TSTP Solution File: PUZ081_8 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : PUZ081_8 : TPTP v8.1.2. Released v8.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n005.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 Apr 30 14:45:46 EDT 2024

% Result   : Theorem 0.21s 0.39s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   76 (  16 unt;   5 typ;   0 def)
%            Number of atoms       :  311 (  59 equ)
%            Maximal formula atoms :    6 (   4 avg)
%            Number of connectives :  145 (  58   ~;  55   |;  19   &)
%                                         (   5 <=>;   7  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :  207 ( 157 fml;  50 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   3   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :   12 (   9 usr;   6 prp; 0-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   63 (  57   !;   6   ?;  42   :)

% Comments : 
%------------------------------------------------------------------------------
tff(func_def_4,type,
    bG0: $o ).

tff(func_def_5,type,
    bG1: $o ).

tff(func_def_6,type,
    bG2: $o > $o ).

tff(func_def_7,type,
    bG3: $o > $o ).

tff(pred_def_3,type,
    says: ( $i * $o ) > $o ).

tff(f168,plain,
    $false,
    inference(trivial_inequality_removal,[],[f161]) ).

tff(f161,plain,
    $true = $false,
    inference(superposition,[],[f92,f150]) ).

tff(f150,plain,
    ! [X0: $o] : ( $true = (X0) ),
    inference(resolution,[],[f148,f95]) ).

tff(f95,plain,
    says(zoey,$false),
    inference(backward_demodulation,[],[f45,f92]) ).

tff(f45,plain,
    says(zoey,bG0),
    inference(cnf_transformation,[],[f11]) ).

tff(f11,plain,
    says(zoey,bG0),
    inference(fool_elimination,[],[f4,f10]) ).

tff(f10,plain,
    ( knave(mel)
  <=> ( $true = bG0 ) ),
    introduced(fool_formula_definition,[new_symbols(definition,[bG0])]) ).

tff(f4,axiom,
    says(zoey,knave(mel)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zoey_speaks) ).

tff(f148,plain,
    ! [X0: $o,X1: $i] :
      ( ~ says(X1,$false)
      | ( $true = (X0) ) ),
    inference(duplicate_literal_removal,[],[f145]) ).

tff(f145,plain,
    ! [X0: $o,X1: $i] :
      ( ~ says(X1,$false)
      | ( $true = (X0) )
      | ( $true = (X0) ) ),
    inference(superposition,[],[f118,f139]) ).

tff(f139,plain,
    ! [X0: $o] :
      ( ( $false = bG2((X0)) )
      | ( $true = (X0) ) ),
    inference(resolution,[],[f118,f136]) ).

tff(f136,plain,
    ! [X0: $o] :
      ( says(mel,(X0))
      | ( $false = (X0) ) ),
    inference(superposition,[],[f121,f9]) ).

tff(f9,plain,
    ! [X0: $o] :
      ( ( $true = (X0) )
      | ( $false = (X0) ) ),
    introduced(fool_axiom,[]) ).

tff(f121,plain,
    says(mel,$true),
    inference(backward_demodulation,[],[f46,f117]) ).

tff(f117,plain,
    $true = bG1,
    inference(subsumption_resolution,[],[f116,f100]) ).

tff(f100,plain,
    ! [X0: $i] : knight(X0),
    inference(trivial_inequality_removal,[],[f97]) ).

tff(f97,plain,
    ! [X0: $i] :
      ( ( $true = $false )
      | knight(X0) ),
    inference(backward_demodulation,[],[f58,f92]) ).

tff(f58,plain,
    ! [X0: $i] :
      ( knight(X0)
      | ( $true = bG0 ) ),
    inference(resolution,[],[f57,f54]) ).

tff(f54,plain,
    ! [X0: $i,X1: $i] :
      ( ~ knight(X1)
      | knight(X0) ),
    inference(resolution,[],[f47,f44]) ).

tff(f44,plain,
    ! [X0: $i,X1: $i] :
      ( ~ knave(X1)
      | ~ knight(X0) ),
    inference(cnf_transformation,[],[f24]) ).

tff(f24,plain,
    ! [X0,X1] :
      ( ~ knave(X1)
      | ~ knight(X0) ),
    inference(ennf_transformation,[],[f22]) ).

tff(f22,plain,
    ~ ? [X0,X1] :
        ( knave(X1)
        & knight(X0) ),
    inference(rectify,[],[f7]) ).

tff(f7,negated_conjecture,
    ~ ? [X2,X3] :
        ( knave(X3)
        & knight(X2) ),
    inference(negated_conjecture,[],[f6]) ).

