TSTP Solution File: DAT046_1 by SnakeForV-SAT---1.0

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%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : DAT046_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 : n004.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 16:04:44 EDT 2022

% Result   : Theorem 0.20s 0.49s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   48 (  15 unt;   6 typ;   0 def)
%            Number of atoms       :   92 (  53 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   82 (  32   ~;  32   |;  10   &)
%                                         (   8 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of FOOLs       :    1 (   1 fml;   0 var)
%            Number arithmetic     :  105 (   0 atm;  14 fun;  60 num;  31 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   4 usr;   5 con; 0-2 aty)
%            Number of variables   :   53 (  53   !;   0   ?;  53   :)

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

tff(f151,plain,
    $false,
    inference(subsumption_resolution,[],[f149,f57]) ).

tff(f57,plain,
    ! [X0: $int] : ~ in(X0,empty),
    inference(cnf_transformation,[],[f1]) ).

tff(f1,axiom,
    ! [X0: $int] : ~ in(X0,empty),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).

tff(f149,plain,
    in(1,empty),
    inference(evaluation,[],[f146]) ).

tff(f146,plain,
    ( ( 1 = 3 )
    | in(1,empty) ),
    inference(resolution,[],[f142,f63]) ).

tff(f63,plain,
    ! [X2: collection,X0: $int,X1: $int] :
      ( ~ in(X0,add(X1,X2))
      | in(X0,X2)
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f45]) ).

tff(f45,plain,
    ! [X0: $int,X1: $int,X2: collection] :
      ( ( in(X0,X2)
        | ( X0 = X1 )
        | ~ in(X0,add(X1,X2)) )
      & ( in(X0,add(X1,X2))
        | ( ~ in(X0,X2)
          & ( X0 != X1 ) ) ) ),
    inference(rectify,[],[f44]) ).

tff(f44,plain,
    ! [X2: $int,X0: $int,X1: collection] :
      ( ( in(X2,X1)
        | ( X0 = X2 )
        | ~ in(X2,add(X0,X1)) )
      & ( in(X2,add(X0,X1))
        | ( ~ in(X2,X1)
          & ( X0 != X2 ) ) ) ),
    inference(flattening,[],[f43]) ).

tff(f43,plain,
    ! [X2: $int,X0: $int,X1: collection] :
      ( ( in(X2,X1)
        | ( X0 = X2 )
        | ~ in(X2,add(X0,X1)) )
      & ( in(X2,add(X0,X1))
        | ( ~ in(X2,X1)
          & ( X0 != X2 ) ) ) ),
    inference(nnf_transformation,[],[f38]) ).

tff(f38,plain,
    ! [X2: $int,X0: $int,X1: collection] :
      ( ( in(X2,X1)
        | ( X0 = X2 ) )
    <=> 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(f142,plain,
    in(1,add(3,empty)),
    inference(subsumption_resolution,[],[f139,f99]) ).

tff(f99,plain,
    ! [X0: $int] : ( 1 = count(add(X0,empty)) ),
    inference(evaluation,[],[f98]) ).

tff(f98,plain,
    ! [X0: $int] : ( count(add(X0,empty)) = $sum(1,0) ),
    inference(forward_demodulation,[],[f95,f80]) ).

tff(f80,plain,
    0 = count(empty),
    inference(equality_resolution,[],[f66]) ).

tff(f66,plain,
    ! [X0: collection] :
      ( ( 0 = count(X0) )
      | ( empty != X0 ) ),
    inference(cnf_transformation,[],[f47]) ).

tff(f47,plain,
    ! [X0: collection] :
      ( ( ( empty = X0 )
        | ( 0 != count(X0) ) )
      & ( ( 0 = count(X0) )
        | ( empty != X0 ) ) ),
    inference(nnf_transformation,[],[f29]) ).

tff(f29,plain,
    ! [X0: collection] :
      ( ( empty = X0 )
    <=> ( 0 = count(X0) ) ),
    inference(rectify,[],[f7]) ).

tff(f7,axiom,
    ! [X12: collection] :
      ( ( 0 = count(X12) )
    <=> ( empty = X12 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).

tff(f95,plain,
    ! [X0: $int] : ( count(add(X0,empty)) = $sum(1,count(empty)) ),
    inference(resolution,[],[f87,f57]) ).

tff(f87,plain,
    ! [X0: $int,X1: collection] :
      ( in(X0,X1)
      | ( count(add(X0,X1)) = $sum(1,count(X1)) ) ),
    inference(forward_demodulation,[],[f78,f17]) ).

tff(f17,plain,
    ! [X0: $int,X1: $int] : ( $sum(X1,X0) = $sum(X0,X1) ),
    introduced(theory_axiom_140,[]) ).

tff(f78,plain,
    ! [X0: $int,X1: collection] :
      ( in(X0,X1)
      | ( count(add(X0,X1)) = $sum(count(X1),1) ) ),
    inference(cnf_transformation,[],[f56]) ).

tff(f56,plain,
    ! [X0: $int,X1: collection] :
      ( ( ( count(add(X0,X1)) = $sum(count(X1),1) )
        | in(X0,X1) )
      & ( ~ in(X0,X1)
        | ( count(add(X0,X1)) != $sum(count(X1),1) ) ) ),
    inference(nnf_transformation,[],[f32]) ).

tff(f32,plain,
    ! [X0: $int,X1: collection] :
      ( ( count(add(X0,X1)) = $sum(count(X1),1) )
    <=> ~ in(X0,X1) ),
    inference(rectify,[],[f8]) ).

