TSTP Solution File: NUM555+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : NUM555+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n022.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 : Thu Aug 31 11:31:25 EDT 2023

% Result   : Theorem 3.84s 1.17s
% Output   : CNFRefutation 3.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   38 (  13 unt;   0 def)
%            Number of atoms       :  189 (  34 equ)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives :  242 (  91   ~;  85   |;  55   &)
%                                         (   9 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-3 aty)
%            Number of variables   :   75 (   1 sgn;  54   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f16,axiom,
    ! [X0,X1] :
      ( ( aElement0(X1)
        & aSet0(X0) )
     => ! [X2] :
          ( sdtmndt0(X0,X1) = X2
        <=> ( ! [X3] :
                ( aElementOf0(X3,X2)
              <=> ( X1 != X3
                  & aElementOf0(X3,X0)
                  & aElement0(X3) ) )
            & aSet0(X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).

fof(f66,axiom,
    ( xk = sbrdtbr0(xQ)
    & isFinite0(xQ)
    & aSet0(xQ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2291) ).

fof(f67,axiom,
    ( aElementOf0(xy,xQ)
    & aElement0(xy) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2304) ).

fof(f69,axiom,
    ~ aElementOf0(xx,xQ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2338) ).

fof(f71,conjecture,
    ~ aElementOf0(xx,sdtmndt0(xQ,xy)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f72,negated_conjecture,
    ~ ~ aElementOf0(xx,sdtmndt0(xQ,xy)),
    inference(negated_conjecture,[],[f71]) ).

fof(f79,plain,
    aElementOf0(xx,sdtmndt0(xQ,xy)),
    inference(flattening,[],[f72]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtmndt0(X0,X1) = X2
        <=> ( ! [X3] :
                ( aElementOf0(X3,X2)
              <=> ( X1 != X3
                  & aElementOf0(X3,X0)
                  & aElement0(X3) ) )
            & aSet0(X2) ) )
      | ~ aElement0(X1)
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f98,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtmndt0(X0,X1) = X2
        <=> ( ! [X3] :
                ( aElementOf0(X3,X2)
              <=> ( X1 != X3
                  & aElementOf0(X3,X0)
                  & aElement0(X3) ) )
            & aSet0(X2) ) )
      | ~ aElement0(X1)
      | ~ aSet0(X0) ),
    inference(flattening,[],[f97]) ).

fof(f165,plain,
    ! [X1,X0,X2] :
      ( sP2(X1,X0,X2)
    <=> ( ! [X3] :
            ( aElementOf0(X3,X2)
          <=> ( X1 != X3
              & aElementOf0(X3,X0)
              & aElement0(X3) ) )
        & aSet0(X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f166,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtmndt0(X0,X1) = X2
        <=> sP2(X1,X0,X2) )
      | ~ sP3(X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

fof(f167,plain,
    ! [X0,X1] :
      ( sP3(X0,X1)
      | ~ aElement0(X1)
      | ~ aSet0(X0) ),
    inference(definition_folding,[],[f98,f166,f165]) ).

fof(f184,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( sdtmndt0(X0,X1) = X2
            | ~ sP2(X1,X0,X2) )
          & ( sP2(X1,X0,X2)
            | sdtmndt0(X0,X1) != X2 ) )
      | ~ sP3(X0,X1) ),
    inference(nnf_transformation,[],[f166]) ).

fof(f185,plain,
    ! [X1,X0,X2] :
      ( ( sP2(X1,X0,X2)
        | ? [X3] :
            ( ( X1 = X3
              | ~ aElementOf0(X3,X0)
              | ~ aElement0(X3)
              | ~ aElementOf0(X3,X2) )
            & ( ( X1 != X3
                & aElementOf0(X3,X0)
                & aElement0(X3) )
              | aElementOf0(X3,X2) ) )
        | ~ aSet0(X2) )
      & ( ( ! [X3] :
              ( ( aElementOf0(X3,X2)
                | X1 = X3
                | ~ aElementOf0(X3,X0)
                | ~ aElement0(X3) )
              & ( ( X1 != X3
                  & aElementOf0(X3,X0)
                  & aElement0(X3) )
                | ~ aElementOf0(X3,X2) ) )
          & aSet0(X2) )
        | ~ sP2(X1,X0,X2) ) ),
    inference(nnf_transformation,[],[f165]) ).

fof(f186,plain,
    ! [X1,X0,X2] :
      ( ( sP2(X1,X0,X2)
        | ? [X3] :
            ( ( X1 = X3
              | ~ aElementOf0(X3,X0)
              | ~ aElement0(X3)
              | ~ aElementOf0(X3,X2) )
            & ( ( X1 != X3
                & aElementOf0(X3,X0)
                & aElement0(X3) )
              | aElementOf0(X3,X2) ) )
        | ~ aSet0(X2) )
      & ( ( ! [X3] :
              ( ( aElementOf0(X3,X2)
                | X1 = X3
                | ~ aElementOf0(X3,X0)
                | ~ aElement0(X3) )
              & ( ( X1 != X3
                  & aElementOf0(X3,X0)
                  & aElement0(X3) )
                | ~ aElementOf0(X3,X2) ) )
          & aSet0(X2) )
        | ~ sP2(X1,X0,X2) ) ),
    inference(flattening,[],[f185]) ).

