TSTP Solution File: DAT097_1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : DAT097_1 : TPTP v8.1.2. Released v6.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n022.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 : Sun May  5 05:04:34 EDT 2024

% Result   : Theorem 0.59s 0.75s
% Output   : Refutation 0.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   62 (  19 unt;  15 typ;   0 def)
%            Number of atoms       :   97 (  57 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   72 (  22   ~;  27   |;  12   &)
%                                         (   5 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number arithmetic     :  149 (   6 atm;  28 fun;  41 num;  74 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :   25 (  13   >;  12   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   3 usr;   1 prp; 0-4 aty)
%            Number of functors    :   15 (  11 usr;   4 con; 0-2 aty)
%            Number of variables   :  141 ( 133   !;   8   ?; 141   :)

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

tff(func_def_0,type,
    nil: list ).

tff(func_def_1,type,
    cons: ( $int * list ) > list ).

tff(func_def_2,type,
    head: list > $int ).

tff(func_def_3,type,
    tail: list > list ).

tff(func_def_5,type,
    length: list > $int ).

tff(func_def_8,type,
    count: ( $int * list ) > $int ).

tff(func_def_9,type,
    append: ( list * list ) > list ).

tff(func_def_11,type,
    sK0: ( $int * list ) > $int ).

tff(func_def_12,type,
    sK1: ( $int * list ) > list ).

tff(func_def_13,type,
    sK2: ( $int * list ) > $int ).

tff(func_def_14,type,
    sK3: ( $int * list ) > list ).

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

tff(pred_def_2,type,
    inRange: ( $int * list ) > $o ).

tff(pred_def_6,type,
    sP4: ( list * $int * list * $int ) > $o ).

tff(f108,plain,
    $false,
    inference(evaluation,[],[f107]) ).

tff(f107,plain,
    1 = $sum(2,0),
    inference(forward_demodulation,[],[f106,f55]) ).

tff(f55,plain,
    ! [X0: $int] : ( 0 = count(X0,nil) ),
    inference(cnf_transformation,[],[f9]) ).

tff(f9,axiom,
    ! [X0: $int] : ( 0 = count(X0,nil) ),
    file('/export/starexec/sandbox/tmp/tmp.5mtB67Ap6O/Vampire---4.8_8286',a) ).

tff(f106,plain,
    ! [X0: $int] : ( 1 = $sum(2,count(X0,nil)) ),
    inference(evaluation,[],[f101]) ).

tff(f101,plain,
    ! [X0: $int] : ( 1 = $sum(1,$sum(count(X0,nil),1)) ),
    inference(superposition,[],[f99,f63]) ).

tff(f63,plain,
    ! [X2: list,X1: $int] : ( count(X1,cons(X1,X2)) = $sum(count(X1,X2),1) ),
    inference(equality_resolution,[],[f53]) ).

tff(f53,plain,
    ! [X2: list,X0: $int,X1: $int] :
      ( ( X0 != X1 )
      | ( count(X0,cons(X1,X2)) = $sum(count(X0,X2),1) ) ),
    inference(cnf_transformation,[],[f41]) ).

tff(f41,plain,
    ! [X0: $int,X1: $int,X2: list] :
      ( ( count(X0,cons(X1,X2)) = $sum(count(X0,X2),1) )
      | ( X0 != X1 ) ),
    inference(ennf_transformation,[],[f35]) ).

tff(f35,plain,
    ! [X0: $int,X1: $int,X2: list] :
      ( ( X0 = X1 )
     => ( count(X0,cons(X1,X2)) = $sum(count(X0,X2),1) ) ),
    inference(rectify,[],[f11]) ).

tff(f11,axiom,
    ! [X0: $int,X3: $int,X4: list,X5: $int] :
      ( ( X0 = X3 )
     => ( count(X0,cons(X3,X4)) = $sum(count(X0,X4),1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.5mtB67Ap6O/Vampire---4.8_8286',a_4) ).

tff(f99,plain,
    ! [X0: $int,X1: $int] : ( 1 = $sum(1,count(X1,cons(X0,nil))) ),
    inference(evaluation,[],[f98]) ).

tff(f98,plain,
    ! [X0: $int,X1: $int] : ( $sum(1,count(X1,cons(X0,nil))) = $sum(1,0) ),
    inference(forward_demodulation,[],[f94,f55]) ).

