TSTP Solution File: COM012+3 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : COM012+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n008.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 : Wed Aug 30 18:42:03 EDT 2023

% Result   : Theorem 1.64s 1.12s
% Output   : CNFRefutation 1.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   44 (  19 unt;   0 def)
%            Number of atoms       :  256 (  34 equ)
%            Maximal formula atoms :   21 (   5 avg)
%            Number of connectives :  299 (  87   ~; 101   |; 104   &)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   6 con; 0-0 aty)
%            Number of variables   :   49 (   0 sgn;  20   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f7,axiom,
    ! [X0,X1,X2,X3] :
      ( ( aElement0(X3)
        & aElement0(X2)
        & aRewritingSystem0(X1)
        & aElement0(X0) )
     => ( ( sdtmndtplgtdt0(X2,X1,X3)
          & sdtmndtplgtdt0(X0,X1,X2) )
       => sdtmndtplgtdt0(X0,X1,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTCTrans) ).

fof(f9,axiom,
    ( aElement0(xz)
    & aElement0(xy)
    & aRewritingSystem0(xR)
    & aElement0(xx) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__349) ).

fof(f10,conjecture,
    ( ( sdtmndtasgtdt0(xy,xR,xz)
      & ( ( sdtmndtplgtdt0(xy,xR,xz)
          & ( ? [X0] :
                ( sdtmndtplgtdt0(X0,xR,xz)
                & aReductOfIn0(X0,xy,xR)
                & aElement0(X0) )
            | aReductOfIn0(xz,xy,xR) ) )
        | xy = xz )
      & sdtmndtasgtdt0(xx,xR,xy)
      & ( ( sdtmndtplgtdt0(xx,xR,xy)
          & ( ? [X0] :
                ( sdtmndtplgtdt0(X0,xR,xy)
                & aReductOfIn0(X0,xx,xR)
                & aElement0(X0) )
            | aReductOfIn0(xy,xx,xR) ) )
        | xx = xy ) )
   => ( sdtmndtasgtdt0(xx,xR,xz)
      | sdtmndtplgtdt0(xx,xR,xz)
      | ? [X0] :
          ( sdtmndtplgtdt0(X0,xR,xz)
          & aReductOfIn0(X0,xx,xR)
          & aElement0(X0) )
      | aReductOfIn0(xz,xx,xR)
      | xx = xz ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(f11,negated_conjecture,
    ~ ( ( sdtmndtasgtdt0(xy,xR,xz)
        & ( ( sdtmndtplgtdt0(xy,xR,xz)
            & ( ? [X0] :
                  ( sdtmndtplgtdt0(X0,xR,xz)
                  & aReductOfIn0(X0,xy,xR)
                  & aElement0(X0) )
              | aReductOfIn0(xz,xy,xR) ) )
          | xy = xz )
        & sdtmndtasgtdt0(xx,xR,xy)
        & ( ( sdtmndtplgtdt0(xx,xR,xy)
            & ( ? [X0] :
                  ( sdtmndtplgtdt0(X0,xR,xy)
                  & aReductOfIn0(X0,xx,xR)
                  & aElement0(X0) )
              | aReductOfIn0(xy,xx,xR) ) )
          | xx = xy ) )
     => ( sdtmndtasgtdt0(xx,xR,xz)
        | sdtmndtplgtdt0(xx,xR,xz)
        | ? [X0] :
            ( sdtmndtplgtdt0(X0,xR,xz)
            & aReductOfIn0(X0,xx,xR)
            & aElement0(X0) )
        | aReductOfIn0(xz,xx,xR)
        | xx = xz ) ),
    inference(negated_conjecture,[],[f10]) ).

