TSTP Solution File: SET635+3 by iProver---3.8

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%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SET635+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n011.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 15:08:49 EDT 2023

% Result   : Theorem 3.78s 1.16s
% Output   : CNFRefutation 3.78s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   42 (  33 unt;   0 def)
%            Number of atoms       :   62 (  43 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   40 (  20   ~;  11   |;   6   &)
%                                         (   2 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   78 (   0 sgn;  43   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [X0,X1] :
      ( difference(X0,X1) = empty_set
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_empty_set) ).

fof(f3,axiom,
    ! [X0] : union(X0,empty_set) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_empty_set) ).

fof(f4,axiom,
    ! [X0,X1,X2] : difference(X0,intersection(X1,X2)) = union(difference(X0,X1),difference(X0,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_and_intersection_and_union) ).

fof(f5,axiom,
    ! [X0,X1,X2] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_and_intersection) ).

fof(f8,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ( subset(X1,X0)
        & subset(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).

fof(f9,axiom,
    ! [X0,X1] : union(X0,X1) = union(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).

fof(f11,axiom,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).

fof(f16,conjecture,
    ! [X0,X1,X2] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),intersection(X0,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th117) ).

fof(f17,negated_conjecture,
    ~ ! [X0,X1,X2] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),intersection(X0,X2)),
    inference(negated_conjecture,[],[f16]) ).

fof(f19,plain,
    ? [X0,X1,X2] : intersection(X0,difference(X1,X2)) != difference(intersection(X0,X1),intersection(X0,X2)),
    inference(ennf_transformation,[],[f17]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( difference(X0,X1) = empty_set
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | difference(X0,X1) != empty_set ) ),
    inference(nnf_transformation,[],[f2]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(flattening,[],[f25]) ).

fof(f35,plain,
    ( ? [X0,X1,X2] : intersection(X0,difference(X1,X2)) != difference(intersection(X0,X1),intersection(X0,X2))
   => intersection(sK2,difference(sK3,sK4)) != difference(intersection(sK2,sK3),intersection(sK2,sK4)) ),
    introduced(choice_axiom,[]) ).

fof(f36,plain,
    intersection(sK2,difference(sK3,sK4)) != difference(intersection(sK2,sK3),intersection(sK2,sK4)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f19,f35]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( difference(X0,X1) = empty_set
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f40,plain,
    ! [X0] : union(X0,empty_set) = X0,
    inference(cnf_transformation,[],[f3]) ).

fof(f41,plain,
    ! [X2,X0,X1] : difference(X0,intersection(X1,X2)) = union(difference(X0,X1),difference(X0,X2)),
    inference(cnf_transformation,[],[f4]) ).

fof(f42,plain,
    ! [X2,X0,X1] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),X2),
    inference(cnf_transformation,[],[f5]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | X0 != X1 ),
    inference(cnf_transformation,[],[f26]) ).

fof(f52,plain,
    ! [X0,X1] : union(X0,X1) = union(X1,X0),
    inference(cnf_transformation,[],[f9]) ).

fof(f54,plain,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    inference(cnf_transformation,[],[f11]) ).

fof(f63,plain,
    intersection(sK2,difference(sK3,sK4)) != difference(intersection(sK2,sK3),intersection(sK2,sK4)),
    inference(cnf_transformation,[],[f36]) ).

fof(f65,plain,
    ! [X1] : subset(X1,X1),
    inference(equality_resolution,[],[f49]) ).

cnf(c_50,plain,
    ( ~ subset(X0,X1)
    | difference(X0,X1) = empty_set ),
    inference(cnf_transformation,[],[f39]) ).

cnf(c_52,plain,
    union(X0,empty_set) = X0,
    inference(cnf_transformation,[],[f40]) ).

cnf(c_53,plain,
    union(difference(X0,X1),difference(X0,X2)) = difference(X0,intersection(X1,X2)),
    inference(cnf_transformation,[],[f41]) ).

cnf(c_54,plain,
    intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),X2),
    inference(cnf_transformation,[],[f42]) ).

cnf(c_63,plain,
    subset(X0,X0),
    inference(cnf_transformation,[],[f65]) ).

cnf(c_64,plain,
    union(X0,X1) = union(X1,X0),
    inference(cnf_transformation,[],[f52]) ).

cnf(c_66,plain,
    intersection(X0,X1) = intersection(X1,X0),
    inference(cnf_transformation,[],[f54]) ).

