TSTP Solution File: ALG070+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : ALG070+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n017.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 02:03:33 EDT 2024

% Result   : Theorem 3.32s 1.23s
% Output   : CNFRefutation 3.32s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   59 (  18 unt;   0 def)
%            Number of atoms       :  212 (  75 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  238 (  85   ~;  70   |;  46   &)
%                                         (   0 <=>;  37  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :  103 (   0 sgn  75   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0] :
      ( sorti1(X0)
     => ! [X1] :
          ( sorti1(X1)
         => sorti1(op1(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).

fof(f2,axiom,
    ! [X0] :
      ( sorti2(X0)
     => ! [X1] :
          ( sorti2(X1)
         => sorti2(op2(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).

fof(f3,axiom,
    ! [X0] :
      ( sorti1(X0)
     => ! [X1] :
          ( sorti1(X1)
         => ( op1(X0,X1) = X0
            | op1(X0,X0) != X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).

fof(f4,axiom,
    ~ ! [X0] :
        ( sorti2(X0)
       => ! [X1] :
            ( sorti2(X1)
           => ( op2(X0,X1) = X0
              | op2(X0,X0) != X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).

fof(f5,conjecture,
    ( ( ! [X1] :
          ( sorti2(X1)
         => sorti1(j(X1)) )
      & ! [X0] :
          ( sorti1(X0)
         => sorti2(h(X0)) ) )
   => ~ ( ! [X7] :
            ( sorti1(X7)
           => j(h(X7)) = X7 )
        & ! [X6] :
            ( sorti2(X6)
           => h(j(X6)) = X6 )
        & ! [X4] :
            ( sorti2(X4)
           => ! [X5] :
                ( sorti2(X5)
               => j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
        & ! [X2] :
            ( sorti1(X2)
           => ! [X3] :
                ( sorti1(X3)
               => h(op1(X2,X3)) = op2(h(X2),h(X3)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

fof(f6,negated_conjecture,
    ~ ( ( ! [X1] :
            ( sorti2(X1)
           => sorti1(j(X1)) )
        & ! [X0] :
            ( sorti1(X0)
           => sorti2(h(X0)) ) )
     => ~ ( ! [X7] :
              ( sorti1(X7)
             => j(h(X7)) = X7 )
          & ! [X6] :
              ( sorti2(X6)
             => h(j(X6)) = X6 )
          & ! [X4] :
              ( sorti2(X4)
             => ! [X5] :
                  ( sorti2(X5)
                 => j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
          & ! [X2] :
              ( sorti1(X2)
             => ! [X3] :
                  ( sorti1(X3)
                 => h(op1(X2,X3)) = op2(h(X2),h(X3)) ) ) ) ),
    inference(negated_conjecture,[],[f5]) ).

fof(f7,plain,
    ~ ( ( ! [X0] :
            ( sorti2(X0)
           => sorti1(j(X0)) )
        & ! [X1] :
            ( sorti1(X1)
           => sorti2(h(X1)) ) )
     => ~ ( ! [X2] :
              ( sorti1(X2)
             => j(h(X2)) = X2 )
          & ! [X3] :
              ( sorti2(X3)
             => h(j(X3)) = X3 )
          & ! [X4] :
              ( sorti2(X4)
             => ! [X5] :
                  ( sorti2(X5)
                 => j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
          & ! [X6] :
              ( sorti1(X6)
             => ! [X7] :
                  ( sorti1(X7)
                 => h(op1(X6,X7)) = op2(h(X6),h(X7)) ) ) ) ),
    inference(rectify,[],[f6]) ).

fof(f8,plain,
    ! [X0] :
      ( ! [X1] :
          ( sorti1(op1(X0,X1))
          | ~ sorti1(X1) )
      | ~ sorti1(X0) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f9,plain,
    ! [X0] :
      ( ! [X1] :
          ( sorti2(op2(X0,X1))
          | ~ sorti2(X1) )
      | ~ sorti2(X0) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f10,plain,
    ! [X0] :
      ( ! [X1] :
          ( op1(X0,X1) = X0
          | op1(X0,X0) != X1
          | ~ sorti1(X1) )
      | ~ sorti1(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f11,plain,
    ! [X0] :
      ( ! [X1] :
          ( op1(X0,X1) = X0
          | op1(X0,X0) != X1
          | ~ sorti1(X1) )
      | ~ sorti1(X0) ),
    inference(flattening,[],[f10]) ).