fof(f16,plain,
    ~ ( ( sdtmndtasgtdt0(xy,xR,xz)
        & ( ( sdtmndtplgtdt0(xy,xR,xz)
            & ( ? [X0] :
                  ( sdtmndtplgtdt0(X0,xR,xz)
                  & aReductOfIn0(X0,xy,xR)
                  & aElement0(X0) )
              | aReductOfIn0(xz,xy,xR) ) )
          | xy = xz )
        & sdtmndtasgtdt0(xx,xR,xy)
        & ( ( sdtmndtplgtdt0(xx,xR,xy)
            & ( ? [X1] :
                  ( sdtmndtplgtdt0(X1,xR,xy)
                  & aReductOfIn0(X1,xx,xR)
                  & aElement0(X1) )
              | aReductOfIn0(xy,xx,xR) ) )
          | xx = xy ) )
     => ( sdtmndtasgtdt0(xx,xR,xz)
        | sdtmndtplgtdt0(xx,xR,xz)
        | ? [X2] :
            ( sdtmndtplgtdt0(X2,xR,xz)
            & aReductOfIn0(X2,xx,xR)
            & aElement0(X2) )
        | aReductOfIn0(xz,xx,xR)
        | xx = xz ) ),
    inference(rectify,[],[f11]) ).

fof(f21,plain,
    ! [X0,X1,X2,X3] :
      ( sdtmndtplgtdt0(X0,X1,X3)
      | ~ sdtmndtplgtdt0(X2,X1,X3)
      | ~ sdtmndtplgtdt0(X0,X1,X2)
      | ~ aElement0(X3)
      | ~ aElement0(X2)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f22,plain,
    ! [X0,X1,X2,X3] :
      ( sdtmndtplgtdt0(X0,X1,X3)
      | ~ sdtmndtplgtdt0(X2,X1,X3)
      | ~ sdtmndtplgtdt0(X0,X1,X2)
      | ~ aElement0(X3)
      | ~ aElement0(X2)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(flattening,[],[f21]) ).

fof(f25,plain,
    ( ~ sdtmndtasgtdt0(xx,xR,xz)
    & ~ sdtmndtplgtdt0(xx,xR,xz)
    & ! [X2] :
        ( ~ sdtmndtplgtdt0(X2,xR,xz)
        | ~ aReductOfIn0(X2,xx,xR)
        | ~ aElement0(X2) )
    & ~ aReductOfIn0(xz,xx,xR)
    & xx != xz
    & sdtmndtasgtdt0(xy,xR,xz)
    & ( ( sdtmndtplgtdt0(xy,xR,xz)
        & ( ? [X0] :
              ( sdtmndtplgtdt0(X0,xR,xz)
              & aReductOfIn0(X0,xy,xR)
              & aElement0(X0) )
          | aReductOfIn0(xz,xy,xR) ) )
      | xy = xz )
    & sdtmndtasgtdt0(xx,xR,xy)
    & ( ( sdtmndtplgtdt0(xx,xR,xy)
        & ( ? [X1] :
              ( sdtmndtplgtdt0(X1,xR,xy)
              & aReductOfIn0(X1,xx,xR)
              & aElement0(X1) )
          | aReductOfIn0(xy,xx,xR) ) )
      | xx = xy ) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f26,plain,
    ( ~ sdtmndtasgtdt0(xx,xR,xz)
    & ~ sdtmndtplgtdt0(xx,xR,xz)
    & ! [X2] :
        ( ~ sdtmndtplgtdt0(X2,xR,xz)
        | ~ aReductOfIn0(X2,xx,xR)
        | ~ aElement0(X2) )
    & ~ aReductOfIn0(xz,xx,xR)
    & xx != xz
    & sdtmndtasgtdt0(xy,xR,xz)
    & ( ( sdtmndtplgtdt0(xy,xR,xz)
        & ( ? [X0] :
              ( sdtmndtplgtdt0(X0,xR,xz)
              & aReductOfIn0(X0,xy,xR)
              & aElement0(X0) )
          | aReductOfIn0(xz,xy,xR) ) )
      | xy = xz )
    & sdtmndtasgtdt0(xx,xR,xy)
    & ( ( sdtmndtplgtdt0(xx,xR,xy)
        & ( ? [X1] :
              ( sdtmndtplgtdt0(X1,xR,xy)
              & aReductOfIn0(X1,xx,xR)
              & aElement0(X1) )
          | aReductOfIn0(xy,xx,xR) ) )
      | xx = xy ) ),
    inference(flattening,[],[f25]) ).

