TSTP Solution File: RNG109+4 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : RNG109+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n029.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 : Fri May  3 02:57:42 EDT 2024

% Result   : Theorem 3.92s 1.11s
% Output   : CNFRefutation 3.92s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f9,axiom,
    ! [X0] :
      ( aElement0(X0)
     => ( sdtpldt0(sz00,X0) = X0
        & sdtpldt0(X0,sz00) = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).

fof(f39,axiom,
    ( aElement0(xb)
    & aElement0(xa) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).

fof(f40,axiom,
    ( sz00 != xb
    | sz00 != xa ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2110) ).

fof(f43,axiom,
    ( aElementOf0(xb,slsdtgt0(xb))
    & ? [X0] :
        ( xb = sdtasdt0(xb,X0)
        & aElement0(X0) )
    & aElementOf0(sz00,slsdtgt0(xb))
    & ? [X0] :
        ( sz00 = sdtasdt0(xb,X0)
        & aElement0(X0) )
    & aElementOf0(xa,slsdtgt0(xa))
    & ? [X0] :
        ( xa = sdtasdt0(xa,X0)
        & aElement0(X0) )
    & aElementOf0(sz00,slsdtgt0(xa))
    & ? [X0] :
        ( sz00 = sdtasdt0(xa,X0)
        & aElement0(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2203) ).

fof(f44,conjecture,
    ? [X0] :
      ( sz00 != X0
      & ( ! [X1] :
            ( aElementOf0(X1,slsdtgt0(xa))
          <=> ? [X2] :
                ( sdtasdt0(xa,X2) = X1
                & aElement0(X2) ) )
       => ( ! [X1] :
              ( aElementOf0(X1,slsdtgt0(xb))
            <=> ? [X2] :
                  ( sdtasdt0(xb,X2) = X1
                  & aElement0(X2) ) )
         => ( aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
            | ? [X1,X2] :
                ( sdtpldt0(X1,X2) = X0
                & aElementOf0(X2,slsdtgt0(xb))
                & aElementOf0(X1,slsdtgt0(xa)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(f45,negated_conjecture,
    ~ ? [X0] :
        ( sz00 != X0
        & ( ! [X1] :
              ( aElementOf0(X1,slsdtgt0(xa))
            <=> ? [X2] :
                  ( sdtasdt0(xa,X2) = X1
                  & aElement0(X2) ) )
         => ( ! [X1] :
                ( aElementOf0(X1,slsdtgt0(xb))
              <=> ? [X2] :
                    ( sdtasdt0(xb,X2) = X1
                    & aElement0(X2) ) )
           => ( aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
              | ? [X1,X2] :
                  ( sdtpldt0(X1,X2) = X0
                  & aElementOf0(X2,slsdtgt0(xb))
                  & aElementOf0(X1,slsdtgt0(xa)) ) ) ) ) ),
    inference(negated_conjecture,[],[f44]) ).

fof(f55,plain,
    ( aElementOf0(xb,slsdtgt0(xb))
    & ? [X0] :
        ( xb = sdtasdt0(xb,X0)
        & aElement0(X0) )
    & aElementOf0(sz00,slsdtgt0(xb))
    & ? [X1] :
        ( sz00 = sdtasdt0(xb,X1)
        & aElement0(X1) )
    & aElementOf0(xa,slsdtgt0(xa))
    & ? [X2] :
        ( xa = sdtasdt0(xa,X2)
        & aElement0(X2) )
    & aElementOf0(sz00,slsdtgt0(xa))
    & ? [X3] :
        ( sz00 = sdtasdt0(xa,X3)
        & aElement0(X3) ) ),
    inference(rectify,[],[f43]) ).

fof(f56,plain,
    ~ ? [X0] :
        ( sz00 != X0
        & ( ! [X1] :
              ( aElementOf0(X1,slsdtgt0(xa))
            <=> ? [X2] :
                  ( sdtasdt0(xa,X2) = X1
                  & aElement0(X2) ) )
         => ( ! [X3] :
                ( aElementOf0(X3,slsdtgt0(xb))
              <=> ? [X4] :
                    ( sdtasdt0(xb,X4) = X3
                    & aElement0(X4) ) )
           => ( aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
              | ? [X5,X6] :
                  ( sdtpldt0(X5,X6) = X0
                  & aElementOf0(X6,slsdtgt0(xb))
                  & aElementOf0(X5,slsdtgt0(xa)) ) ) ) ) ),
    inference(rectify,[],[f45]) ).

