TSTP Solution File: SEU142+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU142+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 : 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 : Sun May  5 09:27:21 EDT 2024

% Result   : Theorem 0.21s 0.40s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   46 (  16 unt;   0 def)
%            Number of atoms       :  164 (  60 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  191 (  73   ~;  74   |;  30   &)
%                                         (  11 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-3 aty)
%            Number of variables   :  109 ( 101   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f751,plain,
    $false,
    inference(unit_resulting_resolution,[],[f73,f325,f297,f43]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | sK5(X0,X1) = X0
      | in(sK5(X0,X1),X1) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ( ( sK5(X0,X1) != X0
            | ~ in(sK5(X0,X1),X1) )
          & ( sK5(X0,X1) = X0
            | in(sK5(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | ~ sP0(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f24,f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( X0 != X2
            | ~ in(X2,X1) )
          & ( X0 = X2
            | in(X2,X1) ) )
     => ( ( sK5(X0,X1) != X0
          | ~ in(sK5(X0,X1),X1) )
        & ( sK5(X0,X1) = X0
          | in(sK5(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | ~ sP0(X0,X1) ) ),
    inference(rectify,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | ~ sP0(X0,X1) ) ),
    inference(nnf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f297,plain,
    sK3 != sK5(sK3,unordered_pair(sK3,sK3)),
    inference(unit_resulting_resolution,[],[f73,f134,f61]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | sK5(X0,X1) != X0
      | sP0(X0,X1) ),
    inference(inner_rewriting,[],[f44]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | sK5(X0,X1) != X0
      | ~ in(sK5(X0,X1),X1) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f134,plain,
    ! [X0,X1] : in(X0,unordered_pair(X1,X0)),
    inference(unit_resulting_resolution,[],[f59,f68,f48]) ).

fof(f48,plain,
    ! [X2,X0,X1,X4] :
      ( ~ sP2(X0,X1,X2)
      | ~ sP1(X4,X1,X0)
      | in(X4,X2) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1,X2] :
      ( ( sP2(X0,X1,X2)
        | ( ( ~ sP1(sK6(X0,X1,X2),X1,X0)
            | ~ in(sK6(X0,X1,X2),X2) )
          & ( sP1(sK6(X0,X1,X2),X1,X0)
            | in(sK6(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ sP1(X4,X1,X0) )
            & ( sP1(X4,X1,X0)
              | ~ in(X4,X2) ) )
        | ~ sP2(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f29,f30]) ).

fof(f30,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ sP1(X3,X1,X0)
            | ~ in(X3,X2) )
          & ( sP1(X3,X1,X0)
            | in(X3,X2) ) )
     => ( ( ~ sP1(sK6(X0,X1,X2),X1,X0)
          | ~ in(sK6(X0,X1,X2),X2) )
        & ( sP1(sK6(X0,X1,X2),X1,X0)
          | in(sK6(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( ( sP2(X0,X1,X2)
        | ? [X3] :
            ( ( ~ sP1(X3,X1,X0)
              | ~ in(X3,X2) )
            & ( sP1(X3,X1,X0)
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ sP1(X4,X1,X0) )
            & ( sP1(X4,X1,X0)
              | ~ in(X4,X2) ) )
        | ~ sP2(X0,X1,X2) ) ),
    inference(rectify,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1,X2] :
      ( ( sP2(X0,X1,X2)
        | ? [X3] :
            ( ( ~ sP1(X3,X1,X0)
              | ~ in(X3,X2) )
            & ( sP1(X3,X1,X0)
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ~ sP1(X3,X1,X0) )
            & ( sP1(X3,X1,X0)
              | ~ in(X3,X2) ) )
        | ~ sP2(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1,X2] :
      ( sP2(X0,X1,X2)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> sP1(X3,X1,X0) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f68,plain,
    ! [X0,X1] : sP2(X0,X1,unordered_pair(X1,X0)),
    inference(superposition,[],[f60,f37]) ).

fof(f37,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(f60,plain,
    ! [X0,X1] : sP2(X0,X1,unordered_pair(X0,X1)),
    inference(equality_resolution,[],[f54]) ).

fof(f54,plain,
    ! [X2,X0,X1] :
      ( sP2(X0,X1,X2)
      | unordered_pair(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X0,X1) = X2
        | ~ sP2(X0,X1,X2) )
      & ( sP2(X0,X1,X2)
        | unordered_pair(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1,X2] :
      ( unordered_pair(X0,X1) = X2
    <=> sP2(X0,X1,X2) ),
    inference(definition_folding,[],[f4,f16,f15]) ).