tff(f6,conjecture,
    ? [X2,X3] :
      ( knave(X3)
      & knight(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',who_is_knight_and_knave) ).

tff(f47,plain,
    ! [X0: $i] :
      ( knave(X0)
      | knight(X0) ),
    inference(cnf_transformation,[],[f34]) ).

tff(f34,plain,
    ! [X0] :
      ( ( ~ knave(X0)
        | ~ knight(X0) )
      & ( knave(X0)
        | knight(X0) ) ),
    inference(nnf_transformation,[],[f1]) ).

tff(f1,axiom,
    ! [X0] :
      ( knight(X0)
    <~> knave(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knights_xor_knaves) ).

tff(f57,plain,
    ( knight(mel)
    | ( $true = bG0 ) ),
    inference(resolution,[],[f42,f47]) ).

tff(f42,plain,
    ( ~ knave(mel)
    | ( $true = bG0 ) ),
    inference(cnf_transformation,[],[f33]) ).

tff(f33,plain,
    ( ( knave(mel)
      | ( $true != bG0 ) )
    & ( ( $true = bG0 )
      | ~ knave(mel) ) ),
    inference(nnf_transformation,[],[f10]) ).

tff(f116,plain,
    ! [X0: $i] :
      ( ( $true = bG1 )
      | ~ knight(X0) ),
    inference(resolution,[],[f114,f44]) ).

tff(f114,plain,
    ( knave(zoey)
    | ( $true = bG1 ) ),
    inference(subsumption_resolution,[],[f39,f102]) ).

tff(f102,plain,
    ~ knave(mel),
    inference(trivial_inequality_removal,[],[f93]) ).

tff(f93,plain,
    ( ( $true = $false )
    | ~ knave(mel) ),
    inference(backward_demodulation,[],[f42,f92]) ).

tff(f39,plain,
    ( ( $true = bG1 )
    | knave(mel)
    | knave(zoey) ),
    inference(cnf_transformation,[],[f32]) ).

tff(f32,plain,
    ( ( ( ~ knave(mel)
        & ~ knave(zoey) )
      | ( $true != bG1 ) )
    & ( ( $true = bG1 )
      | knave(mel)
      | knave(zoey) ) ),
    inference(flattening,[],[f31]) ).

tff(f31,plain,
    ( ( ( ~ knave(mel)
        & ~ knave(zoey) )
      | ( $true != bG1 ) )
    & ( ( $true = bG1 )
      | knave(mel)
      | knave(zoey) ) ),
    inference(nnf_transformation,[],[f12]) ).

tff(f12,plain,
    ( ( ~ knave(mel)
      & ~ knave(zoey) )
  <=> ( $true = bG1 ) ),
    introduced(fool_formula_definition,[new_symbols(definition,[bG1])]) ).

tff(f46,plain,
    says(mel,bG1),
    inference(cnf_transformation,[],[f13]) ).

tff(f13,plain,
    says(mel,bG1),
    inference(fool_elimination,[],[f5,f12]) ).

tff(f5,axiom,
    says(mel,
      ( ~ knave(mel)
      & ~ knave(zoey) )),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mel_speaks) ).

tff(f118,plain,
    ! [X0: $i,X1: $o] :
      ( ~ says(X0,bG2((X1)))
      | ( $true = (X1) ) ),
    inference(subsumption_resolution,[],[f49,f100]) ).

tff(f49,plain,
    ! [X0: $i,X1: $o] :
      ( ( $true = (X1) )
      | ~ says(X0,bG2((X1)))
      | ~ knight(X0) ),
    inference(cnf_transformation,[],[f26]) ).

tff(f26,plain,
    ! [X0,X1: $o] :
      ( ( $true = (X1) )
      | ~ says(X0,bG2((X1)))
      | ~ knight(X0) ),
    inference(flattening,[],[f25]) ).

tff(f25,plain,
    ! [X0,X1: $o] :
      ( ( $true = (X1) )
      | ~ says(X0,bG2((X1)))
      | ~ knight(X0) ),
    inference(ennf_transformation,[],[f16]) ).

tff(f16,plain,
    ! [X0,X1: $o] :
      ( ( says(X0,bG2((X1)))
        & knight(X0) )
     => ( $true = (X1) ) ),
    inference(fool_elimination,[],[f14,f15]) ).

tff(f15,plain,
    ! [X1: $o] :
      ( ( $true = (X1) )
    <=> ( $true = bG2((X1)) ) ),
    introduced(fool_formula_definition,[new_symbols(definition,[bG2])]) ).

