TSTP Solution File: SWW234+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWW234+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 May  3 03:24:36 EDT 2024

% Result   : Theorem 180.65s 24.39s
% Output   : CNFRefutation 180.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   40 (  18 unt;   0 def)
%            Number of atoms       :   88 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   86 (  38   ~;  34   |;   1   &)
%                                         (   3 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-3 aty)
%            Number of variables   :   60 (   1 sgn  48   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f6,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_h) ).

fof(f15,axiom,
    ! [X13,X3] :
      ( class_Groups_Oordered__ab__group__add__abs(X3)
     => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oabs__class_Oabs(X3,X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__ge__zero) ).

fof(f40,axiom,
    ! [X13,X15,X17,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X17)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X15,X13)
         => c_Orderings_Oord__class_Oless__eq(X3,X15,c_Groups_Oplus__class_Oplus(X3,X13,X17)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing2) ).

fof(f53,axiom,
    ! [X19,X18,X16,X3] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X16,X18),c_Groups_Oplus__class_Oplus(X3,X19,X18))
      <=> c_Orderings_Oord__class_Oless__eq(X3,X16,X19) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).

fof(f1113,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(f1120,axiom,
    class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).

fof(f1122,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).

fof(f1274,conjecture,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

fof(f1275,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
    inference(negated_conjecture,[],[f1274]) ).

fof(f1285,plain,
    ! [X0,X1] :
      ( class_Groups_Oordered__ab__group__add__abs(X1)
     => c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0)) ),
    inference(rectify,[],[f15]) ).

fof(f1310,plain,
    ! [X0,X1,X2,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
         => c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X0,X2)) ) ) ),
    inference(rectify,[],[f40]) ).

fof(f1323,plain,
    ! [X0,X1,X2,X3] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
      <=> c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ) ),
    inference(rectify,[],[f53]) ).

fof(f2316,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
    inference(flattening,[],[f1275]) ).

fof(f2331,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0))
      | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(ennf_transformation,[],[f1285]) ).

fof(f2359,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X0,X2))
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
      | ~ class_Groups_Oordered__comm__monoid__add(X3) ),
    inference(ennf_transformation,[],[f1310]) ).

fof(f2360,plain,
    ! [X0,X1,X2,X3] :
      ( c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X0,X2))
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
      | ~ class_Groups_Oordered__comm__monoid__add(X3) ),
    inference(flattening,[],[f2359]) ).

fof(f2383,plain,
    ! [X0,X1,X2,X3] :
      ( ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
      <=> c_Orderings_Oord__class_Oless__eq(X3,X2,X0) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
    inference(ennf_transformation,[],[f1323]) ).

fof(f3430,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
          | ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X0) )
        & ( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
          | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1)) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
    inference(nnf_transformation,[],[f2383]) ).

fof(f3817,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
    inference(cnf_transformation,[],[f6]) ).

fof(f3828,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0))
      | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(cnf_transformation,[],[f2331]) ).

fof(f3864,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X0,X2))
      | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
      | ~ class_Groups_Oordered__comm__monoid__add(X3) ),
    inference(cnf_transformation,[],[f2360]) ).

fof(f3878,plain,
    ! [X2,X3,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
      | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
    inference(cnf_transformation,[],[f3430]) ).

fof(f5326,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1113]) ).

fof(f5333,plain,
    class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1120]) ).

fof(f5335,plain,
    class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1122]) ).

fof(f5487,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
    inference(cnf_transformation,[],[f2316]) ).

cnf(c_54,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
    inference(cnf_transformation,[],[f3817]) ).

cnf(c_63,plain,
    ( ~ class_Groups_Oordered__ab__group__add__abs(X0)
    | c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oabs__class_Oabs(X0,X1)) ),
    inference(cnf_transformation,[],[f3828]) ).

cnf(c_95,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X0,X2,X3)
    | ~ class_Groups_Oordered__comm__monoid__add(X0)
    | c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Oplus__class_Oplus(X0,X3,X1)) ),
    inference(cnf_transformation,[],[f3864]) ).