fof(f15,plain,
    ! [X3,X1,X0] :
      ( sP1(X3,X1,X0)
    <=> ( X1 = X3
        | X0 = X3 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f4,axiom,
    ! [X0,X1,X2] :
      ( unordered_pair(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( X1 = X3
            | X0 = X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).

fof(f59,plain,
    ! [X2,X1] : sP1(X2,X1,X2),
    inference(equality_resolution,[],[f52]) ).

fof(f52,plain,
    ! [X2,X0,X1] :
      ( sP1(X0,X1,X2)
      | X0 != X2 ),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0,X1,X2] :
      ( ( sP1(X0,X1,X2)
        | ( X0 != X1
          & X0 != X2 ) )
      & ( X0 = X1
        | X0 = X2
        | ~ sP1(X0,X1,X2) ) ),
    inference(rectify,[],[f33]) ).

fof(f33,plain,
    ! [X3,X1,X0] :
      ( ( sP1(X3,X1,X0)
        | ( X1 != X3
          & X0 != X3 ) )
      & ( X1 = X3
        | X0 = X3
        | ~ sP1(X3,X1,X0) ) ),
    inference(flattening,[],[f32]) ).

fof(f32,plain,
    ! [X3,X1,X0] :
      ( ( sP1(X3,X1,X0)
        | ( X1 != X3
          & X0 != X3 ) )
      & ( X1 = X3
        | X0 = X3
        | ~ sP1(X3,X1,X0) ) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f325,plain,
    ~ in(sK5(sK3,unordered_pair(sK3,sK3)),unordered_pair(sK3,sK3)),
    inference(unit_resulting_resolution,[],[f68,f315,f47]) ).

fof(f47,plain,
    ! [X2,X0,X1,X4] :
      ( ~ sP2(X0,X1,X2)
      | ~ in(X4,X2)
      | sP1(X4,X1,X0) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f315,plain,
    ~ sP1(sK5(sK3,unordered_pair(sK3,sK3)),sK3,sK3),
    inference(unit_resulting_resolution,[],[f297,f297,f51]) ).

fof(f51,plain,
    ! [X2,X0,X1] :
      ( ~ sP1(X0,X1,X2)
      | X0 = X2
      | X0 = X1 ),
    inference(cnf_transformation,[],[f34]) ).

fof(f73,plain,
    ~ sP0(sK3,unordered_pair(sK3,sK3)),
    inference(unit_resulting_resolution,[],[f36,f46]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | singleton(X0) = X1 ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ~ sP0(X0,X1) )
      & ( sP0(X0,X1)
        | singleton(X0) != X1 ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( singleton(X0) = X1
    <=> sP0(X0,X1) ),
    inference(definition_folding,[],[f3,f13]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( singleton(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).

fof(f36,plain,
    singleton(sK3) != unordered_pair(sK3,sK3),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    singleton(sK3) != unordered_pair(sK3,sK3),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f10,f18]) ).

fof(f18,plain,
    ( ? [X0] : singleton(X0) != unordered_pair(X0,X0)
   => singleton(sK3) != unordered_pair(sK3,sK3) ),
    introduced(choice_axiom,[]) ).

fof(f10,plain,
    ? [X0] : singleton(X0) != unordered_pair(X0,X0),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,negated_conjecture,
    ~ ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    inference(negated_conjecture,[],[f8]) ).

fof(f8,conjecture,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SEU142+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n010.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 11:30:48 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (15507)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (15510)WARNING: value z3 for option sas not known
% 0.14/0.38  % (15512)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  % (15513)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  % (15510)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  % (15509)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  % (15514)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)
% 0.14/0.39  % (15508)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.39  TRYING [1]
% 0.14/0.39  TRYING [2]
% 0.14/0.39  TRYING [3]
% 0.14/0.40  TRYING [1]
% 0.14/0.40  TRYING [2]
% 0.14/0.40  TRYING [4]
% 0.21/0.40  % (15514)First to succeed.
% 0.21/0.40  % (15514)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-15507"
% 0.21/0.40  % (15511)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.40  % (15514)Refutation found. Thanks to Tanya!
% 0.21/0.40  % SZS status Theorem for theBenchmark
% 0.21/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.40  % (15514)------------------------------
% 0.21/0.40  % (15514)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.40  % (15514)Termination reason: Refutation
% 0.21/0.40  
% 0.21/0.40  % (15514)Memory used [KB]: 1000
% 0.21/0.40  % (15514)Time elapsed: 0.022 s
% 0.21/0.40  % (15514)Instructions burned: 34 (million)
% 0.21/0.40  % (15507)Success in time 0.041 s
%------------------------------------------------------------------------------