain,
    ! [X1] : r1(X1),
    inference(subsumption_resolution,[],[f175,f163]) ).

fof(f163,plain,
    ! [X0] : r1(sK14(X0)),
    inference(resolution,[],[f147,f136]) ).

fof(f147,plain,
    ! [X2,X3] :
      ( ~ id(sK19(sK13,X2),X3)
      | r1(sK14(X2)) ),
    inference(resolution,[],[f129,f122]) ).

fof(f122,plain,
    ! [X2,X1,X4] :
      ( ~ r3(sK13,X2,X4)
      | r1(sK14(X2))
      | ~ id(X4,X1) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f175,plain,
    ! [X1] :
      ( ~ r1(sK14(X1))
      | r1(X1) ),
    inference(resolution,[],[f165,f93]) ).

fof(f93,plain,
    ! [X0,X1] :
      ( ~ id(X0,X1)
      | r1(X0)
      | ~ r1(X1) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ~ id(X0,X1)
      | ( ~ r1(X0)
        & ~ r1(X1) )
      | ( r1(X0)
        & r1(X1) ) ),
    inference(rectify,[],[f8]) ).

fof(f8,axiom,
    ! [X19,X20] :
      ( ( r1(X19)
        & r1(X20) )
      | ~ id(X19,X20)
      | ( ~ r1(X20)
        & ~ r1(X19) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).

fof(f209,plain,
    ! [X2,X0,X1] :
      ( ~ r1(X0)
      | ~ id(X0,sK18(X1,X2)) ),
    inference(resolution,[],[f137,f131]) ).

fof(f131,plain,
    ! [X0,X1] : r2(X1,sK18(X0,X1)),
    inference(cnf_transformation,[],[f75]) ).

fof(f137,plain,
    ! [X2,X0,X1] :
      ( ~ r2(X1,X0)
      | ~ r1(X2)
      | ~ id(X2,X0) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ~ r1(X2)
          | ~ id(X2,X0) )
      | ~ r2(X1,X0) ),
    inference(rectify,[],[f18]) ).

fof(f18,axiom,
    ! [X65,X64] :
      ( ~ r2(X64,X65)
      | ! [X66] :
          ( ~ r1(X66)
          | ~ id(X66,X65) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7a) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : NUN062+1 : TPTP v8.1.0. Bugfixed v7.4.0.
% 0.03/0.13  % 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 : n029.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
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 09:53:27 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.49  % (32602)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)
% 0.20/0.49  % (32611)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)
% 0.20/0.50  % (32627)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.20/0.50  % (32608)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.50  TRYING [1]
% 0.20/0.50  TRYING [2]
% 0.20/0.51  % (32618)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.51  % (32630)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.20/0.51  % (32607)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.20/0.51  % (32602)Refutation not found, incomplete strategy% (32602)------------------------------
% 0.20/0.51  % (32602)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (32601)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.20/0.51  % (32602)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (32602)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.51  
% 0.20/0.51  % (32602)Memory used [KB]: 5500
% 0.20/0.51  % (32602)Time elapsed: 0.108 s
% 0.20/0.51  % (32602)Instructions burned: 5 (million)
% 0.20/0.51  % (32602)------------------------------
% 0.20/0.51  % (32602)------------------------------
% 0.20/0.51  % (32613)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.51  TRYING [3]
% 0.20/0.51  % (32619)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.20/0.52  % (32628)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  % (32609)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.52  % (32616)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.52  % (32628)First to succeed.
% 0.20/0.52  % (32634)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)
% 0.20/0.53  % (32606)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.53  % (32604)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.20/0.53  % (32612)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.53  % (32605)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.53  % (32609)Instruction limit reached!
% 0.20/0.53  % (32609)------------------------------
% 0.20/0.53  % (32609)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (32609)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (32609)Termination reason: Unknown
% 0.20/0.53  % (32609)Termination phase: Saturation
% 0.20/0.53  
% 0.20/0.53  % (32609)Memory used [KB]: 5500
% 0.20/0.53  % (32609)Time elapsed: 0.097 s
% 0.20/0.53  % (32609)Instructions burned: 7 (million)
% 0.20/0.53  % (32609)------------------------------
% 0.20/0.53  % (32609)------------------------------
% 0.20/0.53  % (32629)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.20/0.53  % (32626)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.53  % (32628)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  % (32628)------------------------------
% 0.20/0.53  % (32628)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (32628)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (32628)Termination reason: Refutation
% 0.20/0.53  
% 0.20/0.53  % (32628)Memory used [KB]: 5500
% 0.20/0.53  % (32628)Time elapsed: 0.090 s
% 0.20/0.53  % (32628)Instructions burned: 5 (million)
% 0.20/0.53  % (32628)------------------------------
% 0.20/0.53  % (32628)------------------------------
% 0.20/0.53  % (32596)Success in time 0.178 s
%------------------------------------------------------------------------------