TSTP Solution File: ITP330_1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : ITP330_1 : TPTP v8.1.2. Released v8.0.0.
% 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 May  3 02:30:40 EDT 2024

% Result   : Theorem 28.13s 4.73s
% Output   : CNFRefutation 28.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   37 (  18 unt;   0 typ;   0 def)
%            Number of atoms       :  167 (  25 equ)
%            Maximal formula atoms :    4 (   4 avg)
%            Number of connectives :   51 (  24   ~;  18   |;   4   &)
%                                         (   3 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :  103 ( 103 fml;   0 var)
%            Number of types       :    0 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   26 (  23 usr;  14 prp; 0-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   41 (   5 sgn  27   !;   4   ?;  31   :)

% Comments : 
%------------------------------------------------------------------------------
tff(f1,axiom,
    ! [X0: 'A_m_vec$'] :
      ( 'fun_app$'('uua$',X0)
    <=> ? [X1: 'M_a_fun$'] : ( 'sum$'('uu$'(X1),'top$') = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom0) ).

tff(f284,conjecture,
    'thesis$',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture283) ).

tff(f285,negated_conjecture,
    ~ 'thesis$',
    inference(negated_conjecture,[],[f284]) ).

tff(f286,axiom,
    ! [X0: 'M_a_fun$'] :
      ( ( 'sum$'('uu$'(X0),'top$') = 'fun_app$ar'('f$','fun_app$a'('vec_nth$a'('cart_basis_Rn$'),'j$')) )
     => 'thesis$' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis284) ).

tff(f289,axiom,
    'top$b' = 'collect$'('uua$'),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom287) ).

tff(f326,axiom,
    ! [X0: 'A_m_vec$'] :
      ( 'member$a'(X0,'top$b')
    <=> $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom324) ).

tff(f522,axiom,
    ! [X0: 'A_m_vec$',X1: 'A_m_vec_bool_fun$'] :
      ( 'member$a'(X0,'collect$'(X1))
    <=> 'fun_app$'(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom520) ).

tff(f560,axiom,
    ! [X0: 'M_a_m_vec_fun$',X1: 'M_set$'] : ( 'sum$'(X0,X1) = 'vec_lambda$a'('uyx$'(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom558) ).

tff(f929,plain,
    ~ 'thesis$',
    inference(flattening,[],[f285]) ).

tff(f934,plain,
    ! [X0: 'A_m_vec$'] : 'member$a'(X0,'top$b'),
    inference(true_and_false_elimination,[],[f326]) ).

tff(f1053,plain,
    ! [X0: 'M_a_fun$'] :
      ( 'thesis$'
      | ( 'sum$'('uu$'(X0),'top$') != 'fun_app$ar'('f$','fun_app$a'('vec_nth$a'('cart_basis_Rn$'),'j$')) ) ),
    inference(ennf_transformation,[],[f286]) ).

tff(f1385,plain,
    ! [X0: 'A_m_vec$'] :
      ( ( 'fun_app$'('uua$',X0)
        | ! [X1: 'M_a_fun$'] : ( 'sum$'('uu$'(X1),'top$') != X0 ) )
      & ( ? [X1: 'M_a_fun$'] : ( 'sum$'('uu$'(X1),'top$') = X0 )
        | ~ 'fun_app$'('uua$',X0) ) ),
    inference(nnf_transformation,[],[f1]) ).

tff(f1386,plain,
    ! [X0: 'A_m_vec$'] :
      ( ( 'fun_app$'('uua$',X0)
        | ! [X1: 'M_a_fun$'] : ( 'sum$'('uu$'(X1),'top$') != X0 ) )
      & ( ? [X2: 'M_a_fun$'] : ( 'sum$'('uu$'(X2),'top$') = X0 )
        | ~ 'fun_app$'('uua$',X0) ) ),
    inference(rectify,[],[f1385]) ).

tff(f1387,plain,
    ! [X0: 'A_m_vec$'] :
      ( ? [X2: 'M_a_fun$'] : ( 'sum$'('uu$'(X2),'top$') = X0 )
     => ( 'sum$'('uu$'(sK20(X0)),'top$') = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f1388,plain,
    ! [X0: 'A_m_vec$'] :
      ( ( 'fun_app$'('uua$',X0)
        | ! [X1: 'M_a_fun$'] : ( 'sum$'('uu$'(X1),'top$') != X0 ) )
      & ( ( 'sum$'('uu$'(sK20(X0)),'top$') = X0 )
        | ~ 'fun_app$'('uua$',X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f1386,f1387]) ).

