TSTP Solution File: DAT047_1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : DAT047_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_uns --cores 0 -t %d %s

% Computer : n002.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 16:04:00 EDT 2022

% Result   : Theorem 0.18s 0.52s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   65 (  13 unt;   7 typ;   0 def)
%            Number of atoms       :  140 (  46 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  139 (  57   ~;  53   |;  16   &)
%                                         (  13 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of FOOLs       :    1 (   1 fml;   0 var)
%            Number arithmetic     :  144 (   0 atm;  27 fun;  79 num;  38 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :    8 (   5   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :   12 (   4 usr;   6 con; 0-2 aty)
%            Number of variables   :   66 (  66   !;   0   ?;  66   :)

% 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(pred_def_4,type,
    sP0: $int > $o ).

tff(f139,plain,
    $false,
    inference(avatar_sat_refutation,[],[f102,f127,f138]) ).

tff(f138,plain,
    ~ spl1_2,
    inference(avatar_contradiction_clause,[],[f137]) ).

tff(f137,plain,
    ( $false
    | ~ spl1_2 ),
    inference(subsumption_resolution,[],[f136,f55]) ).

tff(f55,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(f136,plain,
    ( in(5,empty)
    | ~ spl1_2 ),
    inference(evaluation,[],[f135]) ).

tff(f135,plain,
    ( ( 5 = 3 )
    | in(5,empty)
    | ~ spl1_2 ),
    inference(resolution,[],[f128,f65]) ).

tff(f65,plain,
    ! [X2: collection,X0: $int,X1: $int] :
      ( ~ in(X1,add(X0,X2))
      | ( X0 = X1 )
      | in(X1,X2) ),
    inference(cnf_transformation,[],[f46]) ).

tff(f46,plain,
    ! [X0: $int,X1: $int,X2: collection] :
      ( ( in(X1,add(X0,X2))
        | ( ( X0 != X1 )
          & ~ in(X1,X2) ) )
      & ( ( X0 = X1 )
        | in(X1,X2)
        | ~ in(X1,add(X0,X2)) ) ),
    inference(flattening,[],[f45]) ).

tff(f45,plain,
    ! [X0: $int,X1: $int,X2: collection] :
      ( ( in(X1,add(X0,X2))
        | ( ( X0 != X1 )
          & ~ in(X1,X2) ) )
      & ( ( X0 = X1 )
        | in(X1,X2)
        | ~ in(X1,add(X0,X2)) ) ),
    inference(nnf_transformation,[],[f29]) ).

tff(f29,plain,
    ! [X0: $int,X1: $int,X2: collection] :
      ( in(X1,add(X0,X2))
    <=> ( ( X0 = X1 )
        | in(X1,X2) ) ),
    inference(rectify,[],[f4]) ).

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

tff(f128,plain,
    ( in(5,add(3,empty))
    | ~ spl1_2 ),
    inference(resolution,[],[f92,f75]) ).

tff(f75,plain,
    ! [X2: collection,X0: $int,X1: $int] :
      ( ~ in(X0,remove(X1,X2))
      | in(X0,X2) ),
    inference(cnf_transformation,[],[f54]) ).

tff(f54,plain,
    ! [X0: $int,X1: $int,X2: collection] :
      ( ( in(X0,remove(X1,X2))
        | ~ in(X0,X2)
        | ( X0 = X1 ) )
      & ( ( in(X0,X2)
          & ( X0 != X1 ) )
        | ~ in(X0,remove(X1,X2)) ) ),
    inference(rectify,[],[f53]) ).

tff(f53,plain,
    ! [X1: $int,X2: $int,X0: collection] :
      ( ( in(X1,remove(X2,X0))
        | ~ in(X1,X0)
        | ( X1 = X2 ) )
      & ( ( in(X1,X0)
          & ( X1 != X2 ) )
        | ~ in(X1,remove(X2,X0)) ) ),
    inference(flattening,[],[f52]) ).

tff(f52,plain,
    ! [X1: $int,X2: $int,X0: collection] :
      ( ( in(X1,remove(X2,X0))
        | ~ in(X1,X0)
        | ( X1 = X2 ) )
      & ( ( in(X1,X0)
          & ( X1 != X2 ) )
        | ~ in(X1,remove(X2,X0)) ) ),
    inference(nnf_transformation,[],[f38]) ).

tff(f38,plain,
    ! [X1: $int,X2: $int,X0: collection] :
      ( in(X1,remove(X2,X0))
    <=> ( in(X1,X0)
        & ( X1 != X2 ) ) ),
    inference(rectify,[],[f5]) ).