fof(f12,plain,
    ? [X0] :
      ( ? [X1] :
          ( op2(X0,X1) != X0
          & op2(X0,X0) = X1
          & sorti2(X1) )
      & sorti2(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f13,plain,
    ? [X0] :
      ( ? [X1] :
          ( op2(X0,X1) != X0
          & op2(X0,X0) = X1
          & sorti2(X1) )
      & sorti2(X0) ),
    inference(flattening,[],[f12]) ).

fof(f14,plain,
    ( ! [X2] :
        ( j(h(X2)) = X2
        | ~ sorti1(X2) )
    & ! [X3] :
        ( h(j(X3)) = X3
        | ~ sorti2(X3) )
    & ! [X4] :
        ( ! [X5] :
            ( j(op2(X4,X5)) = op1(j(X4),j(X5))
            | ~ sorti2(X5) )
        | ~ sorti2(X4) )
    & ! [X6] :
        ( ! [X7] :
            ( h(op1(X6,X7)) = op2(h(X6),h(X7))
            | ~ sorti1(X7) )
        | ~ sorti1(X6) )
    & ! [X0] :
        ( sorti1(j(X0))
        | ~ sorti2(X0) )
    & ! [X1] :
        ( sorti2(h(X1))
        | ~ sorti1(X1) ) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f15,plain,
    ( ! [X2] :
        ( j(h(X2)) = X2
        | ~ sorti1(X2) )
    & ! [X3] :
        ( h(j(X3)) = X3
        | ~ sorti2(X3) )
    & ! [X4] :
        ( ! [X5] :
            ( j(op2(X4,X5)) = op1(j(X4),j(X5))
            | ~ sorti2(X5) )
        | ~ sorti2(X4) )
    & ! [X6] :
        ( ! [X7] :
            ( h(op1(X6,X7)) = op2(h(X6),h(X7))
            | ~ sorti1(X7) )
        | ~ sorti1(X6) )
    & ! [X0] :
        ( sorti1(j(X0))
        | ~ sorti2(X0) )
    & ! [X1] :
        ( sorti2(h(X1))
        | ~ sorti1(X1) ) ),
    inference(flattening,[],[f14]) ).

fof(f16,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( op2(X0,X1) != X0
            & op2(X0,X0) = X1
            & sorti2(X1) )
        & sorti2(X0) )
   => ( ? [X1] :
          ( sK0 != op2(sK0,X1)
          & op2(sK0,sK0) = X1
          & sorti2(X1) )
      & sorti2(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f17,plain,
    ( ? [X1] :
        ( sK0 != op2(sK0,X1)
        & op2(sK0,sK0) = X1
        & sorti2(X1) )
   => ( sK0 != op2(sK0,sK1)
      & op2(sK0,sK0) = sK1
      & sorti2(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ( sK0 != op2(sK0,sK1)
    & op2(sK0,sK0) = sK1
    & sorti2(sK1)
    & sorti2(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f17,f16]) ).

fof(f19,plain,
    ( ! [X0] :
        ( j(h(X0)) = X0
        | ~ sorti1(X0) )
    & ! [X1] :
        ( h(j(X1)) = X1
        | ~ sorti2(X1) )
    & ! [X2] :
        ( ! [X3] :
            ( j(op2(X2,X3)) = op1(j(X2),j(X3))
            | ~ sorti2(X3) )
        | ~ sorti2(X2) )
    & ! [X4] :
        ( ! [X5] :
            ( h(op1(X4,X5)) = op2(h(X4),h(X5))
            | ~ sorti1(X5) )
        | ~ sorti1(X4) )
    & ! [X6] :
        ( sorti1(j(X6))
        | ~ sorti2(X6) )
    & ! [X7] :
        ( sorti2(h(X7))
        | ~ sorti1(X7) ) ),
    inference(rectify,[],[f15]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( sorti1(op1(X0,X1))
      | ~ sorti1(X1)
      | ~ sorti1(X0) ),
    inference(cnf_transformation,[],[f8]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( sorti2(op2(X0,X1))
      | ~ sorti2(X1)
      | ~ sorti2(X0) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( op1(X0,X1) = X0
      | op1(X0,X0) != X1
      | ~ sorti1(X1)
      | ~ sorti1(X0) ),
    inference(cnf_transformation,[],[f11]) ).

fof(f23,plain,
    sorti2(sK0),
    inference(cnf_transformation,[],[f18]) ).

