TSTP Solution File: SET194+3 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET194+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n010.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 03:00:14 EDT 2024

% Result   : Theorem 2.13s 1.14s
% Output   : CNFRefutation 2.13s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1,X2] :
      ( member(X2,union(X0,X1))
    <=> ( member(X2,X1)
        | member(X2,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).

fof(f6,conjecture,
    ! [X0,X1] : subset(X0,union(X0,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_subset_of_union) ).

fof(f7,negated_conjecture,
    ~ ! [X0,X1] : subset(X0,union(X0,X1)),
    inference(negated_conjecture,[],[f6]) ).

fof(f8,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f9,plain,
    ? [X0,X1] : ~ subset(X0,union(X0,X1)),
    inference(ennf_transformation,[],[f7]) ).

fof(f10,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X0,X1))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) )
      & ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X0,X1)) ) ),
    inference(nnf_transformation,[],[f1]) ).

fof(f11,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X0,X1))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) )
      & ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X0,X1)) ) ),
    inference(flattening,[],[f10]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f12]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK0(X0,X1),X1)
          & member(sK0(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f13,f14]) ).

fof(f20,plain,
    ( ? [X0,X1] : ~ subset(X0,union(X0,X1))
   => ~ subset(sK2,union(sK2,sK3)) ),
    introduced(choice_axiom,[]) ).

fof(f21,plain,
    ~ subset(sK2,union(sK2,sK3)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f9,f20]) ).

fof(f23,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f11]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f34,plain,
    ~ subset(sK2,union(sK2,sK3)),
    inference(cnf_transformation,[],[f21]) ).

cnf(c_50,plain,
    ( ~ member(X0,X1)
    | member(X0,union(X1,X2)) ),
    inference(cnf_transformation,[],[f23]) ).

cnf(c_52,plain,
    ( ~ member(sK0(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f27]) ).

cnf(c_53,plain,
    ( member(sK0(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f26]) ).

cnf(c_59,negated_conjecture,
    ~ subset(sK2,union(sK2,sK3)),
    inference(cnf_transformation,[],[f34]) ).

cnf(c_204,plain,
    union(sK2,sK3) = sP0_iProver_def,
    definition ).

cnf(c_205,negated_conjecture,
    ~ subset(sK2,sP0_iProver_def),
    inference(demodulation,[status(thm)],[c_59,c_204]) ).

cnf(c_402,plain,
    ( ~ member(X0,sK2)
    | member(X0,sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_204,c_50]) ).

cnf(c_508,plain,
    ( member(sK0(sK2,X0),sP0_iProver_def)
    | subset(sK2,X0) ),
    inference(superposition,[status(thm)],[c_53,c_402]) ).

cnf(c_526,plain,
    subset(sK2,sP0_iProver_def),
    inference(superposition,[status(thm)],[c_508,c_52]) ).

cnf(c_527,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_526,c_205]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SET194+3 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.12  % Command  : run_iprover %s %d THM
% 0.12/0.32  % Computer : n010.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Thu May  2 20:15:04 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.18/0.44  Running first-order theorem proving
% 0.18/0.44  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.13/1.14  % SZS status Started for theBenchmark.p
% 2.13/1.14  % SZS status Theorem for theBenchmark.p
% 2.13/1.14  
% 2.13/1.14  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 2.13/1.14  
% 2.13/1.14  ------  iProver source info
% 2.13/1.14  
% 2.13/1.14  git: date: 2024-05-02 19:28:25 +0000
% 2.13/1.14  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 2.13/1.14  git: non_committed_changes: false
% 2.13/1.14  
% 2.13/1.14  ------ Parsing...
% 2.13/1.14  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.13/1.14  
% 2.13/1.14  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 2.13/1.14  
% 2.13/1.14  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.13/1.14  
% 2.13/1.14  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.13/1.14  ------ Proving...
% 2.13/1.14  ------ Problem Properties 
% 2.13/1.14  
% 2.13/1.14  
% 2.13/1.14  clauses                                 12
% 2.13/1.14  conjectures                             1
% 2.13/1.14  EPR                                     3
% 2.13/1.14  Horn                                    9
% 2.13/1.14  unary                                   4
% 2.13/1.14  binary                                  4
% 2.13/1.14  lits                                    24
% 2.13/1.14  lits eq                                 4
% 2.13/1.14  fd_pure                                 0
% 2.13/1.14  fd_pseudo                               0
% 2.13/1.14  fd_cond                                 0
% 2.13/1.14  fd_pseudo_cond                          2
% 2.13/1.14  AC symbols                              0
% 2.13/1.14  
% 2.13/1.14  ------ Schedule dynamic 5 is on 
% 2.13/1.14  
% 2.13/1.14  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.13/1.14  
% 2.13/1.14  
% 2.13/1.14  ------ 
% 2.13/1.14  Current options:
% 2.13/1.14  ------ 
% 2.13/1.14  
% 2.13/1.14  
% 2.13/1.14  
% 2.13/1.14  
% 2.13/1.14  ------ Proving...
% 2.13/1.14  
% 2.13/1.14  
% 2.13/1.14  % SZS status Theorem for theBenchmark.p
% 2.13/1.14  
% 2.13/1.14  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.13/1.14  
% 2.13/1.14  
%------------------------------------------------------------------------------