tff(f14,plain,
    ! [X0,X1: $o] :
      ( ( says(X0,(X1))
        & knight(X0) )
     => (X1) ),
    inference(rectify,[],[f2]) ).

tff(f2,axiom,
    ! [X0,X1: $o] :
      ( ( says(X0,(X1))
        & knight(X0) )
     => (X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knights_tell_truth) ).

tff(f92,plain,
    $false = bG0,
    inference(subsumption_resolution,[],[f91,f75]) ).

tff(f75,plain,
    ! [X0: $i] :
      ( ~ knight(X0)
      | ( $false = bG0 ) ),
    inference(resolution,[],[f72,f44]) ).

tff(f72,plain,
    ( knave(mel)
    | ( $false = bG0 ) ),
    inference(trivial_inequality_removal,[],[f64]) ).

tff(f64,plain,
    ( ( $true != $true )
    | knave(mel)
    | ( $false = bG0 ) ),
    inference(superposition,[],[f43,f9]) ).

tff(f43,plain,
    ( ( $true != bG0 )
    | knave(mel) ),
    inference(cnf_transformation,[],[f33]) ).

tff(f91,plain,
    ( ( $false = bG0 )
    | knight(zoey) ),
    inference(resolution,[],[f89,f47]) ).

tff(f89,plain,
    ( ~ knave(zoey)
    | ( $false = bG0 ) ),
    inference(resolution,[],[f65,f82]) ).

tff(f82,plain,
    ! [X0: $i] :
      ( ~ says(X0,$true)
      | ~ knave(X0) ),
    inference(forward_demodulation,[],[f53,f51]) ).

tff(f51,plain,
    $true = bG3($true),
    inference(equality_resolution,[],[f35]) ).

tff(f35,plain,
    ! [X0: $o] :
      ( ( $true = bG3((X0)) )
      | ( $true != (X0) ) ),
    inference(cnf_transformation,[],[f29]) ).

tff(f29,plain,
    ! [X0: $o] :
      ( ( ( $true = (X0) )
        | ( $true != bG3((X0)) ) )
      & ( ( $true = bG3((X0)) )
        | ( $true != (X0) ) ) ),
    inference(nnf_transformation,[],[f20]) ).

tff(f20,plain,
    ! [X0: $o] :
      ( ( $true = (X0) )
    <=> ( $true = bG3((X0)) ) ),
    inference(rectify,[],[f18]) ).

tff(f18,plain,
    ! [X1: $o] :
      ( ( $true = (X1) )
    <=> ( $true = bG3((X1)) ) ),
    introduced(fool_formula_definition,[new_symbols(definition,[bG3])]) ).

tff(f53,plain,
    ! [X0: $i] :
      ( ~ says(X0,bG3($true))
      | ~ knave(X0) ),
    inference(equality_resolution,[],[f50]) ).

tff(f50,plain,
    ! [X0: $i,X1: $o] :
      ( ( $true != (X1) )
      | ~ says(X0,bG3((X1)))
      | ~ knave(X0) ),
    inference(cnf_transformation,[],[f28]) ).

tff(f28,plain,
    ! [X0,X1: $o] :
      ( ( $true != (X1) )
      | ~ says(X0,bG3((X1)))
      | ~ knave(X0) ),
    inference(flattening,[],[f27]) ).

tff(f27,plain,
    ! [X0,X1: $o] :
      ( ( $true != (X1) )
      | ~ says(X0,bG3((X1)))
      | ~ knave(X0) ),
    inference(ennf_transformation,[],[f23]) ).

tff(f23,plain,
    ! [X0,X1: $o] :
      ( ( says(X0,bG3((X1)))
        & knave(X0) )
     => ( $true != (X1) ) ),
    inference(flattening,[],[f19]) ).

tff(f19,plain,
    ! [X0,X1: $o] :
      ( ( says(X0,bG3((X1)))
        & knave(X0) )
     => ( $true != (X1) ) ),
    inference(fool_elimination,[],[f17,f18]) ).

tff(f17,plain,
    ! [X0,X1: $o] :
      ( ( says(X0,(X1))
        & knave(X0) )
     => ~ (X1) ),
    inference(rectify,[],[f3]) ).

tff(f3,axiom,
    ! [X0,X1: $o] :
      ( ( says(X0,(X1))
        & knave(X0) )
     => ~ (X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knaves_lie) ).

