TSTP Solution File: SWW101+1 by Vampire---4.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : SWW101+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d THM

% Computer : n007.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 : Mon Jun 24 18:31:25 EDT 2024

% Result   : Theorem 0.22s 0.45s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   83 (  46 unt;   0 def)
%            Number of atoms       :  163 (  88 equ)
%            Maximal formula atoms :    9 (   1 avg)
%            Number of connectives :  141 (  61   ~;  46   |;  28   &)
%                                         (   4 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :   56 (  50   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f424,plain,
    $false,
    inference(subsumption_resolution,[],[f423,f243]) ).

fof(f243,plain,
    forallprefers(false1,true),
    inference(equality_resolution,[],[f242]) ).

fof(f242,plain,
    ! [X0] :
      ( forallprefers(X0,true)
      | false1 != X0 ),
    inference(equality_resolution,[],[f231]) ).

fof(f231,plain,
    ! [X0,X1] :
      ( forallprefers(X0,X1)
      | true != X1
      | false1 != X0 ),
    inference(definition_unfolding,[],[f180,f129]) ).

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

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

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/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f423,plain,
    ~ forallprefers(false1,true),
    inference(forward_demodulation,[],[f406,f265]) ).

fof(f265,plain,
    true = lazy_and1(true,true),
    inference(resolution,[],[f212,f132]) ).

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

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

fof(f212,plain,
    ! [X0] :
      ( ~ d(X0)
      | lazy_and1(true,X0) = X0 ),
    inference(definition_unfolding,[],[f145,f141]) ).

fof(f141,plain,
    ! [X0] : phi(X0) = lazy_and1(true,X0),
    inference(cnf_transformation,[],[f51]) ).

fof(f51,plain,
    ! [X0] : phi(X0) = lazy_and1(true,X0),
    inference(rectify,[],[f24]) ).

fof(f24,axiom,
    ! [X3] : phi(X3) = lazy_and1(true,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

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/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f406,plain,
    ~ forallprefers(false1,lazy_and1(true,true)),
    inference(backward_demodulation,[],[f367,f399]) ).

fof(f399,plain,
    true = sK6,
    inference(subsumption_resolution,[],[f398,f267]) ).

fof(f267,plain,
    false1 = lazy_and1(true,false1),
    inference(resolution,[],[f212,f204]) ).

fof(f204,plain,
    d(false1),
    inference(definition_unfolding,[],[f133,f129]) ).

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

fof(f398,plain,
    ( false1 != lazy_and1(true,false1)
    | true = sK6 ),
    inference(forward_demodulation,[],[f397,f267]) ).

fof(f397,plain,
    ( false1 != lazy_and1(true,lazy_and1(true,false1))
    | true = sK6 ),
    inference(superposition,[],[f364,f378]) ).

fof(f378,plain,
    ( false1 = sK6
    | true = sK6 ),
    inference(resolution,[],[f370,f218]) ).

fof(f218,plain,
    ! [X0] :
      ( ~ bool(X0)
      | false1 = X0
      | true = X0 ),
    inference(definition_unfolding,[],[f155,f129]) ).

fof(f155,plain,
    ! [X0] :
      ( true = X0
      | false = X0
      | ~ bool(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/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f370,plain,
    bool(sK6),
    inference(trivial_inequality_removal,[],[f369]) ).

fof(f369,plain,
    ( true != true
    | bool(sK6) ),
    inference(superposition,[],[f160,f355]) ).

fof(f355,plain,
    true = prop(sK6),
    inference(subsumption_resolution,[],[f354,f243]) ).

fof(f354,plain,
    ( ~ forallprefers(false1,true)
    | true = prop(sK6) ),
    inference(forward_demodulation,[],[f353,f208]) ).

fof(f208,plain,
    ! [X0] : true = lazy_impl(false1,X0),
    inference(definition_unfolding,[],[f139,f129]) ).

