TSTP Solution File: SWW101+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWW101+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n017.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 17:28:27 EDT 2024

% Result   : Theorem 0.15s 0.40s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   72 (  40 unt;   0 def)
%            Number of atoms       :  149 (  87 equ)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :  123 (  46   ~;  43   |;  28   &)
%                                         (   4 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :   46 (  40   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f846,plain,
    $false,
    inference(trivial_inequality_removal,[],[f845]) ).

fof(f845,plain,
    false != false,
    inference(superposition,[],[f201,f714]) ).

fof(f714,plain,
    false = false2,
    inference(forward_demodulation,[],[f713,f203]) ).

fof(f203,plain,
    false = phi(false),
    inference(resolution,[],[f145,f133]) ).

fof(f133,plain,
    d(false),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ( d(err)
    & d(false)
    & d(true) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',false_true_err_in_d) ).

fof(f145,plain,
    ! [X0] :
      ( ~ d(X0)
      | phi(X0) = X0 ),
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] :
      ( ( err = phi(X0)
        & ~ d(X0) )
      | ( phi(X0) = X0
        & d(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_phi) ).

fof(f713,plain,
    false2 = phi(false),
    inference(forward_demodulation,[],[f674,f220]) ).

fof(f220,plain,
    false = f7(false),
    inference(forward_demodulation,[],[f219,f203]) ).

fof(f219,plain,
    phi(false) = f7(false),
    inference(forward_demodulation,[],[f216,f142]) ).

fof(f142,plain,
    ! [X0] : phi(X0) = lazy_impl(true,X0),
    inference(cnf_transformation,[],[f52]) ).

fof(f52,plain,
    ! [X0] : phi(X0) = lazy_impl(true,X0),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X3] : phi(X3) = lazy_impl(true,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lazy_impl_axiom3) ).

fof(f216,plain,
    f7(false) = lazy_impl(true,false),
    inference(superposition,[],[f143,f207]) ).

fof(f207,plain,
    true = prop(false),
    inference(resolution,[],[f161,f196]) ).

fof(f196,plain,
    bool(false),
    inference(equality_resolution,[],[f156]) ).

fof(f156,plain,
    ! [X0] :
      ( bool(X0)
      | false != X0 ),
    inference(cnf_transformation,[],[f111]) ).

fof(f111,plain,
    ! [X0] :
      ( ( bool(X0)
        | ( true != X0
          & false != X0 ) )
      & ( true = X0
        | false = X0
        | ~ bool(X0) ) ),
    inference(flattening,[],[f110]) ).

fof(f110,plain,
    ! [X0] :
      ( ( bool(X0)
        | ( true != X0
          & false != X0 ) )
      & ( true = X0
        | false = X0
        | ~ bool(X0) ) ),
    inference(nnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] :
      ( bool(X0)
    <=> ( true = X0
        | false = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_bool) ).

fof(f161,plain,
    ! [X0] :
      ( ~ bool(X0)
      | true = prop(X0) ),
    inference(cnf_transformation,[],[f113]) ).

fof(f113,plain,
    ! [X0] :
      ( ( true = prop(X0)
        | ~ bool(X0) )
      & ( bool(X0)
        | true != prop(X0) ) ),
    inference(nnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] :
      ( true = prop(X0)
    <=> bool(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop_true) ).

fof(f143,plain,
    ! [X0] : f7(X0) = lazy_impl(prop(X0),X0),
    inference(cnf_transformation,[],[f53]) ).

fof(f53,plain,
    ! [X0] : f7(X0) = lazy_impl(prop(X0),X0),
    inference(rectify,[],[f39]) ).

fof(f39,axiom,
    ! [X4] : f7(X4) = lazy_impl(prop(X4),X4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_f7) ).

fof(f674,plain,
    false2 = phi(f7(false)),
    inference(backward_demodulation,[],[f193,f671]) ).

fof(f671,plain,
    false = sK6,
    inference(resolution,[],[f650,f200]) ).

fof(f200,plain,
    forallprefers(false,true),
    inference(equality_resolution,[],[f199]) ).

