TSTP Solution File: SWW284+1 by iProver---3.8

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%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SWW284+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n010.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 00:38:43 EDT 2023

% Result   : Theorem 96.75s 13.87s
% Output   : CNFRefutation 96.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   49 (  27 unt;   0 def)
%            Number of atoms       :   89 (  58 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   74 (  34   ~;  27   |;   3   &)
%                                         (   4 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-2 aty)
%            Number of variables   :   49 (   4 sgn;  34   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] :
      ( ! [X2] : hAPP(X1,X2) = hAPP(X0,X2)
     => X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).

fof(f2,axiom,
    v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pe) ).

fof(f3,axiom,
    ! [X3,X4] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => hAPP(c_Polynomial_Opoly(X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))),X3) = c_Groups_Ozero__class_Ozero(X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__0) ).

fof(f4,axiom,
    ! [X5,X4] :
      ( ( class_Rings_Oidom(X4)
        & class_Int_Oring__char__0(X4) )
     => ( c_Polynomial_Opoly(X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))) = c_Polynomial_Opoly(X4,X5)
      <=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X5 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__zero) ).

fof(f1102,axiom,
    class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).

fof(f1115,axiom,
    class_Int_Oring__char__0(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).

fof(f1122,axiom,
    class_Rings_Oidom(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).

fof(f1180,axiom,
    ! [X2] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

fof(f1181,conjecture,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).

fof(f1182,negated_conjecture,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q,
    inference(negated_conjecture,[],[f1181]) ).

fof(f1183,plain,
    ! [X0,X1] :
      ( class_Rings_Ocomm__semiring__0(X1)
     => hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(rectify,[],[f3]) ).

fof(f1184,plain,
    ! [X0,X1] :
      ( ( class_Rings_Oidom(X1)
        & class_Int_Oring__char__0(X1) )
     => ( c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Polynomial_Opoly(X1,X0)
      <=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0 ) ),
    inference(rectify,[],[f4]) ).

fof(f2222,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0),
    inference(rectify,[],[f1180]) ).

fof(f2223,plain,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q,
    inference(flattening,[],[f1182]) ).

fof(f2263,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] : hAPP(X1,X2) != hAPP(X0,X2) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f2264,plain,
    ! [X0,X1] :
      ( hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) = c_Groups_Ozero__class_Ozero(X1)
      | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(ennf_transformation,[],[f1183]) ).

fof(f2265,plain,
    ! [X0,X1] :
      ( ( c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Polynomial_Opoly(X1,X0)
      <=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0 )
      | ~ class_Rings_Oidom(X1)
      | ~ class_Int_Oring__char__0(X1) ),
    inference(ennf_transformation,[],[f1184]) ).

fof(f2266,plain,
    ! [X0,X1] :
      ( ( c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Polynomial_Opoly(X1,X0)
      <=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0 )
      | ~ class_Rings_Oidom(X1)
      | ~ class_Int_Oring__char__0(X1) ),
    inference(flattening,[],[f2265]) ).

fof(f3390,plain,
    ! [X0,X1] :
      ( ? [X2] : hAPP(X1,X2) != hAPP(X0,X2)
     => hAPP(X1,sK4(X0,X1)) != hAPP(X0,sK4(X0,X1)) ),
    introduced(choice_axiom,[]) ).

fof(f3391,plain,
    ! [X0,X1] :
      ( X0 = X1
      | hAPP(X1,sK4(X0,X1)) != hAPP(X0,sK4(X0,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f2263,f3390]) ).

fof(f3392,plain,
    ! [X0,X1] :
      ( ( ( c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Polynomial_Opoly(X1,X0)
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X0 )
        & ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
          | c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) != c_Polynomial_Opoly(X1,X0) ) )
      | ~ class_Rings_Oidom(X1)
      | ~ class_Int_Oring__char__0(X1) ),
    inference(nnf_transformation,[],[f2266]) ).

fof(f3693,plain,
    ! [X0,X1] :
      ( X0 = X1
      | hAPP(X1,sK4(X0,X1)) != hAPP(X0,sK4(X0,X1)) ),
    inference(cnf_transformation,[],[f3391]) ).

fof(f3694,plain,
    v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(cnf_transformation,[],[f2]) ).

fof(f3695,plain,
    ! [X0,X1] :
      ( hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) = c_Groups_Ozero__class_Ozero(X1)
      | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(cnf_transformation,[],[f2264]) ).

fof(f3696,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
      | c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) != c_Polynomial_Opoly(X1,X0)
      | ~ class_Rings_Oidom(X1)
      | ~ class_Int_Oring__char__0(X1) ),
    inference(cnf_transformation,[],[f3392]) ).

fof(f5125,plain,
    class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1102]) ).

fof(f5138,plain,
    class_Int_Oring__char__0(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1115]) ).

fof(f5145,plain,
    class_Rings_Oidom(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1122]) ).

fof(f5203,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0),
    inference(cnf_transformation,[],[f2222]) ).

fof(f5204,plain,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q,
    inference(cnf_transformation,[],[f2223]) ).

cnf(c_49,plain,
    ( hAPP(X0,sK4(X0,X1)) != hAPP(X1,sK4(X0,X1))
    | X0 = X1 ),
    inference(cnf_transformation,[],[f3693]) ).

cnf(c_50,plain,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p,
    inference(cnf_transformation,[],[f3694]) ).