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

tff(f92,plain,
    ( in(5,remove(3,add(3,empty)))
    | ~ spl1_2 ),
    inference(avatar_component_clause,[],[f91]) ).

tff(f91,plain,
    ( spl1_2
  <=> in(5,remove(3,add(3,empty))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).

tff(f127,plain,
    spl1_3,
    inference(avatar_contradiction_clause,[],[f126]) ).

tff(f126,plain,
    ( $false
    | spl1_3 ),
    inference(subsumption_resolution,[],[f125,f78]) ).

tff(f78,plain,
    sP0(1),
    inference(inequality_splitting,[],[f57,f77]) ).

tff(f77,plain,
    ~ sP0(count(add(5,remove(3,add(3,empty))))),
    introduced(inequality_splitting_name_introduction,[new_symbols(naming,[sP0])]) ).

tff(f57,plain,
    1 != count(add(5,remove(3,add(3,empty)))),
    inference(cnf_transformation,[],[f36]) ).

tff(f36,plain,
    1 != count(add(5,remove(3,add(3,empty)))),
    inference(flattening,[],[f14]) ).

tff(f14,negated_conjecture,
    ( ( ~ 1 )
    = count(add(5,remove(3,add(3,empty)))) ),
    inference(negated_conjecture,[],[f13]) ).

tff(f13,conjecture,
    1 = count(add(5,remove(3,add(3,empty)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

tff(f125,plain,
    ( ~ sP0(1)
    | spl1_3 ),
    inference(evaluation,[],[f122]) ).

tff(f122,plain,
    ( ~ sP0($sum(0,1))
    | spl1_3 ),
    inference(superposition,[],[f117,f79]) ).

tff(f79,plain,
    0 = count(empty),
    inference(equality_resolution,[],[f64]) ).

tff(f64,plain,
    ! [X0: collection] :
      ( ( 0 = count(X0) )
      | ( empty != X0 ) ),
    inference(cnf_transformation,[],[f44]) ).

tff(f44,plain,
    ! [X0: collection] :
      ( ( ( 0 = count(X0) )
        | ( empty != X0 ) )
      & ( ( empty = X0 )
        | ( 0 != count(X0) ) ) ),
    inference(nnf_transformation,[],[f30]) ).

tff(f30,plain,
    ! [X0: collection] :
      ( ( 0 = count(X0) )
    <=> ( empty = X0 ) ),
    inference(rectify,[],[f7]) ).

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

tff(f117,plain,
    ( ~ sP0($sum(count(empty),1))
    | spl1_3 ),
    inference(subsumption_resolution,[],[f116,f55]) ).

tff(f116,plain,
    ( ~ sP0($sum(count(empty),1))
    | in(3,empty)
    | spl1_3 ),
    inference(superposition,[],[f114,f69]) ).

tff(f69,plain,
    ! [X0: collection,X1: $int] :
      ( ( $sum(count(X0),1) = count(add(X1,X0)) )
      | in(X1,X0) ),
    inference(cnf_transformation,[],[f49]) ).

tff(f49,plain,
    ! [X0: collection,X1: $int] :
      ( ( ~ in(X1,X0)
        | ( $sum(count(X0),1) != count(add(X1,X0)) ) )
      & ( ( $sum(count(X0),1) = count(add(X1,X0)) )
        | in(X1,X0) ) ),
    inference(rectify,[],[f48]) ).

tff(f48,plain,
    ! [X1: collection,X0: $int] :
      ( ( ~ in(X0,X1)
        | ( count(add(X0,X1)) != $sum(count(X1),1) ) )
      & ( ( count(add(X0,X1)) = $sum(count(X1),1) )
        | in(X0,X1) ) ),
    inference(nnf_transformation,[],[f31]) ).

tff(f31,plain,
    ! [X1: collection,X0: $int] :
      ( ~ in(X0,X1)
    <=> ( count(add(X0,X1)) = $sum(count(X1),1) ) ),
    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(f114,plain,
    ( ~ sP0(count(add(3,empty)))
    | spl1_3 ),
    inference(subsumption_resolution,[],[f113,f80]) ).

tff(f80,plain,
    ! [X2: collection,X1: $int] : in(X1,add(X1,X2)),
    inference(equality_resolution,[],[f67]) ).

tff(f67,plain,
    ! [X2: collection,X0: $int,X1: $int] :
      ( in(X1,add(X0,X2))
      | ( X0 != X1 ) ),
    inference(cnf_transformation,[],[f46]) ).

tff(f113,plain,
    ( ~ sP0(count(add(3,empty)))
    | ~ in(3,add(3,empty))
    | spl1_3 ),
    inference(evaluation,[],[f109]) ).

tff(f109,plain,
    ( ~ sP0($sum($sum(count(add(3,empty)),-1),1))
    | ~ in(3,add(3,empty))
    | spl1_3 ),
    inference(superposition,[],[f101,f83]) ).

tff(f83,plain,
    ! [X0: $int,X1: collection] :
      ( ( count(remove(X0,X1)) = $sum(count(X1),-1) )
      | ~ in(X0,X1) ),
    inference(evaluation,[],[f62]) ).

tff(f62,plain,
    ! [X0: $int,X1: collection] :
      ( ( $sum(count(X1),$uminus(1)) = count(remove(X0,X1)) )
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f43]) ).

