TSTP Solution File: DAT024_1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : DAT024_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 : n021.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 1.69s 0.57s
% Output   : Refutation 1.69s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   49 (  20 unt;   7 typ;   0 def)
%            Number of atoms       :  107 (  15 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  113 (  48   ~;  22   |;  32   &)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :  190 (  46 atm;  23 fun;  85 num;  36 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (   5 usr;   8 con; 0-2 aty)
%            Number of variables   :   43 (  33   !;  10   ?;  43   :)

% 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_8,type,
    sK0: collection ).

tff(func_def_9,type,
    sK1: $int ).

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

tff(f367,plain,
    $false,
    inference(subsumption_resolution,[],[f305,f52]) ).

tff(f52,plain,
    ~ in(0,sK0),
    inference(cnf_transformation,[],[f38]) ).

tff(f38,plain,
    ( ~ in(0,sK0)
    & ~ in(1,sK0)
    & $less(sK1,2)
    & in(sK1,sK0)
    & ! [X2: $int] :
        ( ~ in(X2,sK0)
        | ~ $less(X2,0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f35,f37,f36]) ).

tff(f36,plain,
    ( ? [X0: collection] :
        ( ~ in(0,X0)
        & ~ in(1,X0)
        & ? [X1: $int] :
            ( $less(X1,2)
            & in(X1,X0) )
        & ! [X2: $int] :
            ( ~ in(X2,X0)
            | ~ $less(X2,0) ) )
   => ( ~ in(0,sK0)
      & ~ in(1,sK0)
      & ? [X1: $int] :
          ( $less(X1,2)
          & in(X1,sK0) )
      & ! [X2: $int] :
          ( ~ in(X2,sK0)
          | ~ $less(X2,0) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f37,plain,
    ( ? [X1: $int] :
        ( $less(X1,2)
        & in(X1,sK0) )
   => ( $less(sK1,2)
      & in(sK1,sK0) ) ),
    introduced(choice_axiom,[]) ).

tff(f35,plain,
    ? [X0: collection] :
      ( ~ in(0,X0)
      & ~ in(1,X0)
      & ? [X1: $int] :
          ( $less(X1,2)
          & in(X1,X0) )
      & ! [X2: $int] :
          ( ~ in(X2,X0)
          | ~ $less(X2,0) ) ),
    inference(rectify,[],[f26]) ).

tff(f26,plain,
    ? [X0: collection] :
      ( ~ in(0,X0)
      & ~ in(1,X0)
      & ? [X2: $int] :
          ( $less(X2,2)
          & in(X2,X0) )
      & ! [X1: $int] :
          ( ~ in(X1,X0)
          | ~ $less(X1,0) ) ),
    inference(flattening,[],[f25]) ).

tff(f25,plain,
    ? [X0: collection] :
      ( ? [X2: $int] :
          ( $less(X2,2)
          & in(X2,X0) )
      & ~ in(1,X0)
      & ! [X1: $int] :
          ( ~ in(X1,X0)
          | ~ $less(X1,0) )
      & ~ in(0,X0) ),
    inference(ennf_transformation,[],[f8]) ).

tff(f8,plain,
    ~ ! [X0: collection] :
        ( ( ~ in(1,X0)
          & ! [X1: $int] :
              ( in(X1,X0)
             => ~ $less(X1,0) )
          & ~ in(0,X0) )
       => ! [X2: $int] :
            ( in(X2,X0)
           => ~ $less(X2,2) ) ),
    inference(theory_normalization,[],[f7]) ).

tff(f7,negated_conjecture,
    ~ ! [X0: collection] :
        ( ( ! [X1: $int] :
              ( in(X1,X0)
             => $greatereq(X1,0) )
          & ~ in(0,X0)
          & ~ in(1,X0) )
       => ! [X2: $int] :
            ( in(X2,X0)
           => $greatereq(X2,2) ) ),
    inference(negated_conjecture,[],[f6]) ).

tff(f6,conjecture,
    ! [X0: collection] :
      ( ( ! [X1: $int] :
            ( in(X1,X0)
           => $greatereq(X1,0) )
        & ~ in(0,X0)
        & ~ in(1,X0) )
     => ! [X2: $int] :
          ( in(X2,X0)
         => $greatereq(X2,2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

tff(f305,plain,
    in(0,sK0),
    inference(backward_demodulation,[],[f49,f304]) ).