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

tff(f139,plain,
    ( in(1,add(3,empty))
    | ( 1 != count(add(3,empty)) ) ),
    inference(superposition,[],[f69,f125]) ).

tff(f125,plain,
    1 = count(add(1,add(3,empty))),
    inference(evaluation,[],[f124]) ).

tff(f124,plain,
    ( ( 2 != $sum(1,1) )
    | ( 1 = count(add(1,add(3,empty))) ) ),
    inference(forward_demodulation,[],[f123,f99]) ).

tff(f123,plain,
    ( ( 1 = count(add(1,add(3,empty))) )
    | ( 2 != $sum(1,count(add(3,empty))) ) ),
    inference(forward_demodulation,[],[f115,f99]) ).

tff(f115,plain,
    ( ( count(add(1,add(3,empty))) = count(add(3,empty)) )
    | ( 2 != $sum(1,count(add(3,empty))) ) ),
    inference(superposition,[],[f65,f96]) ).

tff(f96,plain,
    ! [X2: collection,X1: $int] :
      ( ( $sum(1,count(X2)) = count(add(X1,X2)) )
      | ( count(X2) = count(add(X1,X2)) ) ),
    inference(resolution,[],[f87,f68]) ).

tff(f68,plain,
    ! [X0: collection,X1: $int] :
      ( ~ in(X1,X0)
      | ( count(X0) = count(add(X1,X0)) ) ),
    inference(cnf_transformation,[],[f49]) ).

tff(f49,plain,
    ! [X0: collection,X1: $int] :
      ( ( in(X1,X0)
        | ( count(X0) != count(add(X1,X0)) ) )
      & ( ( count(X0) = count(add(X1,X0)) )
        | ~ in(X1,X0) ) ),
    inference(rectify,[],[f48]) ).

tff(f48,plain,
    ! [X1: collection,X0: $int] :
      ( ( in(X0,X1)
        | ( count(add(X0,X1)) != count(X1) ) )
      & ( ( count(add(X0,X1)) = count(X1) )
        | ~ in(X0,X1) ) ),
    inference(nnf_transformation,[],[f40]) ).

tff(f40,plain,
    ! [X1: collection,X0: $int] :
      ( in(X0,X1)
    <=> ( count(add(X0,X1)) = count(X1) ) ),
    inference(rectify,[],[f9]) ).

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

tff(f65,plain,
    count(add(1,add(3,empty))) != 2,
    inference(cnf_transformation,[],[f35]) ).

tff(f35,plain,
    count(add(1,add(3,empty))) != 2,
    inference(flattening,[],[f14]) ).

tff(f14,negated_conjecture,
    ( ( ~ count(add(1,add(3,empty))) )
    = 2 ),
    inference(negated_conjecture,[],[f13]) ).

tff(f13,conjecture,
    count(add(1,add(3,empty))) = 2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

tff(f69,plain,
    ! [X0: collection,X1: $int] :
      ( ( count(X0) != count(add(X1,X0)) )
      | in(X1,X0) ),
    inference(cnf_transformation,[],[f49]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : DAT046=1 : TPTP v8.1.0. Released v5.0.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.35  % Computer : n004.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % 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   : Mon Aug 29 20:14:35 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.20/0.47  % (13771)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 (3000ds/75Mi)
% 0.20/0.47  % (13779)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 (3000ds/467Mi)
% 0.20/0.49  % (13779)First to succeed.
% 0.20/0.49  % (13779)Refutation found. Thanks to Tanya!
% 0.20/0.49  % SZS status Theorem for theBenchmark
% 0.20/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.49  % (13779)------------------------------
% 0.20/0.49  % (13779)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49  % (13779)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49  % (13779)Termination reason: Refutation
% 0.20/0.49  
% 0.20/0.49  % (13779)Memory used [KB]: 5500
% 0.20/0.49  % (13779)Time elapsed: 0.072 s
% 0.20/0.49  % (13779)Instructions burned: 7 (million)
% 0.20/0.49  % (13779)------------------------------
% 0.20/0.49  % (13779)------------------------------
% 0.20/0.49  % (13753)Success in time 0.137 s
%------------------------------------------------------------------------------