%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SET002+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n032.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 : Thu Aug 31 15:05:18 EDT 2023

% Result   : Theorem 0.50s 1.03s
% Output   : CNFRefutation 0.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   17 (  11 unt;   0 def)
%            Number of atoms       :   23 (  13 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   17 (  11   ~;   4   |;   0   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   1 con; 0-2 aty)
%            Number of variables   :   15 (   0 sgn;  10   !;   2   ?)

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

fof(f6,axiom,
    ! [X0] : subset(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).

fof(f8,conjecture,
    ! [X0] : union(X0,X0) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_idempotency_of_union) ).

fof(f9,negated_conjecture,
    ~ ! [X0] : union(X0,X0) = X0,
    inference(negated_conjecture,[],[f8]) ).

fof(f10,plain,
    ! [X0,X1] :
      ( union(X0,X1) = X1
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f12,plain,
    ? [X0] : union(X0,X0) != X0,
    inference(ennf_transformation,[],[f9]) ).

fof(f25,plain,
    ( ? [X0] : union(X0,X0) != X0
   => sK2 != union(sK2,sK2) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    sK2 != union(sK2,sK2),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f12,f25]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( union(X0,X1) = X1
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f10]) ).

fof(f38,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f6]) ).

fof(f43,plain,
    sK2 != union(sK2,sK2),
    inference(cnf_transformation,[],[f26]) ).

cnf(c_49,plain,
    ( ~ subset(X0,X1)
    | union(X0,X1) = X1 ),
    inference(cnf_transformation,[],[f27]) ).

cnf(c_60,plain,
    subset(X0,X0),
    inference(cnf_transformation,[],[f38]) ).

cnf(c_63,negated_conjecture,
    union(sK2,sK2) != sK2,
    inference(cnf_transformation,[],[f43]) ).

cnf(c_64,plain,
    subset(sK2,sK2),
    inference(instantiation,[status(thm)],[c_60]) ).

cnf(c_67,plain,
    ( ~ subset(sK2,sK2)
    | union(sK2,sK2) = sK2 ),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_68,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_67,c_63,c_64]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SET002+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.11  % Command  : run_iprover %s %d THM
% 0.10/0.31  % Computer : n032.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Sat Aug 26 08:59:28 EDT 2023
% 0.10/0.31  % CPUTime  : 
% 0.16/0.39  Running first-order theorem proving
% 0.16/0.39  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.50/1.03  % SZS status Started for theBenchmark.p
% 0.50/1.03  % SZS status Theorem for theBenchmark.p
% 0.50/1.03  
% 0.50/1.03  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.50/1.03  
% 0.50/1.03  ------  iProver source info
% 0.50/1.03  
% 0.50/1.03  git: date: 2023-05-31 18:12:56 +0000
% 0.50/1.03  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.50/1.03  git: non_committed_changes: false
% 0.50/1.03  git: last_make_outside_of_git: false
% 0.50/1.03  
% 0.50/1.03  ------ Parsing...
% 0.50/1.03  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.50/1.03  
% 0.50/1.03  ------ Preprocessing...
% 0.50/1.03  
% 0.50/1.03  % SZS status Theorem for theBenchmark.p
% 0.50/1.03  
% 0.50/1.03  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.50/1.03  
% 0.50/1.03  
%------------------------------------------------------------------------------