TSTP Solution File: SEU124+2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU124+2 : 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 : n032.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 09:27:05 EDT 2024

% Result   : Theorem 0.14s 0.33s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   31 (  10 unt;   0 def)
%            Number of atoms       :  133 (   5 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  163 (  61   ~;  58   |;  33   &)
%                                         (   7 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-3 aty)
%            Number of variables   :   81 (  70   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f722,plain,
    $false,
    inference(resolution,[],[f720,f89]) ).

fof(f89,plain,
    ~ subset(sK2,set_union2(sK2,sK3)),
    inference(cnf_transformation,[],[f57]) ).

fof(f57,plain,
    ~ subset(sK2,set_union2(sK2,sK3)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f38,f56]) ).

fof(f56,plain,
    ( ? [X0,X1] : ~ subset(X0,set_union2(X0,X1))
   => ~ subset(sK2,set_union2(sK2,sK3)) ),
    introduced(choice_axiom,[]) ).

fof(f38,plain,
    ? [X0,X1] : ~ subset(X0,set_union2(X0,X1)),
    inference(ennf_transformation,[],[f31]) ).

fof(f31,negated_conjecture,
    ~ ! [X0,X1] : subset(X0,set_union2(X0,X1)),
    inference(negated_conjecture,[],[f30]) ).

fof(f30,conjecture,
    ! [X0,X1] : subset(X0,set_union2(X0,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).

fof(f720,plain,
    subset(sK2,set_union2(sK2,sK3)),
    inference(resolution,[],[f714,f118]) ).

fof(f118,plain,
    ! [X0,X1] :
      ( in(sK7(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK7(X0,X1),X1)
          & in(sK7(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f70,f71]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK7(X0,X1),X1)
        & in(sK7(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f69]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(f714,plain,
    ~ in(sK7(sK2,set_union2(sK2,sK3)),sK2),
    inference(resolution,[],[f704,f235]) ).

fof(f235,plain,
    ~ in(sK7(sK2,set_union2(sK2,sK3)),set_union2(sK2,sK3)),
    inference(resolution,[],[f119,f89]) ).

fof(f119,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sK7(X0,X1),X1) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f704,plain,
    ! [X2,X0,X1] :
      ( in(X0,set_union2(X1,X2))
      | ~ in(X0,X1) ),
    inference(resolution,[],[f131,f144]) ).

fof(f144,plain,
    ! [X0,X1] : sP1(X1,X0,set_union2(X0,X1)),
    inference(equality_resolution,[],[f136]) ).

fof(f136,plain,
    ! [X2,X0,X1] :
      ( sP1(X1,X0,X2)
      | set_union2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f84]) ).

fof(f84,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ~ sP1(X1,X0,X2) )
      & ( sP1(X1,X0,X2)
        | set_union2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f55]) ).

fof(f55,plain,
    ! [X0,X1,X2] :
      ( set_union2(X0,X1) = X2
    <=> sP1(X1,X0,X2) ),
    inference(definition_folding,[],[f6,f54]) ).

fof(f54,plain,
    ! [X1,X0,X2] :
      ( sP1(X1,X0,X2)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            | in(X3,X0) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f6,axiom,
    ! [X0,X1,X2] :
      ( set_union2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            | in(X3,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).

fof(f131,plain,
    ! [X2,X0,X1,X4] :
      ( ~ sP1(X0,X1,X2)
      | ~ in(X4,X1)
      | in(X4,X2) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f83,plain,
    ! [X0,X1,X2] :
      ( ( sP1(X0,X1,X2)
        | ( ( ( ~ in(sK9(X0,X1,X2),X0)
              & ~ in(sK9(X0,X1,X2),X1) )
            | ~ in(sK9(X0,X1,X2),X2) )
          & ( in(sK9(X0,X1,X2),X0)
            | in(sK9(X0,X1,X2),X1)
            | in(sK9(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( ~ in(X4,X0)
                & ~ in(X4,X1) ) )
            & ( in(X4,X0)
              | in(X4,X1)
              | ~ in(X4,X2) ) )
        | ~ sP1(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f81,f82]) ).

