TSTP Solution File: SET984+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET984+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n018.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 : Mon Jun 24 14:36:46 EDT 2024

% Result   : Theorem 24.53s 4.18s
% Output   : CNFRefutation 24.53s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

fof(f3,axiom,
    ! [X0,X1] : set_intersection2(X0,X0) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( empty_set = cartesian_product2(X0,X1)
    <=> ( empty_set = X1
        | empty_set = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_zfmisc_1) ).

fof(f8,axiom,
    ! [X0,X1,X2,X3] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_zfmisc_1) ).

fof(f9,axiom,
    ! [X0,X1,X2,X3] :
      ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3)
     => ( ( X1 = X3
          & X0 = X2 )
        | empty_set = X1
        | empty_set = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_zfmisc_1) ).

fof(f10,conjecture,
    ! [X0,X1,X2,X3] :
      ( subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))
     => ( ( subset(X1,X3)
          & subset(X0,X2) )
        | empty_set = cartesian_product2(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t138_zfmisc_1) ).

fof(f11,negated_conjecture,
    ~ ! [X0,X1,X2,X3] :
        ( subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))
       => ( ( subset(X1,X3)
            & subset(X0,X2) )
          | empty_set = cartesian_product2(X0,X1) ) ),
    inference(negated_conjecture,[],[f10]) ).

fof(f12,axiom,
    ! [X0,X1] : subset(set_intersection2(X0,X1),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).

fof(f13,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
     => set_intersection2(X0,X1) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).

fof(f14,plain,
    ! [X0] : set_intersection2(X0,X0) = X0,
    inference(rectify,[],[f3]) ).

fof(f16,plain,
    ! [X0,X1,X2,X3] :
      ( ( X1 = X3
        & X0 = X2 )
      | empty_set = X1
      | empty_set = X0
      | cartesian_product2(X0,X1) != cartesian_product2(X2,X3) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f17,plain,
    ! [X0,X1,X2,X3] :
      ( ( X1 = X3
        & X0 = X2 )
      | empty_set = X1
      | empty_set = X0
      | cartesian_product2(X0,X1) != cartesian_product2(X2,X3) ),
    inference(flattening,[],[f16]) ).

fof(f18,plain,
    ? [X0,X1,X2,X3] :
      ( ( ~ subset(X1,X3)
        | ~ subset(X0,X2) )
      & empty_set != cartesian_product2(X0,X1)
      & subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f19,plain,
    ? [X0,X1,X2,X3] :
      ( ( ~ subset(X1,X3)
        | ~ subset(X0,X2) )
      & empty_set != cartesian_product2(X0,X1)
      & subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ),
    inference(flattening,[],[f18]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( set_intersection2(X0,X1) = X0
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ( empty_set = cartesian_product2(X0,X1)
        | ( empty_set != X1
          & empty_set != X0 ) )
      & ( empty_set = X1
        | empty_set = X0
        | empty_set != cartesian_product2(X0,X1) ) ),
    inference(nnf_transformation,[],[f7]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( empty_set = cartesian_product2(X0,X1)
        | ( empty_set != X1
          & empty_set != X0 ) )
      & ( empty_set = X1
        | empty_set = X0
        | empty_set != cartesian_product2(X0,X1) ) ),
    inference(flattening,[],[f25]) ).

fof(f27,plain,
    ( ? [X0,X1,X2,X3] :
        ( ( ~ subset(X1,X3)
          | ~ subset(X0,X2) )
        & empty_set != cartesian_product2(X0,X1)
        & subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) )
   => ( ( ~ subset(sK3,sK5)
        | ~ subset(sK2,sK4) )
      & empty_set != cartesian_product2(sK2,sK3)
      & subset(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5)) ) ),
    introduced(choice_axiom,[]) ).

fof(f28,plain,
    ( ( ~ subset(sK3,sK5)
      | ~ subset(sK2,sK4) )
    & empty_set != cartesian_product2(sK2,sK3)
    & subset(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f19,f27]) ).

fof(f29,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f31,plain,
    ! [X0] : set_intersection2(X0,X0) = X0,
    inference(cnf_transformation,[],[f14]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( empty_set = X1
      | empty_set = X0
      | empty_set != cartesian_product2(X0,X1) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( empty_set = cartesian_product2(X0,X1)
      | empty_set != X0 ),
    inference(cnf_transformation,[],[f26]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( empty_set = cartesian_product2(X0,X1)
      | empty_set != X1 ),
    inference(cnf_transformation,[],[f26]) ).

fof(f38,plain,
    ! [X2,X3,X0,X1] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
    inference(cnf_transformation,[],[f8]) ).

