TSTP Solution File: SEU026+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SEU026+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n023.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 03:04:22 EDT 2024

% Result   : Theorem 4.00s 1.17s
% Output   : CNFRefutation 4.00s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( function(function_inverse(X0))
        & relation(function_inverse(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).

fof(f29,axiom,
    ! [X0,X1] : subset(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

fof(f33,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( relation(X1)
         => ( subset(relation_rng(X0),relation_dom(X1))
           => relation_dom(X0) = relation_dom(relation_composition(X0,X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_relat_1) ).

fof(f34,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( relation(X1)
         => ( subset(relation_dom(X0),relation_rng(X1))
           => relation_rng(X0) = relation_rng(relation_composition(X1,X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_relat_1) ).

fof(f36,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( one_to_one(X0)
       => ( relation_dom(X0) = relation_rng(function_inverse(X0))
          & relation_rng(X0) = relation_dom(function_inverse(X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).

fof(f37,conjecture,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( one_to_one(X0)
       => ( relation_rng(X0) = relation_rng(relation_composition(function_inverse(X0),X0))
          & relation_rng(X0) = relation_dom(relation_composition(function_inverse(X0),X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_funct_1) ).

fof(f38,negated_conjecture,
    ~ ! [X0] :
        ( ( function(X0)
          & relation(X0) )
       => ( one_to_one(X0)
         => ( relation_rng(X0) = relation_rng(relation_composition(function_inverse(X0),X0))
            & relation_rng(X0) = relation_dom(relation_composition(function_inverse(X0),X0)) ) ) ),
    inference(negated_conjecture,[],[f37]) ).

fof(f43,plain,
    ! [X0] : subset(X0,X0),
    inference(rectify,[],[f29]) ).

fof(f51,plain,
    ! [X0] :
      ( ( function(function_inverse(X0))
        & relation(function_inverse(X0)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f52,plain,
    ! [X0] :
      ( ( function(function_inverse(X0))
        & relation(function_inverse(X0)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f51]) ).

fof(f71,plain,
    ! [X0] :
      ( ! [X1] :
          ( relation_dom(X0) = relation_dom(relation_composition(X0,X1))
          | ~ subset(relation_rng(X0),relation_dom(X1))
          | ~ relation(X1) )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f72,plain,
    ! [X0] :
      ( ! [X1] :
          ( relation_dom(X0) = relation_dom(relation_composition(X0,X1))
          | ~ subset(relation_rng(X0),relation_dom(X1))
          | ~ relation(X1) )
      | ~ relation(X0) ),
    inference(flattening,[],[f71]) ).

fof(f73,plain,
    ! [X0] :
      ( ! [X1] :
          ( relation_rng(X0) = relation_rng(relation_composition(X1,X0))
          | ~ subset(relation_dom(X0),relation_rng(X1))
          | ~ relation(X1) )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f74,plain,
    ! [X0] :
      ( ! [X1] :
          ( relation_rng(X0) = relation_rng(relation_composition(X1,X0))
          | ~ subset(relation_dom(X0),relation_rng(X1))
          | ~ relation(X1) )
      | ~ relation(X0) ),
    inference(flattening,[],[f73]) ).

fof(f77,plain,
    ! [X0] :
      ( ( relation_dom(X0) = relation_rng(function_inverse(X0))
        & relation_rng(X0) = relation_dom(function_inverse(X0)) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f78,plain,
    ! [X0] :
      ( ( relation_dom(X0) = relation_rng(function_inverse(X0))
        & relation_rng(X0) = relation_dom(function_inverse(X0)) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f77]) ).

fof(f79,plain,
    ? [X0] :
      ( ( relation_rng(X0) != relation_rng(relation_composition(function_inverse(X0),X0))
        | relation_rng(X0) != relation_dom(relation_composition(function_inverse(X0),X0)) )
      & one_to_one(X0)
      & function(X0)
      & relation(X0) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f80,plain,
    ? [X0] :
      ( ( relation_rng(X0) != relation_rng(relation_composition(function_inverse(X0),X0))
        | relation_rng(X0) != relation_dom(relation_composition(function_inverse(X0),X0)) )
      & one_to_one(X0)
      & function(X0)
      & relation(X0) ),
    inference(flattening,[],[f79]) ).

fof(f108,plain,
    ( ? [X0] :
        ( ( relation_rng(X0) != relation_rng(relation_composition(function_inverse(X0),X0))
          | relation_rng(X0) != relation_dom(relation_composition(function_inverse(X0),X0)) )
        & one_to_one(X0)
        & function(X0)
        & relation(X0) )
   => ( ( relation_rng(sK11) != relation_rng(relation_composition(function_inverse(sK11),sK11))
        | relation_rng(sK11) != relation_dom(relation_composition(function_inverse(sK11),sK11)) )
      & one_to_one(sK11)
      & function(sK11)
      & relation(sK11) ) ),
    introduced(choice_axiom,[]) ).