cnf(c_73,negated_conjecture,
    difference(intersection(sK2,sK3),intersection(sK2,sK4)) != intersection(sK2,difference(sK3,sK4)),
    inference(cnf_transformation,[],[f63]) ).

cnf(c_295,plain,
    intersection(sK2,difference(sK3,intersection(sK2,sK4))) != intersection(sK2,difference(sK3,sK4)),
    inference(demodulation,[status(thm)],[c_73,c_54]) ).

cnf(c_941,plain,
    union(empty_set,X0) = X0,
    inference(superposition,[status(thm)],[c_52,c_64]) ).

cnf(c_996,plain,
    difference(X0,X0) = empty_set,
    inference(superposition,[status(thm)],[c_63,c_50]) ).

cnf(c_1001,plain,
    difference(X0,intersection(X0,X1)) = union(empty_set,difference(X0,X1)),
    inference(superposition,[status(thm)],[c_996,c_53]) ).

cnf(c_1062,plain,
    intersection(X0,difference(X1,X2)) = difference(intersection(X1,X0),X2),
    inference(superposition,[status(thm)],[c_66,c_54]) ).

cnf(c_1236,plain,
    difference(X0,intersection(X0,X1)) = difference(X0,X1),
    inference(demodulation,[status(thm)],[c_1001,c_941]) ).

cnf(c_2594,plain,
    intersection(X0,difference(X1,X2)) = intersection(X1,difference(X0,X2)),
    inference(superposition,[status(thm)],[c_1062,c_54]) ).

cnf(c_6893,plain,
    intersection(X0,difference(X1,intersection(X0,X2))) = intersection(X1,difference(X0,X2)),
    inference(superposition,[status(thm)],[c_1236,c_2594]) ).

cnf(c_7065,plain,
    intersection(sK2,difference(sK3,sK4)) != intersection(sK3,difference(sK2,sK4)),
    inference(demodulation,[status(thm)],[c_295,c_6893]) ).

cnf(c_7066,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_7065,c_2594]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SET635+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n011.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 : Sat Aug 26 12:28:54 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.78/1.16  % SZS status Started for theBenchmark.p
% 3.78/1.16  % SZS status Theorem for theBenchmark.p
% 3.78/1.16  
% 3.78/1.16  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.78/1.16  
% 3.78/1.16  ------  iProver source info
% 3.78/1.16  
% 3.78/1.16  git: date: 2023-05-31 18:12:56 +0000
% 3.78/1.16  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.78/1.16  git: non_committed_changes: false
% 3.78/1.16  git: last_make_outside_of_git: false
% 3.78/1.16  
% 3.78/1.16  ------ Parsing...
% 3.78/1.16  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.78/1.16  
% 3.78/1.16  ------ Preprocessing... sup_sim: 1  sf_s  rm: 1 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 3.78/1.16  
% 3.78/1.16  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.78/1.16  
% 3.78/1.16  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.78/1.16  ------ Proving...
% 3.78/1.16  ------ Problem Properties 
% 3.78/1.16  
% 3.78/1.16  
% 3.78/1.16  clauses                                 23
% 3.78/1.16  conjectures                             0
% 3.78/1.16  EPR                                     4
% 3.78/1.16  Horn                                    20
% 3.78/1.16  unary                                   9
% 3.78/1.16  binary                                  8
% 3.78/1.16  lits                                    43
% 3.78/1.16  lits eq                                 11
% 3.78/1.16  fd_pure                                 0
% 3.78/1.16  fd_pseudo                               0
% 3.78/1.16  fd_cond                                 0
% 3.78/1.16  fd_pseudo_cond                          3
% 3.78/1.16  AC symbols                              0
% 3.78/1.16  
% 3.78/1.16  ------ Schedule dynamic 5 is on 
% 3.78/1.16  
% 3.78/1.16  ------ no conjectures: strip conj schedule 
% 3.78/1.16  
% 3.78/1.16  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.78/1.16  
% 3.78/1.16  
% 3.78/1.16  ------ 
% 3.78/1.16  Current options:
% 3.78/1.16  ------ 
% 3.78/1.16  
% 3.78/1.16  
% 3.78/1.16  
% 3.78/1.16  
% 3.78/1.16  ------ Proving...
% 3.78/1.16  
% 3.78/1.16  
% 3.78/1.16  % SZS status Theorem for theBenchmark.p
% 3.78/1.16  
% 3.78/1.16  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.78/1.17  
% 3.78/1.17  
%------------------------------------------------------------------------------