fof(f24,plain,
    sorti2(sK1),
    inference(cnf_transformation,[],[f18]) ).

fof(f25,plain,
    op2(sK0,sK0) = sK1,
    inference(cnf_transformation,[],[f18]) ).

fof(f26,plain,
    sK0 != op2(sK0,sK1),
    inference(cnf_transformation,[],[f18]) ).

fof(f28,plain,
    ! [X6] :
      ( sorti1(j(X6))
      | ~ sorti2(X6) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f30,plain,
    ! [X2,X3] :
      ( j(op2(X2,X3)) = op1(j(X2),j(X3))
      | ~ sorti2(X3)
      | ~ sorti2(X2) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f31,plain,
    ! [X1] :
      ( h(j(X1)) = X1
      | ~ sorti2(X1) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f33,plain,
    ! [X0] :
      ( op1(X0,op1(X0,X0)) = X0
      | ~ sorti1(op1(X0,X0))
      | ~ sorti1(X0) ),
    inference(equality_resolution,[],[f22]) ).

cnf(c_49,plain,
    ( ~ sorti1(X0)
    | ~ sorti1(X1)
    | sorti1(op1(X0,X1)) ),
    inference(cnf_transformation,[],[f20]) ).

cnf(c_50,plain,
    ( ~ sorti2(X0)
    | ~ sorti2(X1)
    | sorti2(op2(X0,X1)) ),
    inference(cnf_transformation,[],[f21]) ).

cnf(c_51,plain,
    ( ~ sorti1(op1(X0,X0))
    | ~ sorti1(X0)
    | op1(X0,op1(X0,X0)) = X0 ),
    inference(cnf_transformation,[],[f33]) ).

cnf(c_52,plain,
    op2(sK0,sK1) != sK0,
    inference(cnf_transformation,[],[f26]) ).

cnf(c_53,plain,
    op2(sK0,sK0) = sK1,
    inference(cnf_transformation,[],[f25]) ).

cnf(c_54,plain,
    sorti2(sK1),
    inference(cnf_transformation,[],[f24]) ).

cnf(c_55,plain,
    sorti2(sK0),
    inference(cnf_transformation,[],[f23]) ).

cnf(c_57,negated_conjecture,
    ( ~ sorti2(X0)
    | h(j(X0)) = X0 ),
    inference(cnf_transformation,[],[f31]) ).

cnf(c_58,negated_conjecture,
    ( ~ sorti2(X0)
    | ~ sorti2(X1)
    | op1(j(X0),j(X1)) = j(op2(X0,X1)) ),
    inference(cnf_transformation,[],[f30]) ).

cnf(c_60,negated_conjecture,
    ( ~ sorti2(X0)
    | sorti1(j(X0)) ),
    inference(cnf_transformation,[],[f28]) ).

cnf(c_179,negated_conjecture,
    ( ~ sorti2(X0)
    | sorti1(j(X0)) ),
    inference(demodulation,[status(thm)],[c_60]) ).

cnf(c_181,negated_conjecture,
    ( ~ sorti2(X0)
    | ~ sorti2(X1)
    | op1(j(X0),j(X1)) = j(op2(X0,X1)) ),
    inference(demodulation,[status(thm)],[c_58]) ).

cnf(c_182,negated_conjecture,
    ( ~ sorti2(X0)
    | h(j(X0)) = X0 ),
    inference(demodulation,[status(thm)],[c_57]) ).

cnf(c_460,plain,
    ( ~ sorti2(X0)
    | op1(j(X0),j(sK1)) = j(op2(X0,sK1)) ),
    inference(superposition,[status(thm)],[c_54,c_181]) ).

cnf(c_466,plain,
    ( ~ sorti2(X0)
    | op1(j(X0),j(sK0)) = j(op2(X0,sK0)) ),
    inference(superposition,[status(thm)],[c_55,c_181]) ).

cnf(c_468,plain,
    h(j(sK0)) = sK0,
    inference(superposition,[status(thm)],[c_55,c_182]) ).

cnf(c_500,plain,
    op1(j(sK0),j(sK1)) = j(op2(sK0,sK1)),
    inference(superposition,[status(thm)],[c_55,c_460]) ).

cnf(c_510,plain,
    op1(j(sK0),j(sK0)) = j(op2(sK0,sK0)),
    inference(superposition,[status(thm)],[c_55,c_466]) ).

cnf(c_512,plain,
    op1(j(sK0),j(sK0)) = j(sK1),
    inference(light_normalisation,[status(thm)],[c_510,c_53]) ).

