TSTP Solution File: SEU327+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU327+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n027.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 : Sun May  5 09:33:43 EDT 2024

% Result   : Theorem 0.20s 0.44s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   48 (  16 unt;   0 def)
%            Number of atoms       :   98 (  56 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   90 (  40   ~;  28   |;  11   &)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   3 con; 0-3 aty)
%            Number of variables   :   57 (  51   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1777,plain,
    $false,
    inference(trivial_inequality_removal,[],[f1776]) ).

fof(f1776,plain,
    empty_set != empty_set,
    inference(superposition,[],[f144,f1301]) ).

fof(f1301,plain,
    empty_set = sK4,
    inference(trivial_inequality_removal,[],[f1299]) ).

fof(f1299,plain,
    ( set_difference(sK3,union(sK4)) != set_difference(sK3,union(sK4))
    | empty_set = sK4 ),
    inference(superposition,[],[f559,f1297]) ).

fof(f1297,plain,
    ( meet_of_subsets(sK3,complements_of_subsets(sK3,sK4)) = set_difference(sK3,union(sK4))
    | empty_set = sK4 ),
    inference(backward_demodulation,[],[f667,f1293]) ).

fof(f1293,plain,
    set_difference(sK3,union(sK4)) = subset_difference(sK3,sK3,union(sK4)),
    inference(resolution,[],[f1279,f143]) ).

fof(f143,plain,
    element(sK4,powerset(powerset(sK3))),
    inference(cnf_transformation,[],[f129]) ).

fof(f129,plain,
    ( meet_of_subsets(sK3,complements_of_subsets(sK3,sK4)) != subset_complement(sK3,union_of_subsets(sK3,sK4))
    & empty_set != sK4
    & element(sK4,powerset(powerset(sK3))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f79,f128]) ).

fof(f128,plain,
    ( ? [X0,X1] :
        ( meet_of_subsets(X0,complements_of_subsets(X0,X1)) != subset_complement(X0,union_of_subsets(X0,X1))
        & empty_set != X1
        & element(X1,powerset(powerset(X0))) )
   => ( meet_of_subsets(sK3,complements_of_subsets(sK3,sK4)) != subset_complement(sK3,union_of_subsets(sK3,sK4))
      & empty_set != sK4
      & element(sK4,powerset(powerset(sK3))) ) ),
    introduced(choice_axiom,[]) ).

fof(f79,plain,
    ? [X0,X1] :
      ( meet_of_subsets(X0,complements_of_subsets(X0,X1)) != subset_complement(X0,union_of_subsets(X0,X1))
      & empty_set != X1
      & element(X1,powerset(powerset(X0))) ),
    inference(flattening,[],[f78]) ).

fof(f78,plain,
    ? [X0,X1] :
      ( meet_of_subsets(X0,complements_of_subsets(X0,X1)) != subset_complement(X0,union_of_subsets(X0,X1))
      & empty_set != X1
      & element(X1,powerset(powerset(X0))) ),
    inference(ennf_transformation,[],[f49]) ).

fof(f49,negated_conjecture,
    ~ ! [X0,X1] :
        ( element(X1,powerset(powerset(X0)))
       => ( empty_set != X1
         => meet_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_complement(X0,union_of_subsets(X0,X1)) ) ),
    inference(negated_conjecture,[],[f48]) ).

fof(f48,conjecture,
    ! [X0,X1] :
      ( element(X1,powerset(powerset(X0)))
     => ( empty_set != X1
       => meet_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_complement(X0,union_of_subsets(X0,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_tops_2) ).

fof(f1279,plain,
    ( ~ element(sK4,powerset(powerset(sK3)))
    | set_difference(sK3,union(sK4)) = subset_difference(sK3,sK3,union(sK4)) ),
    inference(resolution,[],[f592,f501]) ).

fof(f501,plain,
    ( element(union(sK4),powerset(sK3))
    | ~ element(sK4,powerset(powerset(sK3))) ),
    inference(superposition,[],[f214,f430]) ).

fof(f430,plain,
    union_of_subsets(sK3,sK4) = union(sK4),
    inference(resolution,[],[f212,f143]) ).

fof(f212,plain,
    ! [X0,X1] :
      ( ~ element(X1,powerset(powerset(X0)))
      | union_of_subsets(X0,X1) = union(X1) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f104,plain,
    ! [X0,X1] :
      ( union_of_subsets(X0,X1) = union(X1)
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(ennf_transformation,[],[f44]) ).

fof(f44,axiom,
    ! [X0,X1] :
      ( element(X1,powerset(powerset(X0)))
     => union_of_subsets(X0,X1) = union(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).

fof(f214,plain,
    ! [X0,X1] :
      ( element(union_of_subsets(X0,X1),powerset(X0))
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(cnf_transformation,[],[f106]) ).

fof(f106,plain,
    ! [X0,X1] :
      ( element(union_of_subsets(X0,X1),powerset(X0))
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f26,axiom,
    ! [X0,X1] :
      ( element(X1,powerset(powerset(X0)))
     => element(union_of_subsets(X0,X1),powerset(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_setfam_1) ).

fof(f592,plain,
    ! [X0,X1] :
      ( ~ element(X1,powerset(X0))
      | set_difference(X0,X1) = subset_difference(X0,X0,X1) ),
    inference(resolution,[],[f224,f232]) ).

fof(f232,plain,
    ! [X0] : element(X0,powerset(X0)),
    inference(forward_demodulation,[],[f156,f153]) ).

fof(f153,plain,
    ! [X0] : cast_to_subset(X0) = X0,
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ! [X0] : cast_to_subset(X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).