fof(f109,plain,
    ( ( relation_rng(sK11) != relation_rng(relation_composition(function_inverse(sK11),sK11))
      | relation_rng(sK11) != relation_dom(relation_composition(function_inverse(sK11),sK11)) )
    & one_to_one(sK11)
    & function(sK11)
    & relation(sK11) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f80,f108]) ).

fof(f116,plain,
    ! [X0] :
      ( relation(function_inverse(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f157,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f43]) ).

fof(f162,plain,
    ! [X0,X1] :
      ( relation_dom(X0) = relation_dom(relation_composition(X0,X1))
      | ~ subset(relation_rng(X0),relation_dom(X1))
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f163,plain,
    ! [X0,X1] :
      ( relation_rng(X0) = relation_rng(relation_composition(X1,X0))
      | ~ subset(relation_dom(X0),relation_rng(X1))
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f165,plain,
    ! [X0] :
      ( relation_rng(X0) = relation_dom(function_inverse(X0))
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f78]) ).

fof(f166,plain,
    ! [X0] :
      ( relation_dom(X0) = relation_rng(function_inverse(X0))
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f78]) ).

fof(f167,plain,
    relation(sK11),
    inference(cnf_transformation,[],[f109]) ).

fof(f168,plain,
    function(sK11),
    inference(cnf_transformation,[],[f109]) ).

fof(f169,plain,
    one_to_one(sK11),
    inference(cnf_transformation,[],[f109]) ).

fof(f170,plain,
    ( relation_rng(sK11) != relation_rng(relation_composition(function_inverse(sK11),sK11))
    | relation_rng(sK11) != relation_dom(relation_composition(function_inverse(sK11),sK11)) ),
    inference(cnf_transformation,[],[f109]) ).

cnf(c_54,plain,
    ( ~ function(X0)
    | ~ relation(X0)
    | relation(function_inverse(X0)) ),
    inference(cnf_transformation,[],[f116]) ).

cnf(c_94,plain,
    subset(X0,X0),
    inference(cnf_transformation,[],[f157]) ).

cnf(c_99,plain,
    ( ~ subset(relation_rng(X0),relation_dom(X1))
    | ~ relation(X0)
    | ~ relation(X1)
    | relation_dom(relation_composition(X0,X1)) = relation_dom(X0) ),
    inference(cnf_transformation,[],[f162]) ).

cnf(c_100,plain,
    ( ~ subset(relation_dom(X0),relation_rng(X1))
    | ~ relation(X0)
    | ~ relation(X1)
    | relation_rng(relation_composition(X1,X0)) = relation_rng(X0) ),
    inference(cnf_transformation,[],[f163]) ).

cnf(c_102,plain,
    ( ~ function(X0)
    | ~ relation(X0)
    | ~ one_to_one(X0)
    | relation_rng(function_inverse(X0)) = relation_dom(X0) ),
    inference(cnf_transformation,[],[f166]) ).

cnf(c_103,plain,
    ( ~ function(X0)
    | ~ relation(X0)
    | ~ one_to_one(X0)
    | relation_dom(function_inverse(X0)) = relation_rng(X0) ),
    inference(cnf_transformation,[],[f165]) ).

cnf(c_104,negated_conjecture,
    ( relation_dom(relation_composition(function_inverse(sK11),sK11)) != relation_rng(sK11)
    | relation_rng(relation_composition(function_inverse(sK11),sK11)) != relation_rng(sK11) ),
    inference(cnf_transformation,[],[f170]) ).

cnf(c_105,negated_conjecture,
    one_to_one(sK11),
    inference(cnf_transformation,[],[f169]) ).

cnf(c_106,negated_conjecture,
    function(sK11),
    inference(cnf_transformation,[],[f168]) ).

cnf(c_107,negated_conjecture,
    relation(sK11),
    inference(cnf_transformation,[],[f167]) ).

cnf(c_137,plain,
    ( ~ function(sK11)
    | ~ relation(sK11)
    | ~ one_to_one(sK11)
    | relation_dom(function_inverse(sK11)) = relation_rng(sK11) ),
    inference(instantiation,[status(thm)],[c_103]) ).

cnf(c_138,plain,
    ( ~ function(sK11)
    | ~ relation(sK11)
    | ~ one_to_one(sK11)
    | relation_rng(function_inverse(sK11)) = relation_dom(sK11) ),
    inference(instantiation,[status(thm)],[c_102]) ).