tff(f304,plain,
    0 = sK1,
    inference(subsumption_resolution,[],[f285,f51]) ).

tff(f51,plain,
    ~ in(1,sK0),
    inference(cnf_transformation,[],[f38]) ).

tff(f285,plain,
    ( ( 0 = sK1 )
    | in(1,sK0) ),
    inference(superposition,[],[f49,f284]) ).

tff(f284,plain,
    ( ( 1 = sK1 )
    | ( 0 = sK1 ) ),
    inference(subsumption_resolution,[],[f283,f218]) ).

tff(f218,plain,
    ~ $less(1,sK1),
    inference(evaluation,[],[f217]) ).

tff(f217,plain,
    ~ $less(1,$sum($sum(-1,sK1),1)),
    inference(resolution,[],[f212,f20]) ).

tff(f20,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | ~ $less(X1,$sum(X0,1)) ),
    introduced(theory_axiom_166,[]) ).

tff(f212,plain,
    $less($sum(-1,sK1),1),
    inference(resolution,[],[f209,f68]) ).

tff(f68,plain,
    ! [X2: $int] :
      ( $less(0,X2)
      | $less(X2,1) ),
    inference(superposition,[],[f18,f59]) ).

tff(f59,plain,
    ! [X0: $int] : ( $sum(0,X0) = X0 ),
    inference(superposition,[],[f11,f9]) ).

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

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

tff(f18,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X1,$sum(X0,1))
      | $less(X0,X1) ),
    introduced(theory_axiom_152,[]) ).

tff(f209,plain,
    ~ $less(0,$sum(-1,sK1)),
    inference(evaluation,[],[f208]) ).

tff(f208,plain,
    ~ $less(0,$sum($sum(-2,sK1),1)),
    inference(resolution,[],[f201,f20]) ).

tff(f201,plain,
    $less($sum(-2,sK1),0),
    inference(forward_demodulation,[],[f198,f9]) ).

tff(f198,plain,
    $less($sum(sK1,-2),0),
    inference(evaluation,[],[f195]) ).

tff(f195,plain,
    $less($sum(sK1,$uminus(2)),0),
    inference(superposition,[],[f146,f13]) ).

tff(f13,plain,
    ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
    introduced(theory_axiom_145,[]) ).

tff(f146,plain,
    ! [X0: $int] : $less($sum(sK1,X0),$sum(2,X0)),
    inference(resolution,[],[f17,f50]) ).

tff(f50,plain,
    $less(sK1,2),
    inference(cnf_transformation,[],[f38]) ).

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

tff(f283,plain,
    ( ( 0 = sK1 )
    | ( 1 = sK1 )
    | $less(1,sK1) ),
    inference(resolution,[],[f278,f16]) ).

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

tff(f278,plain,
    ( ~ $less(sK1,1)
    | ( 0 = sK1 ) ),
    inference(evaluation,[],[f277]) ).

tff(f277,plain,
    ( ( 0 = sK1 )
    | ~ $less(sK1,$sum(0,1)) ),
    inference(resolution,[],[f231,f20]) ).

tff(f231,plain,
    ( $less(0,sK1)
    | ( 0 = sK1 ) ),
    inference(resolution,[],[f104,f49]) ).

tff(f104,plain,
    ! [X0: $int] :
      ( ~ in(X0,sK0)
      | $less(0,X0)
      | ( 0 = X0 ) ),
    inference(resolution,[],[f16,f48]) ).

tff(f48,plain,
    ! [X2: $int] :
      ( ~ $less(X2,0)
      | ~ in(X2,sK0) ),
    inference(cnf_transformation,[],[f38]) ).

