TSTP Solution File: DAT033_1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : DAT033_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 : n009.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 16:04:41 EDT 2022

% Result   : Theorem 0.19s 0.53s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   65 (   3 unt;   7 typ;   0 def)
%            Number of atoms       :  130 (  60 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  122 (  50   ~;  49   |;   8   &)
%                                         (  12 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number arithmetic     :  120 (   0 atm;  27 fun;  73 num;  20 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   4 prp; 0-2 aty)
%            Number of functors    :   12 (   5 usr;   6 con; 0-2 aty)
%            Number of variables   :   44 (  42   !;   2   ?;  44   :)

% 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_3,type,
    count: collection > $int ).

tff(func_def_11,type,
    sK0: collection ).

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

tff(f469,plain,
    $false,
    inference(avatar_sat_refutation,[],[f152,f280,f286,f392,f468]) ).

tff(f468,plain,
    ( spl1_3
    | spl1_4
    | ~ spl1_5 ),
    inference(avatar_split_clause,[],[f465,f267,f149,f145]) ).

tff(f145,plain,
    ( spl1_3
  <=> ( count(add(5,sK0)) = count(sK0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).

tff(f149,plain,
    ( spl1_4
  <=> in(3,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).

tff(f267,plain,
    ( spl1_5
  <=> ( count(add(5,sK0)) = $sum(count(sK0),1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).

tff(f465,plain,
    ( ( count(add(5,sK0)) = count(sK0) )
    | spl1_4
    | ~ spl1_5 ),
    inference(backward_demodulation,[],[f268,f460]) ).

tff(f460,plain,
    ( ( $sum(count(sK0),1) = count(sK0) )
    | spl1_4
    | ~ spl1_5 ),
    inference(forward_demodulation,[],[f459,f268]) ).

tff(f459,plain,
    ( ( count(add(5,sK0)) = count(sK0) )
    | spl1_4 ),
    inference(trivial_inequality_removal,[],[f454]) ).

tff(f454,plain,
    ( ( count(sK0) != count(sK0) )
    | ( count(add(5,sK0)) = count(sK0) )
    | spl1_4 ),
    inference(superposition,[],[f406,f190]) ).

tff(f190,plain,
    ! [X6: $int,X5: collection] :
      ( ( count(remove(X6,X5)) = count(X5) )
      | ( count(X5) = count(add(X6,X5)) ) ),
    inference(resolution,[],[f67,f64]) ).

tff(f64,plain,
    ! [X0: collection,X1: $int] :
      ( in(X1,X0)
      | ( count(X0) = count(remove(X1,X0)) ) ),
    inference(cnf_transformation,[],[f44]) ).

tff(f44,plain,
    ! [X0: collection,X1: $int] :
      ( ( ~ in(X1,X0)
        | ( count(X0) != count(remove(X1,X0)) ) )
      & ( ( count(X0) = count(remove(X1,X0)) )
        | in(X1,X0) ) ),
    inference(nnf_transformation,[],[f38]) ).

tff(f38,plain,
    ! [X0: collection,X1: $int] :
      ( ~ in(X1,X0)
    <=> ( count(X0) = count(remove(X1,X0)) ) ),
    inference(rectify,[],[f11]) ).

tff(f11,axiom,
    ! [X20: collection,X19: $int] :
      ( ~ in(X19,X20)
    <=> ( count(remove(X19,X20)) = count(X20) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).

tff(f67,plain,
    ! [X0: collection,X1: $int] :
      ( ~ in(X1,X0)
      | ( count(X0) = count(add(X1,X0)) ) ),
    inference(cnf_transformation,[],[f45]) ).

tff(f45,plain,
    ! [X0: collection,X1: $int] :
      ( ( ( count(X0) = count(add(X1,X0)) )
        | ~ in(X1,X0) )
      & ( in(X1,X0)
        | ( count(X0) != count(add(X1,X0)) ) ) ),
    inference(nnf_transformation,[],[f30]) ).