tff(f94,plain,
    ! [X0: $int,X1: $int] : ( $sum(1,count(X1,nil)) = $sum(1,count(X1,cons(X0,nil))) ),
    inference(superposition,[],[f79,f57]) ).

tff(f57,plain,
    ! [X0: list] : ( append(nil,X0) = X0 ),
    inference(cnf_transformation,[],[f38]) ).

tff(f38,plain,
    ! [X0: list] : ( append(nil,X0) = X0 ),
    inference(rectify,[],[f12]) ).

tff(f12,axiom,
    ! [X1: list] : ( append(nil,X1) = X1 ),
    file('/export/starexec/sandbox/tmp/tmp.5mtB67Ap6O/Vampire---4.8_8286',l_6) ).

tff(f79,plain,
    ! [X2: list,X0: $int,X1: $int] : ( $sum(1,count(X1,append(X2,cons(X0,nil)))) = $sum(1,count(X1,X2)) ),
    inference(evaluation,[],[f78]) ).

tff(f78,plain,
    ! [X2: list,X0: $int,X1: $int] :
      ( $less(0,0)
      | ( $sum(1,count(X1,append(X2,cons(X0,nil)))) = $sum(1,count(X1,X2)) ) ),
    inference(superposition,[],[f72,f55]) ).

tff(f72,plain,
    ! [X2: $int,X3: list,X0: $int,X1: list] :
      ( $less(0,count(X2,X3))
      | ( $sum(1,count(X0,append(X1,cons(X2,X3)))) = $sum(1,count(X0,X1)) ) ),
    inference(resolution,[],[f70,f45]) ).

tff(f45,plain,
    ! [X0: $int,X1: list] :
      ( ~ in(X0,X1)
      | $less(0,count(X0,X1)) ),
    inference(cnf_transformation,[],[f33]) ).

tff(f33,plain,
    ! [X0: $int,X1: list] :
      ( in(X0,X1)
    <=> $less(0,count(X0,X1)) ),
    inference(rectify,[],[f18]) ).

tff(f18,plain,
    ! [X5: $int,X1: list] :
      ( in(X5,X1)
    <=> $less(0,count(X5,X1)) ),
    inference(theory_normalization,[],[f14]) ).

tff(f14,axiom,
    ! [X5: $int,X1: list] :
      ( in(X5,X1)
    <=> $greater(count(X5,X1),0) ),
    file('/export/starexec/sandbox/tmp/tmp.5mtB67Ap6O/Vampire---4.8_8286',a_8) ).

tff(f70,plain,
    ! [X2: $int,X3: list,X0: $int,X1: list] :
      ( in(X0,X1)
      | ( $sum(1,count(X2,append(X3,cons(X0,X1)))) = $sum(1,count(X2,X3)) ) ),
    inference(forward_demodulation,[],[f69,f19]) ).

tff(f19,plain,
    ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
    introduced(theory_axiom_135,[]) ).

tff(f69,plain,
    ! [X2: $int,X3: list,X0: $int,X1: list] :
      ( ( $sum(1,count(X2,append(X3,cons(X0,X1)))) = $sum(count(X2,X3),1) )
      | in(X0,X1) ),
    inference(forward_demodulation,[],[f68,f63]) ).

tff(f68,plain,
    ! [X2: $int,X3: list,X0: $int,X1: list] :
      ( ( count(X2,cons(X2,X3)) = $sum(1,count(X2,append(X3,cons(X0,X1)))) )
      | in(X0,X1) ),
    inference(forward_demodulation,[],[f67,f19]) ).

tff(f67,plain,
    ! [X2: $int,X3: list,X0: $int,X1: list] :
      ( ( count(X2,cons(X2,X3)) = $sum(count(X2,append(X3,cons(X0,X1))),1) )
      | in(X0,X1) ),
    inference(forward_demodulation,[],[f66,f63]) ).

tff(f66,plain,
    ! [X2: $int,X3: list,X0: $int,X1: list] :
      ( ( count(X2,cons(X2,X3)) = count(X2,cons(X2,append(X3,cons(X0,X1)))) )
      | in(X0,X1) ),
    inference(forward_demodulation,[],[f65,f56]) ).

tff(f56,plain,
    ! [X2: list,X0: $int,X1: list] : ( append(cons(X0,X1),X2) = cons(X0,append(X1,X2)) ),
    inference(cnf_transformation,[],[f37]) ).