fof(f199,plain,
    ! [X0] :
      ( forallprefers(X0,true)
      | false != X0 ),
    inference(equality_resolution,[],[f180]) ).

fof(f180,plain,
    ! [X0,X1] :
      ( forallprefers(X0,X1)
      | true != X1
      | false != X0 ),
    inference(cnf_transformation,[],[f104]) ).

fof(f104,plain,
    ! [X0,X1] :
      ( forallprefers(X0,X1)
      | ( ( true != X1
          | false != X0 )
        & ( ~ bool(X1)
          | bool(X0)
          | ~ d(X1)
          | ~ d(X0) )
        & ( ~ d(X1)
          | d(X0) ) ) ),
    inference(ennf_transformation,[],[f82]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( ( ( true = X1
          & false = X0 )
        | ( bool(X1)
          & ~ bool(X0)
          & d(X1)
          & d(X0) )
        | ( d(X1)
          & ~ d(X0) ) )
     => forallprefers(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( forallprefers(X0,X1)
    <=> ( ( true = X1
          & false = X0 )
        | ( bool(X1)
          & ~ bool(X0)
          & d(X1)
          & d(X0) )
        | ( d(X1)
          & ~ d(X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_forallprefers) ).

fof(f650,plain,
    ( ~ forallprefers(false,true)
    | false = sK6 ),
    inference(forward_demodulation,[],[f633,f218]) ).

fof(f218,plain,
    true = f7(true),
    inference(forward_demodulation,[],[f217,f202]) ).

fof(f202,plain,
    true = phi(true),
    inference(resolution,[],[f145,f132]) ).

fof(f132,plain,
    d(true),
    inference(cnf_transformation,[],[f3]) ).

fof(f217,plain,
    phi(true) = f7(true),
    inference(forward_demodulation,[],[f215,f142]) ).

fof(f215,plain,
    f7(true) = lazy_impl(true,true),
    inference(superposition,[],[f143,f206]) ).

fof(f206,plain,
    true = prop(true),
    inference(resolution,[],[f161,f195]) ).

fof(f195,plain,
    bool(true),
    inference(equality_resolution,[],[f157]) ).

fof(f157,plain,
    ! [X0] :
      ( bool(X0)
      | true != X0 ),
    inference(cnf_transformation,[],[f111]) ).

fof(f633,plain,
    ( ~ forallprefers(false,f7(true))
    | false = sK6 ),
    inference(superposition,[],[f222,f626]) ).

fof(f626,plain,
    ( true = sK6
    | false = sK6 ),
    inference(resolution,[],[f533,f200]) ).

fof(f533,plain,
    ( ~ forallprefers(false,true)
    | true = sK6
    | false = sK6 ),
    inference(superposition,[],[f222,f444]) ).

fof(f444,plain,
    ! [X0] :
      ( true = f7(X0)
      | true = X0
      | false = X0 ),
    inference(forward_demodulation,[],[f438,f139]) ).

fof(f139,plain,
    ! [X0] : true = lazy_impl(false,X0),
    inference(cnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0] : true = lazy_impl(false,X0),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ! [X3] : true = lazy_impl(false,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lazy_impl_axiom2) ).

fof(f438,plain,
    ! [X0] :
      ( lazy_impl(false,X0) = f7(X0)
      | true = X0
      | false = X0 ),
    inference(superposition,[],[f143,f279]) ).

fof(f279,plain,
    ! [X0] :
      ( false = prop(X0)
      | true = X0
      | false = X0 ),
    inference(resolution,[],[f155,f159]) ).

fof(f159,plain,
    ! [X0] :
      ( bool(X0)
      | false = prop(X0) ),
    inference(cnf_transformation,[],[f112]) ).

fof(f112,plain,
    ! [X0] :
      ( ( false = prop(X0)
        | bool(X0) )
      & ( ~ bool(X0)
        | false != prop(X0) ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0] :
      ( false = prop(X0)
    <=> ~ bool(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop_false) ).

