%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SET618+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n002.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 15:08:41 EDT 2023

% Result   : Theorem 1.20s 1.18s
% Output   : CNFRefutation 1.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   18 (  17 unt;   0 def)
%            Number of atoms       :   19 (  18 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   10 (   9   ~;   0   |;   0   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   14 (   0 sgn;  10   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_defn) ).

fof(f2,axiom,
    ! [X0] : union(X0,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotency_of_union) ).

fof(f3,axiom,
    ! [X0] : difference(X0,X0) = empty_set,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',self_difference_is_empty_set) ).

fof(f12,conjecture,
    ! [X0] : empty_set = symmetric_difference(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th93) ).

fof(f13,negated_conjecture,
    ~ ! [X0] : empty_set = symmetric_difference(X0,X0),
    inference(negated_conjecture,[],[f12]) ).

fof(f15,plain,
    ? [X0] : empty_set != symmetric_difference(X0,X0),
    inference(ennf_transformation,[],[f13]) ).

fof(f26,plain,
    ( ? [X0] : empty_set != symmetric_difference(X0,X0)
   => empty_set != symmetric_difference(sK2,sK2) ),
    introduced(choice_axiom,[]) ).

fof(f27,plain,
    empty_set != symmetric_difference(sK2,sK2),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f15,f26]) ).

fof(f28,plain,
    ! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
    inference(cnf_transformation,[],[f1]) ).

fof(f29,plain,
    ! [X0] : union(X0,X0) = X0,
    inference(cnf_transformation,[],[f2]) ).

fof(f30,plain,
    ! [X0] : difference(X0,X0) = empty_set,
    inference(cnf_transformation,[],[f3]) ).

fof(f45,plain,
    empty_set != symmetric_difference(sK2,sK2),
    inference(cnf_transformation,[],[f27]) ).

fof(f47,plain,
    empty_set != union(difference(sK2,sK2),difference(sK2,sK2)),
    inference(definition_unfolding,[],[f45,f28]) ).

cnf(c_49,plain,
    union(X0,X0) = X0,
    inference(cnf_transformation,[],[f29]) ).

cnf(c_50,plain,
    difference(X0,X0) = empty_set,
    inference(cnf_transformation,[],[f30]) ).

cnf(c_63,negated_conjecture,
    union(difference(sK2,sK2),difference(sK2,sK2)) != empty_set,
    inference(cnf_transformation,[],[f47]) ).

cnf(c_123,plain,
    empty_set != empty_set,
    inference(demodulation,[status(thm)],[c_63,c_49,c_50]) ).

cnf(c_124,plain,
    $false,
    inference(equality_resolution_simp,[status(thm)],[c_123]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET618+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n002.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sat Aug 26 11:24:18 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 1.20/1.18  % SZS status Started for theBenchmark.p
% 1.20/1.18  % SZS status Theorem for theBenchmark.p
% 1.20/1.18  
% 1.20/1.18  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 1.20/1.18  
% 1.20/1.18  ------  iProver source info
% 1.20/1.18  
% 1.20/1.18  git: date: 2023-05-31 18:12:56 +0000
% 1.20/1.18  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 1.20/1.18  git: non_committed_changes: false
% 1.20/1.18  git: last_make_outside_of_git: false
% 1.20/1.18  
% 1.20/1.18  ------ Parsing...
% 1.20/1.18  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 1.20/1.18  
% 1.20/1.18  ------ Preprocessing...
% 1.20/1.18  
% 1.20/1.18  % SZS status Theorem for theBenchmark.p
% 1.20/1.18  
% 1.20/1.18  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.20/1.18  
% 1.20/1.18  
%------------------------------------------------------------------------------