TSTP Solution File: NUM423+1 by iProver---3.9

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%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : NUM423+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n027.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 02:49:13 EDT 2024

% Result   : Theorem 2.13s 1.16s
% Output   : CNFRefutation 2.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   67 (  16 unt;   0 def)
%            Number of atoms       :  250 ( 100 equ)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  311 ( 128   ~; 134   |;  36   &)
%                                         (   5 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   92 (   0 sgn  60   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    aInteger0(sz00),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntZero) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( ( aInteger0(X1)
        & aInteger0(X0) )
     => aInteger0(sdtasdt0(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntMult) ).

fof(f10,axiom,
    ! [X0] :
      ( aInteger0(X0)
     => ( sz00 = sdtpldt0(smndt0(X0),X0)
        & sz00 = sdtpldt0(X0,smndt0(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).

fof(f15,axiom,
    ! [X0] :
      ( aInteger0(X0)
     => ( sz00 = sdtasdt0(sz00,X0)
        & sz00 = sdtasdt0(X0,sz00) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).

fof(f17,axiom,
    ! [X0,X1] :
      ( ( aInteger0(X1)
        & aInteger0(X0) )
     => ( sz00 = sdtasdt0(X0,X1)
       => ( sz00 = X1
          | sz00 = X0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroDiv) ).

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

fof(f20,axiom,
    ( sz00 != xq
    & aInteger0(xq)
    & aInteger0(xa) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__671) ).

fof(f21,conjecture,
    sdteqdtlpzmzozddtrp0(xa,xa,xq),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f22,negated_conjecture,
    ~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
    inference(negated_conjecture,[],[f21]) ).

fof(f24,plain,
    ~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
    inference(flattening,[],[f22]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( aInteger0(sdtasdt0(X0,X1))
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( aInteger0(sdtasdt0(X0,X1))
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(flattening,[],[f28]) ).

fof(f35,plain,
    ! [X0] :
      ( ( sz00 = sdtpldt0(smndt0(X0),X0)
        & sz00 = sdtpldt0(X0,smndt0(X0)) )
      | ~ aInteger0(X0) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f43,plain,
    ! [X0] :
      ( ( sz00 = sdtasdt0(sz00,X0)
        & sz00 = sdtasdt0(X0,sz00) )
      | ~ aInteger0(X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( sz00 = X1
      | sz00 = X0
      | sz00 != sdtasdt0(X0,X1)
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( sz00 = X1
      | sz00 = X0
      | sz00 != sdtasdt0(X0,X1)
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(flattening,[],[f45]) ).

fof(f47,plain,
    ! [X0] :
      ( ! [X1] :
          ( aDivisorOf0(X1,X0)
        <=> ( ? [X2] :
                ( sdtasdt0(X1,X2) = X0
                & aInteger0(X2) )
            & sz00 != X1
            & aInteger0(X1) ) )
      | ~ aInteger0(X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f48,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(f49,plain,
    ! [X0,X1,X2] :
      ( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
      <=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
      | sz00 = X2
      | ~ aInteger0(X2)
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(flattening,[],[f48]) ).

fof(f50,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,[],[f47]) ).

fof(f51,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,[],[f50]) ).

fof(f52,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,[],[f51]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( sdtasdt0(X1,X3) = X0
          & aInteger0(X3) )
     => ( sdtasdt0(X1,sK0(X0,X1)) = X0
        & aInteger0(sK0(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f54,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])],[f52,f53]) ).

fof(f55,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,[],[f49]) ).

fof(f56,plain,
    aInteger0(sz00),
    inference(cnf_transformation,[],[f2]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( aInteger0(sdtasdt0(X0,X1))
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f65,plain,
    ! [X0] :
      ( sz00 = sdtpldt0(X0,smndt0(X0))
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f73,plain,
    ! [X0] :
      ( sz00 = sdtasdt0(X0,sz00)
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( sz00 = X1
      | sz00 = X0
      | sz00 != sdtasdt0(X0,X1)
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f46]) ).

fof(f82,plain,
    ! [X2,X0,X1] :
      ( aDivisorOf0(X1,X0)
      | sdtasdt0(X1,X2) != X0
      | ~ aInteger0(X2)
      | sz00 = X1
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f54]) ).

fof(f84,plain,
    ! [X2,X0,X1] :
      ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
      | ~ aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
      | sz00 = X2
      | ~ aInteger0(X2)
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f85,plain,
    aInteger0(xa),
    inference(cnf_transformation,[],[f20]) ).

fof(f86,plain,
    aInteger0(xq),
    inference(cnf_transformation,[],[f20]) ).

