TSTP Solution File: SCT172_5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SCT172_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n016.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 : Tue May 21 02:51:53 EDT 2024

% Result   : Theorem 0.14s 0.38s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   61
% Syntax   : Number of formulae    :   80 (  18 unt;  56 typ;   0 def)
%            Number of atoms       :   46 (  15 equ)
%            Maximal formula atoms :    8 (   1 avg)
%            Number of connectives :   40 (  18   ~;   9   |;  10   &)
%                                         (   2 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   93 (  46   >;  47   *;   0   +;   0  <<)
%            Number of predicates  :   15 (  13 usr;   1 prp; 0-6 aty)
%            Number of functors    :   41 (  41 usr;   6 con; 0-5 aty)
%            Number of variables   :   93 (  31   !;  12   ?;  93   :)
%                                         (  50  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    arrow_411405190le_alt: $tType ).

tff(type_def_6,type,
    bool: $tType ).

tff(type_def_7,type,
    list: $tType > $tType ).

tff(type_def_8,type,
    fun: ( $tType * $tType ) > $tType ).

tff(func_def_0,type,
    append: 
      !>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).

tff(func_def_1,type,
    butlast: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

tff(func_def_2,type,
    dropWhile: 
      !>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > list(X0) ) ).

tff(func_def_3,type,
    hd: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

tff(func_def_4,type,
    insert: 
      !>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).

tff(func_def_5,type,
    last: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

tff(func_def_6,type,
    linorder_insort_key: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 * list(X0) ) > list(X0) ) ).

tff(func_def_7,type,
    linorder_sort_key: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X0) ) ).

tff(func_def_8,type,
    cons: 
      !>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).

tff(func_def_9,type,
    nil: 
      !>[X0: $tType] : list(X0) ).

tff(func_def_10,type,
    list_case: 
      !>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).

tff(func_def_11,type,
    list_rec: 
      !>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),fun(X0,X0))) * list(X1) ) > X0 ) ).

tff(func_def_12,type,
    maps: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,list(X1)) * list(X0) ) > list(X1) ) ).

tff(func_def_13,type,
    rev: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

tff(func_def_14,type,
    rotate1: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

tff(func_def_15,type,
    splice: 
      !>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).

tff(func_def_16,type,
    takeWhile: 
      !>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > list(X0) ) ).

tff(func_def_17,type,
    aa: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).

tff(func_def_18,type,
    fFalse: bool ).

tff(func_def_19,type,
    fTrue: bool ).

tff(func_def_20,type,
    a: arrow_411405190le_alt ).

tff(func_def_21,type,
    sK7: ( arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_411405190le_alt ).

tff(func_def_22,type,
    sK8: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

tff(func_def_23,type,
    sK9: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

tff(func_def_24,type,
    sK10: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

tff(func_def_25,type,
    sK11: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

tff(func_def_26,type,
    sK12: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

tff(func_def_27,type,
    sK13: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

tff(func_def_28,type,
    sK14: 
      !>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).

tff(func_def_29,type,
    sK15: 
      !>[X0: $tType] : ( fun(list(X0),bool) > list(X0) ) ).

tff(func_def_30,type,
    sK16: 
      !>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).

tff(func_def_31,type,
    sK17: 
      !>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).

tff(func_def_32,type,
    sK18: 
      !>[X0: $tType] : ( fun(list(X0),bool) > list(X0) ) ).

tff(func_def_33,type,
    sK19: 
      !>[X0: $tType] : ( ( list(X0) * list(X0) * list(X0) * list(X0) ) > list(X0) ) ).

tff(func_def_34,type,
    sK20: 
      !>[X0: $tType] : ( ( list(X0) * list(X0) * list(X0) * X0 ) > list(X0) ) ).

tff(func_def_35,type,
    sK21: 
      !>[X0: $tType] : ( ( list(X0) * list(X0) * list(X0) * X0 ) > list(X0) ) ).

tff(func_def_36,type,
    sK22: arrow_411405190le_alt ).

tff(func_def_37,type,
    sK23: arrow_411405190le_alt ).

tff(func_def_38,type,
    sK24: arrow_411405190le_alt ).

tff(pred_def_1,type,
    linorder: 
      !>[X0: $tType] : $o ).

tff(pred_def_2,type,
    equal_equal: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(pred_def_3,type,
    distinct: 
      !>[X0: $tType] : ( list(X0) > $o ) ).

tff(pred_def_4,type,
    list_ex1: 
      !>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).

