TSTP Solution File: SWV372+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWV372+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n006.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 03:14:16 EDT 2024

% Result   : Theorem 10.13s 2.13s
% Output   : CNFRefutation 10.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   68 (  24 unt;   0 def)
%            Number of atoms       :  126 (  41 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  105 (  47   ~;  38   |;   8   &)
%                                         (   3 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   5 con; 0-3 aty)
%            Number of variables   :  133 (  15 sgn  97   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f39,axiom,
    ! [X0,X1,X2,X3] :
      ( contains_cpq(triple(X0,X1,X2),X3)
    <=> contains_slb(X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).

fof(f40,axiom,
    ! [X0,X1] :
      ( ok(triple(X0,X1,bad))
    <=> $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax40) ).

fof(f46,axiom,
    ! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax46) ).

fof(f47,axiom,
    ! [X0,X1,X2,X3] :
      ( ( ~ contains_slb(X1,findmin_pqp_res(X0))
        & create_slb != X1 )
     => findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax47) ).

fof(f51,axiom,
    ! [X0,X1,X2,X3] :
      ( create_slb != X1
     => findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax51) ).

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',l8_li56) ).

fof(f64,axiom,
    ! [X0,X1,X2] :
      ( ~ contains_cpq(triple(X0,X1,X2),findmin_cpq_res(triple(X0,X1,X2)))
     => ~ ok(findmin_cpq_eff(triple(X0,X1,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l8_l9) ).

fof(f65,axiom,
    ! [X0,X1,X2] :
      ( ~ ok(triple(X0,X1,X2))
     => ~ phi(triple(X0,X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l8_lX) ).

fof(f66,conjecture,
    ! [X0,X1,X2] :
      ( phi(findmin_cpq_eff(triple(X0,X1,X2)))
     => contains_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l8_co) ).

fof(f67,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( phi(findmin_cpq_eff(triple(X0,X1,X2)))
       => contains_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2))) ),
    inference(negated_conjecture,[],[f66]) ).

fof(f70,plain,
    ! [X0,X1] : ~ ok(triple(X0,X1,bad)),
    inference(true_and_false_elimination,[],[f40]) ).

fof(f71,plain,
    ! [X0,X1] : ~ ok(triple(X0,X1,bad)),
    inference(flattening,[],[f70]) ).

fof(f72,plain,
    ! [X0,X1,X2] :
      ( ( ~ contains_slb(X1,findmin_pqp_res(X0))
        & create_slb != X1 )
     => findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
    inference(rectify,[],[f47]) ).

fof(f75,plain,
    ! [X0,X1,X2] :
      ( create_slb != X1
     => findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2)) ),
    inference(rectify,[],[f51]) ).

fof(f111,plain,
    ! [X0,X1,X2] :
      ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
      | contains_slb(X1,findmin_pqp_res(X0))
      | create_slb = X1 ),
    inference(ennf_transformation,[],[f72]) ).

fof(f112,plain,
    ! [X0,X1,X2] :
      ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
      | contains_slb(X1,findmin_pqp_res(X0))
      | create_slb = X1 ),
    inference(flattening,[],[f111]) ).

fof(f117,plain,
    ! [X0,X1,X2] :
      ( findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2))
      | create_slb = X1 ),
    inference(ennf_transformation,[],[f75]) ).

fof(f118,plain,
    ! [X0,X1,X2] :
      ( ~ ok(findmin_cpq_eff(triple(X0,X1,X2)))
      | contains_cpq(triple(X0,X1,X2),findmin_cpq_res(triple(X0,X1,X2))) ),
    inference(ennf_transformation,[],[f64]) ).

fof(f119,plain,
    ! [X0,X1,X2] :
      ( ~ phi(triple(X0,X1,X2))
      | ok(triple(X0,X1,X2)) ),
    inference(ennf_transformation,[],[f65]) ).

fof(f120,plain,
    ? [X0,X1,X2] :
      ( ~ contains_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2)))
      & phi(findmin_cpq_eff(triple(X0,X1,X2))) ),
    inference(ennf_transformation,[],[f67]) ).

fof(f130,plain,
    ! [X0,X1,X2,X3] :
      ( ( contains_cpq(triple(X0,X1,X2),X3)
        | ~ contains_slb(X1,X3) )
      & ( contains_slb(X1,X3)
        | ~ contains_cpq(triple(X0,X1,X2),X3) ) ),
    inference(nnf_transformation,[],[f39]) ).

fof(f135,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(f136,plain,
    ( ? [X0,X1,X2] :
        ( ~ contains_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2)))
        & phi(findmin_cpq_eff(triple(X0,X1,X2))) )
   => ( ~ contains_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(f137,plain,
    ( ~ contains_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])],[f120,f136]) ).

fof(f186,plain,
    ! [X2,X3,X0,X1] :
      ( contains_cpq(triple(X0,X1,X2),X3)
      | ~ contains_slb(X1,X3) ),
    inference(cnf_transformation,[],[f130]) ).