fof(f87,plain,
    sz00 != xq,
    inference(cnf_transformation,[],[f20]) ).

fof(f88,plain,
    ~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
    inference(cnf_transformation,[],[f24]) ).

fof(f89,plain,
    ! [X2,X1] :
      ( aDivisorOf0(X1,sdtasdt0(X1,X2))
      | ~ aInteger0(X2)
      | sz00 = X1
      | ~ aInteger0(X1)
      | ~ aInteger0(sdtasdt0(X1,X2)) ),
    inference(equality_resolution,[],[f82]) ).

cnf(c_49,plain,
    aInteger0(sz00),
    inference(cnf_transformation,[],[f56]) ).

cnf(c_53,plain,
    ( ~ aInteger0(X0)
    | ~ aInteger0(X1)
    | aInteger0(sdtasdt0(X0,X1)) ),
    inference(cnf_transformation,[],[f60]) ).

cnf(c_59,plain,
    ( ~ aInteger0(X0)
    | sdtpldt0(X0,smndt0(X0)) = sz00 ),
    inference(cnf_transformation,[],[f65]) ).

cnf(c_67,plain,
    ( ~ aInteger0(X0)
    | sdtasdt0(X0,sz00) = sz00 ),
    inference(cnf_transformation,[],[f73]) ).

cnf(c_70,plain,
    ( sdtasdt0(X0,X1) != sz00
    | ~ aInteger0(X0)
    | ~ aInteger0(X1)
    | X0 = sz00
    | X1 = sz00 ),
    inference(cnf_transformation,[],[f77]) ).

cnf(c_71,plain,
    ( ~ aInteger0(sdtasdt0(X0,X1))
    | ~ aInteger0(X0)
    | ~ aInteger0(X1)
    | X0 = sz00
    | aDivisorOf0(X0,sdtasdt0(X0,X1)) ),
    inference(cnf_transformation,[],[f89]) ).

cnf(c_76,plain,
    ( ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(X2)))
    | ~ aInteger0(X0)
    | ~ aInteger0(X1)
    | ~ aInteger0(X2)
    | X0 = sz00
    | sdteqdtlpzmzozddtrp0(X1,X2,X0) ),
    inference(cnf_transformation,[],[f84]) ).

cnf(c_78,plain,
    sz00 != xq,
    inference(cnf_transformation,[],[f87]) ).

cnf(c_79,plain,
    aInteger0(xq),
    inference(cnf_transformation,[],[f86]) ).

cnf(c_80,plain,
    aInteger0(xa),
    inference(cnf_transformation,[],[f85]) ).

cnf(c_81,negated_conjecture,
    ~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
    inference(cnf_transformation,[],[f88]) ).

cnf(c_84,plain,
    ( ~ aInteger0(sz00)
    | sdtasdt0(sz00,sz00) = sz00 ),
    inference(instantiation,[status(thm)],[c_67]) ).

cnf(c_97,plain,
    ( sdtasdt0(sz00,sz00) != sz00
    | ~ aInteger0(sz00)
    | sz00 = sz00 ),
    inference(instantiation,[status(thm)],[c_70]) ).

cnf(c_104,plain,
    ( ~ aInteger0(X0)
    | ~ aInteger0(X1)
    | X0 = sz00
    | aDivisorOf0(X0,sdtasdt0(X0,X1)) ),
    inference(global_subsumption_just,[status(thm)],[c_71,c_53,c_71]) ).

cnf(c_456,plain,
    ( X0 != xq
    | X1 != xa
    | X2 != xa
    | ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(X2)))
    | ~ aInteger0(X0)
    | ~ aInteger0(X1)
    | ~ aInteger0(X2)
    | X0 = sz00 ),
    inference(resolution_lifted,[status(thm)],[c_76,c_81]) ).

cnf(c_457,plain,
    ( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
    | ~ aInteger0(xq)
    | ~ aInteger0(xa)
    | xq = sz00 ),
    inference(unflattening,[status(thm)],[c_456]) ).

cnf(c_458,plain,
    ( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
    | xq = sz00 ),
    inference(global_subsumption_just,[status(thm)],[c_457,c_80,c_79,c_457]) ).

cnf(c_508,plain,
    ( sdtpldt0(xa,smndt0(xa)) != sdtasdt0(X0,X1)
    | X0 != xq
    | ~ aInteger0(X0)
    | ~ aInteger0(X1)
    | X0 = sz00
    | sz00 = xq ),
    inference(resolution_lifted,[status(thm)],[c_104,c_458]) ).