tff(pred_def_5,type,
    null: 
      !>[X0: $tType] : ( list(X0) > $o ) ).

tff(pred_def_6,type,
    pp: bool > $o ).

tff(pred_def_7,type,
    sP0: 
      !>[X0: $tType] : ( fun(list(X0),bool) > $o ) ).

tff(pred_def_8,type,
    sP1: 
      !>[X0: $tType] : ( ( list(X0) * list(X0) * list(X0) * list(X0) * list(X0) ) > $o ) ).

tff(pred_def_9,type,
    sP2: 
      !>[X0: $tType] : ( ( list(X0) * list(X0) * list(X0) * list(X0) ) > $o ) ).

tff(pred_def_10,type,
    sP3: 
      !>[X0: $tType] : ( ( list(X0) * list(X0) * X0 * list(X0) ) > $o ) ).

tff(pred_def_11,type,
    sP4: 
      !>[X0: $tType] : ( ( list(X0) * list(X0) * list(X0) * X0 ) > $o ) ).

tff(pred_def_12,type,
    sP5: 
      !>[X0: $tType] : ( ( list(X0) * list(X0) * X0 * list(X0) ) > $o ) ).

tff(pred_def_13,type,
    sP6: 
      !>[X0: $tType] : ( ( list(X0) * list(X0) * list(X0) * X0 ) > $o ) ).

tff(f598,plain,
    $false,
    inference(subsumption_resolution,[],[f597,f539]) ).

tff(f539,plain,
    ! [X0: $tType,X3: X0,X1: list(X0)] : ~ distinct(X0,cons(X0,X3,cons(X0,X3,X1))),
    inference(equality_resolution,[],[f455]) ).

tff(f455,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: list(X0)] :
      ( ( X2 != X3 )
      | ~ distinct(X0,cons(X0,X3,cons(X0,X2,X1))) ),
    inference(cnf_transformation,[],[f296]) ).

tff(f296,plain,
    ! [X0: $tType,X1: list(X0),X2: X0,X3: X0] :
      ( ( distinct(X0,cons(X0,X3,cons(X0,X2,X1)))
        | ~ distinct(X0,cons(X0,X2,X1))
        | ~ distinct(X0,cons(X0,X3,X1))
        | ( X2 = X3 ) )
      & ( ( distinct(X0,cons(X0,X2,X1))
          & distinct(X0,cons(X0,X3,X1))
          & ( X2 != X3 ) )
        | ~ distinct(X0,cons(X0,X3,cons(X0,X2,X1))) ) ),
    inference(flattening,[],[f295]) ).

tff(f295,plain,
    ! [X0: $tType,X1: list(X0),X2: X0,X3: X0] :
      ( ( distinct(X0,cons(X0,X3,cons(X0,X2,X1)))
        | ~ distinct(X0,cons(X0,X2,X1))
        | ~ distinct(X0,cons(X0,X3,X1))
        | ( X2 = X3 ) )
      & ( ( distinct(X0,cons(X0,X2,X1))
          & distinct(X0,cons(X0,X3,X1))
          & ( X2 != X3 ) )
        | ~ distinct(X0,cons(X0,X3,cons(X0,X2,X1))) ) ),
    inference(nnf_transformation,[],[f186]) ).

tff(f186,plain,
    ! [X0: $tType,X1: list(X0),X2: X0,X3: X0] :
      ( distinct(X0,cons(X0,X3,cons(X0,X2,X1)))
    <=> ( distinct(X0,cons(X0,X2,X1))
        & distinct(X0,cons(X0,X3,X1))
        & ( X2 != X3 ) ) ),
    inference(rectify,[],[f6]) ).

tff(f6,axiom,
    ! [X0: $tType,X13: list(X0),X14: X0,X12: X0] :
      ( distinct(X0,cons(X0,X12,cons(X0,X14,X13)))
    <=> ( distinct(X0,cons(X0,X14,X13))
        & distinct(X0,cons(X0,X12,X13))
        & ( X12 != X14 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_distinct__length__2__or__more) ).

tff(f597,plain,
    distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,a,cons(arrow_411405190le_alt,a,insert(arrow_411405190le_alt,a,nil(arrow_411405190le_alt))))),
    inference(forward_demodulation,[],[f596,f335]) ).

tff(f335,plain,
    ! [X0: arrow_411405190le_alt] : ( a = X0 ),
    inference(cnf_transformation,[],[f205]) ).

tff(f205,plain,
    ! [X0: arrow_411405190le_alt] : ( a = X0 ),
    inference(ennf_transformation,[],[f106]) ).