tff(f30,plain,
    ! [X0: collection,X1: $int] :
      ( ( count(X0) = count(add(X1,X0)) )
    <=> in(X1,X0) ),
    inference(rectify,[],[f9]) ).

tff(f9,axiom,
    ! [X16: collection,X15: $int] :
      ( ( count(add(X15,X16)) = count(X16) )
    <=> in(X15,X16) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).

tff(f406,plain,
    ( ( count(remove(5,sK0)) != count(sK0) )
    | spl1_4 ),
    inference(backward_demodulation,[],[f75,f405]) ).

tff(f405,plain,
    ( ( count(remove(3,sK0)) = count(sK0) )
    | spl1_4 ),
    inference(resolution,[],[f150,f64]) ).

tff(f150,plain,
    ( ~ in(3,sK0)
    | spl1_4 ),
    inference(avatar_component_clause,[],[f149]) ).

tff(f75,plain,
    count(remove(3,sK0)) != count(remove(5,sK0)),
    inference(cnf_transformation,[],[f53]) ).

tff(f53,plain,
    ( ( count(add(5,sK0)) = count(add(3,sK0)) )
    & ( count(remove(3,sK0)) != count(remove(5,sK0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f40,f52]) ).

tff(f52,plain,
    ( ? [X0: collection] :
        ( ( count(add(5,X0)) = count(add(3,X0)) )
        & ( count(remove(5,X0)) != count(remove(3,X0)) ) )
   => ( ( count(add(5,sK0)) = count(add(3,sK0)) )
      & ( count(remove(3,sK0)) != count(remove(5,sK0)) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f40,plain,
    ? [X0: collection] :
      ( ( count(add(5,X0)) = count(add(3,X0)) )
      & ( count(remove(5,X0)) != count(remove(3,X0)) ) ),
    inference(ennf_transformation,[],[f14]) ).

tff(f14,negated_conjecture,
    ~ ! [X0: collection] :
        ( ( count(add(5,X0)) = count(add(3,X0)) )
       => ( count(remove(5,X0)) = count(remove(3,X0)) ) ),
    inference(negated_conjecture,[],[f13]) ).

tff(f13,conjecture,
    ! [X0: collection] :
      ( ( count(add(5,X0)) = count(add(3,X0)) )
     => ( count(remove(5,X0)) = count(remove(3,X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

tff(f268,plain,
    ( ( count(add(5,sK0)) = $sum(count(sK0),1) )
    | ~ spl1_5 ),
    inference(avatar_component_clause,[],[f267]) ).

tff(f392,plain,
    ( ~ spl1_3
    | ~ spl1_4 ),
    inference(avatar_contradiction_clause,[],[f391]) ).

tff(f391,plain,
    ( $false
    | ~ spl1_3
    | ~ spl1_4 ),
    inference(trivial_inequality_removal,[],[f390]) ).

tff(f390,plain,
    ( ( $sum(count(sK0),-1) != $sum(count(sK0),-1) )
    | ~ spl1_3
    | ~ spl1_4 ),
    inference(backward_demodulation,[],[f284,f387]) ).

tff(f387,plain,
    ( ( count(remove(5,sK0)) = $sum(count(sK0),-1) )
    | ~ spl1_3 ),
    inference(resolution,[],[f369,f84]) ).

tff(f84,plain,
    ! [X0: collection,X1: $int] :
      ( ~ in(X1,X0)
      | ( $sum(count(X0),-1) = count(remove(X1,X0)) ) ),
    inference(evaluation,[],[f58]) ).

tff(f58,plain,
    ! [X0: collection,X1: $int] :
      ( ( $sum(count(X0),$uminus(1)) = count(remove(X1,X0)) )
      | ~ in(X1,X0) ),
    inference(cnf_transformation,[],[f42]) ).

tff(f42,plain,
    ! [X0: collection,X1: $int] :
      ( ( in(X1,X0)
        | ( $sum(count(X0),$uminus(1)) != count(remove(X1,X0)) ) )
      & ( ( $sum(count(X0),$uminus(1)) = count(remove(X1,X0)) )
        | ~ in(X1,X0) ) ),
    inference(nnf_transformation,[],[f31]) ).