fof(f39,plain,
    ! [X2,X3,X0,X1] :
      ( X0 = X2
      | empty_set = X1
      | empty_set = X0
      | cartesian_product2(X0,X1) != cartesian_product2(X2,X3) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f40,plain,
    ! [X2,X3,X0,X1] :
      ( X1 = X3
      | empty_set = X1
      | empty_set = X0
      | cartesian_product2(X0,X1) != cartesian_product2(X2,X3) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f41,plain,
    subset(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5)),
    inference(cnf_transformation,[],[f28]) ).

fof(f42,plain,
    empty_set != cartesian_product2(sK2,sK3),
    inference(cnf_transformation,[],[f28]) ).

fof(f43,plain,
    ( ~ subset(sK3,sK5)
    | ~ subset(sK2,sK4) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f44,plain,
    ! [X0,X1] : subset(set_intersection2(X0,X1),X0),
    inference(cnf_transformation,[],[f12]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( set_intersection2(X0,X1) = X0
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f46,plain,
    ! [X0] : empty_set = cartesian_product2(X0,empty_set),
    inference(equality_resolution,[],[f37]) ).

fof(f47,plain,
    ! [X1] : empty_set = cartesian_product2(empty_set,X1),
    inference(equality_resolution,[],[f36]) ).

cnf(c_49,plain,
    set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f29]) ).

cnf(c_51,plain,
    set_intersection2(X0,X0) = X0,
    inference(cnf_transformation,[],[f31]) ).

cnf(c_55,plain,
    cartesian_product2(X0,empty_set) = empty_set,
    inference(cnf_transformation,[],[f46]) ).

cnf(c_56,plain,
    cartesian_product2(empty_set,X0) = empty_set,
    inference(cnf_transformation,[],[f47]) ).

cnf(c_57,plain,
    ( cartesian_product2(X0,X1) != empty_set
    | X0 = empty_set
    | X1 = empty_set ),
    inference(cnf_transformation,[],[f35]) ).

cnf(c_58,plain,
    set_intersection2(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = cartesian_product2(set_intersection2(X0,X2),set_intersection2(X1,X3)),
    inference(cnf_transformation,[],[f38]) ).

cnf(c_59,plain,
    ( cartesian_product2(X0,X1) != cartesian_product2(X2,X3)
    | X0 = empty_set
    | X1 = X3
    | X1 = empty_set ),
    inference(cnf_transformation,[],[f40]) ).

cnf(c_60,plain,
    ( cartesian_product2(X0,X1) != cartesian_product2(X2,X3)
    | X0 = X2
    | X0 = empty_set
    | X1 = empty_set ),
    inference(cnf_transformation,[],[f39]) ).

cnf(c_61,negated_conjecture,
    ( ~ subset(sK3,sK5)
    | ~ subset(sK2,sK4) ),
    inference(cnf_transformation,[],[f43]) ).

cnf(c_62,negated_conjecture,
    cartesian_product2(sK2,sK3) != empty_set,
    inference(cnf_transformation,[],[f42]) ).

cnf(c_63,negated_conjecture,
    subset(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5)),
    inference(cnf_transformation,[],[f41]) ).

cnf(c_64,plain,
    subset(set_intersection2(X0,X1),X0),
    inference(cnf_transformation,[],[f44]) ).

cnf(c_65,plain,
    ( ~ subset(X0,X1)
    | set_intersection2(X0,X1) = X0 ),
    inference(cnf_transformation,[],[f45]) ).

cnf(c_173,plain,
    cartesian_product2(sK2,sK3) = sP0_iProver_def,
    definition ).

cnf(c_174,plain,
    cartesian_product2(sK4,sK5) = sP1_iProver_def,
    definition ).

cnf(c_175,negated_conjecture,
    subset(sP0_iProver_def,sP1_iProver_def),
    inference(demodulation,[status(thm)],[c_63,c_174,c_173]) ).

cnf(c_176,negated_conjecture,
    sP0_iProver_def != empty_set,
    inference(demodulation,[status(thm)],[c_62]) ).

cnf(c_178,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_180,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_494,plain,
    ( empty_set != X0
    | sP0_iProver_def != X0
    | sP0_iProver_def = empty_set ),
    inference(instantiation,[status(thm)],[c_180]) ).

cnf(c_584,plain,
    ( empty_set != sP0_iProver_def
    | sP0_iProver_def != sP0_iProver_def
    | sP0_iProver_def = empty_set ),
    inference(instantiation,[status(thm)],[c_494]) ).

cnf(c_585,plain,
    sP0_iProver_def = sP0_iProver_def,
    inference(instantiation,[status(thm)],[c_178]) ).

cnf(c_6545,plain,
    subset(set_intersection2(X0,X1),X1),
    inference(superposition,[status(thm)],[c_49,c_64]) ).