fof(f68,plain,
    ! [X0] :
      ( ( sdtpldt0(sz00,X0) = X0
        & sdtpldt0(X0,sz00) = X0 )
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f111,plain,
    ! [X0] :
      ( sz00 = X0
      | ( ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
        & ! [X5,X6] :
            ( sdtpldt0(X5,X6) != X0
            | ~ aElementOf0(X6,slsdtgt0(xb))
            | ~ aElementOf0(X5,slsdtgt0(xa)) )
        & ! [X3] :
            ( aElementOf0(X3,slsdtgt0(xb))
          <=> ? [X4] :
                ( sdtasdt0(xb,X4) = X3
                & aElement0(X4) ) )
        & ! [X1] :
            ( aElementOf0(X1,slsdtgt0(xa))
          <=> ? [X2] :
                ( sdtasdt0(xa,X2) = X1
                & aElement0(X2) ) ) ) ),
    inference(ennf_transformation,[],[f56]) ).

fof(f112,plain,
    ! [X0] :
      ( sz00 = X0
      | ( ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
        & ! [X5,X6] :
            ( sdtpldt0(X5,X6) != X0
            | ~ aElementOf0(X6,slsdtgt0(xb))
            | ~ aElementOf0(X5,slsdtgt0(xa)) )
        & ! [X3] :
            ( aElementOf0(X3,slsdtgt0(xb))
          <=> ? [X4] :
                ( sdtasdt0(xb,X4) = X3
                & aElement0(X4) ) )
        & ! [X1] :
            ( aElementOf0(X1,slsdtgt0(xa))
          <=> ? [X2] :
                ( sdtasdt0(xa,X2) = X1
                & aElement0(X2) ) ) ) ),
    inference(flattening,[],[f111]) ).

fof(f182,plain,
    ( ? [X0] :
        ( xb = sdtasdt0(xb,X0)
        & aElement0(X0) )
   => ( xb = sdtasdt0(xb,sK31)
      & aElement0(sK31) ) ),
    introduced(choice_axiom,[]) ).

fof(f183,plain,
    ( ? [X1] :
        ( sz00 = sdtasdt0(xb,X1)
        & aElement0(X1) )
   => ( sz00 = sdtasdt0(xb,sK32)
      & aElement0(sK32) ) ),
    introduced(choice_axiom,[]) ).

fof(f184,plain,
    ( ? [X2] :
        ( xa = sdtasdt0(xa,X2)
        & aElement0(X2) )
   => ( xa = sdtasdt0(xa,sK33)
      & aElement0(sK33) ) ),
    introduced(choice_axiom,[]) ).

fof(f185,plain,
    ( ? [X3] :
        ( sz00 = sdtasdt0(xa,X3)
        & aElement0(X3) )
   => ( sz00 = sdtasdt0(xa,sK34)
      & aElement0(sK34) ) ),
    introduced(choice_axiom,[]) ).

fof(f186,plain,
    ( aElementOf0(xb,slsdtgt0(xb))
    & xb = sdtasdt0(xb,sK31)
    & aElement0(sK31)
    & aElementOf0(sz00,slsdtgt0(xb))
    & sz00 = sdtasdt0(xb,sK32)
    & aElement0(sK32)
    & aElementOf0(xa,slsdtgt0(xa))
    & xa = sdtasdt0(xa,sK33)
    & aElement0(sK33)
    & aElementOf0(sz00,slsdtgt0(xa))
    & sz00 = sdtasdt0(xa,sK34)
    & aElement0(sK34) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK31,sK32,sK33,sK34])],[f55,f185,f184,f183,f182]) ).