fof(f82,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ( ~ in(X3,X0)
              & ~ in(X3,X1) )
            | ~ in(X3,X2) )
          & ( in(X3,X0)
            | in(X3,X1)
            | in(X3,X2) ) )
     => ( ( ( ~ in(sK9(X0,X1,X2),X0)
            & ~ in(sK9(X0,X1,X2),X1) )
          | ~ in(sK9(X0,X1,X2),X2) )
        & ( in(sK9(X0,X1,X2),X0)
          | in(sK9(X0,X1,X2),X1)
          | in(sK9(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f81,plain,
    ! [X0,X1,X2] :
      ( ( sP1(X0,X1,X2)
        | ? [X3] :
            ( ( ( ~ in(X3,X0)
                & ~ in(X3,X1) )
              | ~ in(X3,X2) )
            & ( in(X3,X0)
              | in(X3,X1)
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( ~ in(X4,X0)
                & ~ in(X4,X1) ) )
            & ( in(X4,X0)
              | in(X4,X1)
              | ~ in(X4,X2) ) )
        | ~ sP1(X0,X1,X2) ) ),
    inference(rectify,[],[f80]) ).

fof(f80,plain,
    ! [X1,X0,X2] :
      ( ( sP1(X1,X0,X2)
        | ? [X3] :
            ( ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( ~ in(X3,X1)
                & ~ in(X3,X0) ) )
            & ( in(X3,X1)
              | in(X3,X0)
              | ~ in(X3,X2) ) )
        | ~ sP1(X1,X0,X2) ) ),
    inference(flattening,[],[f79]) ).

fof(f79,plain,
    ! [X1,X0,X2] :
      ( ( sP1(X1,X0,X2)
        | ? [X3] :
            ( ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( ~ in(X3,X1)
                & ~ in(X3,X0) ) )
            & ( in(X3,X1)
              | in(X3,X0)
              | ~ in(X3,X2) ) )
        | ~ sP1(X1,X0,X2) ) ),
    inference(nnf_transformation,[],[f54]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : SEU124+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.10  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.09/0.29  % Computer : n032.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit   : 300
% 0.09/0.29  % WCLimit    : 300
% 0.09/0.29  % DateTime   : Fri May  3 11:50:24 EDT 2024
% 0.14/0.29  % CPUTime    : 
% 0.14/0.29  % (31240)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.31  % (31243)WARNING: value z3 for option sas not known
% 0.14/0.31  % (31241)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.31  % (31242)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.31  % (31245)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)
% 0.14/0.31  % (31246)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)
% 0.14/0.31  % (31247)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)
% 0.14/0.31  % (31243)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)
% 0.14/0.31  % (31244)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.31  TRYING [1]
% 0.14/0.31  TRYING [2]
% 0.14/0.32  TRYING [3]
% 0.14/0.32  TRYING [1]
% 0.14/0.32  TRYING [4]
% 0.14/0.32  TRYING [2]
% 0.14/0.33  % (31246)First to succeed.
% 0.14/0.33  % (31246)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-31240"
% 0.14/0.33  % (31246)Refutation found. Thanks to Tanya!
% 0.14/0.33  % SZS status Theorem for theBenchmark
% 0.14/0.33  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.33  % (31246)------------------------------
% 0.14/0.33  % (31246)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.33  % (31246)Termination reason: Refutation
% 0.14/0.33  
% 0.14/0.33  % (31246)Memory used [KB]: 1008
% 0.14/0.33  % (31246)Time elapsed: 0.021 s
% 0.14/0.33  % (31246)Instructions burned: 37 (million)
% 0.14/0.33  % (31240)Success in time 0.036 s
%------------------------------------------------------------------------------