TSTP Solution File: SET083+1 by iProver---3.9

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%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET083+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n012.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 02:59:47 EDT 2024

% Result   : Theorem 3.32s 1.13s
% Output   : CNFRefutation 3.32s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [X2,X0,X1] :
      ( member(X2,unordered_pair(X0,X1))
    <=> ( ( X1 = X2
          | X0 = X2 )
        & member(X2,universal_class) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_defn) ).

fof(f6,axiom,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set_defn) ).

fof(f44,conjecture,
    ! [X0,X1] :
      ( ( member(X0,universal_class)
        & singleton(X0) = singleton(X1) )
     => X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_identified_by_element1) ).

fof(f45,negated_conjecture,
    ~ ! [X0,X1] :
        ( ( member(X0,universal_class)
          & singleton(X0) = singleton(X1) )
       => X0 = X1 ),
    inference(negated_conjecture,[],[f44]) ).

fof(f46,plain,
    ! [X0,X1,X2] :
      ( member(X0,unordered_pair(X1,X2))
    <=> ( ( X0 = X2
          | X0 = X1 )
        & member(X0,universal_class) ) ),
    inference(rectify,[],[f4]) ).

fof(f84,plain,
    ? [X0,X1] :
      ( X0 != X1
      & member(X0,universal_class)
      & singleton(X0) = singleton(X1) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f85,plain,
    ? [X0,X1] :
      ( X0 != X1
      & member(X0,universal_class)
      & singleton(X0) = singleton(X1) ),
    inference(flattening,[],[f84]) ).

fof(f92,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,unordered_pair(X1,X2))
        | ( X0 != X2
          & X0 != X1 )
        | ~ member(X0,universal_class) )
      & ( ( ( X0 = X2
            | X0 = X1 )
          & member(X0,universal_class) )
        | ~ member(X0,unordered_pair(X1,X2)) ) ),
    inference(nnf_transformation,[],[f46]) ).

fof(f93,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,unordered_pair(X1,X2))
        | ( X0 != X2
          & X0 != X1 )
        | ~ member(X0,universal_class) )
      & ( ( ( X0 = X2
            | X0 = X1 )
          & member(X0,universal_class) )
        | ~ member(X0,unordered_pair(X1,X2)) ) ),
    inference(flattening,[],[f92]) ).

fof(f134,plain,
    ( ? [X0,X1] :
        ( X0 != X1
        & member(X0,universal_class)
        & singleton(X0) = singleton(X1) )
   => ( sK6 != sK7
      & member(sK6,universal_class)
      & singleton(sK6) = singleton(sK7) ) ),
    introduced(choice_axiom,[]) ).

fof(f135,plain,
    ( sK6 != sK7
    & member(sK6,universal_class)
    & singleton(sK6) = singleton(sK7) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f85,f134]) ).

fof(f144,plain,
    ! [X2,X0,X1] :
      ( X0 = X2
      | X0 = X1
      | ~ member(X0,unordered_pair(X1,X2)) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f146,plain,
    ! [X2,X0,X1] :
      ( member(X0,unordered_pair(X1,X2))
      | X0 != X2
      | ~ member(X0,universal_class) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f148,plain,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    inference(cnf_transformation,[],[f6]) ).

fof(f223,plain,
    singleton(sK6) = singleton(sK7),
    inference(cnf_transformation,[],[f135]) ).

fof(f224,plain,
    member(sK6,universal_class),
    inference(cnf_transformation,[],[f135]) ).

fof(f225,plain,
    sK6 != sK7,
    inference(cnf_transformation,[],[f135]) ).

fof(f263,plain,
    unordered_pair(sK6,sK6) = unordered_pair(sK7,sK7),
    inference(definition_unfolding,[],[f223,f148,f148]) ).

fof(f266,plain,
    ! [X2,X1] :
      ( member(X2,unordered_pair(X1,X2))
      | ~ member(X2,universal_class) ),
    inference(equality_resolution,[],[f146]) ).

cnf(c_56,plain,
    ( ~ member(X0,universal_class)
    | member(X0,unordered_pair(X1,X0)) ),
    inference(cnf_transformation,[],[f266]) ).

cnf(c_58,plain,
    ( ~ member(X0,unordered_pair(X1,X2))
    | X0 = X1
    | X0 = X2 ),
    inference(cnf_transformation,[],[f144]) ).

cnf(c_128,negated_conjecture,
    sK6 != sK7,
    inference(cnf_transformation,[],[f225]) ).