fof(f187,plain,
    ! [X0,X1,X2] :
      ( ( sP2(X0,X1,X2)
        | ? [X3] :
            ( ( X0 = X3
              | ~ aElementOf0(X3,X1)
              | ~ aElement0(X3)
              | ~ aElementOf0(X3,X2) )
            & ( ( X0 != X3
                & aElementOf0(X3,X1)
                & aElement0(X3) )
              | aElementOf0(X3,X2) ) )
        | ~ aSet0(X2) )
      & ( ( ! [X4] :
              ( ( aElementOf0(X4,X2)
                | X0 = X4
                | ~ aElementOf0(X4,X1)
                | ~ aElement0(X4) )
              & ( ( X0 != X4
                  & aElementOf0(X4,X1)
                  & aElement0(X4) )
                | ~ aElementOf0(X4,X2) ) )
          & aSet0(X2) )
        | ~ sP2(X0,X1,X2) ) ),
    inference(rectify,[],[f186]) ).

fof(f188,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( X0 = X3
            | ~ aElementOf0(X3,X1)
            | ~ aElement0(X3)
            | ~ aElementOf0(X3,X2) )
          & ( ( X0 != X3
              & aElementOf0(X3,X1)
              & aElement0(X3) )
            | aElementOf0(X3,X2) ) )
     => ( ( sK7(X0,X1,X2) = X0
          | ~ aElementOf0(sK7(X0,X1,X2),X1)
          | ~ aElement0(sK7(X0,X1,X2))
          | ~ aElementOf0(sK7(X0,X1,X2),X2) )
        & ( ( sK7(X0,X1,X2) != X0
            & aElementOf0(sK7(X0,X1,X2),X1)
            & aElement0(sK7(X0,X1,X2)) )
          | aElementOf0(sK7(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f189,plain,
    ! [X0,X1,X2] :
      ( ( sP2(X0,X1,X2)
        | ( ( sK7(X0,X1,X2) = X0
            | ~ aElementOf0(sK7(X0,X1,X2),X1)
            | ~ aElement0(sK7(X0,X1,X2))
            | ~ aElementOf0(sK7(X0,X1,X2),X2) )
          & ( ( sK7(X0,X1,X2) != X0
              & aElementOf0(sK7(X0,X1,X2),X1)
              & aElement0(sK7(X0,X1,X2)) )
            | aElementOf0(sK7(X0,X1,X2),X2) ) )
        | ~ aSet0(X2) )
      & ( ( ! [X4] :
              ( ( aElementOf0(X4,X2)
                | X0 = X4
                | ~ aElementOf0(X4,X1)
                | ~ aElement0(X4) )
              & ( ( X0 != X4
                  & aElementOf0(X4,X1)
                  & aElement0(X4) )
                | ~ aElementOf0(X4,X2) ) )
          & aSet0(X2) )
        | ~ sP2(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f187,f188]) ).

fof(f249,plain,
    ! [X2,X0,X1] :
      ( sP2(X1,X0,X2)
      | sdtmndt0(X0,X1) != X2
      | ~ sP3(X0,X1) ),
    inference(cnf_transformation,[],[f184]) ).

fof(f253,plain,
    ! [X2,X0,X1,X4] :
      ( aElementOf0(X4,X1)
      | ~ aElementOf0(X4,X2)
      | ~ sP2(X0,X1,X2) ),
    inference(cnf_transformation,[],[f189]) ).

fof(f260,plain,
    ! [X0,X1] :
      ( sP3(X0,X1)
      | ~ aElement0(X1)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f167]) ).

fof(f339,plain,
    aSet0(xQ),
    inference(cnf_transformation,[],[f66]) ).

fof(f342,plain,
    aElement0(xy),
    inference(cnf_transformation,[],[f67]) ).

fof(f345,plain,
    ~ aElementOf0(xx,xQ),
    inference(cnf_transformation,[],[f69]) ).

fof(f347,plain,
    aElementOf0(xx,sdtmndt0(xQ,xy)),
    inference(cnf_transformation,[],[f79]) ).

fof(f353,plain,
    ! [X0,X1] :
      ( sP2(X1,X0,sdtmndt0(X0,X1))
      | ~ sP3(X0,X1) ),
    inference(equality_resolution,[],[f249]) ).

cnf(c_77,plain,
    ( ~ sP3(X0,X1)
    | sP2(X1,X0,sdtmndt0(X0,X1)) ),
    inference(cnf_transformation,[],[f353]) ).