cnf(c_110,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oplus__class_Oplus(X0,X1,X2),c_Groups_Oplus__class_Oplus(X0,X3,X2))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X0)
    | c_Orderings_Oord__class_Oless__eq(X0,X1,X3) ),
    inference(cnf_transformation,[],[f3878]) ).

cnf(c_1522,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f5326]) ).

cnf(c_1529,plain,
    class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f5333]) ).

cnf(c_1531,plain,
    class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f5335]) ).

cnf(c_1683,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
    inference(cnf_transformation,[],[f5487]) ).

cnf(c_92931,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),X0))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_93440,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
    | ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),X0)) ),
    inference(instantiation,[status(thm)],[c_95]) ).

cnf(c_106546,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____))
    | ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____))) ),
    inference(instantiation,[status(thm)],[c_93440]) ).

cnf(c_154221,plain,
    ( ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) ),
    inference(instantiation,[status(thm)],[c_63]) ).

cnf(c_172753,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ),
    inference(instantiation,[status(thm)],[c_92931]) ).

cnf(c_172754,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_172753,c_154221,c_106546,c_54,c_1683,c_1522,c_1529,c_1531]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13  % Problem  : SWW234+1 : TPTP v8.1.2. Released v5.2.0.
% 0.05/0.14  % Command  : run_iprover %s %d THM
% 0.14/0.36  % Computer : n010.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu May  2 22:11:34 EDT 2024
% 0.14/0.36  % CPUTime  : 
% 0.22/0.50  Running first-order theorem proving
% 0.22/0.50  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
% 180.65/24.39  % SZS status Started for theBenchmark.p
% 180.65/24.39  % SZS status Theorem for theBenchmark.p
% 180.65/24.39  
% 180.65/24.39  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 180.65/24.39  
% 180.65/24.39  ------  iProver source info
% 180.65/24.39  
% 180.65/24.39  git: date: 2024-05-02 19:28:25 +0000
% 180.65/24.39  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 180.65/24.39  git: non_committed_changes: false
% 180.65/24.39  
% 180.65/24.39  ------ Parsing...
% 180.65/24.39  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 180.65/24.39  
% 180.65/24.39  ------ Preprocessing... sup_sim: 65  sf_s  rm: 7 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e  sup_sim: 50  sf_s  rm: 12 0s  sf_e  pe_s  pe_e  sup_sim: 3  sf_s  rm: 12 0s  sf_e  pe_s  pe_e 
% 180.65/24.39  
% 180.65/24.39  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 180.65/24.39  
% 180.65/24.39  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 180.65/24.39  ------ Proving...
% 180.65/24.39  ------ Problem Properties 
% 180.65/24.39  
% 180.65/24.39  
% 180.65/24.39  clauses                                 1350
% 180.65/24.39  conjectures                             1
% 180.65/24.39  EPR                                     231
% 180.65/24.39  Horn                                    1196
% 180.65/24.39  unary                                   410
% 180.65/24.39  binary                                  456
% 180.65/24.39  lits                                    3007
% 180.65/24.39  lits eq                                 647
% 180.65/24.39  fd_pure                                 0
% 180.65/24.39  fd_pseudo                               0
% 180.65/24.39  fd_cond                                 69
% 180.65/24.39  fd_pseudo_cond                          87
% 180.65/24.39  AC symbols                              0
% 180.65/24.39  
% 180.65/24.39  ------ Input Options Time Limit: Unbounded
% 180.65/24.39  
% 180.65/24.39  
% 180.65/24.39  ------ 
% 180.65/24.39  Current options:
% 180.65/24.39  ------ 
% 180.65/24.39  
% 180.65/24.39  
% 180.65/24.39  
% 180.65/24.39  
% 180.65/24.39  ------ Proving...
% 180.65/24.39  
% 180.65/24.39  
% 180.65/24.39  % SZS status Theorem for theBenchmark.p
% 180.65/24.39  
% 180.65/24.39  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 180.65/24.39  
% 180.65/24.40  
%------------------------------------------------------------------------------