tff(f1822,plain,
    ! [X0: 'A_m_vec$',X1: 'A_m_vec_bool_fun$'] :
      ( ( 'member$a'(X0,'collect$'(X1))
        | ~ 'fun_app$'(X1,X0) )
      & ( 'fun_app$'(X1,X0)
        | ~ 'member$a'(X0,'collect$'(X1)) ) ),
    inference(nnf_transformation,[],[f522]) ).

tff(f1982,plain,
    ! [X0: 'A_m_vec$'] :
      ( ( 'sum$'('uu$'(sK20(X0)),'top$') = X0 )
      | ~ 'fun_app$'('uua$',X0) ),
    inference(cnf_transformation,[],[f1388]) ).

tff(f2347,plain,
    ~ 'thesis$',
    inference(cnf_transformation,[],[f929]) ).

tff(f2348,plain,
    ! [X0: 'M_a_fun$'] :
      ( 'thesis$'
      | ( 'sum$'('uu$'(X0),'top$') != 'fun_app$ar'('f$','fun_app$a'('vec_nth$a'('cart_basis_Rn$'),'j$')) ) ),
    inference(cnf_transformation,[],[f1053]) ).

tff(f2351,plain,
    'top$b' = 'collect$'('uua$'),
    inference(cnf_transformation,[],[f289]) ).

tff(f2392,plain,
    ! [X0: 'A_m_vec$'] : 'member$a'(X0,'top$b'),
    inference(cnf_transformation,[],[f934]) ).

tff(f2859,plain,
    ! [X0: 'A_m_vec$',X1: 'A_m_vec_bool_fun$'] :
      ( 'fun_app$'(X1,X0)
      | ~ 'member$a'(X0,'collect$'(X1)) ),
    inference(cnf_transformation,[],[f1822]) ).

tff(f2912,plain,
    ! [X0: 'M_a_m_vec_fun$',X1: 'M_set$'] : ( 'sum$'(X0,X1) = 'vec_lambda$a'('uyx$'(X0,X1)) ),
    inference(cnf_transformation,[],[f560]) ).

tff(f3375,plain,
    ! [X0: 'A_m_vec$'] :
      ( ( 'vec_lambda$a'('uyx$'('uu$'(sK20(X0)),'top$')) = X0 )
      | ~ 'fun_app$'('uua$',X0) ),
    inference(definition_unfolding,[],[f1982,f2912]) ).

tff(f3431,plain,
    ! [X0: 'M_a_fun$'] :
      ( 'thesis$'
      | ( 'fun_app$ar'('f$','fun_app$a'('vec_nth$a'('cart_basis_Rn$'),'j$')) != 'vec_lambda$a'('uyx$'('uu$'(X0),'top$')) ) ),
    inference(definition_unfolding,[],[f2348,f2912]) ).

cnf(c_50,plain,
    ( ~ 'fun_app$'('uua$',X0_52)
    | 'vec_lambda$a'('uyx$'('uu$'(sK20(X0_52)),'top$')) = X0_52 ),
    inference(cnf_transformation,[],[f3375]) ).

cnf(c_414,negated_conjecture,
    ~ 'thesis$',
    inference(cnf_transformation,[],[f2347]) ).

cnf(c_415,plain,
    ( 'fun_app$ar'('f$','fun_app$a'('vec_nth$a'('cart_basis_Rn$'),'j$')) != 'vec_lambda$a'('uyx$'('uu$'(X0_48),'top$'))
    | 'thesis$' ),
    inference(cnf_transformation,[],[f3431]) ).

cnf(c_416,plain,
    'collect$'('uua$') = 'top$b',
    inference(cnf_transformation,[],[f2351]) ).

cnf(c_457,plain,
    'member$a'(X0_52,'top$b'),
    inference(cnf_transformation,[],[f2392]) ).

cnf(c_873,plain,
    ( ~ 'member$a'(X0_52,'collect$'(X0_22))
    | 'fun_app$'(X0_22,X0_52) ),
    inference(cnf_transformation,[],[f2859]) ).

cnf(c_2373,plain,
    'fun_app$ar'('f$','fun_app$a'('vec_nth$a'('cart_basis_Rn$'),'j$')) != 'vec_lambda$a'('uyx$'('uu$'(X0_48),'top$')),
    inference(global_subsumption_just,[status(thm)],[c_415,c_414,c_415]) ).