fof(f187,plain,
    ! [X0] :
      ( sz00 = X0
      | ( ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
        & ! [X5,X6] :
            ( sdtpldt0(X5,X6) != X0
            | ~ aElementOf0(X6,slsdtgt0(xb))
            | ~ aElementOf0(X5,slsdtgt0(xa)) )
        & ! [X3] :
            ( ( aElementOf0(X3,slsdtgt0(xb))
              | ! [X4] :
                  ( sdtasdt0(xb,X4) != X3
                  | ~ aElement0(X4) ) )
            & ( ? [X4] :
                  ( sdtasdt0(xb,X4) = X3
                  & aElement0(X4) )
              | ~ aElementOf0(X3,slsdtgt0(xb)) ) )
        & ! [X1] :
            ( ( aElementOf0(X1,slsdtgt0(xa))
              | ! [X2] :
                  ( sdtasdt0(xa,X2) != X1
                  | ~ aElement0(X2) ) )
            & ( ? [X2] :
                  ( sdtasdt0(xa,X2) = X1
                  & aElement0(X2) )
              | ~ aElementOf0(X1,slsdtgt0(xa)) ) ) ) ),
    inference(nnf_transformation,[],[f112]) ).

fof(f188,plain,
    ! [X0] :
      ( sz00 = X0
      | ( ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
        & ! [X1,X2] :
            ( sdtpldt0(X1,X2) != X0
            | ~ aElementOf0(X2,slsdtgt0(xb))
            | ~ aElementOf0(X1,slsdtgt0(xa)) )
        & ! [X3] :
            ( ( aElementOf0(X3,slsdtgt0(xb))
              | ! [X4] :
                  ( sdtasdt0(xb,X4) != X3
                  | ~ aElement0(X4) ) )
            & ( ? [X5] :
                  ( sdtasdt0(xb,X5) = X3
                  & aElement0(X5) )
              | ~ aElementOf0(X3,slsdtgt0(xb)) ) )
        & ! [X6] :
            ( ( aElementOf0(X6,slsdtgt0(xa))
              | ! [X7] :
                  ( sdtasdt0(xa,X7) != X6
                  | ~ aElement0(X7) ) )
            & ( ? [X8] :
                  ( sdtasdt0(xa,X8) = X6
                  & aElement0(X8) )
              | ~ aElementOf0(X6,slsdtgt0(xa)) ) ) ) ),
    inference(rectify,[],[f187]) ).

fof(f189,plain,
    ! [X3] :
      ( ? [X5] :
          ( sdtasdt0(xb,X5) = X3
          & aElement0(X5) )
     => ( sdtasdt0(xb,sK35(X3)) = X3
        & aElement0(sK35(X3)) ) ),
    introduced(choice_axiom,[]) ).

fof(f190,plain,
    ! [X6] :
      ( ? [X8] :
          ( sdtasdt0(xa,X8) = X6
          & aElement0(X8) )
     => ( sdtasdt0(xa,sK36(X6)) = X6
        & aElement0(sK36(X6)) ) ),
    introduced(choice_axiom,[]) ).

fof(f191,plain,
    ! [X0] :
      ( sz00 = X0
      | ( ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
        & ! [X1,X2] :
            ( sdtpldt0(X1,X2) != X0
            | ~ aElementOf0(X2,slsdtgt0(xb))
            | ~ aElementOf0(X1,slsdtgt0(xa)) )
        & ! [X3] :
            ( ( aElementOf0(X3,slsdtgt0(xb))
              | ! [X4] :
                  ( sdtasdt0(xb,X4) != X3
                  | ~ aElement0(X4) ) )
            & ( ( sdtasdt0(xb,sK35(X3)) = X3
                & aElement0(sK35(X3)) )
              | ~ aElementOf0(X3,slsdtgt0(xb)) ) )
        & ! [X6] :
            ( ( aElementOf0(X6,slsdtgt0(xa))
              | ! [X7] :
                  ( sdtasdt0(xa,X7) != X6
                  | ~ aElement0(X7) ) )
            & ( ( sdtasdt0(xa,sK36(X6)) = X6
                & aElement0(sK36(X6)) )
              | ~ aElementOf0(X6,slsdtgt0(xa)) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK35,sK36])],[f188,f190,f189]) ).

fof(f199,plain,
    ! [X0] :
      ( sdtpldt0(X0,sz00) = X0
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f200,plain,
    ! [X0] :
      ( sdtpldt0(sz00,X0) = X0
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f282,plain,
    aElement0(xa),
    inference(cnf_transformation,[],[f39]) ).