cnf(c_750,plain,
    ( X0 != sK11
    | ~ function(X0)
    | ~ relation(X0)
    | relation_dom(function_inverse(X0)) = relation_rng(X0) ),
    inference(resolution_lifted,[status(thm)],[c_103,c_105]) ).

cnf(c_751,plain,
    ( ~ function(sK11)
    | ~ relation(sK11)
    | relation_dom(function_inverse(sK11)) = relation_rng(sK11) ),
    inference(unflattening,[status(thm)],[c_750]) ).

cnf(c_752,plain,
    relation_dom(function_inverse(sK11)) = relation_rng(sK11),
    inference(global_subsumption_just,[status(thm)],[c_751,c_107,c_106,c_105,c_137]) ).

cnf(c_757,plain,
    ( X0 != sK11
    | ~ function(X0)
    | ~ relation(X0)
    | relation_rng(function_inverse(X0)) = relation_dom(X0) ),
    inference(resolution_lifted,[status(thm)],[c_102,c_105]) ).

cnf(c_758,plain,
    ( ~ function(sK11)
    | ~ relation(sK11)
    | relation_rng(function_inverse(sK11)) = relation_dom(sK11) ),
    inference(unflattening,[status(thm)],[c_757]) ).

cnf(c_759,plain,
    relation_rng(function_inverse(sK11)) = relation_dom(sK11),
    inference(global_subsumption_just,[status(thm)],[c_758,c_107,c_106,c_105,c_138]) ).

cnf(c_1816,plain,
    function_inverse(sK11) = sP0_iProver_def,
    definition ).

cnf(c_1817,plain,
    relation_composition(sP0_iProver_def,sK11) = sP1_iProver_def,
    definition ).

cnf(c_1818,plain,
    relation_dom(sP1_iProver_def) = sP2_iProver_def,
    definition ).

cnf(c_1819,plain,
    relation_rng(sK11) = sP3_iProver_def,
    definition ).

cnf(c_1820,plain,
    relation_rng(sP1_iProver_def) = sP4_iProver_def,
    definition ).

cnf(c_1821,negated_conjecture,
    relation(sK11),
    inference(demodulation,[status(thm)],[c_107]) ).

cnf(c_1822,negated_conjecture,
    function(sK11),
    inference(demodulation,[status(thm)],[c_106]) ).

cnf(c_1823,negated_conjecture,
    ( sP2_iProver_def != sP3_iProver_def
    | sP4_iProver_def != sP3_iProver_def ),
    inference(demodulation,[status(thm)],[c_104,c_1820,c_1819,c_1816,c_1817,c_1818]) ).

cnf(c_2777,plain,
    relation_dom(sP0_iProver_def) = sP3_iProver_def,
    inference(light_normalisation,[status(thm)],[c_752,c_1816,c_1819]) ).

cnf(c_2778,plain,
    relation_dom(sK11) = relation_rng(sP0_iProver_def),
    inference(light_normalisation,[status(thm)],[c_759,c_1816]) ).

cnf(c_3055,plain,
    ( ~ function(sK11)
    | ~ relation(sK11)
    | relation(sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_1816,c_54]) ).

cnf(c_3056,plain,
    relation(sP0_iProver_def),
    inference(forward_subsumption_resolution,[status(thm)],[c_3055,c_1821,c_1822]) ).

cnf(c_3728,plain,
    ( ~ subset(relation_rng(X0),relation_rng(sP0_iProver_def))
    | ~ relation(X0)
    | ~ relation(sK11)
    | relation_dom(relation_composition(X0,sK11)) = relation_dom(X0) ),
    inference(superposition,[status(thm)],[c_2778,c_99]) ).

cnf(c_3755,plain,
    ( ~ subset(relation_rng(X0),relation_rng(sP0_iProver_def))
    | ~ relation(X0)
    | relation_dom(relation_composition(X0,sK11)) = relation_dom(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_3728,c_1821]) ).

cnf(c_3791,plain,
    ( ~ subset(relation_rng(sP0_iProver_def),relation_rng(X0))
    | ~ relation(X0)
    | ~ relation(sK11)
    | relation_rng(relation_composition(X0,sK11)) = relation_rng(sK11) ),
    inference(superposition,[status(thm)],[c_2778,c_100]) ).

cnf(c_3819,plain,
    ( ~ subset(relation_rng(sP0_iProver_def),relation_rng(X0))
    | ~ relation(X0)
    | ~ relation(sK11)
    | relation_rng(relation_composition(X0,sK11)) = sP3_iProver_def ),
    inference(light_normalisation,[status(thm)],[c_3791,c_1819]) ).