cnf(c_84,plain,
    ( ~ sP2(X0,X1,X2)
    | ~ aElementOf0(X3,X2)
    | aElementOf0(X3,X1) ),
    inference(cnf_transformation,[],[f253]) ).

cnf(c_87,plain,
    ( ~ aElement0(X0)
    | ~ aSet0(X1)
    | sP3(X1,X0) ),
    inference(cnf_transformation,[],[f260]) ).

cnf(c_168,plain,
    aSet0(xQ),
    inference(cnf_transformation,[],[f339]) ).

cnf(c_170,plain,
    aElement0(xy),
    inference(cnf_transformation,[],[f342]) ).

cnf(c_172,plain,
    ~ aElementOf0(xx,xQ),
    inference(cnf_transformation,[],[f345]) ).

cnf(c_174,negated_conjecture,
    aElementOf0(xx,sdtmndt0(xQ,xy)),
    inference(cnf_transformation,[],[f347]) ).

cnf(c_1868,plain,
    ( X0 != X1
    | X2 != X3
    | ~ aElement0(X0)
    | ~ aSet0(X2)
    | sP2(X1,X3,sdtmndt0(X3,X1)) ),
    inference(resolution_lifted,[status(thm)],[c_87,c_77]) ).

cnf(c_1869,plain,
    ( ~ aElement0(X0)
    | ~ aSet0(X1)
    | sP2(X0,X1,sdtmndt0(X1,X0)) ),
    inference(unflattening,[status(thm)],[c_1868]) ).

cnf(c_11194,plain,
    ( ~ aElementOf0(X0,sdtmndt0(X1,X2))
    | ~ aElement0(X2)
    | ~ aSet0(X1)
    | aElementOf0(X0,X1) ),
    inference(superposition,[status(thm)],[c_1869,c_84]) ).

cnf(c_11407,plain,
    ( ~ aElement0(xy)
    | ~ aSet0(xQ)
    | aElementOf0(xx,xQ) ),
    inference(superposition,[status(thm)],[c_174,c_11194]) ).

cnf(c_11408,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_11407,c_172,c_168,c_170]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM555+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.16/0.35  % Computer : n022.cluster.edu
% 0.16/0.35  % Model    : x86_64 x86_64
% 0.16/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35  % Memory   : 8042.1875MB
% 0.16/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35  % CPULimit : 300
% 0.16/0.35  % WCLimit  : 300
% 0.16/0.35  % DateTime : Fri Aug 25 11:01:40 EDT 2023
% 0.16/0.35  % CPUTime  : 
% 0.21/0.48  Running first-order theorem proving
% 0.21/0.48  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.84/1.17  % SZS status Started for theBenchmark.p
% 3.84/1.17  % SZS status Theorem for theBenchmark.p
% 3.84/1.17  
% 3.84/1.17  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.84/1.17  
% 3.84/1.17  ------  iProver source info
% 3.84/1.17  
% 3.84/1.17  git: date: 2023-05-31 18:12:56 +0000
% 3.84/1.17  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.84/1.17  git: non_committed_changes: false
% 3.84/1.17  git: last_make_outside_of_git: false
% 3.84/1.17  
% 3.84/1.17  ------ Parsing...
% 3.84/1.17  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.84/1.17  
% 3.84/1.17  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 3.84/1.17  
% 3.84/1.17  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.84/1.17  
% 3.84/1.17  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.84/1.17  ------ Proving...
% 3.84/1.17  ------ Problem Properties 
% 3.84/1.17  
% 3.84/1.17  
% 3.84/1.17  clauses                                 123
% 3.84/1.17  conjectures                             1
% 3.84/1.17  EPR                                     39
% 3.84/1.17  Horn                                    93
% 3.84/1.17  unary                                   25
% 3.84/1.17  binary                                  16
% 3.84/1.17  lits                                    393
% 3.84/1.17  lits eq                                 59
% 3.84/1.17  fd_pure                                 0
% 3.84/1.17  fd_pseudo                               0
% 3.84/1.17  fd_cond                                 9
% 3.84/1.17  fd_pseudo_cond                          18
% 3.84/1.17  AC symbols                              0
% 3.84/1.17  
% 3.84/1.17  ------ Input Options Time Limit: Unbounded
% 3.84/1.17  
% 3.84/1.17  
% 3.84/1.17  ------ 
% 3.84/1.17  Current options:
% 3.84/1.17  ------ 
% 3.84/1.17  
% 3.84/1.17  
% 3.84/1.17  
% 3.84/1.17  
% 3.84/1.17  ------ Proving...
% 3.84/1.17  
% 3.84/1.17  
% 3.84/1.17  ------ Proving...
% 3.84/1.17  
% 3.84/1.17  
% 3.84/1.17  % SZS status Theorem for theBenchmark.p
% 3.84/1.17  
% 3.84/1.17  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.84/1.18  
% 3.84/1.18  
%------------------------------------------------------------------------------