TSTP Solution File: RNG105+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : RNG105+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n023.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 13:55:19 EDT 2023

% Result   : Theorem 7.89s 1.66s
% Output   : CNFRefutation 7.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   56 (  17 unt;   0 def)
%            Number of atoms       :  198 (  47 equ)
%            Maximal formula atoms :   17 (   3 avg)
%            Number of connectives :  235 (  93   ~;  88   |;  44   &)
%                                         (   4 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   6 con; 0-2 aty)
%            Number of variables   :   81 (   0 sgn;  59   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,axiom,
    ! [X0,X1] :
      ( ( aElement0(X1)
        & aElement0(X0) )
     => aElement0(sdtpldt0(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( ( aElement0(X1)
        & aElement0(X0) )
     => aElement0(sdtasdt0(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).

fof(f37,axiom,
    ! [X0] :
      ( aElement0(X0)
     => ! [X1] :
          ( slsdtgt0(X0) = X1
        <=> ( ! [X2] :
                ( aElementOf0(X2,X1)
              <=> ? [X3] :
                    ( sdtasdt0(X0,X3) = X2
                    & aElement0(X3) ) )
            & aSet0(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrIdeal) ).

fof(f38,axiom,
    aElement0(xc),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1905) ).

fof(f39,axiom,
    ( aElement0(xz)
    & aElementOf0(xy,slsdtgt0(xc))
    & aElementOf0(xx,slsdtgt0(xc)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1933) ).

fof(f40,axiom,
    ( xx = sdtasdt0(xc,xu)
    & aElement0(xu) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1956) ).

fof(f41,axiom,
    ( xy = sdtasdt0(xc,xv)
    & aElement0(xv) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1979) ).

fof(f42,axiom,
    sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2010) ).

fof(f43,axiom,
    sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2043) ).

fof(f44,conjecture,
    ( aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
    & aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f45,negated_conjecture,
    ~ ( aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
      & aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) ),
    inference(negated_conjecture,[],[f44]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( aElement0(sdtpldt0(X0,X1))
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( aElement0(sdtpldt0(X0,X1))
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(flattening,[],[f56]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( aElement0(sdtasdt0(X0,X1))
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( aElement0(sdtasdt0(X0,X1))
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(flattening,[],[f58]) ).

fof(f102,plain,
    ! [X0] :
      ( ! [X1] :
          ( slsdtgt0(X0) = X1
        <=> ( ! [X2] :
                ( aElementOf0(X2,X1)
              <=> ? [X3] :
                    ( sdtasdt0(X0,X3) = X2
                    & aElement0(X3) ) )
            & aSet0(X1) ) )
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f103,plain,
    ( ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
    | ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f149,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( slsdtgt0(X0) = X1
            | ? [X2] :
                ( ( ! [X3] :
                      ( sdtasdt0(X0,X3) != X2
                      | ~ aElement0(X3) )
                  | ~ aElementOf0(X2,X1) )
                & ( ? [X3] :
                      ( sdtasdt0(X0,X3) = X2
                      & aElement0(X3) )
                  | aElementOf0(X2,X1) ) )
            | ~ aSet0(X1) )
          & ( ( ! [X2] :
                  ( ( aElementOf0(X2,X1)
                    | ! [X3] :
                        ( sdtasdt0(X0,X3) != X2
                        | ~ aElement0(X3) ) )
                  & ( ? [X3] :
                        ( sdtasdt0(X0,X3) = X2
                        & aElement0(X3) )
                    | ~ aElementOf0(X2,X1) ) )
              & aSet0(X1) )
            | slsdtgt0(X0) != X1 ) )
      | ~ aElement0(X0) ),
    inference(nnf_transformation,[],[f102]) ).

