TSTP Solution File: DAT027_1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : DAT027_1 : TPTP v8.1.0. Released v5.0.0.
% 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 : 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 : Wed Aug 31 16:04:39 EDT 2022

% Result   : Theorem 1.74s 0.59s
% Output   : Refutation 1.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   64 (  16 unt;  10 typ;   0 def)
%            Number of atoms       :  181 (  42 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  190 (  63   ~;  51   |;  58   &)
%                                         (   4 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :  209 (  55 atm;  23 fun;  49 num;  82 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (   8 usr;   7 con; 0-2 aty)
%            Number of variables   :  112 (  90   !;  22   ?; 112   :)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    collection: $tType ).

tff(func_def_0,type,
    empty: collection ).

tff(func_def_1,type,
    add: ( $int * collection ) > collection ).

tff(func_def_2,type,
    remove: ( $int * collection ) > collection ).

tff(func_def_7,type,
    sK0: $int ).

tff(func_def_8,type,
    sK1: $int ).

tff(func_def_9,type,
    sK2: collection ).

tff(func_def_10,type,
    sK3: collection ).

tff(func_def_11,type,
    sK4: $int ).

tff(pred_def_1,type,
    in: ( $int * collection ) > $o ).

tff(f637,plain,
    $false,
    inference(subsumption_resolution,[],[f635,f41]) ).

tff(f41,plain,
    ~ $less(sK1,0),
    inference(cnf_transformation,[],[f31]) ).

tff(f31,plain,
    ( in(sK4,sK3)
    & ~ $less(0,sK4)
    & ! [X5: $int] :
        ( ~ in(X5,sK2)
        | $less(0,X5) )
    & ( add($sum(sK0,sK1),remove(sK0,sK2)) = sK3 )
    & ~ $less(sK1,0)
    & in(sK0,sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f28,f30,f29]) ).

tff(f29,plain,
    ( ? [X0: $int,X1: $int,X2: collection,X3: collection] :
        ( ? [X4: $int] :
            ( in(X4,X3)
            & ~ $less(0,X4) )
        & ! [X5: $int] :
            ( ~ in(X5,X2)
            | $less(0,X5) )
        & ( add($sum(X0,X1),remove(X0,X2)) = X3 )
        & ~ $less(X1,0)
        & in(X0,X2) )
   => ( ? [X4: $int] :
          ( in(X4,sK3)
          & ~ $less(0,X4) )
      & ! [X5: $int] :
          ( ~ in(X5,sK2)
          | $less(0,X5) )
      & ( add($sum(sK0,sK1),remove(sK0,sK2)) = sK3 )
      & ~ $less(sK1,0)
      & in(sK0,sK2) ) ),
    introduced(choice_axiom,[]) ).

tff(f30,plain,
    ( ? [X4: $int] :
        ( in(X4,sK3)
        & ~ $less(0,X4) )
   => ( in(sK4,sK3)
      & ~ $less(0,sK4) ) ),
    introduced(choice_axiom,[]) ).

tff(f28,plain,
    ? [X0: $int,X1: $int,X2: collection,X3: collection] :
      ( ? [X4: $int] :
          ( in(X4,X3)
          & ~ $less(0,X4) )
      & ! [X5: $int] :
          ( ~ in(X5,X2)
          | $less(0,X5) )
      & ( add($sum(X0,X1),remove(X0,X2)) = X3 )
      & ~ $less(X1,0)
      & in(X0,X2) ),
    inference(rectify,[],[f27]) ).

tff(f27,plain,
    ? [X3: $int,X2: $int,X1: collection,X0: collection] :
      ( ? [X5: $int] :
          ( in(X5,X0)
          & ~ $less(0,X5) )
      & ! [X4: $int] :
          ( ~ in(X4,X1)
          | $less(0,X4) )
      & ( add($sum(X3,X2),remove(X3,X1)) = X0 )
      & ~ $less(X2,0)
      & in(X3,X1) ),
    inference(flattening,[],[f26]) ).

tff(f26,plain,
    ? [X3: $int,X0: collection,X2: $int,X1: collection] :
      ( ? [X5: $int] :
          ( in(X5,X0)
          & ~ $less(0,X5) )
      & ~ $less(X2,0)
      & in(X3,X1)
      & ( add($sum(X3,X2),remove(X3,X1)) = X0 )
      & ! [X4: $int] :
          ( ~ in(X4,X1)
          | $less(0,X4) ) ),
    inference(ennf_transformation,[],[f24]) ).