cnf(c_73001,plain,
    ( ~ 'member$a'(X0_52,'top$b')
    | 'fun_app$'('uua$',X0_52) ),
    inference(superposition,[status(thm)],[c_416,c_873]) ).

cnf(c_73006,plain,
    'fun_app$'('uua$',X0_52),
    inference(forward_subsumption_resolution,[status(thm)],[c_73001,c_457]) ).

cnf(c_77457,plain,
    'vec_lambda$a'('uyx$'('uu$'(sK20(X0_52)),'top$')) = X0_52,
    inference(global_subsumption_just,[status(thm)],[c_50,c_50,c_73006]) ).

cnf(c_88629,plain,
    'fun_app$ar'('f$','fun_app$a'('vec_nth$a'('cart_basis_Rn$'),'j$')) != X0_52,
    inference(superposition,[status(thm)],[c_77457,c_2373]) ).

cnf(c_88632,plain,
    $false,
    inference(equality_resolution,[status(thm)],[c_88629]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.15  % Problem  : ITP330_1 : TPTP v8.1.2. Released v8.0.0.
% 0.12/0.16  % Command  : run_iprover %s %d THM
% 0.14/0.37  % Computer : n008.cluster.edu
% 0.14/0.37  % Model    : x86_64 x86_64
% 0.14/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37  % Memory   : 8042.1875MB
% 0.14/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.38  % CPULimit : 300
% 0.14/0.38  % WCLimit  : 300
% 0.14/0.38  % DateTime : Thu May  2 21:57:43 EDT 2024
% 0.14/0.38  % CPUTime  : 
% 0.20/0.51  Running first-order theorem proving
% 0.20/0.51  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
% 28.13/4.73  % SZS status Started for theBenchmark.p
% 28.13/4.73  % SZS status Theorem for theBenchmark.p
% 28.13/4.73  
% 28.13/4.73  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 28.13/4.73  
% 28.13/4.73  ------  iProver source info
% 28.13/4.73  
% 28.13/4.73  git: date: 2024-05-02 19:28:25 +0000
% 28.13/4.73  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 28.13/4.73  git: non_committed_changes: false
% 28.13/4.73  
% 28.13/4.73  ------ Parsing...
% 28.13/4.73  ------ Clausification by vclausify_rel  & Parsing by iProver...------  preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 28.13/4.73  
% 28.13/4.73  
% 28.13/4.73  ------ Preprocessing... sup_sim: 290  pe_s  pe:1:0s pe:2:0s pe:4:0s pe_e  sup_sim: 2  pe_s  pe_e  sup_sim: 0  pe_s  pe_e 
% 28.13/4.73  
% 28.13/4.73  ------ Preprocessing...------  preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 28.13/4.73   gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e ------  preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 28.13/4.73  
% 28.13/4.73  
% 28.13/4.73  ------ Preprocessing...
% 28.13/4.73  ------ Proving...
% 28.13/4.73  ------ Problem Properties 
% 28.13/4.73  
% 28.13/4.73  
% 28.13/4.73  clauses                                 1062
% 28.13/4.73  conjectures                             0
% 28.13/4.73  EPR                                     22
% 28.13/4.73  Horn                                    743
% 28.13/4.73  unary                                   502
% 28.13/4.73  binary                                  325
% 28.13/4.73  lits                                    2320
% 28.13/4.73  lits eq                                 1404
% 28.13/4.73  fd_pure                                 1
% 28.13/4.73  fd_pseudo                               0
% 28.13/4.73  fd_cond                                 7
% 28.13/4.73  fd_pseudo_cond                          106
% 28.13/4.73  AC symbols                              0
% 28.13/4.73  
% 28.13/4.73  ------ Schedule dynamic 5 is on 
% 28.13/4.73  
% 28.13/4.73  ------ no conjectures: strip conj schedule 
% 28.13/4.73  
% 28.13/4.73  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 28.13/4.73  
% 28.13/4.73  
% 28.13/4.73  ------ 
% 28.13/4.73  Current options:
% 28.13/4.73  ------ 
% 28.13/4.73  
% 28.13/4.73  
% 28.13/4.73  
% 28.13/4.73  
% 28.13/4.73  ------ Proving...
% 28.13/4.73  
% 28.13/4.73  
% 28.13/4.73  % SZS status Theorem for theBenchmark.p
% 28.13/4.73  
% 28.13/4.73  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 28.13/4.73  
% 28.13/4.73  
%------------------------------------------------------------------------------