TSTP Solution File: SWV381+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SWV381+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : Thu Aug 31 22:32:47 EDT 2023

% Result   : Theorem 3.69s 1.13s
% Output   : CNFRefutation 3.69s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   55 (  10 unt;   0 def)
%            Number of atoms       :  129 (   8 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  129 (  55   ~;  50   |;  12   &)
%                                         (   3 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-3 aty)
%            Number of variables   :  117 (   0 sgn;  65   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [X0,X1] :
      ( less_than(X1,X0)
      | less_than(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( strictly_less_than(X0,X1)
    <=> ( ~ less_than(X1,X0)
        & less_than(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricly_smaller_definition) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( issmallestelement_pq(X0,X1)
    <=> ! [X2] :
          ( contains_pq(X0,X2)
         => less_than(X1,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10) ).

fof(f53,axiom,
    ! [X0] : findmin_cpq_res(X0) = removemin_cpq_res(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax53) ).

fof(f63,axiom,
    ! [X0,X1,X2,X3] :
      ( contains_cpq(triple(X0,X1,X2),X3)
    <=> contains_pq(i(triple(X0,X1,X2)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l17_li56) ).

fof(f64,axiom,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
          & contains_cpq(triple(X0,X1,X2),X3) )
     => ~ phi(findmin_cpq_eff(triple(X0,X1,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l17_l18) ).

fof(f65,conjecture,
    ! [X0,X1,X2] :
      ( phi(findmin_cpq_eff(triple(X0,X1,X2)))
     => issmallestelement_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l17_co) ).

fof(f66,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( phi(findmin_cpq_eff(triple(X0,X1,X2)))
       => issmallestelement_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2))) ),
    inference(negated_conjecture,[],[f65]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( contains_pq(X0,X2)
         => less_than(X1,X2) )
     => issmallestelement_pq(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f10]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( ( ~ less_than(X1,X0)
        & less_than(X0,X1) )
     => strictly_less_than(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f4]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( strictly_less_than(X0,X1)
      | less_than(X1,X0)
      | ~ less_than(X0,X1) ),
    inference(ennf_transformation,[],[f76]) ).

fof(f80,plain,
    ! [X0,X1] :
      ( strictly_less_than(X0,X1)
      | less_than(X1,X0)
      | ~ less_than(X0,X1) ),
    inference(flattening,[],[f79]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( issmallestelement_pq(X0,X1)
      | ? [X2] :
          ( ~ less_than(X1,X2)
          & contains_pq(X0,X2) ) ),
    inference(ennf_transformation,[],[f75]) ).

fof(f117,plain,
    ! [X0,X1,X2] :
      ( ~ phi(findmin_cpq_eff(triple(X0,X1,X2)))
      | ! [X3] :
          ( ~ strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
          | ~ contains_cpq(triple(X0,X1,X2),X3) ) ),
    inference(ennf_transformation,[],[f64]) ).

fof(f118,plain,
    ? [X0,X1,X2] :
      ( ~ issmallestelement_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2)))
      & phi(findmin_cpq_eff(triple(X0,X1,X2))) ),
    inference(ennf_transformation,[],[f66]) ).

fof(f121,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ less_than(X1,X2)
          & contains_pq(X0,X2) )
     => ( ~ less_than(X1,sK0(X0,X1))
        & contains_pq(X0,sK0(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f122,plain,
    ! [X0,X1] :
      ( issmallestelement_pq(X0,X1)
      | ( ~ less_than(X1,sK0(X0,X1))
        & contains_pq(X0,sK0(X0,X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f81,f121]) ).

fof(f133,plain,
    ! [X0,X1,X2,X3] :
      ( ( contains_cpq(triple(X0,X1,X2),X3)
        | ~ contains_pq(i(triple(X0,X1,X2)),X3) )
      & ( contains_pq(i(triple(X0,X1,X2)),X3)
        | ~ contains_cpq(triple(X0,X1,X2),X3) ) ),
    inference(nnf_transformation,[],[f63]) ).