tff(f24,plain,
    ~ ! [X3: $int,X0: collection,X2: $int,X1: collection] :
        ( ( ~ $less(X2,0)
          & in(X3,X1)
          & ( add($sum(X3,X2),remove(X3,X1)) = X0 )
          & ! [X4: $int] :
              ( in(X4,X1)
             => $less(0,X4) ) )
       => ! [X5: $int] :
            ( in(X5,X0)
           => $less(0,X5) ) ),
    inference(rectify,[],[f8]) ).

tff(f8,plain,
    ~ ! [X0: collection,X1: collection,X3: $int,X2: $int] :
        ( ( ( add($sum(X2,X3),remove(X2,X1)) = X0 )
          & ~ $less(X3,0)
          & ! [X4: $int] :
              ( in(X4,X1)
             => $less(0,X4) )
          & in(X2,X1) )
       => ! [X5: $int] :
            ( in(X5,X0)
           => $less(0,X5) ) ),
    inference(theory_normalization,[],[f7]) ).

tff(f7,negated_conjecture,
    ~ ! [X0: collection,X1: collection,X3: $int,X2: $int] :
        ( ( ( add($sum(X2,X3),remove(X2,X1)) = X0 )
          & $greatereq(X3,0)
          & ! [X4: $int] :
              ( in(X4,X1)
             => $greater(X4,0) )
          & in(X2,X1) )
       => ! [X5: $int] :
            ( in(X5,X0)
           => $greater(X5,0) ) ),
    inference(negated_conjecture,[],[f6]) ).

tff(f6,conjecture,
    ! [X0: collection,X1: collection,X3: $int,X2: $int] :
      ( ( ( add($sum(X2,X3),remove(X2,X1)) = X0 )
        & $greatereq(X3,0)
        & ! [X4: $int] :
            ( in(X4,X1)
           => $greater(X4,0) )
        & in(X2,X1) )
     => ! [X5: $int] :
          ( in(X5,X0)
         => $greater(X5,0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

tff(f635,plain,
    $less(sK1,0),
    inference(superposition,[],[f585,f617]) ).

tff(f617,plain,
    0 = sK4,
    inference(subsumption_resolution,[],[f612,f41]) ).

tff(f612,plain,
    ( $less(sK1,0)
    | ( 0 = sK4 ) ),
    inference(resolution,[],[f585,f104]) ).

tff(f104,plain,
    ! [X0: $int] :
      ( ~ $less(X0,sK4)
      | $less(X0,0)
      | ( 0 = sK4 ) ),
    inference(resolution,[],[f99,f15]) ).

tff(f15,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X1,X2)
      | ~ $less(X0,X1)
      | $less(X0,X2) ),
    introduced(theory_axiom_148,[]) ).

tff(f99,plain,
    ( $less(sK4,0)
    | ( 0 = sK4 ) ),
    inference(resolution,[],[f16,f44]) ).

tff(f44,plain,
    ~ $less(0,sK4),
    inference(cnf_transformation,[],[f31]) ).

tff(f16,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X1,X0)
      | $less(X0,X1)
      | ( X0 = X1 ) ),
    introduced(theory_axiom_149,[]) ).

tff(f585,plain,
    $less(sK1,sK4),
    inference(subsumption_resolution,[],[f581,f69]) ).

tff(f69,plain,
    $less(0,sK0),
    inference(resolution,[],[f56,f65]) ).

tff(f65,plain,
    ~ in(sK0,sK2),
    inference(consistent_polarity_flipping,[],[f40]) ).

tff(f40,plain,
    in(sK0,sK2),
    inference(cnf_transformation,[],[f31]) ).

tff(f56,plain,
    ! [X5: $int] :
      ( in(X5,sK2)
      | $less(0,X5) ),
    inference(consistent_polarity_flipping,[],[f43]) ).

tff(f43,plain,
    ! [X5: $int] :
      ( $less(0,X5)
      | ~ in(X5,sK2) ),
    inference(cnf_transformation,[],[f31]) ).

tff(f581,plain,
    ( $less(sK1,sK4)
    | ~ $less(0,sK0) ),
    inference(superposition,[],[f354,f74]) ).

tff(f74,plain,
    ! [X0: $int] : ( $sum(0,X0) = X0 ),
    inference(superposition,[],[f9,f11]) ).