fof(f155,plain,
    ! [X0] :
      ( ~ bool(X0)
      | false = X0
      | true = X0 ),
    inference(cnf_transformation,[],[f111]) ).

fof(f222,plain,
    ~ forallprefers(false,f7(sK6)),
    inference(superposition,[],[f194,f220]) ).

fof(f194,plain,
    ! [X1] : ~ forallprefers(f7(X1),f7(sK6)),
    inference(cnf_transformation,[],[f127]) ).

fof(f127,plain,
    ( ! [X1] : ~ forallprefers(f7(X1),f7(sK6))
    & false2 = phi(f7(sK6)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f109,f126]) ).

fof(f126,plain,
    ( ? [X0] :
        ( ! [X1] : ~ forallprefers(f7(X1),f7(X0))
        & false2 = phi(f7(X0)) )
   => ( ! [X1] : ~ forallprefers(f7(X1),f7(sK6))
      & false2 = phi(f7(sK6)) ) ),
    introduced(choice_axiom,[]) ).

fof(f109,plain,
    ? [X0] :
      ( ! [X1] : ~ forallprefers(f7(X1),f7(X0))
      & false2 = phi(f7(X0)) ),
    inference(ennf_transformation,[],[f80]) ).

fof(f80,plain,
    ? [X0] :
      ( ~ ? [X1] : forallprefers(f7(X1),f7(X0))
      & false2 = phi(f7(X0)) ),
    inference(rectify,[],[f40]) ).

fof(f40,axiom,
    ? [X4] :
      ( ~ ? [X9] : forallprefers(f7(X9),f7(X4))
      & false2 = phi(f7(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_false2) ).

fof(f193,plain,
    false2 = phi(f7(sK6)),
    inference(cnf_transformation,[],[f127]) ).

fof(f201,plain,
    false != false2,
    inference(forward_demodulation,[],[f128,f129]) ).

fof(f129,plain,
    false = false1,
    inference(cnf_transformation,[],[f38]) ).

fof(f38,axiom,
    false = false1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_false1) ).

fof(f128,plain,
    false1 != false2,
    inference(cnf_transformation,[],[f47]) ).

fof(f47,plain,
    false1 != false2,
    inference(flattening,[],[f46]) ).

fof(f46,negated_conjecture,
    false1 != false2,
    inference(negated_conjecture,[],[f45]) ).

fof(f45,conjecture,
    false1 = false2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',false1_false2) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : SWW101+1 : TPTP v8.1.2. Released v5.2.0.
% 0.13/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n017.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Tue Apr 30 02:37:48 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.36  % (25134)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37  % (25137)WARNING: value z3 for option sas not known
% 0.15/0.37  % (25136)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.37  % (25138)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.37  % (25135)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.37  % (25140)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)
% 0.15/0.37  % (25139)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)
% 0.15/0.37  % (25137)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)
% 0.15/0.37  % (25141)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)
% 0.15/0.38  Detected minimum model sizes of [3]
% 0.15/0.38  Detected maximum model sizes of [max]
% 0.15/0.38  TRYING [3]
% 0.15/0.39  Detected minimum model sizes of [3]
% 0.15/0.39  Detected maximum model sizes of [max]
% 0.15/0.39  TRYING [3]
% 0.15/0.40  % (25140)First to succeed.
% 0.15/0.40  % (25140)Refutation found. Thanks to Tanya!
% 0.15/0.40  % SZS status Theorem for theBenchmark
% 0.15/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.40  % (25140)------------------------------
% 0.15/0.40  % (25140)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.40  % (25140)Termination reason: Refutation
% 0.15/0.40  
% 0.15/0.40  % (25140)Memory used [KB]: 1117
% 0.15/0.40  % (25140)Time elapsed: 0.024 s
% 0.15/0.40  % (25140)Instructions burned: 40 (million)
% 0.15/0.40  % (25140)------------------------------
% 0.15/0.40  % (25140)------------------------------
% 0.15/0.40  % (25134)Success in time 0.031 s
%------------------------------------------------------------------------------