cnf(c_3820,plain,
    ( ~ subset(relation_rng(sP0_iProver_def),relation_rng(X0))
    | ~ relation(X0)
    | relation_rng(relation_composition(X0,sK11)) = sP3_iProver_def ),
    inference(forward_subsumption_resolution,[status(thm)],[c_3819,c_1821]) ).

cnf(c_3997,plain,
    ( ~ relation(sP0_iProver_def)
    | relation_rng(relation_composition(sP0_iProver_def,sK11)) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_94,c_3820]) ).

cnf(c_4002,plain,
    ( ~ relation(sP0_iProver_def)
    | sP3_iProver_def = sP4_iProver_def ),
    inference(light_normalisation,[status(thm)],[c_3997,c_1817,c_1820]) ).

cnf(c_4003,plain,
    sP3_iProver_def = sP4_iProver_def,
    inference(forward_subsumption_resolution,[status(thm)],[c_4002,c_3056]) ).

cnf(c_4018,plain,
    ( sP2_iProver_def != sP3_iProver_def
    | sP3_iProver_def != sP3_iProver_def ),
    inference(demodulation,[status(thm)],[c_1823,c_4003]) ).

cnf(c_4019,plain,
    sP2_iProver_def != sP3_iProver_def,
    inference(equality_resolution_simp,[status(thm)],[c_4018]) ).

cnf(c_4032,plain,
    ( ~ relation(sP0_iProver_def)
    | relation_dom(relation_composition(sP0_iProver_def,sK11)) = relation_dom(sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_94,c_3755]) ).

cnf(c_4036,plain,
    ( ~ relation(sP0_iProver_def)
    | sP2_iProver_def = sP3_iProver_def ),
    inference(light_normalisation,[status(thm)],[c_4032,c_1817,c_1818,c_2777]) ).

cnf(c_4037,plain,
    sP2_iProver_def = sP3_iProver_def,
    inference(forward_subsumption_resolution,[status(thm)],[c_4036,c_3056]) ).

cnf(c_4092,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_4037,c_4019]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU026+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13  % Command  : run_iprover %s %d THM
% 0.14/0.34  % Computer : n023.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu May  2 18:07:39 EDT 2024
% 0.21/0.34  % CPUTime  : 
% 0.21/0.47  Running first-order theorem proving
% 0.21/0.47  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
% 4.00/1.17  % SZS status Started for theBenchmark.p
% 4.00/1.17  % SZS status Theorem for theBenchmark.p
% 4.00/1.17  
% 4.00/1.17  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 4.00/1.17  
% 4.00/1.17  ------  iProver source info
% 4.00/1.17  
% 4.00/1.17  git: date: 2024-05-02 19:28:25 +0000
% 4.00/1.17  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 4.00/1.17  git: non_committed_changes: false
% 4.00/1.17  
% 4.00/1.17  ------ Parsing...
% 4.00/1.17  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 4.00/1.17  
% 4.00/1.17  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e 
% 4.00/1.17  
% 4.00/1.17  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 4.00/1.17  
% 4.00/1.17  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 4.00/1.17  ------ Proving...
% 4.00/1.17  ------ Problem Properties 
% 4.00/1.17  
% 4.00/1.17  
% 4.00/1.17  clauses                                 65
% 4.00/1.17  conjectures                             3
% 4.00/1.17  EPR                                     30
% 4.00/1.17  Horn                                    63
% 4.00/1.17  unary                                   32
% 4.00/1.17  binary                                  17
% 4.00/1.17  lits                                    118
% 4.00/1.17  lits eq                                 17
% 4.00/1.17  fd_pure                                 0
% 4.00/1.17  fd_pseudo                               0
% 4.00/1.17  fd_cond                                 1
% 4.00/1.17  fd_pseudo_cond                          1
% 4.00/1.17  AC symbols                              0
% 4.00/1.17  
% 4.00/1.17  ------ Schedule dynamic 5 is on 
% 4.00/1.17  
% 4.00/1.17  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.00/1.17  
% 4.00/1.17  
% 4.00/1.17  ------ 
% 4.00/1.17  Current options:
% 4.00/1.17  ------ 
% 4.00/1.17  
% 4.00/1.17  
% 4.00/1.17  
% 4.00/1.17  
% 4.00/1.17  ------ Proving...
% 4.00/1.17  
% 4.00/1.17  
% 4.00/1.17  % SZS status Theorem for theBenchmark.p
% 4.00/1.17  
% 4.00/1.17  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.00/1.17  
% 4.00/1.17  
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