TSTP Solution File: NUM337+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : NUM337+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n020.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 02:48:42 EDT 2024

% Result   : Theorem 107.32s 15.20s
% Output   : CNFRefutation 107.32s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   57 (  21 unt;   0 def)
%            Number of atoms       :  145 (  19 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  158 (  70   ~;  63   |;  15   &)
%                                         (   1 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-4 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-1 aty)
%            Number of variables   :  118 (   0 sgn  86   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    rdn_translate(n2,rdn_pos(rdnn(n2))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn2) ).

fof(f4,axiom,
    rdn_translate(n3,rdn_pos(rdnn(n3))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn3) ).

fof(f6,axiom,
    rdn_translate(n5,rdn_pos(rdnn(n5))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn5) ).

fof(f287,axiom,
    ! [X0,X1,X2,X9,X10,X11] :
      ( ( rdn_translate(X2,rdn_pos(X11))
        & rdn_add_with_carry(rdnn(n0),X9,X10,X11)
        & rdn_translate(X1,rdn_pos(X10))
        & rdn_translate(X0,rdn_pos(X9)) )
     => sum(X0,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_entry_point_pos_pos) ).

fof(f294,axiom,
    ! [X16,X17,X1,X2] :
      ( ( sum(X17,X1,X2)
        & sum(X16,X1,X2) )
     => X16 = X17 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_LHS) ).

fof(f296,axiom,
    ! [X0,X1,X2] :
      ( sum(X1,X2,X0)
    <=> difference(X0,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',minus_entry_point) ).

fof(f297,axiom,
    ! [X20,X21,X22,X23,X24] :
      ( ( rdn_digit_add(rdnn(X24),rdnn(X20),rdnn(X23),rdnn(n0))
        & rdn_digit_add(rdnn(X21),rdnn(X22),rdnn(X24),rdnn(n0)) )
     => rdn_add_with_carry(rdnn(X20),rdnn(X21),rdnn(X22),rdnn(X23)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_digit_digit_digit) ).

fof(f334,axiom,
    rdn_digit_add(rdnn(n3),rdnn(n2),rdnn(n5),rdnn(n0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n3_n2_n5_n0) ).

fof(f352,axiom,
    rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n5_n0_n5_n0) ).

fof(f402,conjecture,
    ! [X0] :
      ( difference(n5,X0,n2)
     => n3 = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',diff_n5_only_n3_n2) ).

fof(f403,negated_conjecture,
    ~ ! [X0] :
        ( difference(n5,X0,n2)
       => n3 = X0 ),
    inference(negated_conjecture,[],[f402]) ).

fof(f411,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ( rdn_translate(X2,rdn_pos(X5))
        & rdn_add_with_carry(rdnn(n0),X3,X4,X5)
        & rdn_translate(X1,rdn_pos(X4))
        & rdn_translate(X0,rdn_pos(X3)) )
     => sum(X0,X1,X2) ),
    inference(rectify,[],[f287]) ).

fof(f418,plain,
    ! [X0,X1,X2,X3] :
      ( ( sum(X1,X2,X3)
        & sum(X0,X2,X3) )
     => X0 = X1 ),
    inference(rectify,[],[f294]) ).

fof(f420,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
        & rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0)) )
     => rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3)) ),
    inference(rectify,[],[f297]) ).

fof(f444,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( sum(X0,X1,X2)
      | ~ rdn_translate(X2,rdn_pos(X5))
      | ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
      | ~ rdn_translate(X1,rdn_pos(X4))
      | ~ rdn_translate(X0,rdn_pos(X3)) ),
    inference(ennf_transformation,[],[f411]) ).

fof(f445,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( sum(X0,X1,X2)
      | ~ rdn_translate(X2,rdn_pos(X5))
      | ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
      | ~ rdn_translate(X1,rdn_pos(X4))
      | ~ rdn_translate(X0,rdn_pos(X3)) ),
    inference(flattening,[],[f444]) ).

