TSTP Solution File: NUM425+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : NUM425+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n031.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 11:30:22 EDT 2023

% Result   : Theorem 2.93s 1.16s
% Output   : CNFRefutation 2.93s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   60 (  14 unt;   0 def)
%            Number of atoms       :  211 (  69 equ)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  257 ( 106   ~; 107   |;  34   &)
%                                         (   5 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   83 (   0 sgn;  50   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [X0] :
      ( aInteger0(X0)
     => aInteger0(smndt0(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( ( aInteger0(X1)
        & aInteger0(X0) )
     => aInteger0(sdtpldt0(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntPlus) ).

fof(f18,axiom,
    ! [X0] :
      ( aInteger0(X0)
     => ! [X1] :
          ( aDivisorOf0(X1,X0)
        <=> ( ? [X2] :
                ( sdtasdt0(X1,X2) = X0
                & aInteger0(X2) )
            & sz00 != X1
            & aInteger0(X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivisor) ).

fof(f19,axiom,
    ! [X0,X1,X2] :
      ( ( sz00 != X2
        & aInteger0(X2)
        & aInteger0(X1)
        & aInteger0(X0) )
     => ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
      <=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquMod) ).

fof(f21,axiom,
    ( sz00 != xq
    & aInteger0(xq)
    & aInteger0(xb)
    & aInteger0(xa) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__704) ).

fof(f22,axiom,
    sdteqdtlpzmzozddtrp0(xa,xb,xq),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__724) ).

fof(f23,conjecture,
    ? [X0] :
      ( sdtasdt0(xq,X0) = sdtpldt0(xa,smndt0(xb))
      & aInteger0(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(f24,negated_conjecture,
    ~ ? [X0] :
        ( sdtasdt0(xq,X0) = sdtpldt0(xa,smndt0(xb))
        & aInteger0(X0) ),
    inference(negated_conjecture,[],[f23]) ).

fof(f26,plain,
    ! [X0] :
      ( aInteger0(smndt0(X0))
      | ~ aInteger0(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( aInteger0(sdtpldt0(X0,X1))
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( aInteger0(sdtpldt0(X0,X1))
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(flattening,[],[f27]) ).

fof(f48,plain,
    ! [X0] :
      ( ! [X1] :
          ( aDivisorOf0(X1,X0)
        <=> ( ? [X2] :
                ( sdtasdt0(X1,X2) = X0
                & aInteger0(X2) )
            & sz00 != X1
            & aInteger0(X1) ) )
      | ~ aInteger0(X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f49,plain,
    ! [X0,X1,X2] :
      ( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
      <=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
      | sz00 = X2
      | ~ aInteger0(X2)
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f50,plain,
    ! [X0,X1,X2] :
      ( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
      <=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
      | sz00 = X2
      | ~ aInteger0(X2)
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(flattening,[],[f49]) ).

fof(f53,plain,
    ! [X0] :
      ( sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xb))
      | ~ aInteger0(X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f54,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aDivisorOf0(X1,X0)
            | ! [X2] :
                ( sdtasdt0(X1,X2) != X0
                | ~ aInteger0(X2) )
            | sz00 = X1
            | ~ aInteger0(X1) )
          & ( ( ? [X2] :
                  ( sdtasdt0(X1,X2) = X0
                  & aInteger0(X2) )
              & sz00 != X1
              & aInteger0(X1) )
            | ~ aDivisorOf0(X1,X0) ) )
      | ~ aInteger0(X0) ),
    inference(nnf_transformation,[],[f48]) ).

fof(f55,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aDivisorOf0(X1,X0)
            | ! [X2] :
                ( sdtasdt0(X1,X2) != X0
                | ~ aInteger0(X2) )
            | sz00 = X1
            | ~ aInteger0(X1) )
          & ( ( ? [X2] :
                  ( sdtasdt0(X1,X2) = X0
                  & aInteger0(X2) )
              & sz00 != X1
              & aInteger0(X1) )
            | ~ aDivisorOf0(X1,X0) ) )
      | ~ aInteger0(X0) ),
    inference(flattening,[],[f54]) ).

fof(f56,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aDivisorOf0(X1,X0)
            | ! [X2] :
                ( sdtasdt0(X1,X2) != X0
                | ~ aInteger0(X2) )
            | sz00 = X1
            | ~ aInteger0(X1) )
          & ( ( ? [X3] :
                  ( sdtasdt0(X1,X3) = X0
                  & aInteger0(X3) )
              & sz00 != X1
              & aInteger0(X1) )
            | ~ aDivisorOf0(X1,X0) ) )
      | ~ aInteger0(X0) ),
    inference(rectify,[],[f55]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( sdtasdt0(X1,X3) = X0
          & aInteger0(X3) )
     => ( sdtasdt0(X1,sK0(X0,X1)) = X0
        & aInteger0(sK0(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f58,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aDivisorOf0(X1,X0)
            | ! [X2] :
                ( sdtasdt0(X1,X2) != X0
                | ~ aInteger0(X2) )
            | sz00 = X1
            | ~ aInteger0(X1) )
          & ( ( sdtasdt0(X1,sK0(X0,X1)) = X0
              & aInteger0(sK0(X0,X1))
              & sz00 != X1
              & aInteger0(X1) )
            | ~ aDivisorOf0(X1,X0) ) )
      | ~ aInteger0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f56,f57]) ).