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/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f353,plain,
    ( ~ forallprefers(false1,lazy_impl(false1,sK6))
    | true = prop(sK6) ),
    inference(superposition,[],[f346,f252]) ).

fof(f252,plain,
    ! [X0] :
      ( prop(X0) = false1
      | true = prop(X0) ),
    inference(resolution,[],[f219,f161]) ).

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/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f219,plain,
    ! [X0] :
      ( bool(X0)
      | prop(X0) = false1 ),
    inference(definition_unfolding,[],[f159,f129]) ).

fof(f159,plain,
    ! [X0] :
      ( false = prop(X0)
      | bool(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/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f346,plain,
    ~ forallprefers(false1,lazy_impl(prop(sK6),sK6)),
    inference(forward_demodulation,[],[f345,f267]) ).

fof(f345,plain,
    ~ forallprefers(lazy_and1(true,false1),lazy_impl(prop(sK6),sK6)),
    inference(forward_demodulation,[],[f339,f209]) ).

fof(f209,plain,
    ! [X0] : lazy_and1(true,X0) = lazy_impl(true,X0),
    inference(definition_unfolding,[],[f142,f141]) ).

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/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f339,plain,
    ~ forallprefers(lazy_impl(true,false1),lazy_impl(prop(sK6),sK6)),
    inference(superposition,[],[f236,f249]) ).

fof(f249,plain,
    true = prop(false1),
    inference(resolution,[],[f161,f239]) ).

fof(f239,plain,
    bool(false1),
    inference(equality_resolution,[],[f217]) ).

fof(f217,plain,
    ! [X0] :
      ( bool(X0)
      | false1 != X0 ),
    inference(definition_unfolding,[],[f156,f129]) ).

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

fof(f236,plain,
    ! [X1] : ~ forallprefers(lazy_impl(prop(X1),X1),lazy_impl(prop(sK6),sK6)),
    inference(definition_unfolding,[],[f194,f143,f143]) ).

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/sandbox/benchmark/theBenchmark.p',unknown) ).

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/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f160,plain,
    ! [X0] :
      ( true != prop(X0)
      | bool(X0) ),
    inference(cnf_transformation,[],[f113]) ).

fof(f364,plain,
    false1 != lazy_and1(true,lazy_and1(true,sK6)),
    inference(forward_demodulation,[],[f358,f209]) ).

fof(f358,plain,
    false1 != lazy_and1(true,lazy_impl(true,sK6)),
    inference(backward_demodulation,[],[f289,f355]) ).

fof(f289,plain,
    false1 != lazy_and1(true,lazy_impl(prop(sK6),sK6)),
    inference(superposition,[],[f128,f237]) ).

fof(f237,plain,
    false2 = lazy_and1(true,lazy_impl(prop(sK6),sK6)),
    inference(definition_unfolding,[],[f193,f141,f143]) ).

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

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/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f367,plain,
    ~ forallprefers(false1,lazy_and1(true,sK6)),
    inference(forward_demodulation,[],[f361,f209]) ).