cnf(c_509,plain,
    ( sdtpldt0(xa,smndt0(xa)) != sdtasdt0(xq,X0)
    | ~ aInteger0(X0)
    | ~ aInteger0(xq)
    | sz00 = xq
    | xq = sz00 ),
    inference(unflattening,[status(thm)],[c_508]) ).

cnf(c_511,plain,
    ( sdtpldt0(xa,smndt0(xa)) != sdtasdt0(xq,X0)
    | ~ aInteger0(X0)
    | xq = sz00 ),
    inference(global_subsumption_just,[status(thm)],[c_509,c_79,c_78,c_509]) ).

cnf(c_513,plain,
    ( sdtpldt0(xa,smndt0(xa)) != sdtasdt0(xq,sz00)
    | ~ aInteger0(sz00)
    | xq = sz00 ),
    inference(instantiation,[status(thm)],[c_511]) ).

cnf(c_816,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_1256,plain,
    sdtasdt0(xq,sz00) = sz00,
    inference(superposition,[status(thm)],[c_79,c_67]) ).

cnf(c_1347,plain,
    ( sz00 != X0
    | xq != X0
    | sz00 = xq ),
    inference(instantiation,[status(thm)],[c_816]) ).

cnf(c_1348,plain,
    ( sz00 != sz00
    | xq != sz00
    | sz00 = xq ),
    inference(instantiation,[status(thm)],[c_1347]) ).

cnf(c_1349,plain,
    ( sdtpldt0(xa,smndt0(xa)) != X0
    | sdtasdt0(xq,X1) != X0
    | sdtpldt0(xa,smndt0(xa)) = sdtasdt0(xq,X1) ),
    inference(instantiation,[status(thm)],[c_816]) ).

cnf(c_1350,plain,
    ( sdtpldt0(xa,smndt0(xa)) != sz00
    | sdtasdt0(xq,sz00) != sz00
    | sdtpldt0(xa,smndt0(xa)) = sdtasdt0(xq,sz00) ),
    inference(instantiation,[status(thm)],[c_1349]) ).

cnf(c_1385,plain,
    ( ~ aInteger0(xa)
    | sdtpldt0(xa,smndt0(xa)) = sz00 ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_1386,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_1385,c_1350,c_1348,c_1256,c_513,c_97,c_84,c_78,c_49,c_80]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : NUM423+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n027.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 : Thu May  2 19:51:35 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.19/0.47  Running first-order theorem proving
% 0.19/0.47  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.13/1.16  % SZS status Started for theBenchmark.p
% 2.13/1.16  % SZS status Theorem for theBenchmark.p
% 2.13/1.16  
% 2.13/1.16  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 2.13/1.16  
% 2.13/1.16  ------  iProver source info
% 2.13/1.16  
% 2.13/1.16  git: date: 2024-05-02 19:28:25 +0000
% 2.13/1.16  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 2.13/1.16  git: non_committed_changes: false
% 2.13/1.16  
% 2.13/1.16  ------ Parsing...
% 2.13/1.16  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.13/1.16  
% 2.13/1.16  ------ 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 
% 2.13/1.16  
% 2.13/1.16  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.13/1.16  
% 2.13/1.16  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.13/1.16  ------ Proving...
% 2.13/1.16  ------ Problem Properties 
% 2.13/1.16  
% 2.13/1.16  
% 2.13/1.16  clauses                                 28
% 2.13/1.16  conjectures                             0
% 2.13/1.16  EPR                                     5
% 2.13/1.16  Horn                                    25
% 2.13/1.16  unary                                   5
% 2.13/1.16  binary                                  11
% 2.13/1.16  lits                                    71
% 2.13/1.16  lits eq                                 25
% 2.13/1.16  fd_pure                                 0
% 2.13/1.16  fd_pseudo                               0
% 2.13/1.16  fd_cond                                 3
% 2.13/1.16  fd_pseudo_cond                          0
% 2.13/1.16  AC symbols                              0
% 2.13/1.16  
% 2.13/1.16  ------ Schedule dynamic 5 is on 
% 2.13/1.16  
% 2.13/1.16  ------ no conjectures: strip conj schedule 
% 2.13/1.16  
% 2.13/1.16  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.13/1.16  
% 2.13/1.16  
% 2.13/1.16  ------ 
% 2.13/1.16  Current options:
% 2.13/1.16  ------ 
% 2.13/1.16  
% 2.13/1.16  
% 2.13/1.16  
% 2.13/1.16  
% 2.13/1.16  ------ Proving...
% 2.13/1.16  
% 2.13/1.16  
% 2.13/1.16  % SZS status Theorem for theBenchmark.p
% 2.13/1.16  
% 2.13/1.16  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.13/1.16  
% 2.13/1.16  
%------------------------------------------------------------------------------