tff(f31,plain,
    ! [X0: collection,X1: $int] :
      ( in(X1,X0)
    <=> ( $sum(count(X0),$uminus(1)) = count(remove(X1,X0)) ) ),
    inference(rectify,[],[f15]) ).

tff(f15,plain,
    ! [X18: collection,X17: $int] :
      ( in(X17,X18)
    <=> ( count(remove(X17,X18)) = $sum(count(X18),$uminus(1)) ) ),
    inference(theory_normalization,[],[f10]) ).

tff(f10,axiom,
    ! [X18: collection,X17: $int] :
      ( in(X17,X18)
    <=> ( count(remove(X17,X18)) = $difference(count(X18),1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).

tff(f369,plain,
    ( in(5,sK0)
    | ~ spl1_3 ),
    inference(trivial_inequality_removal,[],[f365]) ).

tff(f365,plain,
    ( ( count(sK0) != count(sK0) )
    | in(5,sK0)
    | ~ spl1_3 ),
    inference(superposition,[],[f66,f146]) ).

tff(f146,plain,
    ( ( count(add(5,sK0)) = count(sK0) )
    | ~ spl1_3 ),
    inference(avatar_component_clause,[],[f145]) ).

tff(f66,plain,
    ! [X0: collection,X1: $int] :
      ( ( count(X0) != count(add(X1,X0)) )
      | in(X1,X0) ),
    inference(cnf_transformation,[],[f45]) ).

tff(f284,plain,
    ( ( count(remove(5,sK0)) != $sum(count(sK0),-1) )
    | ~ spl1_4 ),
    inference(backward_demodulation,[],[f75,f281]) ).

tff(f281,plain,
    ( ( count(remove(3,sK0)) = $sum(count(sK0),-1) )
    | ~ spl1_4 ),
    inference(resolution,[],[f151,f84]) ).

tff(f151,plain,
    ( in(3,sK0)
    | ~ spl1_4 ),
    inference(avatar_component_clause,[],[f149]) ).

tff(f286,plain,
    ( spl1_3
    | ~ spl1_4 ),
    inference(avatar_split_clause,[],[f285,f149,f145]) ).

tff(f285,plain,
    ( ( count(add(5,sK0)) = count(sK0) )
    | ~ spl1_4 ),
    inference(forward_demodulation,[],[f283,f76]) ).

tff(f76,plain,
    count(add(5,sK0)) = count(add(3,sK0)),
    inference(cnf_transformation,[],[f53]) ).

tff(f283,plain,
    ( ( count(add(3,sK0)) = count(sK0) )
    | ~ spl1_4 ),
    inference(resolution,[],[f151,f67]) ).

tff(f280,plain,
    ( spl1_5
    | spl1_4 ),
    inference(avatar_split_clause,[],[f279,f149,f267]) ).

tff(f279,plain,
    ( ( count(add(5,sK0)) = $sum(count(sK0),1) )
    | spl1_4 ),
    inference(forward_demodulation,[],[f276,f76]) ).

tff(f276,plain,
    ( ( count(add(3,sK0)) = $sum(count(sK0),1) )
    | spl1_4 ),
    inference(resolution,[],[f150,f61]) ).

tff(f61,plain,
    ! [X0: $int,X1: collection] :
      ( in(X0,X1)
      | ( $sum(count(X1),1) = count(add(X0,X1)) ) ),
    inference(cnf_transformation,[],[f43]) ).

tff(f43,plain,
    ! [X0: $int,X1: collection] :
      ( ( ~ in(X0,X1)
        | ( $sum(count(X1),1) != count(add(X0,X1)) ) )
      & ( ( $sum(count(X1),1) = count(add(X0,X1)) )
        | in(X0,X1) ) ),
    inference(nnf_transformation,[],[f33]) ).

tff(f33,plain,
    ! [X0: $int,X1: collection] :
      ( ~ in(X0,X1)
    <=> ( $sum(count(X1),1) = count(add(X0,X1)) ) ),
    inference(rectify,[],[f8]) ).