fof(f283,plain,
    aElement0(xb),
    inference(cnf_transformation,[],[f39]) ).

fof(f284,plain,
    ( sz00 != xb
    | sz00 != xa ),
    inference(cnf_transformation,[],[f40]) ).

fof(f322,plain,
    aElementOf0(sz00,slsdtgt0(xa)),
    inference(cnf_transformation,[],[f186]) ).

fof(f325,plain,
    aElementOf0(xa,slsdtgt0(xa)),
    inference(cnf_transformation,[],[f186]) ).

fof(f328,plain,
    aElementOf0(sz00,slsdtgt0(xb)),
    inference(cnf_transformation,[],[f186]) ).

fof(f331,plain,
    aElementOf0(xb,slsdtgt0(xb)),
    inference(cnf_transformation,[],[f186]) ).

fof(f338,plain,
    ! [X2,X0,X1] :
      ( sz00 = X0
      | sdtpldt0(X1,X2) != X0
      | ~ aElementOf0(X2,slsdtgt0(xb))
      | ~ aElementOf0(X1,slsdtgt0(xa)) ),
    inference(cnf_transformation,[],[f191]) ).

fof(f355,plain,
    ! [X2,X1] :
      ( sz00 = sdtpldt0(X1,X2)
      | ~ aElementOf0(X2,slsdtgt0(xb))
      | ~ aElementOf0(X1,slsdtgt0(xa)) ),
    inference(equality_resolution,[],[f338]) ).

cnf(c_56,plain,
    ( ~ aElement0(X0)
    | sdtpldt0(sz00,X0) = X0 ),
    inference(cnf_transformation,[],[f200]) ).

cnf(c_57,plain,
    ( ~ aElement0(X0)
    | sdtpldt0(X0,sz00) = X0 ),
    inference(cnf_transformation,[],[f199]) ).

cnf(c_139,plain,
    aElement0(xb),
    inference(cnf_transformation,[],[f283]) ).

cnf(c_140,plain,
    aElement0(xa),
    inference(cnf_transformation,[],[f282]) ).

cnf(c_141,plain,
    ( sz00 != xb
    | sz00 != xa ),
    inference(cnf_transformation,[],[f284]) ).

cnf(c_177,plain,
    aElementOf0(xb,slsdtgt0(xb)),
    inference(cnf_transformation,[],[f331]) ).

cnf(c_180,plain,
    aElementOf0(sz00,slsdtgt0(xb)),
    inference(cnf_transformation,[],[f328]) ).

cnf(c_183,plain,
    aElementOf0(xa,slsdtgt0(xa)),
    inference(cnf_transformation,[],[f325]) ).

cnf(c_186,plain,
    aElementOf0(sz00,slsdtgt0(xa)),
    inference(cnf_transformation,[],[f322]) ).

cnf(c_190,negated_conjecture,
    ( ~ aElementOf0(X0,slsdtgt0(xa))
    | ~ aElementOf0(X1,slsdtgt0(xb))
    | sdtpldt0(X0,X1) = sz00 ),
    inference(cnf_transformation,[],[f355]) ).

cnf(c_7062,plain,
    slsdtgt0(xa) = sP5_iProver_def,
    definition ).

cnf(c_7063,plain,
    slsdtgt0(xb) = sP6_iProver_def,
    definition ).

cnf(c_7076,negated_conjecture,
    ( ~ aElementOf0(X0,sP5_iProver_def)
    | ~ aElementOf0(X1,sP6_iProver_def)
    | sdtpldt0(X0,X1) = sz00 ),
    inference(demodulation,[status(thm)],[c_190]) ).

cnf(c_9067,plain,
    aElementOf0(xb,sP6_iProver_def),
    inference(light_normalisation,[status(thm)],[c_177,c_7063]) ).

cnf(c_9074,plain,
    aElementOf0(sz00,sP6_iProver_def),
    inference(light_normalisation,[status(thm)],[c_180,c_7063]) ).

cnf(c_9081,plain,
    aElementOf0(xa,sP5_iProver_def),
    inference(light_normalisation,[status(thm)],[c_183,c_7062]) ).

