TSTP Solution File: SWW229+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWW229+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n031.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 03:24:35 EDT 2024

% Result   : Theorem 7.61s 1.66s
% Output   : CNFRefutation 7.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   17 (  10 unt;   0 def)
%            Number of atoms       :   24 (   1 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   16 (   9   ~;   5   |;   0   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   15 (  15 usr;   8 con; 0-3 aty)
%            Number of variables   :   23 (   0 sgn  12   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f6,axiom,
    ! [X4,X5,X6] :
      ( class_RealVector_Oreal__normed__vector(X6)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,X5),c_RealVector_Onorm__class_Onorm(X6,X4))),c_RealVector_Onorm__class_Onorm(X6,c_Groups_Ominus__class_Ominus(X6,X5,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__triangle__ineq3) ).

fof(f1169,axiom,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).

fof(f1254,conjecture,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

fof(f1255,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),
    inference(negated_conjecture,[],[f1254]) ).

fof(f1257,plain,
    ! [X0,X1,X2] :
      ( class_RealVector_Oreal__normed__vector(X2)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X0))),c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0))) ),
    inference(rectify,[],[f6]) ).

fof(f2255,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),
    inference(flattening,[],[f1255]) ).

fof(f2257,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X0))),c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)))
      | ~ class_RealVector_Oreal__normed__vector(X2) ),
    inference(ennf_transformation,[],[f1257]) ).

fof(f3682,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X0))),c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)))
      | ~ class_RealVector_Oreal__normed__vector(X2) ),
    inference(cnf_transformation,[],[f2257]) ).

fof(f5254,plain,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1169]) ).

fof(f5339,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),
    inference(cnf_transformation,[],[f2255]) ).

cnf(c_54,plain,
    ( ~ class_RealVector_Oreal__normed__vector(X0)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1),c_RealVector_Onorm__class_Onorm(X0,X2))),c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ominus__class_Ominus(X0,X1,X2))) ),
    inference(cnf_transformation,[],[f3682]) ).

cnf(c_1583,plain,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f5254]) ).

cnf(c_1668,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),
    inference(cnf_transformation,[],[f5339]) ).

cnf(c_2692,plain,
    ( ~ class_RealVector_Oreal__normed__vector(X0)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1),c_RealVector_Onorm__class_Onorm(X0,X2))),c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ominus__class_Ominus(X0,X1,X2))) ),
    inference(prop_impl_just,[status(thm)],[c_54]) ).

cnf(c_11758,plain,
    ( X0 != tc_Complex_Ocomplex
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1),c_RealVector_Onorm__class_Onorm(X0,X2))),c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ominus__class_Ominus(X0,X1,X2))) ),
    inference(resolution_lifted,[status(thm)],[c_2692,c_1583]) ).

cnf(c_11759,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1))),
    inference(unflattening,[status(thm)],[c_11758]) ).

cnf(c_11889,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[c_1668,c_11759]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWW229+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.13  % Command  : run_iprover %s %d THM
% 0.14/0.34  % Computer : n031.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu May  2 22:56:46 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.21/0.47  Running first-order theorem proving
% 0.21/0.47  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
% 7.61/1.66  % SZS status Started for theBenchmark.p
% 7.61/1.66  % SZS status Theorem for theBenchmark.p
% 7.61/1.66  
% 7.61/1.66  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 7.61/1.66  
% 7.61/1.66  ------  iProver source info
% 7.61/1.66  
% 7.61/1.66  git: date: 2024-05-02 19:28:25 +0000
% 7.61/1.66  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 7.61/1.66  git: non_committed_changes: false
% 7.61/1.66  
% 7.61/1.66  ------ Parsing...
% 7.61/1.66  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 7.61/1.66  
% 7.61/1.66  ------ Preprocessing... sup_sim: 7  pe_s  pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s
% 7.61/1.66  
% 7.61/1.66  % SZS status Theorem for theBenchmark.p
% 7.61/1.66  
% 7.61/1.66  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.61/1.66  
% 7.61/1.66  
%------------------------------------------------------------------------------