tff(f106,plain,
    ~ ? [X0: arrow_411405190le_alt] : ( a != X0 ),
    inference(rectify,[],[f105]) ).

tff(f105,negated_conjecture,
    ~ ? [X44: arrow_411405190le_alt] : ( a != X44 ),
    inference(negated_conjecture,[],[f104]) ).

tff(f104,conjecture,
    ? [X44: arrow_411405190le_alt] : ( a != X44 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

tff(f596,plain,
    distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,sK22,cons(arrow_411405190le_alt,a,insert(arrow_411405190le_alt,a,nil(arrow_411405190le_alt))))),
    inference(forward_demodulation,[],[f595,f335]) ).

tff(f595,plain,
    distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,sK22,cons(arrow_411405190le_alt,sK23,insert(arrow_411405190le_alt,a,nil(arrow_411405190le_alt))))),
    inference(forward_demodulation,[],[f594,f335]) ).

tff(f594,plain,
    distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,sK22,cons(arrow_411405190le_alt,sK23,insert(arrow_411405190le_alt,sK24,nil(arrow_411405190le_alt))))),
    inference(forward_demodulation,[],[f510,f351]) ).

tff(f351,plain,
    ! [X0: $tType,X1: X0] : ( cons(X0,X1,nil(X0)) = insert(X0,X1,nil(X0)) ),
    inference(cnf_transformation,[],[f117]) ).

tff(f117,plain,
    ! [X0: $tType,X1: X0] : ( cons(X0,X1,nil(X0)) = insert(X0,X1,nil(X0)) ),
    inference(rectify,[],[f13]) ).

tff(f13,axiom,
    ! [X0: $tType,X8: X0] : ( cons(X0,X8,nil(X0)) = insert(X0,X8,nil(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_insert__Nil) ).

tff(f510,plain,
    distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,sK22,cons(arrow_411405190le_alt,sK23,cons(arrow_411405190le_alt,sK24,nil(arrow_411405190le_alt))))),
    inference(cnf_transformation,[],[f334]) ).

tff(f334,plain,
    distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,sK22,cons(arrow_411405190le_alt,sK23,cons(arrow_411405190le_alt,sK24,nil(arrow_411405190le_alt))))),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23,sK24])],[f203,f333]) ).

tff(f333,plain,
    ( ? [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: arrow_411405190le_alt] : distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,X0,cons(arrow_411405190le_alt,X1,cons(arrow_411405190le_alt,X2,nil(arrow_411405190le_alt)))))
   => distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,sK22,cons(arrow_411405190le_alt,sK23,cons(arrow_411405190le_alt,sK24,nil(arrow_411405190le_alt))))) ),
    introduced(choice_axiom,[]) ).

tff(f203,plain,
    ? [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: arrow_411405190le_alt] : distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,X0,cons(arrow_411405190le_alt,X1,cons(arrow_411405190le_alt,X2,nil(arrow_411405190le_alt))))),
    inference(rectify,[],[f1]) ).

tff(f1,axiom,
    ? [X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] : distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,X3,cons(arrow_411405190le_alt,X4,cons(arrow_411405190le_alt,X5,nil(arrow_411405190le_alt))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_alt3) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SCT172_5 : TPTP v8.2.0. Released v6.0.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n016.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 May 20 00:06:22 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (9199)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (9203)WARNING: value z3 for option sas not known
% 0.14/0.37  % (9201)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37  % (9204)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37  % (9205)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.37  % (9207)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.37  % (9203)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37  % (9206)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.37  % (9200)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38  % (9207)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.38  % Exception at run slice level% Exception at run slice level
% 0.14/0.38  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.38  
% 0.14/0.38  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.38  % Exception at run slice level
% 0.14/0.38  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.38  % (9207)First to succeed.
% 0.14/0.38  % (9207)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-9199"
% 0.14/0.38  % (9207)Refutation found. Thanks to Tanya!
% 0.14/0.38  % SZS status Theorem for theBenchmark
% 0.14/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.38  % (9207)------------------------------
% 0.14/0.38  % (9207)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.38  % (9207)Termination reason: Refutation
% 0.14/0.38  
% 0.14/0.38  % (9207)Memory used [KB]: 1082
% 0.14/0.38  % (9207)Time elapsed: 0.011 s
% 0.14/0.38  % (9207)Instructions burned: 21 (million)
% 0.14/0.38  % (9199)Success in time 0.029 s
%------------------------------------------------------------------------------