fof(f150,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( slsdtgt0(X0) = X1
            | ? [X2] :
                ( ( ! [X3] :
                      ( sdtasdt0(X0,X3) != X2
                      | ~ aElement0(X3) )
                  | ~ aElementOf0(X2,X1) )
                & ( ? [X3] :
                      ( sdtasdt0(X0,X3) = X2
                      & aElement0(X3) )
                  | aElementOf0(X2,X1) ) )
            | ~ aSet0(X1) )
          & ( ( ! [X2] :
                  ( ( aElementOf0(X2,X1)
                    | ! [X3] :
                        ( sdtasdt0(X0,X3) != X2
                        | ~ aElement0(X3) ) )
                  & ( ? [X3] :
                        ( sdtasdt0(X0,X3) = X2
                        & aElement0(X3) )
                    | ~ aElementOf0(X2,X1) ) )
              & aSet0(X1) )
            | slsdtgt0(X0) != X1 ) )
      | ~ aElement0(X0) ),
    inference(flattening,[],[f149]) ).

fof(f151,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( slsdtgt0(X0) = X1
            | ? [X2] :
                ( ( ! [X3] :
                      ( sdtasdt0(X0,X3) != X2
                      | ~ aElement0(X3) )
                  | ~ aElementOf0(X2,X1) )
                & ( ? [X4] :
                      ( sdtasdt0(X0,X4) = X2
                      & aElement0(X4) )
                  | aElementOf0(X2,X1) ) )
            | ~ aSet0(X1) )
          & ( ( ! [X5] :
                  ( ( aElementOf0(X5,X1)
                    | ! [X6] :
                        ( sdtasdt0(X0,X6) != X5
                        | ~ aElement0(X6) ) )
                  & ( ? [X7] :
                        ( sdtasdt0(X0,X7) = X5
                        & aElement0(X7) )
                    | ~ aElementOf0(X5,X1) ) )
              & aSet0(X1) )
            | slsdtgt0(X0) != X1 ) )
      | ~ aElement0(X0) ),
    inference(rectify,[],[f150]) ).

fof(f152,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ! [X3] :
                ( sdtasdt0(X0,X3) != X2
                | ~ aElement0(X3) )
            | ~ aElementOf0(X2,X1) )
          & ( ? [X4] :
                ( sdtasdt0(X0,X4) = X2
                & aElement0(X4) )
            | aElementOf0(X2,X1) ) )
     => ( ( ! [X3] :
              ( sdtasdt0(X0,X3) != sK19(X0,X1)
              | ~ aElement0(X3) )
          | ~ aElementOf0(sK19(X0,X1),X1) )
        & ( ? [X4] :
              ( sdtasdt0(X0,X4) = sK19(X0,X1)
              & aElement0(X4) )
          | aElementOf0(sK19(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f153,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( sdtasdt0(X0,X4) = sK19(X0,X1)
          & aElement0(X4) )
     => ( sK19(X0,X1) = sdtasdt0(X0,sK20(X0,X1))
        & aElement0(sK20(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f154,plain,
    ! [X0,X5] :
      ( ? [X7] :
          ( sdtasdt0(X0,X7) = X5
          & aElement0(X7) )
     => ( sdtasdt0(X0,sK21(X0,X5)) = X5
        & aElement0(sK21(X0,X5)) ) ),
    introduced(choice_axiom,[]) ).

fof(f155,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( slsdtgt0(X0) = X1
            | ( ( ! [X3] :
                    ( sdtasdt0(X0,X3) != sK19(X0,X1)
                    | ~ aElement0(X3) )
                | ~ aElementOf0(sK19(X0,X1),X1) )
              & ( ( sK19(X0,X1) = sdtasdt0(X0,sK20(X0,X1))
                  & aElement0(sK20(X0,X1)) )
                | aElementOf0(sK19(X0,X1),X1) ) )
            | ~ aSet0(X1) )
          & ( ( ! [X5] :
                  ( ( aElementOf0(X5,X1)
                    | ! [X6] :
                        ( sdtasdt0(X0,X6) != X5
                        | ~ aElement0(X6) ) )
                  & ( ( sdtasdt0(X0,sK21(X0,X5)) = X5
                      & aElement0(sK21(X0,X5)) )
                    | ~ aElementOf0(X5,X1) ) )
              & aSet0(X1) )
            | slsdtgt0(X0) != X1 ) )
      | ~ aElement0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20,sK21])],[f151,f154,f153,f152]) ).