fof(f361,plain,
    ~ forallprefers(false1,lazy_impl(true,sK6)),
    inference(backward_demodulation,[],[f346,f355]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : SWW101+1 : TPTP v8.2.0. Released v5.2.0.
% 0.11/0.13  % Command    : run_vampire %s %d THM
% 0.13/0.34  % Computer : n007.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Wed Jun 19 06:19:09 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.13/0.36  Running first-order theorem proving
% 0.13/0.36  Running /export/starexec/sandbox/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.43  % (15330)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43  % (15334)lrs+1011_1:1_sil=2000:i=103:ep=RS:nm=32:ss=axioms:sos=on_0 on theBenchmark for (2999ds/103Mi)
% 0.22/0.43  % (15330)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43  % (15333)lrs+11_1:16_to=lpo:drc=off:bsd=on:sp=frequency:i=172350:bs=on:av=off:fsd=on:sil=256000:fdi=50_0 on theBenchmark for (2999ds/172350Mi)
% 0.22/0.43  % (15330)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43  % (15335)lrs+1011_1:1_sil=32000:rnwc=on:nwc=10.0:lwlo=on:i=121:bd=off:av=off_0 on theBenchmark for (2999ds/121Mi)
% 0.22/0.43  % (15330)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43  % (15336)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=113:sd=1:ep=RS:ss=axioms_0 on theBenchmark for (2999ds/113Mi)
% 0.22/0.43  % (15330)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43  % (15337)lrs+1010_1:1_to=lpo:sil=2000:plsq=on:plsqr=32,1:sp=reverse_arity:sos=on:spb=goal_then_units:i=128:ss=axioms:sgt=50:bd=off:sd=3_0 on theBenchmark for (2999ds/128Mi)
% 0.22/0.43  % (15330)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43  % (15331)lrs+2_5:39_bsr=unit_only:to=lpo:drc=off:sil=128000:plsq=on:plsqr=2,19:sp=frequency:lcm=reverse:fd=preordered:s2a=on:i=38749:s2at=-1.0:fsr=off:uhcvi=on:rawr=on:aer=off:lwlo=on:add=off:bce=on:acc=model:afr=on_0 on theBenchmark for (2999ds/38749Mi)
% 0.22/0.43  % (15330)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43  % (15332)lrs+1002_74:59_drc=off:tgt=full:sos=all:cond=fast:i=124987:kws=inv_frequency:afp=300:afq=2.0744697298148953:rawr=on:urr=full:sil=128000:si=on:rtra=on:random_seed=3250543_0 on theBenchmark for (2999ds/124987Mi)
% 0.22/0.43  % (15334)Refutation not found, incomplete strategy% (15334)------------------------------
% 0.22/0.43  % (15334)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.43  % (15334)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.43  % (15334)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.43  
% 0.22/0.43  % (15334)Memory used [KB]: 1150
% 0.22/0.43  % (15334)Time elapsed: 0.003 s
% 0.22/0.43  % (15334)Instructions burned: 1 (million)
% 0.22/0.43  % (15336)Refutation not found, incomplete strategy% (15336)------------------------------
% 0.22/0.43  % (15336)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.43  % (15336)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.43  % (15336)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.43  
% 0.22/0.43  % (15336)Memory used [KB]: 1154
% 0.22/0.43  % (15336)Time elapsed: 0.003 s
% 0.22/0.43  % (15336)Instructions burned: 2 (million)
% 0.22/0.43  % (15334)------------------------------
% 0.22/0.43  % (15334)------------------------------
% 0.22/0.43  % (15336)------------------------------
% 0.22/0.43  % (15336)------------------------------
% 0.22/0.43  % (15332)Refutation not found, incomplete strategy% (15332)------------------------------
% 0.22/0.43  % (15332)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.43  % (15332)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.43  % (15332)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.43  
% 0.22/0.43  % (15332)Memory used [KB]: 1252
% 0.22/0.43  % (15332)Time elapsed: 0.006 s
% 0.22/0.43  % (15332)Instructions burned: 7 (million)
% 0.22/0.43  % (15332)------------------------------
% 0.22/0.43  % (15332)------------------------------
% 0.22/0.45  % (15333)First to succeed.
% 0.22/0.45  % (15333)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-15330"
% 0.22/0.45  % (15330)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.45  % (15333)Refutation found. Thanks to Tanya!
% 0.22/0.45  % SZS status Theorem for theBenchmark
% 0.22/0.45  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.45  % (15333)------------------------------
% 0.22/0.45  % (15333)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.45  % (15333)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.45  % (15333)Termination reason: Refutation
% 0.22/0.45  
% 0.22/0.45  % (15333)Memory used [KB]: 1406
% 0.22/0.45  % (15333)Time elapsed: 0.021 s
% 0.22/0.45  % (15333)Instructions burned: 32 (million)
% 0.22/0.45  % (15333)------------------------------
% 0.22/0.45  % (15333)------------------------------
% 0.22/0.45  % (15330)Success in time 0.08 s
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