TSTP Solution File: ALG069+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : ALG069+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n014.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 3.76s 1.17s
% Output   : CNFRefutation 3.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   55 (  10 unt;   0 def)
%            Number of atoms       :  187 (  56 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  209 (  77   ~;  64   |;  37   &)
%                                         (   0 <=>;  31  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-2 aty)
%            Number of variables   :   93 (   0 sgn  66   !;   6   ?)

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

fof(f4,axiom,
    ~ ! [X0] :
        ( sorti2(X0)
       => ? [X1] :
            ( op2(X1,X1) = X0
            & sorti2(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(f10,plain,
    ! [X0] :
      ( ? [X1] :
          ( op1(X1,X1) = X0
          & sorti1(X1) )
      | ~ sorti1(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f11,plain,
    ? [X0] :
      ( ! [X1] :
          ( op2(X1,X1) != X0
          | ~ sorti2(X1) )
      & sorti2(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f12,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(f13,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,[],[f12]) ).

fof(f14,plain,
    ! [X0] :
      ( ? [X1] :
          ( op1(X1,X1) = X0
          & sorti1(X1) )
     => ( op1(sK0(X0),sK0(X0)) = X0
        & sorti1(sK0(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f15,plain,
    ! [X0] :
      ( ( op1(sK0(X0),sK0(X0)) = X0
        & sorti1(sK0(X0)) )
      | ~ sorti1(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f10,f14]) ).

fof(f16,plain,
    ( ? [X0] :
        ( ! [X1] :
            ( op2(X1,X1) != X0
            | ~ sorti2(X1) )
        & sorti2(X0) )
   => ( ! [X1] :
          ( op2(X1,X1) != sK1
          | ~ sorti2(X1) )
      & sorti2(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f17,plain,
    ( ! [X1] :
        ( op2(X1,X1) != sK1
        | ~ sorti2(X1) )
    & sorti2(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f11,f16]) ).

fof(f18,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,[],[f13]) ).

fof(f21,plain,
    ! [X0] :
      ( sorti1(sK0(X0))
      | ~ sorti1(X0) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f22,plain,
    ! [X0] :
      ( op1(sK0(X0),sK0(X0)) = X0
      | ~ sorti1(X0) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f23,plain,
    sorti2(sK1),
    inference(cnf_transformation,[],[f17]) ).

fof(f24,plain,
    ! [X1] :
      ( op2(X1,X1) != sK1
      | ~ sorti2(X1) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f25,plain,
    ! [X7] :
      ( sorti2(h(X7))
      | ~ sorti1(X7) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f26,plain,
    ! [X6] :
      ( sorti1(j(X6))
      | ~ sorti2(X6) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f27,plain,
    ! [X4,X5] :
      ( h(op1(X4,X5)) = op2(h(X4),h(X5))
      | ~ sorti1(X5)
      | ~ sorti1(X4) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f29,plain,
    ! [X1] :
      ( h(j(X1)) = X1
      | ~ sorti2(X1) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f30,plain,
    ! [X0] :
      ( j(h(X0)) = X0
      | ~ sorti1(X0) ),
    inference(cnf_transformation,[],[f18]) ).

cnf(c_51,plain,
    ( ~ sorti1(X0)
    | op1(sK0(X0),sK0(X0)) = X0 ),
    inference(cnf_transformation,[],[f22]) ).

cnf(c_52,plain,
    ( ~ sorti1(X0)
    | sorti1(sK0(X0)) ),
    inference(cnf_transformation,[],[f21]) ).

cnf(c_53,plain,
    ( op2(X0,X0) != sK1
    | ~ sorti2(X0) ),
    inference(cnf_transformation,[],[f24]) ).

cnf(c_54,plain,
    sorti2(sK1),
    inference(cnf_transformation,[],[f23]) ).

cnf(c_55,negated_conjecture,
    ( ~ sorti1(X0)
    | j(h(X0)) = X0 ),
    inference(cnf_transformation,[],[f30]) ).

cnf(c_56,negated_conjecture,
    ( ~ sorti2(X0)
    | h(j(X0)) = X0 ),
    inference(cnf_transformation,[],[f29]) ).

cnf(c_58,negated_conjecture,
    ( ~ sorti1(X0)
    | ~ sorti1(X1)
    | op2(h(X0),h(X1)) = h(op1(X0,X1)) ),
    inference(cnf_transformation,[],[f27]) ).

cnf(c_59,negated_conjecture,
    ( ~ sorti2(X0)
    | sorti1(j(X0)) ),
    inference(cnf_transformation,[],[f26]) ).

cnf(c_60,negated_conjecture,
    ( ~ sorti1(X0)
    | sorti2(h(X0)) ),
    inference(cnf_transformation,[],[f25]) ).

cnf(c_62,plain,
    ( ~ sorti2(sK1)
    | sorti1(j(sK1)) ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_185,negated_conjecture,
    ( ~ sorti1(X0)
    | sorti2(h(X0)) ),
    inference(demodulation,[status(thm)],[c_60]) ).

cnf(c_186,negated_conjecture,
    ( ~ sorti2(X0)
    | sorti1(j(X0)) ),
    inference(demodulation,[status(thm)],[c_59]) ).

cnf(c_187,negated_conjecture,
    ( ~ sorti1(X0)
    | ~ sorti1(X1)
    | op2(h(X0),h(X1)) = h(op1(X0,X1)) ),
    inference(demodulation,[status(thm)],[c_58]) ).

cnf(c_189,negated_conjecture,
    ( ~ sorti2(X0)
    | h(j(X0)) = X0 ),
    inference(demodulation,[status(thm)],[c_56]) ).