fof(f134,plain,
    ( ? [X0,X1,X2] :
        ( ~ issmallestelement_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2)))
        & phi(findmin_cpq_eff(triple(X0,X1,X2))) )
   => ( ~ issmallestelement_pq(i(triple(sK2,sK3,sK4)),findmin_cpq_res(triple(sK2,sK3,sK4)))
      & phi(findmin_cpq_eff(triple(sK2,sK3,sK4))) ) ),
    introduced(choice_axiom,[]) ).

fof(f135,plain,
    ( ~ issmallestelement_pq(i(triple(sK2,sK3,sK4)),findmin_cpq_res(triple(sK2,sK3,sK4)))
    & phi(findmin_cpq_eff(triple(sK2,sK3,sK4))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f118,f134]) ).

fof(f137,plain,
    ! [X0,X1] :
      ( less_than(X1,X0)
      | less_than(X0,X1) ),
    inference(cnf_transformation,[],[f2]) ).

fof(f139,plain,
    ! [X0,X1] :
      ( strictly_less_than(X0,X1)
      | less_than(X1,X0)
      | ~ less_than(X0,X1) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( issmallestelement_pq(X0,X1)
      | contains_pq(X0,sK0(X0,X1)) ),
    inference(cnf_transformation,[],[f122]) ).

fof(f148,plain,
    ! [X0,X1] :
      ( issmallestelement_pq(X0,X1)
      | ~ less_than(X1,sK0(X0,X1)) ),
    inference(cnf_transformation,[],[f122]) ).

fof(f198,plain,
    ! [X0] : findmin_cpq_res(X0) = removemin_cpq_res(X0),
    inference(cnf_transformation,[],[f53]) ).

fof(f206,plain,
    ! [X2,X3,X0,X1] :
      ( contains_cpq(triple(X0,X1,X2),X3)
      | ~ contains_pq(i(triple(X0,X1,X2)),X3) ),
    inference(cnf_transformation,[],[f133]) ).

fof(f207,plain,
    ! [X2,X3,X0,X1] :
      ( ~ phi(findmin_cpq_eff(triple(X0,X1,X2)))
      | ~ strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
      | ~ contains_cpq(triple(X0,X1,X2),X3) ),
    inference(cnf_transformation,[],[f117]) ).

fof(f208,plain,
    phi(findmin_cpq_eff(triple(sK2,sK3,sK4))),
    inference(cnf_transformation,[],[f135]) ).

fof(f209,plain,
    ~ issmallestelement_pq(i(triple(sK2,sK3,sK4)),findmin_cpq_res(triple(sK2,sK3,sK4))),
    inference(cnf_transformation,[],[f135]) ).

fof(f214,plain,
    ! [X2,X3,X0,X1] :
      ( ~ phi(findmin_cpq_eff(triple(X0,X1,X2)))
      | ~ strictly_less_than(X3,removemin_cpq_res(triple(X0,X1,X2)))
      | ~ contains_cpq(triple(X0,X1,X2),X3) ),
    inference(definition_unfolding,[],[f207,f198]) ).

fof(f215,plain,
    ~ issmallestelement_pq(i(triple(sK2,sK3,sK4)),removemin_cpq_res(triple(sK2,sK3,sK4))),
    inference(definition_unfolding,[],[f209,f198]) ).

cnf(c_50,plain,
    ( less_than(X0,X1)
    | less_than(X1,X0) ),
    inference(cnf_transformation,[],[f137]) ).

cnf(c_52,plain,
    ( ~ less_than(X0,X1)
    | less_than(X1,X0)
    | strictly_less_than(X0,X1) ),
    inference(cnf_transformation,[],[f139]) ).

cnf(c_60,plain,
    ( ~ less_than(X0,sK0(X1,X0))
    | issmallestelement_pq(X1,X0) ),
    inference(cnf_transformation,[],[f148]) ).

cnf(c_61,plain,
    ( contains_pq(X0,sK0(X0,X1))
    | issmallestelement_pq(X0,X1) ),
    inference(cnf_transformation,[],[f147]) ).

cnf(c_116,plain,
    ( ~ contains_pq(i(triple(X0,X1,X2)),X3)
    | contains_cpq(triple(X0,X1,X2),X3) ),
    inference(cnf_transformation,[],[f206]) ).