cnf(c_51,plain,
    ( ~ class_Rings_Ocomm__semiring__0(X0)
    | hAPP(c_Polynomial_Opoly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1) = c_Groups_Ozero__class_Ozero(X0) ),
    inference(cnf_transformation,[],[f3695]) ).

cnf(c_52,plain,
    ( c_Polynomial_Opoly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) != c_Polynomial_Opoly(X0,X1)
    | ~ class_Rings_Oidom(X0)
    | ~ class_Int_Oring__char__0(X0)
    | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1 ),
    inference(cnf_transformation,[],[f3696]) ).

cnf(c_1422,plain,
    class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f5125]) ).

cnf(c_1435,plain,
    class_Int_Oring__char__0(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f5138]) ).

cnf(c_1442,plain,
    class_Rings_Oidom(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f5145]) ).

cnf(c_1500,plain,
    hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f5203]) ).

cnf(c_1501,negated_conjecture,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q,
    inference(cnf_transformation,[],[f5204]) ).

cnf(c_3532,plain,
    v_p != v_q,
    inference(demodulation,[status(thm)],[c_1501,c_50]) ).

cnf(c_3535,plain,
    ( hAPP(X0,sK4(X0,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q))) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q) = X0 ),
    inference(superposition,[status(thm)],[c_1500,c_49]) ).

cnf(c_3637,plain,
    hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(superposition,[status(thm)],[c_1422,c_51]) ).

cnf(c_3639,plain,
    hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(demodulation,[status(thm)],[c_3637,c_50]) ).

cnf(c_3662,plain,
    c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p) = c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),
    inference(superposition,[status(thm)],[c_3639,c_3535]) ).

cnf(c_10201,plain,
    ( c_Polynomial_Opoly(tc_Complex_Ocomplex,X0) != c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p)
    | ~ class_Rings_Oidom(tc_Complex_Ocomplex)
    | ~ class_Int_Oring__char__0(tc_Complex_Ocomplex)
    | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0 ),
    inference(superposition,[status(thm)],[c_50,c_52]) ).

cnf(c_10204,plain,
    ( c_Polynomial_Opoly(tc_Complex_Ocomplex,X0) != c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p)
    | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0 ),
    inference(global_subsumption_just,[status(thm)],[c_10201,c_1442,c_1435,c_10201]) ).

cnf(c_10209,plain,
    ( c_Polynomial_Opoly(tc_Complex_Ocomplex,X0) != c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q)
    | X0 = v_p ),
    inference(light_normalisation,[status(thm)],[c_10204,c_50,c_3662]) ).

cnf(c_61816,plain,
    v_p = v_q,
    inference(equality_resolution,[status(thm)],[c_10209]) ).

cnf(c_61817,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_61816,c_3532]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWW284+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n010.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 17:55:34 EDT 2023
% 0.19/0.34  % CPUTime  : 
% 0.19/0.46  Running first-order theorem proving
% 0.19/0.46  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 96.75/13.87  % SZS status Started for theBenchmark.p
% 96.75/13.87  % SZS status Theorem for theBenchmark.p
% 96.75/13.87  
% 96.75/13.87  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 96.75/13.87  
% 96.75/13.87  ------  iProver source info
% 96.75/13.87  
% 96.75/13.87  git: date: 2023-05-31 18:12:56 +0000
% 96.75/13.87  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 96.75/13.87  git: non_committed_changes: false
% 96.75/13.87  git: last_make_outside_of_git: false
% 96.75/13.87  
% 96.75/13.87  ------ Parsing...
% 96.75/13.87  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 96.75/13.87  
% 96.75/13.87  ------ Preprocessing... sf_s  rm: 6 0s  sf_e  sf_s  rm: 2 0s  sf_e 
% 96.75/13.87  
% 96.75/13.87  ------ Preprocessing...
% 96.75/13.87  
% 96.75/13.87  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 96.75/13.87  ------ Proving...
% 96.75/13.87  ------ Problem Properties 
% 96.75/13.87  
% 96.75/13.87  
% 96.75/13.87  clauses                                 1256
% 96.75/13.87  conjectures                             1
% 96.75/13.87  EPR                                     149
% 96.75/13.87  Horn                                    1080
% 96.75/13.87  unary                                   276
% 96.75/13.87  binary                                  480
% 96.75/13.87  lits                                    2964
% 96.75/13.87  lits eq                                 944
% 96.75/13.87  fd_pure                                 0
% 96.75/13.87  fd_pseudo                               0
% 96.75/13.87  fd_cond                                 48
% 96.75/13.87  fd_pseudo_cond                          165
% 96.75/13.87  AC symbols                              0
% 96.75/13.87  
% 96.75/13.87  ------ Input Options Time Limit: Unbounded
% 96.75/13.87  
% 96.75/13.87  
% 96.75/13.87  ------ 
% 96.75/13.87  Current options:
% 96.75/13.87  ------ 
% 96.75/13.87  
% 96.75/13.87  
% 96.75/13.87  
% 96.75/13.87  
% 96.75/13.87  ------ Proving...
% 96.75/13.87  
% 96.75/13.87  
% 96.75/13.87  % SZS status Theorem for theBenchmark.p
% 96.75/13.87  
% 96.75/13.87  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 96.75/13.87  
% 96.75/13.88  
%------------------------------------------------------------------------------