TSTP Solution File: SWW198+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SWW198+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n008.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 Sep  1 00:38:28 EDT 2023

% Result   : Theorem 19.48s 3.68s
% Output   : CNFRefutation 19.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   31 (  21 unt;   0 def)
%            Number of atoms       :   47 (  31 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   34 (  18   ~;  10   |;   3   &)
%                                         (   2 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   4 con; 0-3 aty)
%            Number of variables   :   33 (   1 sgn;  23   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o) ).

fof(f49,axiom,
    ! [X2] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    <=> ? [X22] : c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X22)) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__Suc__mult__two__ex) ).

fof(f224,axiom,
    ! [X7] : c_Int_OBit0(X7) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,X7),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__def) ).

fof(f736,axiom,
    ! [X12] : c_Nat_OSuc(X12) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).

fof(f741,axiom,
    ! [X7] : c_Int_OBit1(X7) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X7),X7),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit1__def) ).

fof(f1186,conjecture,
    ? [X22] : v_na____ = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

fof(f1187,negated_conjecture,
    ~ ? [X22] : v_na____ = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X22)),
    inference(negated_conjecture,[],[f1186]) ).

fof(f1224,plain,
    ! [X0] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0)
    <=> ? [X1] : c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)) = X0 ),
    inference(rectify,[],[f49]) ).

fof(f1376,plain,
    ! [X0] : c_Int_OBit0(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
    inference(rectify,[],[f224]) ).

fof(f1836,plain,
    ! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
    inference(rectify,[],[f736]) ).

fof(f1839,plain,
    ! [X0] : c_Int_OBit1(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),
    inference(rectify,[],[f741]) ).

fof(f2078,plain,
    ~ ? [X0] : v_na____ = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0)),
    inference(rectify,[],[f1187]) ).

fof(f3087,plain,
    ! [X0] : v_na____ != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0)),
    inference(ennf_transformation,[],[f2078]) ).

fof(f3131,plain,
    ! [X0] :
      ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0)
        | ! [X1] : c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)) != X0 )
      & ( ? [X1] : c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)) = X0
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0) ) ),
    inference(nnf_transformation,[],[f1224]) ).

fof(f3132,plain,
    ! [X0] :
      ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0)
        | ! [X1] : c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)) != X0 )
      & ( ? [X2] : c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = X0
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0) ) ),
    inference(rectify,[],[f3131]) ).

fof(f3133,plain,
    ! [X0] :
      ( ? [X2] : c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = X0
     => c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),sK14(X0))) = X0 ),
    introduced(choice_axiom,[]) ).

fof(f3134,plain,
    ! [X0] :
      ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0)
        | ! [X1] : c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)) != X0 )
      & ( c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),sK14(X0))) = X0
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f3132,f3133]) ).

fof(f3566,plain,
    ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
    inference(cnf_transformation,[],[f1]) ).

fof(f3630,plain,
    ! [X0] :
      ( c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),sK14(X0))) = X0
      | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0) ),
    inference(cnf_transformation,[],[f3134]) ).

fof(f3876,plain,
    ! [X0] : c_Int_OBit0(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
    inference(cnf_transformation,[],[f1376]) ).

fof(f4646,plain,
    ! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
    inference(cnf_transformation,[],[f1836]) ).

fof(f4651,plain,
    ! [X0] : c_Int_OBit1(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),
    inference(cnf_transformation,[],[f1839]) ).

fof(f5339,plain,
    ! [X0] : v_na____ != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0)),
    inference(cnf_transformation,[],[f3087]) ).

fof(f5377,plain,
    ! [X0] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),sK14(X0))) = X0
      | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0) ),
    inference(definition_unfolding,[],[f3630,f4646,f3876,f4651]) ).

fof(f5688,plain,
    ! [X0] : v_na____ != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X0)),
    inference(definition_unfolding,[],[f5339,f4646,f3876,f4651]) ).

cnf(c_49,negated_conjecture,
    ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
    inference(cnf_transformation,[],[f3566]) ).

cnf(c_105,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),sK14(X0))) = X0
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0) ),
    inference(cnf_transformation,[],[f5377]) ).

cnf(c_1752,negated_conjecture,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X0)) != v_na____,
    inference(cnf_transformation,[],[f5688]) ).

cnf(c_3246,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),sK14(v_na____))) = v_na____
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____) ),
    inference(instantiation,[status(thm)],[c_105]) ).

cnf(c_6737,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),sK14(v_na____))) != v_na____,
    inference(instantiation,[status(thm)],[c_1752]) ).

cnf(c_6738,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_6737,c_3246,c_49]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWW198+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n008.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 : Sun Aug 27 19:51:17 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 19.48/3.68  % SZS status Started for theBenchmark.p
% 19.48/3.68  % SZS status Theorem for theBenchmark.p
% 19.48/3.68  
% 19.48/3.68  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 19.48/3.68  
% 19.48/3.68  ------  iProver source info
% 19.48/3.68  
% 19.48/3.68  git: date: 2023-05-31 18:12:56 +0000
% 19.48/3.68  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 19.48/3.68  git: non_committed_changes: false
% 19.48/3.68  git: last_make_outside_of_git: false
% 19.48/3.68  
% 19.48/3.68  ------ Parsing...
% 19.48/3.68  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 19.48/3.68  
% 19.48/3.68  ------ Preprocessing... sup_sim: 0  sf_s  rm: 31 0s  sf_e  sup_sim: 0  sf_s  rm: 6 0s  sf_e 
% 19.48/3.68  
% 19.48/3.68  ------ Preprocessing...
% 19.48/3.68  
% 19.48/3.68  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 19.48/3.68  ------ Proving...
% 19.48/3.68  ------ Problem Properties 
% 19.48/3.68  
% 19.48/3.68  
% 19.48/3.68  clauses                                 1419
% 19.48/3.68  conjectures                             71
% 19.48/3.68  EPR                                     242
% 19.48/3.68  Horn                                    1207
% 19.48/3.68  unary                                   374
% 19.48/3.68  binary                                  437
% 19.48/3.68  lits                                    3520
% 19.48/3.68  lits eq                                 664
% 19.48/3.68  fd_pure                                 0
% 19.48/3.68  fd_pseudo                               0
% 19.48/3.68  fd_cond                                 53
% 19.48/3.68  fd_pseudo_cond                          96
% 19.48/3.68  AC symbols                              0
% 19.48/3.68  
% 19.48/3.68  ------ Input Options Time Limit: Unbounded
% 19.48/3.68  
% 19.48/3.68  
% 19.48/3.68  ------ 
% 19.48/3.68  Current options:
% 19.48/3.68  ------ 
% 19.48/3.68  
% 19.48/3.68  
% 19.48/3.68  
% 19.48/3.68  
% 19.48/3.68  ------ Proving...
% 19.48/3.68  
% 19.48/3.68  
% 19.48/3.68  % SZS status Theorem for theBenchmark.p
% 19.48/3.68  
% 19.48/3.68  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 19.48/3.68  
% 19.48/3.69  
%------------------------------------------------------------------------------