cnf(c_628,plain,
    ( ~ sorti2(X0)
    | ~ sorti2(X1)
    | h(j(op2(X0,X1))) = op2(X0,X1) ),
    inference(superposition,[status(thm)],[c_50,c_182]) ).

cnf(c_678,plain,
    ( ~ sorti1(X0)
    | op1(X0,op1(X0,X0)) = X0 ),
    inference(superposition,[status(thm)],[c_49,c_51]) ).

cnf(c_890,plain,
    ( ~ sorti2(X0)
    | h(j(op2(X0,sK1))) = op2(X0,sK1) ),
    inference(superposition,[status(thm)],[c_54,c_628]) ).

cnf(c_1064,plain,
    ( ~ sorti2(X0)
    | op1(j(X0),op1(j(X0),j(X0))) = j(X0) ),
    inference(superposition,[status(thm)],[c_179,c_678]) ).

cnf(c_1104,plain,
    h(j(op2(sK0,sK1))) = op2(sK0,sK1),
    inference(superposition,[status(thm)],[c_55,c_890]) ).

cnf(c_1206,plain,
    op1(j(sK0),op1(j(sK0),j(sK0))) = j(sK0),
    inference(superposition,[status(thm)],[c_55,c_1064]) ).

cnf(c_1210,plain,
    j(op2(sK0,sK1)) = j(sK0),
    inference(light_normalisation,[status(thm)],[c_1206,c_500,c_512]) ).

cnf(c_1217,plain,
    op2(sK0,sK1) = h(j(sK0)),
    inference(demodulation,[status(thm)],[c_1104,c_1210]) ).

cnf(c_1220,plain,
    op2(sK0,sK1) = sK0,
    inference(light_normalisation,[status(thm)],[c_1217,c_468]) ).

cnf(c_1221,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_1220,c_52]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : ALG070+1 : TPTP v8.1.2. Released v2.7.0.
% 0.08/0.15  % Command  : run_iprover %s %d THM
% 0.15/0.36  % Computer : n017.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Thu May  2 22:14:36 EDT 2024
% 0.15/0.37  % CPUTime  : 
% 0.23/0.51  Running first-order theorem proving
% 0.23/0.51  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
% 3.32/1.23  % SZS status Started for theBenchmark.p
% 3.32/1.23  % SZS status Theorem for theBenchmark.p
% 3.32/1.23  
% 3.32/1.23  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.32/1.23  
% 3.32/1.23  ------  iProver source info
% 3.32/1.23  
% 3.32/1.23  git: date: 2024-05-02 19:28:25 +0000
% 3.32/1.23  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.32/1.23  git: non_committed_changes: false
% 3.32/1.23  
% 3.32/1.23  ------ Parsing...
% 3.32/1.23  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.32/1.23  
% 3.32/1.23  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 3.32/1.23  
% 3.32/1.23  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.32/1.23  
% 3.32/1.23  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.32/1.23  ------ Proving...
% 3.32/1.23  ------ Problem Properties 
% 3.32/1.23  
% 3.32/1.23  
% 3.32/1.23  clauses                                 13
% 3.32/1.23  conjectures                             6
% 3.32/1.23  EPR                                     2
% 3.32/1.23  Horn                                    13
% 3.32/1.23  unary                                   4
% 3.32/1.23  binary                                  4
% 3.32/1.23  lits                                    27
% 3.32/1.23  lits eq                                 7
% 3.32/1.23  fd_pure                                 0
% 3.32/1.23  fd_pseudo                               0
% 3.32/1.23  fd_cond                                 0
% 3.32/1.23  fd_pseudo_cond                          0
% 3.32/1.23  AC symbols                              0
% 3.32/1.23  
% 3.32/1.23  ------ Schedule dynamic 5 is on 
% 3.32/1.23  
% 3.32/1.23  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.32/1.23  
% 3.32/1.23  
% 3.32/1.23  ------ 
% 3.32/1.23  Current options:
% 3.32/1.23  ------ 
% 3.32/1.23  
% 3.32/1.23  
% 3.32/1.23  
% 3.32/1.23  
% 3.32/1.23  ------ Proving...
% 3.32/1.23  
% 3.32/1.23  
% 3.32/1.23  % SZS status Theorem for theBenchmark.p
% 3.32/1.23  
% 3.32/1.23  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.32/1.23  
% 3.32/1.23  
%------------------------------------------------------------------------------