fof(f34,plain,
    ( ~ sdtmndtasgtdt0(xx,xR,xz)
    & ~ sdtmndtplgtdt0(xx,xR,xz)
    & ! [X0] :
        ( ~ sdtmndtplgtdt0(X0,xR,xz)
        | ~ aReductOfIn0(X0,xx,xR)
        | ~ aElement0(X0) )
    & ~ aReductOfIn0(xz,xx,xR)
    & xx != xz
    & sdtmndtasgtdt0(xy,xR,xz)
    & ( ( sdtmndtplgtdt0(xy,xR,xz)
        & ( ? [X1] :
              ( sdtmndtplgtdt0(X1,xR,xz)
              & aReductOfIn0(X1,xy,xR)
              & aElement0(X1) )
          | aReductOfIn0(xz,xy,xR) ) )
      | xy = xz )
    & sdtmndtasgtdt0(xx,xR,xy)
    & ( ( sdtmndtplgtdt0(xx,xR,xy)
        & ( ? [X2] :
              ( sdtmndtplgtdt0(X2,xR,xy)
              & aReductOfIn0(X2,xx,xR)
              & aElement0(X2) )
          | aReductOfIn0(xy,xx,xR) ) )
      | xx = xy ) ),
    inference(rectify,[],[f26]) ).

fof(f35,plain,
    ( ? [X1] :
        ( sdtmndtplgtdt0(X1,xR,xz)
        & aReductOfIn0(X1,xy,xR)
        & aElement0(X1) )
   => ( sdtmndtplgtdt0(sK1,xR,xz)
      & aReductOfIn0(sK1,xy,xR)
      & aElement0(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f36,plain,
    ( ? [X2] :
        ( sdtmndtplgtdt0(X2,xR,xy)
        & aReductOfIn0(X2,xx,xR)
        & aElement0(X2) )
   => ( sdtmndtplgtdt0(sK2,xR,xy)
      & aReductOfIn0(sK2,xx,xR)
      & aElement0(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f37,plain,
    ( ~ sdtmndtasgtdt0(xx,xR,xz)
    & ~ sdtmndtplgtdt0(xx,xR,xz)
    & ! [X0] :
        ( ~ sdtmndtplgtdt0(X0,xR,xz)
        | ~ aReductOfIn0(X0,xx,xR)
        | ~ aElement0(X0) )
    & ~ aReductOfIn0(xz,xx,xR)
    & xx != xz
    & sdtmndtasgtdt0(xy,xR,xz)
    & ( ( sdtmndtplgtdt0(xy,xR,xz)
        & ( ( sdtmndtplgtdt0(sK1,xR,xz)
            & aReductOfIn0(sK1,xy,xR)
            & aElement0(sK1) )
          | aReductOfIn0(xz,xy,xR) ) )
      | xy = xz )
    & sdtmndtasgtdt0(xx,xR,xy)
    & ( ( sdtmndtplgtdt0(xx,xR,xy)
        & ( ( sdtmndtplgtdt0(sK2,xR,xy)
            & aReductOfIn0(sK2,xx,xR)
            & aElement0(sK2) )
          | aReductOfIn0(xy,xx,xR) ) )
      | xx = xy ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f34,f36,f35]) ).

fof(f44,plain,
    ! [X2,X3,X0,X1] :
      ( sdtmndtplgtdt0(X0,X1,X3)
      | ~ sdtmndtplgtdt0(X2,X1,X3)
      | ~ sdtmndtplgtdt0(X0,X1,X2)
      | ~ aElement0(X3)
      | ~ aElement0(X2)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f48,plain,
    aElement0(xx),
    inference(cnf_transformation,[],[f9]) ).

fof(f49,plain,
    aRewritingSystem0(xR),
    inference(cnf_transformation,[],[f9]) ).

fof(f50,plain,
    aElement0(xy),
    inference(cnf_transformation,[],[f9]) ).