tff(f8,axiom,
    ! [X13: $int,X14: collection] :
      ( ( count(add(X13,X14)) = $sum(count(X14),1) )
    <=> ~ in(X13,X14) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).

tff(f152,plain,
    ( ~ spl1_3
    | spl1_4 ),
    inference(avatar_split_clause,[],[f143,f149,f145]) ).

tff(f143,plain,
    ( in(3,sK0)
    | ( count(add(5,sK0)) != count(sK0) ) ),
    inference(superposition,[],[f66,f76]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : DAT033=1 : TPTP v8.1.0. Released v5.0.0.
% 0.06/0.13  % 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 : n009.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 20:14:50 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.45  % (26350)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)
% 0.19/0.47  % (26342)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.48  % (26342)Instruction limit reached!
% 0.19/0.48  % (26342)------------------------------
% 0.19/0.48  % (26342)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.48  % (26342)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.48  % (26342)Termination reason: Unknown
% 0.19/0.48  % (26342)Termination phase: Saturation
% 0.19/0.48  
% 0.19/0.48  % (26342)Memory used [KB]: 5500
% 0.19/0.48  % (26342)Time elapsed: 0.092 s
% 0.19/0.48  % (26342)Instructions burned: 7 (million)
% 0.19/0.48  % (26342)------------------------------
% 0.19/0.48  % (26342)------------------------------
% 0.19/0.48  % (26364)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)
% 0.19/0.49  % (26336)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)
% 0.19/0.50  % (26335)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)
% 0.19/0.50  % (26335)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.19/0.50  % (26335)Terminated due to inappropriate strategy.
% 0.19/0.50  % (26335)------------------------------
% 0.19/0.50  % (26335)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (26335)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (26335)Termination reason: Inappropriate
% 0.19/0.50  
% 0.19/0.50  % (26335)Memory used [KB]: 895
% 0.19/0.50  % (26335)Time elapsed: 0.002 s
% 0.19/0.50  % (26335)Instructions burned: 2 (million)
% 0.19/0.50  % (26335)------------------------------
% 0.19/0.50  % (26335)------------------------------
% 0.19/0.51  % (26348)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.51  % (26360)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.19/0.51  % (26352)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.19/0.51  % (26364)First to succeed.
% 0.19/0.52  % (26337)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)
% 0.19/0.52  % (26357)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)
% 0.19/0.52  % (26339)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.52  % (26352)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.19/0.52  % (26344)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)
% 0.19/0.52  % (26352)Terminated due to inappropriate strategy.
% 0.19/0.52  % (26352)------------------------------
% 0.19/0.52  % (26352)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (26352)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (26352)Termination reason: Inappropriate
% 0.19/0.52  
% 0.19/0.52  % (26352)Memory used [KB]: 895
% 0.19/0.52  % (26352)Time elapsed: 0.004 s
% 0.19/0.52  % (26352)Instructions burned: 3 (million)
% 0.19/0.52  % (26352)------------------------------
% 0.19/0.52  % (26352)------------------------------
% 0.19/0.53  % (26340)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)
% 0.19/0.53  % (26338)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)
% 0.19/0.53  % (26351)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)
% 0.19/0.53  % (26349)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)
% 0.19/0.53  % (26364)Refutation found. Thanks to Tanya!
% 0.19/0.53  % SZS status Theorem for theBenchmark
% 0.19/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.53  % (26364)------------------------------
% 0.19/0.53  % (26364)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53  % (26364)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53  % (26364)Termination reason: Refutation
% 0.19/0.53  
% 0.19/0.53  % (26364)Memory used [KB]: 5756
% 0.19/0.53  % (26364)Time elapsed: 0.124 s
% 0.19/0.53  % (26364)Instructions burned: 18 (million)
% 0.19/0.53  % (26364)------------------------------
% 0.19/0.53  % (26364)------------------------------
% 0.19/0.53  % (26334)Success in time 0.18 s
%------------------------------------------------------------------------------