cnf(c_129,negated_conjecture,
    member(sK6,universal_class),
    inference(cnf_transformation,[],[f224]) ).

cnf(c_130,negated_conjecture,
    unordered_pair(sK6,sK6) = unordered_pair(sK7,sK7),
    inference(cnf_transformation,[],[f263]) ).

cnf(c_1562,plain,
    unordered_pair(sK6,sK6) = sP0_iProver_def,
    definition ).

cnf(c_1563,plain,
    unordered_pair(sK7,sK7) = sP1_iProver_def,
    definition ).

cnf(c_1564,negated_conjecture,
    sP0_iProver_def = sP1_iProver_def,
    inference(demodulation,[status(thm)],[c_130,c_1563,c_1562]) ).

cnf(c_1565,negated_conjecture,
    member(sK6,universal_class),
    inference(demodulation,[status(thm)],[c_129]) ).

cnf(c_1566,negated_conjecture,
    sK6 != sK7,
    inference(demodulation,[status(thm)],[c_128]) ).

cnf(c_2385,plain,
    unordered_pair(sK7,sK7) = sP0_iProver_def,
    inference(light_normalisation,[status(thm)],[c_1563,c_1564]) ).

cnf(c_2485,plain,
    ( ~ member(sK6,universal_class)
    | member(sK6,sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_1562,c_56]) ).

cnf(c_2489,plain,
    member(sK6,sP0_iProver_def),
    inference(forward_subsumption_resolution,[status(thm)],[c_2485,c_1565]) ).

cnf(c_3210,plain,
    ( ~ member(X0,sP0_iProver_def)
    | X0 = sK7 ),
    inference(superposition,[status(thm)],[c_2385,c_58]) ).

cnf(c_3350,plain,
    sK6 = sK7,
    inference(superposition,[status(thm)],[c_2489,c_3210]) ).

cnf(c_3352,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_3350,c_1566]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SET083+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.03/0.12  % Command  : run_iprover %s %d THM
% 0.11/0.32  % Computer : n012.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Thu May  2 20:08:25 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.17/0.44  Running first-order theorem proving
% 0.17/0.44  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
% 3.32/1.13  % SZS status Started for theBenchmark.p
% 3.32/1.13  % SZS status Theorem for theBenchmark.p
% 3.32/1.13  
% 3.32/1.13  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.32/1.13  
% 3.32/1.13  ------  iProver source info
% 3.32/1.13  
% 3.32/1.13  git: date: 2024-05-02 19:28:25 +0000
% 3.32/1.13  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.32/1.13  git: non_committed_changes: false
% 3.32/1.13  
% 3.32/1.13  ------ Parsing...
% 3.32/1.13  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.32/1.13  
% 3.32/1.13  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sup_sim: 0  sf_s  rm: 4 0s  sf_e  pe_s  pe_e 
% 3.32/1.13  
% 3.32/1.13  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.32/1.13  
% 3.32/1.13  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.32/1.13  ------ Proving...
% 3.32/1.13  ------ Problem Properties 
% 3.32/1.13  
% 3.32/1.13  
% 3.32/1.13  clauses                                 79
% 3.32/1.13  conjectures                             3
% 3.32/1.13  EPR                                     10
% 3.32/1.13  Horn                                    71
% 3.32/1.13  unary                                   19
% 3.32/1.13  binary                                  39
% 3.32/1.13  lits                                    161
% 3.32/1.13  lits eq                                 18
% 3.32/1.13  fd_pure                                 0
% 3.32/1.13  fd_pseudo                               0
% 3.32/1.13  fd_cond                                 4
% 3.32/1.13  fd_pseudo_cond                          3
% 3.32/1.13  AC symbols                              0
% 3.32/1.13  
% 3.32/1.13  ------ Schedule dynamic 5 is on 
% 3.32/1.13  
% 3.32/1.13  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.32/1.13  
% 3.32/1.13  
% 3.32/1.13  ------ 
% 3.32/1.13  Current options:
% 3.32/1.13  ------ 
% 3.32/1.13  
% 3.32/1.13  
% 3.32/1.13  
% 3.32/1.13  
% 3.32/1.13  ------ Proving...
% 3.32/1.13  
% 3.32/1.13  
% 3.32/1.13  % SZS status Theorem for theBenchmark.p
% 3.32/1.13  
% 3.32/1.13  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.32/1.13  
% 3.32/1.13  
%------------------------------------------------------------------------------