cnf(c_6556,plain,
    set_intersection2(sP0_iProver_def,sP1_iProver_def) = sP0_iProver_def,
    inference(superposition,[status(thm)],[c_175,c_65]) ).

cnf(c_6579,plain,
    cartesian_product2(set_intersection2(sK2,X0),set_intersection2(sK3,X1)) = set_intersection2(sP0_iProver_def,cartesian_product2(X0,X1)),
    inference(superposition,[status(thm)],[c_173,c_58]) ).

cnf(c_6586,plain,
    subset(cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)),cartesian_product2(X1,X3)),
    inference(superposition,[status(thm)],[c_58,c_6545]) ).

cnf(c_6703,plain,
    subset(cartesian_product2(set_intersection2(X0,X1),X2),cartesian_product2(X1,X2)),
    inference(superposition,[status(thm)],[c_51,c_6586]) ).

cnf(c_26079,plain,
    ( set_intersection2(sP0_iProver_def,cartesian_product2(X0,X1)) != cartesian_product2(X2,X3)
    | set_intersection2(sK2,X0) = X2
    | X2 = empty_set
    | X3 = empty_set ),
    inference(superposition,[status(thm)],[c_6579,c_60]) ).

cnf(c_26080,plain,
    ( set_intersection2(sP0_iProver_def,cartesian_product2(X0,X1)) != cartesian_product2(X2,X3)
    | set_intersection2(sK3,X1) = X3
    | X2 = empty_set
    | X3 = empty_set ),
    inference(superposition,[status(thm)],[c_6579,c_59]) ).

cnf(c_26087,plain,
    subset(set_intersection2(sP0_iProver_def,cartesian_product2(X0,X1)),cartesian_product2(X0,set_intersection2(sK3,X1))),
    inference(superposition,[status(thm)],[c_6579,c_6703]) ).

cnf(c_26623,plain,
    subset(set_intersection2(sP0_iProver_def,sP1_iProver_def),cartesian_product2(sK4,set_intersection2(sK3,sK5))),
    inference(superposition,[status(thm)],[c_174,c_26087]) ).

cnf(c_26635,plain,
    subset(sP0_iProver_def,cartesian_product2(sK4,set_intersection2(sK3,sK5))),
    inference(light_normalisation,[status(thm)],[c_26623,c_6556]) ).

cnf(c_40884,plain,
    ( cartesian_product2(X0,X1) != set_intersection2(sP0_iProver_def,sP1_iProver_def)
    | set_intersection2(sK2,sK4) = X0
    | X0 = empty_set
    | X1 = empty_set ),
    inference(superposition,[status(thm)],[c_174,c_26079]) ).

cnf(c_40897,plain,
    ( cartesian_product2(X0,X1) != sP0_iProver_def
    | set_intersection2(sK2,sK4) = X0
    | X0 = empty_set
    | X1 = empty_set ),
    inference(light_normalisation,[status(thm)],[c_40884,c_6556]) ).

cnf(c_41009,plain,
    ( cartesian_product2(X0,X1) != set_intersection2(sP0_iProver_def,sP1_iProver_def)
    | set_intersection2(sK3,sK5) = X1
    | X0 = empty_set
    | X1 = empty_set ),
    inference(superposition,[status(thm)],[c_174,c_26080]) ).

cnf(c_41022,plain,
    ( cartesian_product2(X0,X1) != sP0_iProver_def
    | set_intersection2(sK3,sK5) = X1
    | X0 = empty_set
    | X1 = empty_set ),
    inference(light_normalisation,[status(thm)],[c_41009,c_6556]) ).

cnf(c_42842,plain,
    ( set_intersection2(sK2,sK4) = sK2
    | empty_set = sK3
    | empty_set = sK2 ),
    inference(superposition,[status(thm)],[c_173,c_40897]) ).

cnf(c_43569,plain,
    ( set_intersection2(sK3,sK5) = sK3
    | empty_set = sK3
    | empty_set = sK2 ),
    inference(superposition,[status(thm)],[c_173,c_41022]) ).

cnf(c_43806,plain,
    ( empty_set = sK3
    | empty_set = sK2
    | subset(sK2,sK4) ),
    inference(superposition,[status(thm)],[c_42842,c_6545]) ).

cnf(c_45586,plain,
    ( empty_set = sK3
    | empty_set = sK2
    | subset(sK3,sK5) ),
    inference(superposition,[status(thm)],[c_43569,c_6545]) ).

cnf(c_45648,plain,
    ( empty_set = sK3
    | empty_set = sK2
    | subset(sP0_iProver_def,cartesian_product2(sK4,sK3)) ),
    inference(superposition,[status(thm)],[c_43569,c_26635]) ).