tff(f11,plain,
    ! [X0: $int] : ( $sum(X0,0) = X0 ),
    introduced(theory_axiom_142,[]) ).

tff(f9,plain,
    ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
    introduced(theory_axiom_140,[]) ).

tff(f354,plain,
    ! [X1: $int] :
      ( $less($sum(X1,sK1),sK4)
      | ~ $less(X1,sK0) ),
    inference(superposition,[],[f17,f304]) ).

tff(f304,plain,
    $sum(sK0,sK1) = sK4,
    inference(subsumption_resolution,[],[f303,f44]) ).

tff(f303,plain,
    ( $less(0,sK4)
    | ( $sum(sK0,sK1) = sK4 ) ),
    inference(resolution,[],[f302,f56]) ).

tff(f302,plain,
    ( ~ in(sK4,sK2)
    | ( $sum(sK0,sK1) = sK4 ) ),
    inference(resolution,[],[f232,f64]) ).

tff(f64,plain,
    ~ in(sK4,sK3),
    inference(consistent_polarity_flipping,[],[f45]) ).

tff(f45,plain,
    in(sK4,sK3),
    inference(cnf_transformation,[],[f31]) ).

tff(f232,plain,
    ! [X1: $int] :
      ( in(X1,sK3)
      | ( $sum(sK0,sK1) = X1 )
      | ~ in(X1,sK2) ),
    inference(resolution,[],[f229,f61]) ).

tff(f61,plain,
    ! [X2: $int,X0: collection,X1: $int] :
      ( in(X2,remove(X1,X0))
      | ~ in(X2,X0) ),
    inference(consistent_polarity_flipping,[],[f47]) ).

tff(f47,plain,
    ! [X2: $int,X0: collection,X1: $int] :
      ( ~ in(X2,remove(X1,X0))
      | in(X2,X0) ),
    inference(cnf_transformation,[],[f34]) ).

tff(f34,plain,
    ! [X0: collection,X1: $int,X2: $int] :
      ( ( ( ( X1 != X2 )
          & in(X2,X0) )
        | ~ in(X2,remove(X1,X0)) )
      & ( in(X2,remove(X1,X0))
        | ( X1 = X2 )
        | ~ in(X2,X0) ) ),
    inference(rectify,[],[f33]) ).

tff(f33,plain,
    ! [X1: collection,X2: $int,X0: $int] :
      ( ( ( ( X0 != X2 )
          & in(X0,X1) )
        | ~ in(X0,remove(X2,X1)) )
      & ( in(X0,remove(X2,X1))
        | ( X0 = X2 )
        | ~ in(X0,X1) ) ),
    inference(flattening,[],[f32]) ).

tff(f32,plain,
    ! [X1: collection,X2: $int,X0: $int] :
      ( ( ( ( X0 != X2 )
          & in(X0,X1) )
        | ~ in(X0,remove(X2,X1)) )
      & ( in(X0,remove(X2,X1))
        | ( X0 = X2 )
        | ~ in(X0,X1) ) ),
    inference(nnf_transformation,[],[f25]) ).

tff(f25,plain,
    ! [X1: collection,X2: $int,X0: $int] :
      ( ( ( X0 != X2 )
        & in(X0,X1) )
    <=> in(X0,remove(X2,X1)) ),
    inference(rectify,[],[f5]) ).

tff(f5,axiom,
    ! [X8: $int,X9: collection,X10: $int] :
      ( ( in(X8,X9)
        & ( X8 != X10 ) )
    <=> in(X8,remove(X10,X9)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).

tff(f229,plain,
    ! [X0: $int] :
      ( ~ in(X0,remove(sK0,sK2))
      | in(X0,sK3)
      | ( $sum(sK0,sK1) = X0 ) ),
    inference(superposition,[],[f66,f42]) ).

tff(f42,plain,
    add($sum(sK0,sK1),remove(sK0,sK2)) = sK3,
    inference(cnf_transformation,[],[f31]) ).

tff(f66,plain,
    ! [X2: $int,X0: collection,X1: $int] :
      ( in(X2,add(X1,X0))
      | ( X1 = X2 )
      | ~ in(X2,X0) ),
    inference(consistent_polarity_flipping,[],[f51]) ).

tff(f51,plain,
    ! [X2: $int,X0: collection,X1: $int] :
      ( in(X2,X0)
      | ( X1 = X2 )
      | ~ in(X2,add(X1,X0)) ),
    inference(cnf_transformation,[],[f37]) ).