fof(f51,plain,
    aElement0(xz),
    inference(cnf_transformation,[],[f9]) ).

fof(f55,plain,
    ( sdtmndtplgtdt0(xx,xR,xy)
    | xx = xy ),
    inference(cnf_transformation,[],[f37]) ).

fof(f56,plain,
    sdtmndtasgtdt0(xx,xR,xy),
    inference(cnf_transformation,[],[f37]) ).

fof(f60,plain,
    ( sdtmndtplgtdt0(xy,xR,xz)
    | xy = xz ),
    inference(cnf_transformation,[],[f37]) ).

fof(f61,plain,
    sdtmndtasgtdt0(xy,xR,xz),
    inference(cnf_transformation,[],[f37]) ).

fof(f65,plain,
    ~ sdtmndtplgtdt0(xx,xR,xz),
    inference(cnf_transformation,[],[f37]) ).

fof(f66,plain,
    ~ sdtmndtasgtdt0(xx,xR,xz),
    inference(cnf_transformation,[],[f37]) ).

cnf(c_55,plain,
    ( ~ sdtmndtplgtdt0(X0,X1,X2)
    | ~ sdtmndtplgtdt0(X3,X1,X0)
    | ~ aElement0(X0)
    | ~ aElement0(X2)
    | ~ aElement0(X3)
    | ~ aRewritingSystem0(X1)
    | sdtmndtplgtdt0(X3,X1,X2) ),
    inference(cnf_transformation,[],[f44]) ).

cnf(c_59,plain,
    aElement0(xz),
    inference(cnf_transformation,[],[f51]) ).

cnf(c_60,plain,
    aElement0(xy),
    inference(cnf_transformation,[],[f50]) ).

cnf(c_61,plain,
    aRewritingSystem0(xR),
    inference(cnf_transformation,[],[f49]) ).

cnf(c_62,plain,
    aElement0(xx),
    inference(cnf_transformation,[],[f48]) ).

cnf(c_63,negated_conjecture,
    ~ sdtmndtasgtdt0(xx,xR,xz),
    inference(cnf_transformation,[],[f66]) ).

cnf(c_64,negated_conjecture,
    ~ sdtmndtplgtdt0(xx,xR,xz),
    inference(cnf_transformation,[],[f65]) ).

cnf(c_68,negated_conjecture,
    sdtmndtasgtdt0(xy,xR,xz),
    inference(cnf_transformation,[],[f61]) ).

cnf(c_69,negated_conjecture,
    ( xz = xy
    | sdtmndtplgtdt0(xy,xR,xz) ),
    inference(cnf_transformation,[],[f60]) ).

cnf(c_73,negated_conjecture,
    sdtmndtasgtdt0(xx,xR,xy),
    inference(cnf_transformation,[],[f56]) ).

cnf(c_74,negated_conjecture,
    ( xy = xx
    | sdtmndtplgtdt0(xx,xR,xy) ),
    inference(cnf_transformation,[],[f55]) ).

cnf(c_455,plain,
    ( xz != xz
    | xy != xx
    | xR != xR ),
    inference(resolution_lifted,[status(thm)],[c_63,c_68]) ).

cnf(c_465,plain,
    ( xz != xy
    | xR != xR
    | xx != xx ),
    inference(resolution_lifted,[status(thm)],[c_63,c_73]) ).

cnf(c_525,plain,
    ( X0 != xR
    | ~ sdtmndtplgtdt0(X1,X0,X2)
    | ~ sdtmndtplgtdt0(X3,X0,X1)
    | ~ aElement0(X1)
    | ~ aElement0(X2)
    | ~ aElement0(X3)
    | sdtmndtplgtdt0(X3,X0,X2) ),
    inference(resolution_lifted,[status(thm)],[c_55,c_61]) ).

cnf(c_526,plain,
    ( ~ sdtmndtplgtdt0(X0,xR,X1)
    | ~ sdtmndtplgtdt0(X2,xR,X0)
    | ~ aElement0(X0)
    | ~ aElement0(X1)
    | ~ aElement0(X2)
    | sdtmndtplgtdt0(X2,xR,X1) ),
    inference(unflattening,[status(thm)],[c_525]) ).