fof(f458,plain,
    ! [X0,X1,X2,X3] :
      ( X0 = X1
      | ~ sum(X1,X2,X3)
      | ~ sum(X0,X2,X3) ),
    inference(ennf_transformation,[],[f418]) ).

fof(f459,plain,
    ! [X0,X1,X2,X3] :
      ( X0 = X1
      | ~ sum(X1,X2,X3)
      | ~ sum(X0,X2,X3) ),
    inference(flattening,[],[f458]) ).

fof(f462,plain,
    ! [X0,X1,X2,X3,X4] :
      ( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3))
      | ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
      | ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0)) ),
    inference(ennf_transformation,[],[f420]) ).

fof(f463,plain,
    ! [X0,X1,X2,X3,X4] :
      ( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3))
      | ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
      | ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0)) ),
    inference(flattening,[],[f462]) ).

fof(f471,plain,
    ? [X0] :
      ( n3 != X0
      & difference(n5,X0,n2) ),
    inference(ennf_transformation,[],[f403]) ).

fof(f474,plain,
    ! [X0,X1,X2] :
      ( ( sum(X1,X2,X0)
        | ~ difference(X0,X1,X2) )
      & ( difference(X0,X1,X2)
        | ~ sum(X1,X2,X0) ) ),
    inference(nnf_transformation,[],[f296]) ).

fof(f475,plain,
    ( ? [X0] :
        ( n3 != X0
        & difference(n5,X0,n2) )
   => ( n3 != sK0
      & difference(n5,sK0,n2) ) ),
    introduced(choice_axiom,[]) ).

fof(f476,plain,
    ( n3 != sK0
    & difference(n5,sK0,n2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f471,f475]) ).

fof(f479,plain,
    rdn_translate(n2,rdn_pos(rdnn(n2))),
    inference(cnf_transformation,[],[f3]) ).

fof(f480,plain,
    rdn_translate(n3,rdn_pos(rdnn(n3))),
    inference(cnf_transformation,[],[f4]) ).

fof(f482,plain,
    rdn_translate(n5,rdn_pos(rdnn(n5))),
    inference(cnf_transformation,[],[f6]) ).

fof(f765,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( sum(X0,X1,X2)
      | ~ rdn_translate(X2,rdn_pos(X5))
      | ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
      | ~ rdn_translate(X1,rdn_pos(X4))
      | ~ rdn_translate(X0,rdn_pos(X3)) ),
    inference(cnf_transformation,[],[f445]) ).

fof(f772,plain,
    ! [X2,X3,X0,X1] :
      ( X0 = X1
      | ~ sum(X1,X2,X3)
      | ~ sum(X0,X2,X3) ),
    inference(cnf_transformation,[],[f459]) ).

fof(f775,plain,
    ! [X2,X0,X1] :
      ( sum(X1,X2,X0)
      | ~ difference(X0,X1,X2) ),
    inference(cnf_transformation,[],[f474]) ).

fof(f776,plain,
    ! [X2,X3,X0,X1,X4] :
      ( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3))
      | ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
      | ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0)) ),
    inference(cnf_transformation,[],[f463]) ).

fof(f813,plain,
    rdn_digit_add(rdnn(n3),rdnn(n2),rdnn(n5),rdnn(n0)),
    inference(cnf_transformation,[],[f334]) ).

fof(f831,plain,
    rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
    inference(cnf_transformation,[],[f352]) ).

fof(f881,plain,
    difference(n5,sK0,n2),
    inference(cnf_transformation,[],[f476]) ).

fof(f882,plain,
    n3 != sK0,
    inference(cnf_transformation,[],[f476]) ).

cnf(c_51,plain,
    rdn_translate(n2,rdn_pos(rdnn(n2))),
    inference(cnf_transformation,[],[f479]) ).

cnf(c_52,plain,
    rdn_translate(n3,rdn_pos(rdnn(n3))),
    inference(cnf_transformation,[],[f480]) ).