fof(f59,plain,
    ! [X0,X1,X2] :
      ( ( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
          | ~ aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
        & ( aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
          | ~ sdteqdtlpzmzozddtrp0(X0,X1,X2) ) )
      | sz00 = X2
      | ~ aInteger0(X2)
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(nnf_transformation,[],[f50]) ).

fof(f62,plain,
    ! [X0] :
      ( aInteger0(smndt0(X0))
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( aInteger0(sdtpldt0(X0,X1))
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( aInteger0(sK0(X0,X1))
      | ~ aDivisorOf0(X1,X0)
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( sdtasdt0(X1,sK0(X0,X1)) = X0
      | ~ aDivisorOf0(X1,X0)
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f87,plain,
    ! [X2,X0,X1] :
      ( aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
      | ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
      | sz00 = X2
      | ~ aInteger0(X2)
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f90,plain,
    aInteger0(xa),
    inference(cnf_transformation,[],[f21]) ).

fof(f91,plain,
    aInteger0(xb),
    inference(cnf_transformation,[],[f21]) ).

fof(f92,plain,
    aInteger0(xq),
    inference(cnf_transformation,[],[f21]) ).

fof(f93,plain,
    sz00 != xq,
    inference(cnf_transformation,[],[f21]) ).

fof(f94,plain,
    sdteqdtlpzmzozddtrp0(xa,xb,xq),
    inference(cnf_transformation,[],[f22]) ).

fof(f95,plain,
    ! [X0] :
      ( sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xb))
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f53]) ).

cnf(c_51,plain,
    ( ~ aInteger0(X0)
    | aInteger0(smndt0(X0)) ),
    inference(cnf_transformation,[],[f62]) ).

cnf(c_52,plain,
    ( ~ aInteger0(X0)
    | ~ aInteger0(X1)
    | aInteger0(sdtpldt0(X0,X1)) ),
    inference(cnf_transformation,[],[f63]) ).

cnf(c_72,plain,
    ( ~ aDivisorOf0(X0,X1)
    | ~ aInteger0(X1)
    | sdtasdt0(X0,sK0(X1,X0)) = X1 ),
    inference(cnf_transformation,[],[f85]) ).

cnf(c_73,plain,
    ( ~ aDivisorOf0(X0,X1)
    | ~ aInteger0(X1)
    | aInteger0(sK0(X1,X0)) ),
    inference(cnf_transformation,[],[f84]) ).

cnf(c_77,plain,
    ( ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
    | ~ aInteger0(X0)
    | ~ aInteger0(X1)
    | ~ aInteger0(X2)
    | X2 = sz00
    | aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ),
    inference(cnf_transformation,[],[f87]) ).

cnf(c_79,plain,
    sz00 != xq,
    inference(cnf_transformation,[],[f93]) ).

cnf(c_80,plain,
    aInteger0(xq),
    inference(cnf_transformation,[],[f92]) ).

cnf(c_81,plain,
    aInteger0(xb),
    inference(cnf_transformation,[],[f91]) ).

cnf(c_82,plain,
    aInteger0(xa),
    inference(cnf_transformation,[],[f90]) ).

cnf(c_83,plain,
    sdteqdtlpzmzozddtrp0(xa,xb,xq),
    inference(cnf_transformation,[],[f94]) ).

cnf(c_84,negated_conjecture,
    ( sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,X0)
    | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f95]) ).

cnf(c_501,plain,
    ( X0 != xa
    | X1 != xb
    | X2 != xq
    | ~ aInteger0(X0)
    | ~ aInteger0(X1)
    | ~ aInteger0(X2)
    | X2 = sz00
    | aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ),
    inference(resolution_lifted,[status(thm)],[c_77,c_83]) ).

cnf(c_502,plain,
    ( ~ aInteger0(xq)
    | ~ aInteger0(xb)
    | ~ aInteger0(xa)
    | xq = sz00
    | aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb))) ),
    inference(unflattening,[status(thm)],[c_501]) ).

cnf(c_503,plain,
    ( xq = sz00
    | aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb))) ),
    inference(global_subsumption_just,[status(thm)],[c_502,c_82,c_81,c_80,c_502]) ).

cnf(c_597,plain,
    ( sdtpldt0(xa,smndt0(xb)) != X1
    | X0 != xq
    | ~ aInteger0(X1)
    | sz00 = xq
    | aInteger0(sK0(X1,X0)) ),
    inference(resolution_lifted,[status(thm)],[c_73,c_503]) ).

cnf(c_598,plain,
    ( ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
    | sz00 = xq
    | aInteger0(sK0(sdtpldt0(xa,smndt0(xb)),xq)) ),
    inference(unflattening,[status(thm)],[c_597]) ).