cnf(c_190,negated_conjecture,
    ( ~ sorti1(X0)
    | j(h(X0)) = X0 ),
    inference(demodulation,[status(thm)],[c_55]) ).

cnf(c_469,plain,
    h(j(sK1)) = sK1,
    inference(superposition,[status(thm)],[c_54,c_189]) ).

cnf(c_479,plain,
    ( ~ sorti1(X0)
    | j(h(sK0(X0))) = sK0(X0) ),
    inference(superposition,[status(thm)],[c_52,c_190]) ).

cnf(c_556,plain,
    ( ~ sorti2(X0)
    | op1(sK0(j(X0)),sK0(j(X0))) = j(X0) ),
    inference(superposition,[status(thm)],[c_186,c_51]) ).

cnf(c_575,plain,
    ( ~ sorti2(X0)
    | j(h(sK0(j(X0)))) = sK0(j(X0)) ),
    inference(superposition,[status(thm)],[c_186,c_479]) ).

cnf(c_589,plain,
    ( ~ sorti1(j(X0))
    | sorti1(sK0(j(X0))) ),
    inference(instantiation,[status(thm)],[c_52]) ).

cnf(c_590,plain,
    ( ~ sorti1(j(sK1))
    | sorti1(sK0(j(sK1))) ),
    inference(instantiation,[status(thm)],[c_589]) ).

cnf(c_634,plain,
    j(h(sK0(j(sK1)))) = sK0(j(sK1)),
    inference(superposition,[status(thm)],[c_54,c_575]) ).

cnf(c_651,plain,
    ( ~ sorti1(sK0(j(X0)))
    | sorti2(h(sK0(j(X0)))) ),
    inference(instantiation,[status(thm)],[c_185]) ).

cnf(c_652,plain,
    ( ~ sorti1(sK0(j(sK1)))
    | sorti2(h(sK0(j(sK1)))) ),
    inference(instantiation,[status(thm)],[c_651]) ).

cnf(c_676,plain,
    op1(sK0(j(sK1)),sK0(j(sK1))) = j(sK1),
    inference(superposition,[status(thm)],[c_54,c_556]) ).

cnf(c_747,plain,
    ( ~ sorti2(h(sK0(j(sK1))))
    | sorti1(sK0(j(sK1))) ),
    inference(superposition,[status(thm)],[c_634,c_186]) ).

cnf(c_764,plain,
    sorti1(sK0(j(sK1))),
    inference(global_subsumption_just,[status(thm)],[c_747,c_54,c_62,c_590]) ).

cnf(c_766,plain,
    ( ~ sorti1(X0)
    | op2(h(X0),h(sK0(j(sK1)))) = h(op1(X0,sK0(j(sK1)))) ),
    inference(superposition,[status(thm)],[c_764,c_187]) ).

cnf(c_1860,plain,
    op2(h(sK0(j(sK1))),h(sK0(j(sK1)))) = h(op1(sK0(j(sK1)),sK0(j(sK1)))),
    inference(superposition,[status(thm)],[c_764,c_766]) ).

cnf(c_1865,plain,
    op2(h(sK0(j(sK1))),h(sK0(j(sK1)))) = sK1,
    inference(light_normalisation,[status(thm)],[c_1860,c_469,c_676]) ).

cnf(c_2106,plain,
    ~ sorti2(h(sK0(j(sK1)))),
    inference(superposition,[status(thm)],[c_1865,c_53]) ).

cnf(c_2107,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_2106,c_652,c_590,c_62,c_54]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : ALG069+1 : TPTP v8.1.2. Released v2.7.0.
% 0.12/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n014.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu May  2 22:42:17 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  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
% 3.76/1.17  % SZS status Started for theBenchmark.p
% 3.76/1.17  % SZS status Theorem for theBenchmark.p
% 3.76/1.17  
% 3.76/1.17  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.76/1.17  
% 3.76/1.17  ------  iProver source info
% 3.76/1.17  
% 3.76/1.17  git: date: 2024-05-02 19:28:25 +0000
% 3.76/1.17  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.76/1.17  git: non_committed_changes: false
% 3.76/1.17  
% 3.76/1.17  ------ Parsing...
% 3.76/1.17  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.76/1.17  
% 3.76/1.17  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 3.76/1.17  
% 3.76/1.17  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.76/1.17  
% 3.76/1.17  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.76/1.17  ------ Proving...
% 3.76/1.17  ------ Problem Properties 
% 3.76/1.17  
% 3.76/1.17  
% 3.76/1.17  clauses                                 12
% 3.76/1.17  conjectures                             6
% 3.76/1.17  EPR                                     1
% 3.76/1.17  Horn                                    12
% 3.76/1.17  unary                                   1
% 3.76/1.17  binary                                  7
% 3.76/1.17  lits                                    27
% 3.76/1.17  lits eq                                 6
% 3.76/1.17  fd_pure                                 0
% 3.76/1.17  fd_pseudo                               0
% 3.76/1.17  fd_cond                                 0
% 3.76/1.17  fd_pseudo_cond                          0
% 3.76/1.17  AC symbols                              0
% 3.76/1.17  
% 3.76/1.17  ------ Schedule dynamic 5 is on 
% 3.76/1.17  
% 3.76/1.17  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.76/1.17  
% 3.76/1.17  
% 3.76/1.17  ------ 
% 3.76/1.17  Current options:
% 3.76/1.17  ------ 
% 3.76/1.17  
% 3.76/1.17  
% 3.76/1.17  
% 3.76/1.17  
% 3.76/1.17  ------ Proving...
% 3.76/1.17  
% 3.76/1.17  
% 3.76/1.17  % SZS status Theorem for theBenchmark.p
% 3.76/1.17  
% 3.76/1.17  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.76/1.17  
% 3.76/1.17  
%------------------------------------------------------------------------------