cnf(c_54,plain,
    rdn_translate(n5,rdn_pos(rdnn(n5))),
    inference(cnf_transformation,[],[f482]) ).

cnf(c_337,plain,
    ( ~ rdn_add_with_carry(rdnn(n0),X0,X1,X2)
    | ~ rdn_translate(X3,rdn_pos(X0))
    | ~ rdn_translate(X4,rdn_pos(X2))
    | ~ rdn_translate(X5,rdn_pos(X1))
    | sum(X3,X5,X4) ),
    inference(cnf_transformation,[],[f765]) ).

cnf(c_344,plain,
    ( ~ sum(X0,X1,X2)
    | ~ sum(X3,X1,X2)
    | X0 = X3 ),
    inference(cnf_transformation,[],[f772]) ).

cnf(c_346,plain,
    ( ~ difference(X0,X1,X2)
    | sum(X1,X2,X0) ),
    inference(cnf_transformation,[],[f775]) ).

cnf(c_348,plain,
    ( ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0))
    | ~ rdn_digit_add(rdnn(X2),rdnn(X3),rdnn(X4),rdnn(n0))
    | rdn_add_with_carry(rdnn(X3),rdnn(X0),rdnn(X1),rdnn(X4)) ),
    inference(cnf_transformation,[],[f776]) ).

cnf(c_385,plain,
    rdn_digit_add(rdnn(n3),rdnn(n2),rdnn(n5),rdnn(n0)),
    inference(cnf_transformation,[],[f813]) ).

cnf(c_403,plain,
    rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
    inference(cnf_transformation,[],[f831]) ).

cnf(c_453,negated_conjecture,
    n3 != sK0,
    inference(cnf_transformation,[],[f882]) ).

cnf(c_454,negated_conjecture,
    difference(n5,sK0,n2),
    inference(cnf_transformation,[],[f881]) ).

cnf(c_1452,plain,
    ( X0 != n5
    | X1 != sK0
    | X2 != n2
    | sum(X1,X2,X0) ),
    inference(resolution_lifted,[status(thm)],[c_346,c_454]) ).

cnf(c_1453,plain,
    sum(sK0,n2,n5),
    inference(unflattening,[status(thm)],[c_1452]) ).

cnf(c_5144,plain,
    ( ~ sum(X0,n2,n5)
    | ~ sum(sK0,n2,n5)
    | X0 = sK0 ),
    inference(instantiation,[status(thm)],[c_344]) ).

cnf(c_5186,plain,
    ( ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n5),rdnn(n0))
    | ~ rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0))
    | rdn_add_with_carry(rdnn(n0),rdnn(X0),rdnn(X1),rdnn(n5)) ),
    inference(instantiation,[status(thm)],[c_348]) ).

cnf(c_7208,plain,
    ( ~ rdn_digit_add(rdnn(n3),rdnn(n2),rdnn(n5),rdnn(n0))
    | ~ rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0))
    | rdn_add_with_carry(rdnn(n0),rdnn(n3),rdnn(n2),rdnn(n5)) ),
    inference(instantiation,[status(thm)],[c_5186]) ).

cnf(c_13948,plain,
    ( ~ sum(n3,n2,n5)
    | ~ sum(sK0,n2,n5)
    | n3 = sK0 ),
    inference(instantiation,[status(thm)],[c_5144]) ).

cnf(c_62761,plain,
    ( ~ rdn_add_with_carry(rdnn(n0),rdnn(n3),rdnn(n2),rdnn(n5))
    | ~ rdn_translate(X0,rdn_pos(rdnn(n3)))
    | ~ rdn_translate(X1,rdn_pos(rdnn(n5)))
    | ~ rdn_translate(X2,rdn_pos(rdnn(n2)))
    | sum(X0,X2,X1) ),
    inference(instantiation,[status(thm)],[c_337]) ).