cnf(c_607,plain,
    ( sdtpldt0(xa,smndt0(xb)) != X1
    | X0 != xq
    | ~ aInteger0(X1)
    | sdtasdt0(X0,sK0(X1,X0)) = X1
    | sz00 = xq ),
    inference(resolution_lifted,[status(thm)],[c_72,c_503]) ).

cnf(c_608,plain,
    ( ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
    | sdtasdt0(xq,sK0(sdtpldt0(xa,smndt0(xb)),xq)) = sdtpldt0(xa,smndt0(xb))
    | sz00 = xq ),
    inference(unflattening,[status(thm)],[c_607]) ).

cnf(c_1093,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_1095,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_1655,plain,
    ( sdtpldt0(xa,smndt0(xb)) != X0
    | sdtasdt0(xq,X1) != X0
    | sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,X1) ),
    inference(instantiation,[status(thm)],[c_1095]) ).

cnf(c_1689,plain,
    ( sdtpldt0(xa,smndt0(xb)) != sdtpldt0(xa,smndt0(xb))
    | sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xb))
    | sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,X0) ),
    inference(instantiation,[status(thm)],[c_1655]) ).

cnf(c_1690,plain,
    sdtpldt0(xa,smndt0(xb)) = sdtpldt0(xa,smndt0(xb)),
    inference(instantiation,[status(thm)],[c_1093]) ).

cnf(c_1815,plain,
    ( ~ aInteger0(xb)
    | aInteger0(smndt0(xb)) ),
    inference(instantiation,[status(thm)],[c_51]) ).

cnf(c_1852,plain,
    ( ~ aInteger0(smndt0(xb))
    | ~ aInteger0(xa)
    | aInteger0(sdtpldt0(xa,smndt0(xb))) ),
    inference(instantiation,[status(thm)],[c_52]) ).

cnf(c_2567,plain,
    ( sdtasdt0(xq,sK0(sdtpldt0(xa,smndt0(xb)),xq)) != sdtpldt0(xa,smndt0(xb))
    | sdtpldt0(xa,smndt0(xb)) != sdtpldt0(xa,smndt0(xb))
    | sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sK0(sdtpldt0(xa,smndt0(xb)),xq)) ),
    inference(instantiation,[status(thm)],[c_1689]) ).

cnf(c_3928,plain,
    ( sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,sK0(sdtpldt0(xa,smndt0(xb)),xq))
    | ~ aInteger0(sK0(sdtpldt0(xa,smndt0(xb)),xq)) ),
    inference(instantiation,[status(thm)],[c_84]) ).

cnf(c_3929,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_3928,c_2567,c_1852,c_1815,c_1690,c_608,c_598,c_79,c_81,c_82]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM425+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.12/0.34  % Computer : n031.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Fri Aug 25 14:09:22 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.46  Running first-order theorem proving
% 0.19/0.46  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.93/1.16  % SZS status Started for theBenchmark.p
% 2.93/1.16  % SZS status Theorem for theBenchmark.p
% 2.93/1.16  
% 2.93/1.16  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.93/1.16  
% 2.93/1.16  ------  iProver source info
% 2.93/1.16  
% 2.93/1.16  git: date: 2023-05-31 18:12:56 +0000
% 2.93/1.16  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.93/1.16  git: non_committed_changes: false
% 2.93/1.16  git: last_make_outside_of_git: false
% 2.93/1.16  
% 2.93/1.16  ------ Parsing...
% 2.93/1.16  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.93/1.16  
% 2.93/1.16  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e 
% 2.93/1.16  
% 2.93/1.16  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.93/1.16  
% 2.93/1.16  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.93/1.16  ------ Proving...
% 2.93/1.16  ------ Problem Properties 
% 2.93/1.16  
% 2.93/1.16  
% 2.93/1.16  clauses                                 34
% 2.93/1.16  conjectures                             1
% 2.93/1.16  EPR                                     8
% 2.93/1.16  Horn                                    30
% 2.93/1.16  unary                                   6
% 2.93/1.16  binary                                  14
% 2.93/1.16  lits                                    84
% 2.93/1.16  lits eq                                 25
% 2.93/1.16  fd_pure                                 0
% 2.93/1.16  fd_pseudo                               0
% 2.93/1.16  fd_cond                                 3
% 2.93/1.16  fd_pseudo_cond                          0
% 2.93/1.16  AC symbols                              0
% 2.93/1.16  
% 2.93/1.16  ------ Schedule dynamic 5 is on 
% 2.93/1.16  
% 2.93/1.16  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.93/1.16  
% 2.93/1.16  
% 2.93/1.16  ------ 
% 2.93/1.16  Current options:
% 2.93/1.16  ------ 
% 2.93/1.16  
% 2.93/1.16  
% 2.93/1.16  
% 2.93/1.16  
% 2.93/1.16  ------ Proving...
% 2.93/1.16  
% 2.93/1.16  
% 2.93/1.16  % SZS status Theorem for theBenchmark.p
% 2.93/1.16  
% 2.93/1.16  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.93/1.16  
% 2.93/1.16  
%------------------------------------------------------------------------------