fof(f156,plain,
    ! [X0] : element(cast_to_subset(X0),powerset(X0)),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,axiom,
    ! [X0] : element(cast_to_subset(X0),powerset(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).

fof(f224,plain,
    ! [X2,X0,X1] :
      ( ~ element(X2,powerset(X0))
      | ~ element(X1,powerset(X0))
      | subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f120,plain,
    ! [X0,X1,X2] :
      ( subset_difference(X0,X1,X2) = set_difference(X1,X2)
      | ~ element(X2,powerset(X0))
      | ~ element(X1,powerset(X0)) ),
    inference(flattening,[],[f119]) ).

fof(f119,plain,
    ! [X0,X1,X2] :
      ( subset_difference(X0,X1,X2) = set_difference(X1,X2)
      | ~ element(X2,powerset(X0))
      | ~ element(X1,powerset(X0)) ),
    inference(ennf_transformation,[],[f46]) ).

fof(f46,axiom,
    ! [X0,X1,X2] :
      ( ( element(X2,powerset(X0))
        & element(X1,powerset(X0)) )
     => subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).

fof(f667,plain,
    ( meet_of_subsets(sK3,complements_of_subsets(sK3,sK4)) = subset_difference(sK3,sK3,union(sK4))
    | empty_set = sK4 ),
    inference(forward_demodulation,[],[f663,f430]) ).

fof(f663,plain,
    ( empty_set = sK4
    | meet_of_subsets(sK3,complements_of_subsets(sK3,sK4)) = subset_difference(sK3,sK3,union_of_subsets(sK3,sK4)) ),
    inference(resolution,[],[f233,f143]) ).

fof(f233,plain,
    ! [X0,X1] :
      ( ~ element(X1,powerset(powerset(X0)))
      | empty_set = X1
      | meet_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,X0,union_of_subsets(X0,X1)) ),
    inference(forward_demodulation,[],[f218,f153]) ).

fof(f218,plain,
    ! [X0,X1] :
      ( meet_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1))
      | empty_set = X1
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f111,plain,
    ! [X0,X1] :
      ( meet_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1))
      | empty_set = X1
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(flattening,[],[f110]) ).

fof(f110,plain,
    ! [X0,X1] :
      ( meet_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1))
      | empty_set = X1
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(ennf_transformation,[],[f54]) ).

fof(f54,axiom,
    ! [X0,X1] :
      ( element(X1,powerset(powerset(X0)))
     => ( empty_set != X1
       => meet_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_setfam_1) ).

fof(f559,plain,
    meet_of_subsets(sK3,complements_of_subsets(sK3,sK4)) != set_difference(sK3,union(sK4)),
    inference(backward_demodulation,[],[f433,f555]) ).

fof(f555,plain,
    subset_complement(sK3,union(sK4)) = set_difference(sK3,union(sK4)),
    inference(resolution,[],[f526,f143]) ).

fof(f526,plain,
    ( ~ element(sK4,powerset(powerset(sK3)))
    | subset_complement(sK3,union(sK4)) = set_difference(sK3,union(sK4)) ),
    inference(resolution,[],[f501,f210]) ).

fof(f210,plain,
    ! [X0,X1] :
      ( ~ element(X1,powerset(X0))
      | subset_complement(X0,X1) = set_difference(X0,X1) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f102,plain,
    ! [X0,X1] :
      ( subset_complement(X0,X1) = set_difference(X0,X1)
      | ~ element(X1,powerset(X0)) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,axiom,
    ! [X0,X1] :
      ( element(X1,powerset(X0))
     => subset_complement(X0,X1) = set_difference(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).

fof(f433,plain,
    meet_of_subsets(sK3,complements_of_subsets(sK3,sK4)) != subset_complement(sK3,union(sK4)),
    inference(backward_demodulation,[],[f145,f430]) ).

fof(f145,plain,
    meet_of_subsets(sK3,complements_of_subsets(sK3,sK4)) != subset_complement(sK3,union_of_subsets(sK3,sK4)),
    inference(cnf_transformation,[],[f129]) ).

fof(f144,plain,
    empty_set != sK4,
    inference(cnf_transformation,[],[f129]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SEU327+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n027.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   : Fri May  3 11:41:36 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (32047)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (32050)WARNING: value z3 for option sas not known
% 0.14/0.37  % (32053)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)
% 0.14/0.38  % (32051)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38  % (32050)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)
% 0.14/0.38  % (32048)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38  % (32052)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)
% 0.14/0.38  % (32049)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38  % (32054)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)
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [3]
% 0.14/0.39  TRYING [1]
% 0.14/0.39  TRYING [2]
% 0.14/0.39  TRYING [4]
% 0.14/0.41  TRYING [3]
% 0.20/0.42  TRYING [5]
% 0.20/0.44  % (32053)First to succeed.
% 0.20/0.44  % (32053)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-32047"
% 0.20/0.44  % (32053)Refutation found. Thanks to Tanya!
% 0.20/0.44  % SZS status Theorem for theBenchmark
% 0.20/0.44  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.44  % (32053)------------------------------
% 0.20/0.44  % (32053)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.44  % (32053)Termination reason: Refutation
% 0.20/0.44  
% 0.20/0.44  % (32053)Memory used [KB]: 1656
% 0.20/0.44  % (32053)Time elapsed: 0.069 s
% 0.20/0.44  % (32053)Instructions burned: 137 (million)
% 0.20/0.44  % (32047)Success in time 0.085 s
%------------------------------------------------------------------------------