cnf(c_631,plain,
    xz != xy,
    inference(equality_resolution_simp,[status(thm)],[c_465]) ).

cnf(c_632,plain,
    xy != xx,
    inference(equality_resolution_simp,[status(thm)],[c_455]) ).

cnf(c_1154,plain,
    ( ~ sdtmndtplgtdt0(X0,xR,xy)
    | ~ sdtmndtplgtdt0(xy,xR,xz)
    | ~ aElement0(X0)
    | ~ aElement0(xz)
    | ~ aElement0(xy)
    | sdtmndtplgtdt0(X0,xR,xz) ),
    inference(instantiation,[status(thm)],[c_526]) ).

cnf(c_1195,plain,
    ( ~ sdtmndtplgtdt0(xy,xR,xz)
    | ~ sdtmndtplgtdt0(xx,xR,xy)
    | ~ aElement0(xz)
    | ~ aElement0(xy)
    | ~ aElement0(xx)
    | sdtmndtplgtdt0(xx,xR,xz) ),
    inference(instantiation,[status(thm)],[c_1154]) ).

cnf(c_1196,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_1195,c_632,c_631,c_69,c_74,c_64,c_59,c_60,c_62]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : COM012+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command  : run_iprover %s %d THM
% 0.14/0.35  % Computer : n008.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 : Tue Aug 29 13:31:32 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 1.64/1.12  % SZS status Started for theBenchmark.p
% 1.64/1.12  % SZS status Theorem for theBenchmark.p
% 1.64/1.12  
% 1.64/1.12  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 1.64/1.12  
% 1.64/1.12  ------  iProver source info
% 1.64/1.12  
% 1.64/1.12  git: date: 2023-05-31 18:12:56 +0000
% 1.64/1.12  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 1.64/1.12  git: non_committed_changes: false
% 1.64/1.12  git: last_make_outside_of_git: false
% 1.64/1.12  
% 1.64/1.12  ------ Parsing...
% 1.64/1.12  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 1.64/1.12  
% 1.64/1.12  ------ 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: 3 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 3 0s  sf_e  pe_s  pe:1:0s pe_e  sf_s  rm: 3 0s  sf_e  pe_s  pe_e 
% 1.64/1.12  
% 1.64/1.12  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 1.64/1.12  ------ Proving...
% 1.64/1.12  ------ Problem Properties 
% 1.64/1.12  
% 1.64/1.12  
% 1.64/1.12  clauses                                 21
% 1.64/1.12  conjectures                             11
% 1.64/1.12  EPR                                     18
% 1.64/1.12  Horn                                    15
% 1.64/1.12  unary                                   10
% 1.64/1.12  binary                                  3
% 1.64/1.12  lits                                    51
% 1.64/1.12  lits eq                                 0
% 1.64/1.12  fd_pure                                 0
% 1.64/1.12  fd_pseudo                               0
% 1.64/1.12  fd_cond                                 0
% 1.64/1.12  fd_pseudo_cond                          0
% 1.64/1.12  AC symbols                              0
% 1.64/1.12  
% 1.64/1.12  ------ Schedule dynamic 5 is on 
% 1.64/1.12  
% 1.64/1.12  ------ no equalities: superposition off 
% 1.64/1.12  
% 1.64/1.12  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.64/1.12  
% 1.64/1.12  
% 1.64/1.12  ------ 
% 1.64/1.12  Current options:
% 1.64/1.12  ------ 
% 1.64/1.12  
% 1.64/1.12  
% 1.64/1.12  
% 1.64/1.12  
% 1.64/1.12  ------ Proving...
% 1.64/1.12  
% 1.64/1.12  
% 1.64/1.12  % SZS status Theorem for theBenchmark.p
% 1.64/1.12  
% 1.64/1.12  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.64/1.12  
% 1.64/1.12  
%------------------------------------------------------------------------------