TSTP Solution File: SET162+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET162+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n010.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 15:06:51 EDT 2024

% Result   : Theorem 0.22s 0.39s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   36 (  12 unt;   0 def)
%            Number of atoms       :   97 (  16 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  101 (  40   ~;  37   |;  17   &)
%                                         (   4 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   70 (  65   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f360,plain,
    $false,
    inference(trivial_inequality_removal,[],[f359]) ).

fof(f359,plain,
    sK0 != sK0,
    inference(superposition,[],[f27,f282]) ).

fof(f282,plain,
    ! [X0] : union(X0,empty_set) = X0,
    inference(resolution,[],[f259,f77]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( ~ subset(union(X0,X1),X0)
      | union(X0,X1) = X0 ),
    inference(resolution,[],[f75,f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | X0 = X1
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(flattening,[],[f15]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ( subset(X1,X0)
        & subset(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).

fof(f75,plain,
    ! [X0,X1] : subset(X0,union(X0,X1)),
    inference(duplicate_literal_removal,[],[f70]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( subset(X0,union(X0,X1))
      | subset(X0,union(X0,X1)) ),
    inference(resolution,[],[f53,f39]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( member(sK2(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK2(X0,X1),X1)
          & member(sK2(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f22,f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK2(X0,X1),X1)
        & member(sK2(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).

fof(f53,plain,
    ! [X2,X0,X1] :
      ( ~ member(sK2(X0,union(X1,X2)),X1)
      | subset(X0,union(X1,X2)) ),
    inference(resolution,[],[f42,f40]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( ~ member(sK2(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f42,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X0,X1))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) )
      & ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X0,X1)) ) ),
    inference(flattening,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X0,X1))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) )
      & ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X0,X1)) ) ),
    inference(nnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1,X2] :
      ( member(X2,union(X0,X1))
    <=> ( member(X2,X1)
        | member(X2,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).

fof(f259,plain,
    ! [X0] : subset(union(X0,empty_set),X0),
    inference(duplicate_literal_removal,[],[f246]) ).

fof(f246,plain,
    ! [X0] :
      ( subset(union(X0,empty_set),X0)
      | subset(union(X0,empty_set),X0) ),
    inference(resolution,[],[f141,f40]) ).

fof(f141,plain,
    ! [X0,X1] :
      ( member(sK2(union(X0,empty_set),X1),X0)
      | subset(union(X0,empty_set),X1) ),
    inference(resolution,[],[f65,f28]) ).

fof(f28,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] : ~ member(X0,empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).

fof(f65,plain,
    ! [X2,X0,X1] :
      ( member(sK2(union(X0,X1),X2),X1)
      | member(sK2(union(X0,X1),X2),X0)
      | subset(union(X0,X1),X2) ),
    inference(resolution,[],[f41,f39]) ).

fof(f41,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,union(X0,X1))
      | member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f27,plain,
    sK0 != union(sK0,empty_set),
    inference(cnf_transformation,[],[f14]) ).

fof(f14,plain,
    sK0 != union(sK0,empty_set),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f11,f13]) ).

fof(f13,plain,
    ( ? [X0] : union(X0,empty_set) != X0
   => sK0 != union(sK0,empty_set) ),
    introduced(choice_axiom,[]) ).

fof(f11,plain,
    ? [X0] : union(X0,empty_set) != X0,
    inference(ennf_transformation,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X0] : union(X0,empty_set) = X0,
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X0] : union(X0,empty_set) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_union_empty_set) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SET162+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n010.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 01:24:05 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (27834)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38  % (27837)WARNING: value z3 for option sas not known
% 0.15/0.38  % (27838)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38  % (27836)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38  % (27835)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38  % (27839)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)
% 0.15/0.38  % (27840)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)
% 0.15/0.38  % (27837)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)
% 0.15/0.38  % (27841)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  TRYING [1]
% 0.15/0.38  TRYING [2]
% 0.15/0.38  TRYING [3]
% 0.22/0.38  TRYING [1]
% 0.22/0.38  TRYING [2]
% 0.22/0.38  TRYING [4]
% 0.22/0.39  TRYING [5]
% 0.22/0.39  TRYING [3]
% 0.22/0.39  TRYING [1]
% 0.22/0.39  TRYING [2]
% 0.22/0.39  TRYING [3]
% 0.22/0.39  % (27837)First to succeed.
% 0.22/0.39  TRYING [4]
% 0.22/0.39  % (27837)Refutation found. Thanks to Tanya!
% 0.22/0.39  % SZS status Theorem for theBenchmark
% 0.22/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.39  % (27837)------------------------------
% 0.22/0.39  % (27837)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.39  % (27837)Termination reason: Refutation
% 0.22/0.39  
% 0.22/0.39  % (27837)Memory used [KB]: 912
% 0.22/0.39  % (27837)Time elapsed: 0.014 s
% 0.22/0.39  % (27837)Instructions burned: 17 (million)
% 0.22/0.39  % (27837)------------------------------
% 0.22/0.39  % (27837)------------------------------
% 0.22/0.39  % (27834)Success in time 0.03 s
%------------------------------------------------------------------------------