cnf(c_9082,plain,
    ( ~ aElementOf0(X0,sP6_iProver_def)
    | sdtpldt0(xa,X0) = sz00 ),
    inference(superposition,[status(thm)],[c_9081,c_7076]) ).

cnf(c_9219,plain,
    aElementOf0(sz00,sP5_iProver_def),
    inference(light_normalisation,[status(thm)],[c_186,c_7062]) ).

cnf(c_9220,plain,
    ( ~ aElementOf0(X0,sP6_iProver_def)
    | sdtpldt0(sz00,X0) = sz00 ),
    inference(superposition,[status(thm)],[c_9219,c_7076]) ).

cnf(c_9273,plain,
    sdtpldt0(xa,sz00) = sz00,
    inference(superposition,[status(thm)],[c_9074,c_9082]) ).

cnf(c_9280,plain,
    sdtpldt0(sz00,xb) = sz00,
    inference(superposition,[status(thm)],[c_9067,c_9220]) ).

cnf(c_9799,plain,
    sdtpldt0(sz00,xb) = xb,
    inference(superposition,[status(thm)],[c_139,c_56]) ).

cnf(c_9817,plain,
    sz00 = xb,
    inference(light_normalisation,[status(thm)],[c_9799,c_9280]) ).

cnf(c_9867,plain,
    sdtpldt0(xa,sz00) = xa,
    inference(superposition,[status(thm)],[c_140,c_57]) ).

cnf(c_9882,plain,
    sz00 = xa,
    inference(light_normalisation,[status(thm)],[c_9867,c_9273]) ).

cnf(c_9934,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_9882,c_9817,c_141]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem  : RNG109+4 : TPTP v8.1.2. Released v4.0.0.
% 0.05/0.11  % Command  : run_iprover %s %d THM
% 0.11/0.32  % Computer : n029.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Thu May  2 21:41:22 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.16/0.43  Running first-order theorem proving
% 0.16/0.43  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.92/1.11  % SZS status Started for theBenchmark.p
% 3.92/1.11  % SZS status Theorem for theBenchmark.p
% 3.92/1.11  
% 3.92/1.11  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.92/1.11  
% 3.92/1.11  ------  iProver source info
% 3.92/1.11  
% 3.92/1.11  git: date: 2024-05-02 19:28:25 +0000
% 3.92/1.11  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.92/1.11  git: non_committed_changes: false
% 3.92/1.11  
% 3.92/1.11  ------ Parsing...
% 3.92/1.11  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.92/1.11  
% 3.92/1.11  ------ Preprocessing... sup_sim: 1  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 
% 3.92/1.11  
% 3.92/1.11  ------ Preprocessing... gs_s  sp: 8 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.92/1.11  
% 3.92/1.11  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.92/1.11  ------ Proving...
% 3.92/1.11  ------ Problem Properties 
% 3.92/1.11  
% 3.92/1.11  
% 3.92/1.11  clauses                                 147
% 3.92/1.11  conjectures                             10
% 3.92/1.11  EPR                                     40
% 3.92/1.11  Horn                                    117
% 3.92/1.11  unary                                   32
% 3.92/1.11  binary                                  34
% 3.92/1.11  lits                                    431
% 3.92/1.11  lits eq                                 64
% 3.92/1.11  fd_pure                                 0
% 3.92/1.11  fd_pseudo                               0
% 3.92/1.11  fd_cond                                 5
% 3.92/1.11  fd_pseudo_cond                          11
% 3.92/1.11  AC symbols                              0
% 3.92/1.11  
% 3.92/1.11  ------ Schedule dynamic 5 is on 
% 3.92/1.11  
% 3.92/1.11  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.92/1.11  
% 3.92/1.11  
% 3.92/1.11  ------ 
% 3.92/1.11  Current options:
% 3.92/1.11  ------ 
% 3.92/1.11  
% 3.92/1.11  
% 3.92/1.11  
% 3.92/1.11  
% 3.92/1.11  ------ Proving...
% 3.92/1.11  
% 3.92/1.11  
% 3.92/1.11  % SZS status Theorem for theBenchmark.p
% 3.92/1.11  
% 3.92/1.11  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.92/1.11  
% 3.92/1.12  
%------------------------------------------------------------------------------