tff(f37,plain,
    ! [X0: $int,X1: list,X2: list] : ( append(cons(X0,X1),X2) = cons(X0,append(X1,X2)) ),
    inference(rectify,[],[f13]) ).

tff(f13,axiom,
    ! [X6: $int,X0: list,X1: list] : ( append(cons(X6,X0),X1) = cons(X6,append(X0,X1)) ),
    file('/export/starexec/sandbox/tmp/tmp.5mtB67Ap6O/Vampire---4.8_8286',l_7) ).

tff(f65,plain,
    ! [X2: $int,X3: list,X0: $int,X1: list] :
      ( in(X0,X1)
      | ( count(X2,cons(X2,X3)) = count(X2,append(cons(X2,X3),cons(X0,X1))) ) ),
    inference(resolution,[],[f59,f61]) ).

tff(f61,plain,
    ! [X4: $int,X5: list] : in(X4,cons(X4,X5)),
    inference(equality_resolution,[],[f60]) ).

tff(f60,plain,
    ! [X0: $int,X4: $int,X5: list] :
      ( ( X0 != X4 )
      | in(X0,cons(X4,X5)) ),
    inference(equality_resolution,[],[f49]) ).

tff(f49,plain,
    ! [X0: $int,X1: list,X4: $int,X5: list] :
      ( ( cons(X4,X5) != X1 )
      | ( X0 != X4 )
      | in(X0,X1) ),
    inference(cnf_transformation,[],[f34]) ).

tff(f34,plain,
    ! [X0: $int,X1: list] :
      ( in(X0,X1)
    <=> ( ? [X2: $int,X3: list] :
            ( in(X0,X3)
            & ( cons(X2,X3) = X1 ) )
        | ? [X4: $int,X5: list] :
            ( ( X0 = X4 )
            & ( cons(X4,X5) = X1 ) ) ) ),
    inference(rectify,[],[f5]) ).

tff(f5,axiom,
    ! [X2: $int,X1: list] :
      ( in(X2,X1)
    <=> ( ? [X3: $int,X4: list] :
            ( in(X2,X4)
            & ( cons(X3,X4) = X1 ) )
        | ? [X3: $int,X4: list] :
            ( ( X2 = X3 )
            & ( cons(X3,X4) = X1 ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.5mtB67Ap6O/Vampire---4.8_8286',in_conv) ).

tff(f59,plain,
    ! [X2: list,X3: list,X0: $int,X1: $int] :
      ( ~ in(X1,X3)
      | in(X0,X2)
      | ( count(X1,X3) = count(X1,append(X3,cons(X0,X2))) ) ),
    inference(equality_resolution,[],[f43]) ).

tff(f43,plain,
    ! [X2: list,X3: list,X0: $int,X1: $int,X4: list] :
      ( ~ in(X1,X3)
      | in(X0,X2)
      | ( append(X3,cons(X0,X2)) != X4 )
      | ( count(X1,X3) = count(X1,X4) ) ),
    inference(cnf_transformation,[],[f40]) ).

tff(f40,plain,
    ! [X0: $int,X1: $int,X2: list,X3: list,X4: list] :
      ( ( count(X1,X3) = count(X1,X4) )
      | ( append(X3,cons(X0,X2)) != X4 )
      | in(X0,X2)
      | ~ in(X1,X3) ),
    inference(flattening,[],[f39]) ).

tff(f39,plain,
    ! [X0: $int,X1: $int,X2: list,X3: list,X4: list] :
      ( ( count(X1,X3) = count(X1,X4) )
      | ( append(X3,cons(X0,X2)) != X4 )
      | in(X0,X2)
      | ~ in(X1,X3) ),
    inference(ennf_transformation,[],[f32]) ).

tff(f32,plain,
    ! [X0: $int,X1: $int,X2: list,X3: list,X4: list] :
      ( ( ( append(X3,cons(X0,X2)) = X4 )
        & ~ in(X0,X2)
        & in(X1,X3) )
     => ( count(X1,X3) = count(X1,X4) ) ),
    inference(flattening,[],[f31]) ).