tff(f37,plain,
    ! [X0: collection,X1: $int,X2: $int] :
      ( ( ( X1 = X2 )
        | in(X2,X0)
        | ~ in(X2,add(X1,X0)) )
      & ( in(X2,add(X1,X0))
        | ( ( X1 != X2 )
          & ~ in(X2,X0) ) ) ),
    inference(rectify,[],[f36]) ).

tff(f36,plain,
    ! [X1: collection,X0: $int,X2: $int] :
      ( ( ( X0 = X2 )
        | in(X2,X1)
        | ~ in(X2,add(X0,X1)) )
      & ( in(X2,add(X0,X1))
        | ( ( X0 != X2 )
          & ~ in(X2,X1) ) ) ),
    inference(flattening,[],[f35]) ).

tff(f35,plain,
    ! [X1: collection,X0: $int,X2: $int] :
      ( ( ( X0 = X2 )
        | in(X2,X1)
        | ~ in(X2,add(X0,X1)) )
      & ( in(X2,add(X0,X1))
        | ( ( X0 != X2 )
          & ~ in(X2,X1) ) ) ),
    inference(nnf_transformation,[],[f23]) ).

tff(f23,plain,
    ! [X1: collection,X0: $int,X2: $int] :
      ( ( ( X0 = X2 )
        | in(X2,X1) )
    <=> in(X2,add(X0,X1)) ),
    inference(rectify,[],[f4]) ).

tff(f4,axiom,
    ! [X7: $int,X6: collection,X5: $int] :
      ( ( ( X5 = X7 )
        | in(X5,X6) )
    <=> in(X5,add(X7,X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).

tff(f17,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less($sum(X0,X2),$sum(X1,X2))
      | ~ $less(X0,X1) ),
    introduced(theory_axiom_150,[]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : DAT027=1 : TPTP v8.1.0. Released v5.0.0.
% 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 : n006.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   : Mon Aug 29 20:15:40 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.52  % (1197)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)
% 0.20/0.54  % (1209)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.54  % (1211)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.54  % (1209)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.20/0.54  % (1209)Terminated due to inappropriate strategy.
% 0.20/0.54  % (1209)------------------------------
% 0.20/0.54  % (1209)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54  % (1209)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54  % (1209)Termination reason: Inappropriate
% 0.20/0.54  
% 0.20/0.54  % (1209)Memory used [KB]: 895
% 0.20/0.54  % (1209)Time elapsed: 0.003 s
% 0.20/0.54  % (1209)Instructions burned: 2 (million)
% 0.20/0.54  % (1209)------------------------------
% 0.20/0.54  % (1209)------------------------------
% 0.20/0.55  % (1217)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.20/0.55  % (1201)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)
% 0.20/0.57  % (1194)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)
% 0.20/0.58  % (1197)Instruction limit reached!
% 0.20/0.58  % (1197)------------------------------
% 0.20/0.58  % (1197)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.58  % (1196)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.58  % (1193)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)
% 1.74/0.58  % (1221)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)
% 1.74/0.58  % (1197)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.74/0.58  % (1197)Termination reason: Unknown
% 1.74/0.58  % (1197)Termination phase: Saturation
% 1.74/0.58  
% 1.74/0.58  % (1197)Memory used [KB]: 5884
% 1.74/0.58  % (1197)Time elapsed: 0.167 s
% 1.74/0.58  % (1197)Instructions burned: 48 (million)
% 1.74/0.58  % (1197)------------------------------
% 1.74/0.58  % (1197)------------------------------
% 1.74/0.59  % (1211)First to succeed.
% 1.74/0.59  % (1211)Refutation found. Thanks to Tanya!
% 1.74/0.59  % SZS status Theorem for theBenchmark
% 1.74/0.59  % SZS output start Proof for theBenchmark
% See solution above
% 1.74/0.59  % (1211)------------------------------
% 1.74/0.59  % (1211)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.74/0.59  % (1211)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.74/0.59  % (1211)Termination reason: Refutation
% 1.74/0.59  
% 1.74/0.59  % (1211)Memory used [KB]: 1535
% 1.74/0.59  % (1211)Time elapsed: 0.171 s
% 1.74/0.59  % (1211)Instructions burned: 41 (million)
% 1.74/0.59  % (1211)------------------------------
% 1.74/0.59  % (1211)------------------------------
% 1.74/0.59  % (1191)Success in time 0.234 s
%------------------------------------------------------------------------------