cnf(c_118,plain,
    ( ~ strictly_less_than(X0,removemin_cpq_res(triple(X1,X2,X3)))
    | ~ contains_cpq(triple(X1,X2,X3),X0)
    | ~ phi(findmin_cpq_eff(triple(X1,X2,X3))) ),
    inference(cnf_transformation,[],[f214]) ).

cnf(c_119,negated_conjecture,
    ~ issmallestelement_pq(i(triple(sK2,sK3,sK4)),removemin_cpq_res(triple(sK2,sK3,sK4))),
    inference(cnf_transformation,[],[f215]) ).

cnf(c_120,negated_conjecture,
    phi(findmin_cpq_eff(triple(sK2,sK3,sK4))),
    inference(cnf_transformation,[],[f208]) ).

cnf(c_176,plain,
    ( less_than(X1,X0)
    | strictly_less_than(X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_52,c_50,c_52]) ).

cnf(c_177,plain,
    ( less_than(X0,X1)
    | strictly_less_than(X1,X0) ),
    inference(renaming,[status(thm)],[c_176]) ).

cnf(c_189,plain,
    ( less_than(X0,X1)
    | strictly_less_than(X1,X0) ),
    inference(prop_impl_just,[status(thm)],[c_177]) ).

cnf(c_197,plain,
    ( ~ less_than(X0,sK0(X1,X0))
    | issmallestelement_pq(X1,X0) ),
    inference(prop_impl_just,[status(thm)],[c_60]) ).

cnf(c_199,plain,
    ( issmallestelement_pq(X0,X1)
    | contains_pq(X0,sK0(X0,X1)) ),
    inference(prop_impl_just,[status(thm)],[c_61]) ).

cnf(c_200,plain,
    ( contains_pq(X0,sK0(X0,X1))
    | issmallestelement_pq(X0,X1) ),
    inference(renaming,[status(thm)],[c_199]) ).

cnf(c_1023,plain,
    ( removemin_cpq_res(triple(X0,X1,X2)) != X3
    | X4 != X5
    | ~ contains_cpq(triple(X0,X1,X2),X4)
    | ~ phi(findmin_cpq_eff(triple(X0,X1,X2)))
    | less_than(X3,X5) ),
    inference(resolution_lifted,[status(thm)],[c_118,c_189]) ).

cnf(c_1024,plain,
    ( ~ contains_cpq(triple(X0,X1,X2),X3)
    | ~ phi(findmin_cpq_eff(triple(X0,X1,X2)))
    | less_than(removemin_cpq_res(triple(X0,X1,X2)),X3) ),
    inference(unflattening,[status(thm)],[c_1023]) ).

cnf(c_1351,plain,
    ( removemin_cpq_res(triple(sK2,sK3,sK4)) != X0
    | i(triple(sK2,sK3,sK4)) != X1
    | ~ less_than(X0,sK0(X1,X0)) ),
    inference(resolution_lifted,[status(thm)],[c_197,c_119]) ).

cnf(c_1352,plain,
    ~ less_than(removemin_cpq_res(triple(sK2,sK3,sK4)),sK0(i(triple(sK2,sK3,sK4)),removemin_cpq_res(triple(sK2,sK3,sK4)))),
    inference(unflattening,[status(thm)],[c_1351]) ).

cnf(c_1356,plain,
    ( removemin_cpq_res(triple(sK2,sK3,sK4)) != X1
    | i(triple(sK2,sK3,sK4)) != X0
    | contains_pq(X0,sK0(X0,X1)) ),
    inference(resolution_lifted,[status(thm)],[c_200,c_119]) ).

cnf(c_1357,plain,
    contains_pq(i(triple(sK2,sK3,sK4)),sK0(i(triple(sK2,sK3,sK4)),removemin_cpq_res(triple(sK2,sK3,sK4)))),
    inference(unflattening,[status(thm)],[c_1356]) ).

cnf(c_4580,plain,
    ( ~ contains_cpq(triple(sK2,sK3,sK4),X0)
    | ~ phi(findmin_cpq_eff(triple(sK2,sK3,sK4)))
    | less_than(removemin_cpq_res(triple(sK2,sK3,sK4)),X0) ),
    inference(instantiation,[status(thm)],[c_1024]) ).