tff(f31,plain,
    ~ ~ ! [X0: $int,X1: $int,X2: list,X3: list,X4: list] :
          ( ( ( append(X3,cons(X0,X2)) = X4 )
            & ~ in(X0,X2)
            & in(X1,X3) )
         => ( count(X1,X3) = count(X1,X4) ) ),
    inference(rectify,[],[f16]) ).

tff(f16,negated_conjecture,
    ~ ~ ! [X7: $int,X5: $int,X0: list,X1: list,X8: list] :
          ( ( ( append(X1,cons(X7,X0)) = X8 )
            & ~ in(X7,X0)
            & in(X5,X1) )
         => ( count(X5,X1) = count(X5,X8) ) ),
    inference(negated_conjecture,[],[f15]) ).

tff(f15,conjecture,
    ~ ! [X7: $int,X5: $int,X0: list,X1: list,X8: list] :
        ( ( ( append(X1,cons(X7,X0)) = X8 )
          & ~ in(X7,X0)
          & in(X5,X1) )
       => ( count(X5,X1) = count(X5,X8) ) ),
    file('/export/starexec/sandbox/tmp/tmp.5mtB67Ap6O/Vampire---4.8_8286',c) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : DAT097_1 : TPTP v8.1.2. Released v6.1.0.
% 0.13/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.36  % Computer : n022.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Fri May  3 12:54:42 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a TF0_THM_EQU_ARI problem
% 0.15/0.37  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.5mtB67Ap6O/Vampire---4.8_8286
% 0.59/0.74  % (8556)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.59/0.74  % (8558)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.59/0.74  % (8559)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.59/0.74  % (8557)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.59/0.74  % (8560)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.59/0.74  % (8561)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.59/0.74  % (8563)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.59/0.74  % (8562)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.59/0.75  % (8556)Refutation not found, incomplete strategy% (8556)------------------------------
% 0.59/0.75  % (8556)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.59/0.75  % (8556)Termination reason: Refutation not found, incomplete strategy
% 0.59/0.75  
% 0.59/0.75  % (8556)Memory used [KB]: 1063
% 0.59/0.75  % (8556)Time elapsed: 0.003 s
% 0.59/0.75  % (8556)Instructions burned: 5 (million)
% 0.59/0.75  % (8563)Refutation not found, incomplete strategy% (8563)------------------------------
% 0.59/0.75  % (8563)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.59/0.75  % (8563)Termination reason: Refutation not found, incomplete strategy
% 0.59/0.75  
% 0.59/0.75  % (8563)Memory used [KB]: 1028
% 0.59/0.75  % (8563)Time elapsed: 0.004 s
% 0.59/0.75  % (8556)------------------------------
% 0.59/0.75  % (8556)------------------------------
% 0.59/0.75  % (8563)Instructions burned: 3 (million)
% 0.59/0.75  % (8563)------------------------------
% 0.59/0.75  % (8563)------------------------------
% 0.59/0.75  % (8560)Refutation not found, incomplete strategy% (8560)------------------------------
% 0.59/0.75  % (8560)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.59/0.75  % (8560)Termination reason: Refutation not found, incomplete strategy
% 0.59/0.75  
% 0.59/0.75  % (8560)Memory used [KB]: 1051
% 0.59/0.75  % (8560)Time elapsed: 0.004 s
% 0.59/0.75  % (8560)Instructions burned: 4 (million)
% 0.59/0.75  % (8560)------------------------------
% 0.59/0.75  % (8560)------------------------------
% 0.59/0.75  % (8564)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2996ds/55Mi)
% 0.59/0.75  % (8562)First to succeed.
% 0.59/0.75  % (8562)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-8542"
% 0.59/0.75  % (8566)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/208Mi)
% 0.59/0.75  % (8562)Refutation found. Thanks to Tanya!
% 0.59/0.75  % SZS status Theorem for Vampire---4
% 0.59/0.75  % SZS output start Proof for Vampire---4
% See solution above
% 0.59/0.75  % (8562)------------------------------
% 0.59/0.75  % (8562)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.59/0.75  % (8562)Termination reason: Refutation
% 0.59/0.75  
% 0.59/0.75  % (8562)Memory used [KB]: 1066
% 0.59/0.75  % (8562)Time elapsed: 0.007 s
% 0.59/0.75  % (8562)Instructions burned: 9 (million)
% 0.59/0.75  % (8542)Success in time 0.379 s
% 0.59/0.75  % Vampire---4.8 exiting
%------------------------------------------------------------------------------