fof(f159,plain,
    ! [X0,X1] :
      ( aElement0(sdtpldt0(X0,X1))
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f57]) ).

fof(f160,plain,
    ! [X0,X1] :
      ( aElement0(sdtasdt0(X0,X1))
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f241,plain,
    ! [X0,X1,X6,X5] :
      ( aElementOf0(X5,X1)
      | sdtasdt0(X0,X6) != X5
      | ~ aElement0(X6)
      | slsdtgt0(X0) != X1
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f155]) ).

fof(f245,plain,
    aElement0(xc),
    inference(cnf_transformation,[],[f38]) ).

fof(f248,plain,
    aElement0(xz),
    inference(cnf_transformation,[],[f39]) ).

fof(f249,plain,
    aElement0(xu),
    inference(cnf_transformation,[],[f40]) ).

fof(f251,plain,
    aElement0(xv),
    inference(cnf_transformation,[],[f41]) ).

fof(f253,plain,
    sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
    inference(cnf_transformation,[],[f42]) ).

fof(f254,plain,
    sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
    inference(cnf_transformation,[],[f43]) ).

fof(f255,plain,
    ( ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
    | ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) ),
    inference(cnf_transformation,[],[f103]) ).

fof(f263,plain,
    ! [X0,X1,X6] :
      ( aElementOf0(sdtasdt0(X0,X6),X1)
      | ~ aElement0(X6)
      | slsdtgt0(X0) != X1
      | ~ aElement0(X0) ),
    inference(equality_resolution,[],[f241]) ).

fof(f264,plain,
    ! [X0,X6] :
      ( aElementOf0(sdtasdt0(X0,X6),slsdtgt0(X0))
      | ~ aElement0(X6)
      | ~ aElement0(X0) ),
    inference(equality_resolution,[],[f263]) ).

cnf(c_52,plain,
    ( ~ aElement0(X0)
    | ~ aElement0(X1)
    | aElement0(sdtpldt0(X0,X1)) ),
    inference(cnf_transformation,[],[f159]) ).

cnf(c_53,plain,
    ( ~ aElement0(X0)
    | ~ aElement0(X1)
    | aElement0(sdtasdt0(X0,X1)) ),
    inference(cnf_transformation,[],[f160]) ).

cnf(c_134,plain,
    ( ~ aElement0(X0)
    | ~ aElement0(X1)
    | aElementOf0(sdtasdt0(X0,X1),slsdtgt0(X0)) ),
    inference(cnf_transformation,[],[f264]) ).

cnf(c_138,plain,
    aElement0(xc),
    inference(cnf_transformation,[],[f245]) ).

cnf(c_139,plain,
    aElement0(xz),
    inference(cnf_transformation,[],[f248]) ).

cnf(c_143,plain,
    aElement0(xu),
    inference(cnf_transformation,[],[f249]) ).

cnf(c_145,plain,
    aElement0(xv),
    inference(cnf_transformation,[],[f251]) ).

cnf(c_146,plain,
    sdtasdt0(xc,sdtpldt0(xu,xv)) = sdtpldt0(xx,xy),
    inference(cnf_transformation,[],[f253]) ).

cnf(c_147,plain,
    sdtasdt0(xc,sdtasdt0(xu,xz)) = sdtasdt0(xz,xx),
    inference(cnf_transformation,[],[f254]) ).

cnf(c_148,negated_conjecture,
    ( ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
    | ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ),
    inference(cnf_transformation,[],[f255]) ).

cnf(c_7668,plain,
    ( ~ aElement0(sdtpldt0(xu,xv))
    | ~ aElement0(xc)
    | aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) ),
    inference(superposition,[status(thm)],[c_146,c_134]) ).

cnf(c_7669,plain,
    ( ~ aElement0(sdtasdt0(xu,xz))
    | ~ aElement0(xc)
    | aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ),
    inference(superposition,[status(thm)],[c_147,c_134]) ).