tff(f49,plain,
    in(sK1,sK0),
    inference(cnf_transformation,[],[f38]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : DAT024=1 : TPTP v8.1.0. Released v5.0.0.
% 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
% 0.12/0.33  % Computer : n021.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Mon Aug 29 20:13:25 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.20/0.47  % (17535)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.48  % (17544)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.49  % (17552)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.50  % (17551)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.20/0.50  % (17553)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  % (17560)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)
% 0.20/0.50  % (17542)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)
% 0.20/0.50  % (17545)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)
% 0.20/0.50  % (17559)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.51  % (17537)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)
% 0.20/0.51  % (17537)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.20/0.51  % (17537)Terminated due to inappropriate strategy.
% 0.20/0.51  % (17537)------------------------------
% 0.20/0.51  % (17537)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (17537)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (17537)Termination reason: Inappropriate
% 0.20/0.51  
% 0.20/0.51  % (17537)Memory used [KB]: 895
% 0.20/0.51  % (17537)Time elapsed: 0.005 s
% 0.20/0.51  % (17537)Instructions burned: 2 (million)
% 0.20/0.51  % (17537)------------------------------
% 0.20/0.51  % (17537)------------------------------
% 0.20/0.52  % (17538)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  % (17534)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)
% 0.20/0.52  % (17532)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)
% 0.20/0.52  % (17538)Instruction limit reached!
% 0.20/0.52  % (17538)------------------------------
% 0.20/0.52  % (17538)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (17538)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (17538)Termination reason: Unknown
% 0.20/0.52  % (17538)Termination phase: Saturation
% 0.20/0.52  
% 0.20/0.52  % (17538)Memory used [KB]: 5500
% 0.20/0.52  % (17538)Time elapsed: 0.128 s
% 0.20/0.52  % (17538)Instructions burned: 7 (million)
% 0.20/0.52  % (17538)------------------------------
% 0.20/0.52  % (17538)------------------------------
% 0.20/0.52  % (17533)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)
% 0.20/0.52  % (17536)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)
% 0.20/0.52  % (17539)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.53  % (17539)Instruction limit reached!
% 0.20/0.53  % (17539)------------------------------
% 0.20/0.53  % (17539)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (17539)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (17539)Termination reason: Unknown
% 0.20/0.53  % (17539)Termination phase: Saturation
% 0.20/0.53  
% 0.20/0.53  % (17539)Memory used [KB]: 5373
% 0.20/0.53  % (17539)Time elapsed: 0.136 s
% 0.20/0.53  % (17539)Instructions burned: 3 (million)
% 0.20/0.53  % (17539)------------------------------
% 0.20/0.53  % (17539)------------------------------
% 0.20/0.53  % (17540)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)
% 0.20/0.53  % (17531)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)
% 0.20/0.53  % (17547)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.53  % (17531)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.20/0.53  % (17531)Terminated due to inappropriate strategy.
% 0.20/0.53  % (17531)------------------------------
% 0.20/0.53  % (17531)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (17531)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (17531)Termination reason: Inappropriate
% 0.20/0.53  
% 0.20/0.53  % (17531)Memory used [KB]: 895
% 0.20/0.53  % (17531)Time elapsed: 0.002 s
% 0.20/0.53  % (17531)Instructions burned: 2 (million)
% 0.20/0.53  % (17531)------------------------------
% 0.20/0.53  % (17531)------------------------------
% 0.20/0.53  % (17557)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)
% 0.20/0.53  % (17548)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.53  % (17548)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.20/0.53  % (17548)Terminated due to inappropriate strategy.
% 0.20/0.53  % (17548)------------------------------
% 0.20/0.53  % (17548)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (17548)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (17548)Termination reason: Inappropriate
% 0.20/0.53  
% 0.20/0.53  % (17548)Memory used [KB]: 895
% 0.20/0.53  % (17548)Time elapsed: 0.002 s
% 0.20/0.53  % (17548)------------------------------
% 0.20/0.53  % (17548)------------------------------
% 0.20/0.53  % (17541)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.54  % (17558)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.20/0.54  % (17549)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.54  % (17555)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.20/0.54  % (17543)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.54  % (17556)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 1.51/0.54  % (17550)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)
% 1.51/0.55  % (17554)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)
% 1.51/0.55  % (17546)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)
% 1.69/0.56  % (17558)First to succeed.
% 1.69/0.57  % (17558)Refutation found. Thanks to Tanya!
% 1.69/0.57  % SZS status Theorem for theBenchmark
% 1.69/0.57  % SZS output start Proof for theBenchmark
% See solution above
% 1.69/0.57  % (17558)------------------------------
% 1.69/0.57  % (17558)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.69/0.57  % (17558)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.69/0.57  % (17558)Termination reason: Refutation
% 1.69/0.57  
% 1.69/0.57  % (17558)Memory used [KB]: 1151
% 1.69/0.57  % (17558)Time elapsed: 0.179 s
% 1.69/0.57  % (17558)Instructions burned: 14 (million)
% 1.69/0.57  % (17558)------------------------------
% 1.69/0.57  % (17558)------------------------------
% 1.69/0.57  % (17530)Success in time 0.221 s
%------------------------------------------------------------------------------