tff(f65,plain,
    ( says(zoey,$true)
    | ( $false = bG0 ) ),
    inference(superposition,[],[f45,f9]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : PUZ081_8 : TPTP v8.1.2. Released v8.0.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n005.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Tue Apr 30 01:56:41 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (16456)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.38  % (16457)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.21/0.38  % (16459)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.21/0.38  % (16461)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.21/0.38  % (16458)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.38  % (16460)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.21/0.38  Detected minimum model sizes of [1,1]
% 0.21/0.38  Detected maximum model sizes of [2,2]
% 0.21/0.38  % (16463)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.21/0.38  % (16462)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.21/0.38  TRYING [1,1]
% 0.21/0.38  Detected minimum model sizes of [1,1]
% 0.21/0.38  Detected maximum model sizes of [2,2]
% 0.21/0.38  TRYING [1,1]
% 0.21/0.38  Detected minimum model sizes of [1,1]
% 0.21/0.38  Detected maximum model sizes of [2,2]
% 0.21/0.38  TRYING [1,1]
% 0.21/0.38  TRYING [1,2]
% 0.21/0.38  TRYING [1,2]
% 0.21/0.38  Detected minimum model sizes of [1,1]
% 0.21/0.38  Detected maximum model sizes of [2,2]
% 0.21/0.38  TRYING [2,2]
% 0.21/0.38  TRYING [1,1]
% 0.21/0.38  TRYING [1,2]
% 0.21/0.38  TRYING [2,2]
% 0.21/0.38  Cannot enumerate next child to try in an incomplete setup
% 0.21/0.38  % (16457)Refutation not found, incomplete strategy% (16457)------------------------------
% 0.21/0.38  % (16457)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.38  % (16457)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.38  
% 0.21/0.38  % (16457)Memory used [KB]: 733
% 0.21/0.38  % (16457)Time elapsed: 0.005 s
% 0.21/0.38  % (16457)Instructions burned: 5 (million)
% 0.21/0.38  % (16457)------------------------------
% 0.21/0.38  % (16457)------------------------------
% 0.21/0.38  TRYING [2,2]
% 0.21/0.38  Cannot enumerate next child to try in an incomplete setup
% 0.21/0.38  % (16458)Refutation not found, incomplete strategy% (16458)------------------------------
% 0.21/0.38  % (16458)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.38  % (16458)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.38  
% 0.21/0.38  % (16458)Memory used [KB]: 734
% 0.21/0.38  % (16458)Time elapsed: 0.005 s
% 0.21/0.38  % (16458)Instructions burned: 5 (million)
% 0.21/0.38  % (16458)------------------------------
% 0.21/0.38  % (16458)------------------------------
% 0.21/0.38  Cannot enumerate next child to try in an incomplete setup
% 0.21/0.38  % (16460)Refutation not found, incomplete strategy% (16460)------------------------------
% 0.21/0.38  % (16460)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.38  % (16460)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.38  
% 0.21/0.38  % (16460)Memory used [KB]: 735
% 0.21/0.38  % (16460)Time elapsed: 0.005 s
% 0.21/0.38  % (16460)Instructions burned: 5 (million)
% 0.21/0.38  % (16460)------------------------------
% 0.21/0.38  % (16460)------------------------------
% 0.21/0.39  TRYING [1,2]
% 0.21/0.39  % (16461)First to succeed.
% 0.21/0.39  TRYING [2,2]
% 0.21/0.39  Cannot enumerate next child to try in an incomplete setup
% 0.21/0.39  % (16463)Refutation not found, incomplete strategy% (16463)------------------------------
% 0.21/0.39  % (16463)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.39  % (16463)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.39  
% 0.21/0.39  % (16463)Memory used [KB]: 734
% 0.21/0.39  % (16463)Time elapsed: 0.005 s
% 0.21/0.39  % (16463)Instructions burned: 5 (million)
% 0.21/0.39  % (16463)------------------------------
% 0.21/0.39  % (16463)------------------------------
% 0.21/0.39  % (16462)Also succeeded, but the first one will report.
% 0.21/0.39  % (16461)Refutation found. Thanks to Tanya!
% 0.21/0.39  % SZS status Theorem for theBenchmark
% 0.21/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.39  % (16461)------------------------------
% 0.21/0.39  % (16461)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.39  % (16461)Termination reason: Refutation
% 0.21/0.39  
% 0.21/0.39  % (16461)Memory used [KB]: 768
% 0.21/0.39  % (16461)Time elapsed: 0.007 s
% 0.21/0.39  % (16461)Instructions burned: 8 (million)
% 0.21/0.39  % (16461)------------------------------
% 0.21/0.39  % (16461)------------------------------
% 0.21/0.39  % (16456)Success in time 0.021 s
%------------------------------------------------------------------------------