cnf(c_7741,plain,
    ( ~ aElement0(sdtasdt0(xu,xz))
    | aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ),
    inference(global_subsumption_just,[status(thm)],[c_7669,c_138,c_7669]) ).

cnf(c_7745,plain,
    ( ~ aElement0(sdtpldt0(xu,xv))
    | aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) ),
    inference(global_subsumption_just,[status(thm)],[c_7668,c_138,c_7668]) ).

cnf(c_8285,plain,
    ( ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
    | ~ aElement0(sdtasdt0(xu,xz)) ),
    inference(superposition,[status(thm)],[c_7741,c_148]) ).

cnf(c_8296,plain,
    ( ~ aElement0(sdtpldt0(xu,xv))
    | ~ aElement0(sdtasdt0(xu,xz)) ),
    inference(superposition,[status(thm)],[c_7745,c_8285]) ).

cnf(c_8303,plain,
    ( ~ aElement0(sdtasdt0(xu,xz))
    | ~ aElement0(xu)
    | ~ aElement0(xv) ),
    inference(superposition,[status(thm)],[c_52,c_8296]) ).

cnf(c_8304,plain,
    ~ aElement0(sdtasdt0(xu,xz)),
    inference(global_subsumption_just,[status(thm)],[c_8303,c_145,c_143,c_8303]) ).

cnf(c_8306,plain,
    ( ~ aElement0(xz)
    | ~ aElement0(xu) ),
    inference(superposition,[status(thm)],[c_53,c_8304]) ).

cnf(c_8307,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_8306,c_139,c_143]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : RNG105+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n023.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sun Aug 27 02:44:41 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.19/0.48  Running first-order theorem proving
% 0.19/0.48  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.89/1.66  % SZS status Started for theBenchmark.p
% 7.89/1.66  % SZS status Theorem for theBenchmark.p
% 7.89/1.66  
% 7.89/1.66  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 7.89/1.66  
% 7.89/1.66  ------  iProver source info
% 7.89/1.66  
% 7.89/1.66  git: date: 2023-05-31 18:12:56 +0000
% 7.89/1.66  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 7.89/1.66  git: non_committed_changes: false
% 7.89/1.66  git: last_make_outside_of_git: false
% 7.89/1.66  
% 7.89/1.66  ------ Parsing...
% 7.89/1.66  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 7.89/1.66  
% 7.89/1.66  ------ 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: 2 0s  sf_e  pe_s  pe_e 
% 7.89/1.66  
% 7.89/1.66  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 7.89/1.66  
% 7.89/1.66  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 7.89/1.66  ------ Proving...
% 7.89/1.66  ------ Problem Properties 
% 7.89/1.66  
% 7.89/1.66  
% 7.89/1.66  clauses                                 95
% 7.89/1.66  conjectures                             1
% 7.89/1.66  EPR                                     16
% 7.89/1.66  Horn                                    72
% 7.89/1.66  unary                                   13
% 7.89/1.66  binary                                  15
% 7.89/1.66  lits                                    331
% 7.89/1.66  lits eq                                 46
% 7.89/1.66  fd_pure                                 0
% 7.89/1.66  fd_pseudo                               0
% 7.89/1.66  fd_cond                                 3
% 7.89/1.66  fd_pseudo_cond                          11
% 7.89/1.66  AC symbols                              0
% 7.89/1.66  
% 7.89/1.66  ------ Input Options Time Limit: Unbounded
% 7.89/1.66  
% 7.89/1.66  
% 7.89/1.66  ------ 
% 7.89/1.66  Current options:
% 7.89/1.66  ------ 
% 7.89/1.66  
% 7.89/1.66  
% 7.89/1.66  
% 7.89/1.66  
% 7.89/1.66  ------ Proving...
% 7.89/1.66  
% 7.89/1.66  
% 7.89/1.66  % SZS status Theorem for theBenchmark.p
% 7.89/1.66  
% 7.89/1.66  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.89/1.66  
% 7.89/1.67  
%------------------------------------------------------------------------------