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

tff(f33,plain,
    ! [X0: $int,X1: collection] :
      ( ( $sum(count(X1),$uminus(1)) = count(remove(X0,X1)) )
    <=> in(X0,X1) ),
    inference(rectify,[],[f15]) ).

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

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

tff(f101,plain,
    ( ~ sP0($sum(count(remove(3,add(3,empty))),1))
    | spl1_3 ),
    inference(avatar_component_clause,[],[f99]) ).

tff(f99,plain,
    ( spl1_3
  <=> sP0($sum(count(remove(3,add(3,empty))),1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).

tff(f102,plain,
    ( ~ spl1_3
    | spl1_2 ),
    inference(avatar_split_clause,[],[f85,f91,f99]) ).

tff(f85,plain,
    ( in(5,remove(3,add(3,empty)))
    | ~ sP0($sum(count(remove(3,add(3,empty))),1)) ),
    inference(superposition,[],[f77,f69]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : DAT047=1 : TPTP v8.1.0. Released v5.0.0.
% 0.11/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.33  % Computer : n002.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon Aug 29 20:30:13 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.18/0.49  % (24427)dis+2_1:1_av=off:bsr=on:erd=off:s2pl=on:sgt=16:sos=on:sp=frequency:ss=axioms:i=46:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/46Mi)
% 0.18/0.49  % (24419)lrs+22_1:1_amm=sco:fsr=off:gve=force:sos=on:uwa=all:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.18/0.49  % (24427)Refutation not found, incomplete strategy% (24427)------------------------------
% 0.18/0.49  % (24427)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.49  % (24419)Refutation not found, incomplete strategy% (24419)------------------------------
% 0.18/0.49  % (24419)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.49  % (24427)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.49  % (24427)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.49  
% 0.18/0.49  % (24427)Memory used [KB]: 1023
% 0.18/0.49  % (24427)Time elapsed: 0.055 s
% 0.18/0.49  % (24427)Instructions burned: 3 (million)
% 0.18/0.49  % (24427)------------------------------
% 0.18/0.49  % (24427)------------------------------
% 0.18/0.49  % (24411)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=32:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/32Mi)
% 0.18/0.49  % (24419)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.49  % (24419)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.49  
% 0.18/0.49  % (24419)Memory used [KB]: 5628
% 0.18/0.49  % (24419)Time elapsed: 0.054 s
% 0.18/0.49  % (24419)Instructions burned: 3 (million)
% 0.18/0.49  % (24419)------------------------------
% 0.18/0.49  % (24419)------------------------------
% 0.18/0.50  % (24414)lrs+10_1:8_ep=R:erd=off:fs=off:fsr=off:gve=force:nwc=2.0:uwa=one_side_interpreted:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.18/0.50  % (24412)lrs+1010_1:1_bd=off:fd=off:fde=none:ins=3:sac=on:sos=on:spb=goal:to=lpo:i=36:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/36Mi)
% 0.18/0.50  % (24408)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.18/0.51  % (24413)lrs+1010_1:1_ep=RST:s2a=on:s2at=5.0:sos=all:i=26:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/26Mi)
% 0.18/0.51  % (24405)dis+1010_1:4_aac=none:abs=on:atotf=0.5:avsq=on:avsqc=2:avsqr=215,247:awrs=converge:awrsf=128:bsd=on:erd=off:fde=none:gve=cautious:newcnf=on:nwc=5.0:rnwc=on:sac=on:sas=z3:sp=const_min:tgt=ground:thsq=on:thsqc=64:thsqr=1,4:i=59848:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59848Mi)
% 0.18/0.51  % (24412)First to succeed.
% 0.18/0.51  % (24407)dis+1011_1:64_drc=off:flr=on:nwc=2.0:sac=on:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.18/0.52  % (24406)lrs+1010_1:1_aac=none:bce=on:nicw=on:nm=0:plsq=on:plsql=on:sac=on:sos=on:sp=frequency:spb=units:to=lpo:i=34:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/34Mi)
% 0.18/0.52  % (24417)lrs+10_1:1_ep=R:gve=force:plsq=on:plsqr=32,1:uwa=one_side_interpreted:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.18/0.52  % (24412)Refutation found. Thanks to Tanya!
% 0.18/0.52  % SZS status Theorem for theBenchmark
% 0.18/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.52  % (24412)------------------------------
% 0.18/0.52  % (24412)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.52  % (24412)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.52  % (24412)Termination reason: Refutation
% 0.18/0.52  
% 0.18/0.52  % (24412)Memory used [KB]: 5500
% 0.18/0.52  % (24412)Time elapsed: 0.119 s
% 0.18/0.52  % (24412)Instructions burned: 3 (million)
% 0.18/0.52  % (24412)------------------------------
% 0.18/0.52  % (24412)------------------------------
% 0.18/0.52  % (24404)Success in time 0.173 s
%------------------------------------------------------------------------------