cnf(c_5021,plain,
    ( ~ contains_pq(i(triple(sK2,sK3,sK4)),sK0(i(triple(sK2,sK3,sK4)),removemin_cpq_res(triple(sK2,sK3,sK4))))
    | contains_cpq(triple(sK2,sK3,sK4),sK0(i(triple(sK2,sK3,sK4)),removemin_cpq_res(triple(sK2,sK3,sK4)))) ),
    inference(instantiation,[status(thm)],[c_116]) ).

cnf(c_8494,plain,
    ( ~ contains_cpq(triple(sK2,sK3,sK4),sK0(i(triple(sK2,sK3,sK4)),removemin_cpq_res(triple(sK2,sK3,sK4))))
    | ~ phi(findmin_cpq_eff(triple(sK2,sK3,sK4)))
    | less_than(removemin_cpq_res(triple(sK2,sK3,sK4)),sK0(i(triple(sK2,sK3,sK4)),removemin_cpq_res(triple(sK2,sK3,sK4)))) ),
    inference(instantiation,[status(thm)],[c_4580]) ).

cnf(c_8495,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_8494,c_5021,c_1357,c_1352,c_120]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15  % Problem  : SWV381+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.16  % Command  : run_iprover %s %d THM
% 0.12/0.37  % Computer : n010.cluster.edu
% 0.12/0.37  % Model    : x86_64 x86_64
% 0.12/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37  % Memory   : 8042.1875MB
% 0.12/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.37  % CPULimit : 300
% 0.12/0.37  % WCLimit  : 300
% 0.12/0.37  % DateTime : Tue Aug 29 03:30:19 EDT 2023
% 0.12/0.37  % CPUTime  : 
% 0.19/0.48  Running first-order theorem proving
% 0.19/0.48  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.69/1.13  % SZS status Started for theBenchmark.p
% 3.69/1.13  % SZS status Theorem for theBenchmark.p
% 3.69/1.13  
% 3.69/1.13  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.69/1.13  
% 3.69/1.13  ------  iProver source info
% 3.69/1.13  
% 3.69/1.13  git: date: 2023-05-31 18:12:56 +0000
% 3.69/1.13  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.69/1.13  git: non_committed_changes: false
% 3.69/1.13  git: last_make_outside_of_git: false
% 3.69/1.13  
% 3.69/1.13  ------ Parsing...
% 3.69/1.13  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.69/1.13  
% 3.69/1.13  ------ 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 
% 3.69/1.13  
% 3.69/1.13  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.69/1.13  
% 3.69/1.13  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.69/1.13  ------ Proving...
% 3.69/1.13  ------ Problem Properties 
% 3.69/1.13  
% 3.69/1.13  
% 3.69/1.13  clauses                                 69
% 3.69/1.13  conjectures                             2
% 3.69/1.13  EPR                                     9
% 3.69/1.13  Horn                                    52
% 3.69/1.13  unary                                   25
% 3.69/1.13  binary                                  24
% 3.69/1.13  lits                                    135
% 3.69/1.13  lits eq                                 40
% 3.69/1.13  fd_pure                                 0
% 3.69/1.13  fd_pseudo                               0
% 3.69/1.13  fd_cond                                 5
% 3.69/1.13  fd_pseudo_cond                          7
% 3.69/1.13  AC symbols                              0
% 3.69/1.13  
% 3.69/1.13  ------ Schedule dynamic 5 is on 
% 3.69/1.13  
% 3.69/1.13  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.69/1.13  
% 3.69/1.13  
% 3.69/1.13  ------ 
% 3.69/1.13  Current options:
% 3.69/1.13  ------ 
% 3.69/1.13  
% 3.69/1.13  
% 3.69/1.13  
% 3.69/1.13  
% 3.69/1.13  ------ Proving...
% 3.69/1.13  
% 3.69/1.13  
% 3.69/1.13  % SZS status Theorem for theBenchmark.p
% 3.69/1.13  
% 3.69/1.13  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.69/1.13  
% 3.69/1.13  
%------------------------------------------------------------------------------