cnf(c_72984,plain,
    ( ~ rdn_add_with_carry(rdnn(n0),rdnn(n3),rdnn(n2),rdnn(n5))
    | ~ rdn_translate(X0,rdn_pos(rdnn(n3)))
    | ~ rdn_translate(X1,rdn_pos(rdnn(n5)))
    | ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
    | sum(X0,n2,X1) ),
    inference(instantiation,[status(thm)],[c_62761]) ).

cnf(c_92175,plain,
    ( ~ rdn_add_with_carry(rdnn(n0),rdnn(n3),rdnn(n2),rdnn(n5))
    | ~ rdn_translate(X0,rdn_pos(rdnn(n3)))
    | ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
    | ~ rdn_translate(n5,rdn_pos(rdnn(n5)))
    | sum(X0,n2,n5) ),
    inference(instantiation,[status(thm)],[c_72984]) ).

cnf(c_131116,plain,
    ( ~ rdn_add_with_carry(rdnn(n0),rdnn(n3),rdnn(n2),rdnn(n5))
    | ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
    | ~ rdn_translate(n3,rdn_pos(rdnn(n3)))
    | ~ rdn_translate(n5,rdn_pos(rdnn(n5)))
    | sum(n3,n2,n5) ),
    inference(instantiation,[status(thm)],[c_92175]) ).

cnf(c_131117,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_131116,c_13948,c_7208,c_1453,c_385,c_403,c_51,c_52,c_54,c_453]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem  : NUM337+1 : TPTP v8.1.2. Released v3.1.0.
% 0.05/0.11  % Command  : run_iprover %s %d THM
% 0.11/0.31  % Computer : n020.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Thu May  2 19:45:16 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.17/0.42  Running first-order theorem proving
% 0.17/0.42  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
% 107.32/15.20  % SZS status Started for theBenchmark.p
% 107.32/15.20  % SZS status Theorem for theBenchmark.p
% 107.32/15.20  
% 107.32/15.20  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 107.32/15.20  
% 107.32/15.20  ------  iProver source info
% 107.32/15.20  
% 107.32/15.20  git: date: 2024-05-02 19:28:25 +0000
% 107.32/15.20  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 107.32/15.20  git: non_committed_changes: false
% 107.32/15.20  
% 107.32/15.20  ------ Parsing...
% 107.32/15.20  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 107.32/15.20  
% 107.32/15.20  ------ 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: 2 0s  sf_e  pe_s  pe_e 
% 107.32/15.20  
% 107.32/15.20  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 107.32/15.20  
% 107.32/15.20  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 107.32/15.20  ------ Proving...
% 107.32/15.20  ------ Problem Properties 
% 107.32/15.20  
% 107.32/15.20  
% 107.32/15.20  clauses                                 403
% 107.32/15.20  conjectures                             1
% 107.32/15.20  EPR                                     9
% 107.32/15.20  Horn                                    401
% 107.32/15.20  unary                                   377
% 107.32/15.20  binary                                  6
% 107.32/15.20  lits                                    473
% 107.32/15.20  lits eq                                 6
% 107.32/15.20  fd_pure                                 0
% 107.32/15.20  fd_pseudo                               0
% 107.32/15.20  fd_cond                                 0
% 107.32/15.20  fd_pseudo_cond                          5
% 107.32/15.20  AC symbols                              0
% 107.32/15.20  
% 107.32/15.20  ------ Input Options Time Limit: Unbounded
% 107.32/15.20  
% 107.32/15.20  
% 107.32/15.20  ------ 
% 107.32/15.20  Current options:
% 107.32/15.20  ------ 
% 107.32/15.20  
% 107.32/15.20  
% 107.32/15.20  
% 107.32/15.20  
% 107.32/15.20  ------ Proving...
% 107.32/15.20  
% 107.32/15.20  
% 107.32/15.20  % SZS status Theorem for theBenchmark.p
% 107.32/15.20  
% 107.32/15.20  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 107.32/15.20  
% 107.32/15.20  
%------------------------------------------------------------------------------