TSTP Solution File: SET904+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET904+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n005.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 03:01:57 EDT 2024

% Result   : Theorem 2.26s 1.22s
% Output   : CNFRefutation 2.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   21 (  11 unt;   0 def)
%            Number of atoms       :   33 (   3 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   24 (  12   ~;   4   |;   4   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   24 (   0 sgn  14   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

fof(f9,conjecture,
    ! [X0,X1] :
      ( subset(set_union2(singleton(X0),X1),X1)
     => in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_zfmisc_1) ).

fof(f10,negated_conjecture,
    ~ ! [X0,X1] :
        ( subset(set_union2(singleton(X0),X1),X1)
       => in(X0,X1) ),
    inference(negated_conjecture,[],[f9]) ).

fof(f11,axiom,
    ! [X0,X1] :
      ( subset(set_union2(singleton(X0),X1),X1)
     => in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l21_zfmisc_1) ).

fof(f17,plain,
    ? [X0,X1] :
      ( ~ in(X0,X1)
      & subset(set_union2(singleton(X0),X1),X1) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | ~ subset(set_union2(singleton(X0),X1),X1) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f23,plain,
    ( ? [X0,X1] :
        ( ~ in(X0,X1)
        & subset(set_union2(singleton(X0),X1),X1) )
   => ( ~ in(sK2,sK3)
      & subset(set_union2(singleton(sK2),sK3),sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ( ~ in(sK2,sK3)
    & subset(set_union2(singleton(sK2),sK3),sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f17,f23]) ).

fof(f27,plain,
    ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
    inference(cnf_transformation,[],[f3]) ).

fof(f33,plain,
    subset(set_union2(singleton(sK2),sK3),sK3),
    inference(cnf_transformation,[],[f24]) ).

fof(f34,plain,
    ~ in(sK2,sK3),
    inference(cnf_transformation,[],[f24]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | ~ subset(set_union2(singleton(X0),X1),X1) ),
    inference(cnf_transformation,[],[f18]) ).

cnf(c_51,plain,
    set_union2(X0,X1) = set_union2(X1,X0),
    inference(cnf_transformation,[],[f27]) ).

cnf(c_57,negated_conjecture,
    ~ in(sK2,sK3),
    inference(cnf_transformation,[],[f34]) ).

cnf(c_58,negated_conjecture,
    subset(set_union2(singleton(sK2),sK3),sK3),
    inference(cnf_transformation,[],[f33]) ).

cnf(c_59,plain,
    ( ~ subset(set_union2(singleton(X0),X1),X1)
    | in(X0,X1) ),
    inference(cnf_transformation,[],[f35]) ).

cnf(c_106,plain,
    subset(set_union2(sK3,singleton(sK2)),sK3),
    inference(demodulation,[status(thm)],[c_58,c_51]) ).

cnf(c_141,negated_conjecture,
    ~ in(sK2,sK3),
    inference(demodulation,[status(thm)],[c_57]) ).

cnf(c_315,plain,
    ( ~ subset(set_union2(X0,singleton(X1)),X0)
    | in(X1,X0) ),
    inference(superposition,[status(thm)],[c_51,c_59]) ).

cnf(c_329,plain,
    in(sK2,sK3),
    inference(superposition,[status(thm)],[c_106,c_315]) ).

cnf(c_333,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_329,c_141]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SET904+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.14  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n005.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu May  2 20:20:56 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.21/0.49  Running first-order theorem proving
% 0.21/0.49  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
% 2.26/1.22  % SZS status Started for theBenchmark.p
% 2.26/1.22  % SZS status Theorem for theBenchmark.p
% 2.26/1.22  
% 2.26/1.22  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 2.26/1.22  
% 2.26/1.22  ------  iProver source info
% 2.26/1.22  
% 2.26/1.22  git: date: 2024-05-02 19:28:25 +0000
% 2.26/1.22  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 2.26/1.22  git: non_committed_changes: false
% 2.26/1.22  
% 2.26/1.22  ------ Parsing...
% 2.26/1.22  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.26/1.22  
% 2.26/1.22  ------ Preprocessing... sup_sim: 1  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 2.26/1.22  
% 2.26/1.22  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.26/1.22  
% 2.26/1.22  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.26/1.22  ------ Proving...
% 2.26/1.22  ------ Problem Properties 
% 2.26/1.22  
% 2.26/1.22  
% 2.26/1.22  clauses                                 11
% 2.26/1.22  conjectures                             1
% 2.26/1.22  EPR                                     5
% 2.26/1.22  Horn                                    11
% 2.26/1.22  unary                                   7
% 2.26/1.22  binary                                  4
% 2.26/1.22  lits                                    15
% 2.26/1.22  lits eq                                 2
% 2.26/1.22  fd_pure                                 0
% 2.26/1.22  fd_pseudo                               0
% 2.26/1.22  fd_cond                                 0
% 2.26/1.22  fd_pseudo_cond                          0
% 2.26/1.22  AC symbols                              0
% 2.26/1.22  
% 2.26/1.22  ------ Schedule dynamic 5 is on 
% 2.26/1.22  
% 2.26/1.22  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.26/1.22  
% 2.26/1.22  
% 2.26/1.22  ------ 
% 2.26/1.22  Current options:
% 2.26/1.22  ------ 
% 2.26/1.22  
% 2.26/1.22  
% 2.26/1.22  
% 2.26/1.22  
% 2.26/1.22  ------ Proving...
% 2.26/1.22  
% 2.26/1.22  
% 2.26/1.22  % SZS status Theorem for theBenchmark.p
% 2.26/1.22  
% 2.26/1.22  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.26/1.22  
% 2.26/1.22  
%------------------------------------------------------------------------------