cnf(c_52907,plain,
    ( empty_set = sK2
    | empty_set = sK3 ),
    inference(global_subsumption_just,[status(thm)],[c_45648,c_61,c_43806,c_45586]) ).

cnf(c_52908,plain,
    ( empty_set = sK3
    | empty_set = sK2 ),
    inference(renaming,[status(thm)],[c_52907]) ).

cnf(c_60484,plain,
    ( empty_set != sP0_iProver_def
    | empty_set = sK3
    | empty_set = sK2 ),
    inference(superposition,[status(thm)],[c_173,c_57]) ).

cnf(c_60492,plain,
    ( empty_set = sK3
    | empty_set = sK2 ),
    inference(global_subsumption_just,[status(thm)],[c_60484,c_52908]) ).

cnf(c_60498,plain,
    ( cartesian_product2(empty_set,sK3) = sP0_iProver_def
    | empty_set = sK3 ),
    inference(superposition,[status(thm)],[c_60492,c_173]) ).

cnf(c_60511,plain,
    ( empty_set = sK3
    | empty_set = sP0_iProver_def ),
    inference(demodulation,[status(thm)],[c_60498,c_56]) ).

cnf(c_60518,plain,
    ( cartesian_product2(sK2,empty_set) = sP0_iProver_def
    | empty_set = sP0_iProver_def ),
    inference(superposition,[status(thm)],[c_60511,c_173]) ).

cnf(c_60547,plain,
    cartesian_product2(sK2,empty_set) = sP0_iProver_def,
    inference(global_subsumption_just,[status(thm)],[c_60518,c_176,c_584,c_585,c_60518]) ).

cnf(c_60549,plain,
    empty_set = sP0_iProver_def,
    inference(demodulation,[status(thm)],[c_60547,c_55]) ).

cnf(c_60558,plain,
    sP0_iProver_def != sP0_iProver_def,
    inference(demodulation,[status(thm)],[c_176,c_60549]) ).

cnf(c_60559,plain,
    $false,
    inference(equality_resolution_simp,[status(thm)],[c_60558]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET984+1 : TPTP v8.2.0. Released v3.2.0.
% 0.07/0.12  % Command  : run_iprover %s %d THM
% 0.12/0.33  % Computer : n018.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sun Jun 23 13:32:54 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.19/0.47  Running first-order theorem proving
% 0.19/0.47  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
% 24.53/4.18  % SZS status Started for theBenchmark.p
% 24.53/4.18  % SZS status Theorem for theBenchmark.p
% 24.53/4.18  
% 24.53/4.18  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 24.53/4.18  
% 24.53/4.18  ------  iProver source info
% 24.53/4.18  
% 24.53/4.18  git: date: 2024-06-12 09:56:46 +0000
% 24.53/4.18  git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 24.53/4.18  git: non_committed_changes: false
% 24.53/4.18  
% 24.53/4.18  ------ Parsing...
% 24.53/4.18  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 24.53/4.18  
% 24.53/4.18  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 24.53/4.18  
% 24.53/4.18  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 24.53/4.18  
% 24.53/4.18  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 24.53/4.18  ------ Proving...
% 24.53/4.18  ------ Problem Properties 
% 24.53/4.18  
% 24.53/4.18  
% 24.53/4.18  clauses                                 19
% 24.53/4.18  conjectures                             3
% 24.53/4.18  EPR                                     7
% 24.53/4.18  Horn                                    16
% 24.53/4.18  unary                                   14
% 24.53/4.18  binary                                  2
% 24.53/4.18  lits                                    29
% 24.53/4.18  lits eq                                 20
% 24.53/4.18  fd_pure                                 0
% 24.53/4.18  fd_pseudo                               0
% 24.53/4.18  fd_cond                                 1
% 24.53/4.18  fd_pseudo_cond                          2
% 24.53/4.18  AC symbols                              0
% 24.53/4.18  
% 24.53/4.18  ------ Schedule dynamic 5 is on 
% 24.53/4.18  
% 24.53/4.18  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 24.53/4.18  
% 24.53/4.18  
% 24.53/4.18  ------ 
% 24.53/4.18  Current options:
% 24.53/4.18  ------ 
% 24.53/4.18  
% 24.53/4.18  
% 24.53/4.18  
% 24.53/4.18  
% 24.53/4.18  ------ Proving...
% 24.53/4.18  
% 24.53/4.18  
% 24.53/4.18  % SZS status Theorem for theBenchmark.p
% 24.53/4.18  
% 24.53/4.18  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 24.53/4.18  
% 24.53/4.19  
%------------------------------------------------------------------------------