fof(f187,plain,
    ! [X0,X1] : ~ ok(triple(X0,X1,bad)),
    inference(cnf_transformation,[],[f71]) ).

fof(f193,plain,
    ! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad),
    inference(cnf_transformation,[],[f46]) ).

fof(f194,plain,
    ! [X2,X0,X1] :
      ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
      | contains_slb(X1,findmin_pqp_res(X0))
      | create_slb = X1 ),
    inference(cnf_transformation,[],[f112]) ).

fof(f198,plain,
    ! [X2,X0,X1] :
      ( findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2))
      | create_slb = X1 ),
    inference(cnf_transformation,[],[f117]) ).

fof(f200,plain,
    ! [X0] : findmin_cpq_res(X0) = removemin_cpq_res(X0),
    inference(cnf_transformation,[],[f53]) ).

fof(f207,plain,
    ! [X2,X3,X0,X1] :
      ( contains_pq(i(triple(X0,X1,X2)),X3)
      | ~ contains_cpq(triple(X0,X1,X2),X3) ),
    inference(cnf_transformation,[],[f135]) ).

fof(f209,plain,
    ! [X2,X0,X1] :
      ( ~ ok(findmin_cpq_eff(triple(X0,X1,X2)))
      | contains_cpq(triple(X0,X1,X2),findmin_cpq_res(triple(X0,X1,X2))) ),
    inference(cnf_transformation,[],[f118]) ).

fof(f210,plain,
    ! [X2,X0,X1] :
      ( ~ phi(triple(X0,X1,X2))
      | ok(triple(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f119]) ).

fof(f211,plain,
    phi(findmin_cpq_eff(triple(sK2,sK3,sK4))),
    inference(cnf_transformation,[],[f137]) ).

fof(f212,plain,
    ~ contains_pq(i(triple(sK2,sK3,sK4)),findmin_cpq_res(triple(sK2,sK3,sK4))),
    inference(cnf_transformation,[],[f137]) ).

fof(f216,plain,
    ! [X2,X0,X1] :
      ( findmin_pqp_res(X0) = removemin_cpq_res(triple(X0,X1,X2))
      | create_slb = X1 ),
    inference(definition_unfolding,[],[f198,f200]) ).

fof(f217,plain,
    ! [X2,X0,X1] :
      ( ~ ok(findmin_cpq_eff(triple(X0,X1,X2)))
      | contains_cpq(triple(X0,X1,X2),removemin_cpq_res(triple(X0,X1,X2))) ),
    inference(definition_unfolding,[],[f209,f200]) ).

fof(f218,plain,
    ~ contains_pq(i(triple(sK2,sK3,sK4)),removemin_cpq_res(triple(sK2,sK3,sK4))),
    inference(definition_unfolding,[],[f212,f200]) ).

cnf(c_96,plain,
    ( ~ contains_slb(X0,X1)
    | contains_cpq(triple(X2,X0,X3),X1) ),
    inference(cnf_transformation,[],[f186]) ).

cnf(c_98,plain,
    ~ ok(triple(X0,X1,bad)),
    inference(cnf_transformation,[],[f187]) ).

cnf(c_104,plain,
    findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad),
    inference(cnf_transformation,[],[f193]) ).

cnf(c_105,plain,
    ( triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) = findmin_cpq_eff(triple(X0,X1,X2))
    | X1 = create_slb
    | contains_slb(X1,findmin_pqp_res(X0)) ),
    inference(cnf_transformation,[],[f194]) ).

cnf(c_109,plain,
    ( removemin_cpq_res(triple(X0,X1,X2)) = findmin_pqp_res(X0)
    | X1 = create_slb ),
    inference(cnf_transformation,[],[f216]) ).

cnf(c_117,plain,
    ( ~ contains_cpq(triple(X0,X1,X2),X3)
    | contains_pq(i(triple(X0,X1,X2)),X3) ),
    inference(cnf_transformation,[],[f207]) ).

cnf(c_118,plain,
    ( ~ ok(findmin_cpq_eff(triple(X0,X1,X2)))
    | contains_cpq(triple(X0,X1,X2),removemin_cpq_res(triple(X0,X1,X2))) ),
    inference(cnf_transformation,[],[f217]) ).

cnf(c_119,plain,
    ( ~ phi(triple(X0,X1,X2))
    | ok(triple(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f210]) ).

cnf(c_120,negated_conjecture,
    ~ contains_pq(i(triple(sK2,sK3,sK4)),removemin_cpq_res(triple(sK2,sK3,sK4))),
    inference(cnf_transformation,[],[f218]) ).

cnf(c_121,negated_conjecture,
    phi(findmin_cpq_eff(triple(sK2,sK3,sK4))),
    inference(cnf_transformation,[],[f211]) ).

cnf(c_9007,plain,
    ~ contains_cpq(triple(sK2,sK3,sK4),removemin_cpq_res(triple(sK2,sK3,sK4))),
    inference(superposition,[status(thm)],[c_117,c_120]) ).

cnf(c_9075,plain,
    ~ contains_slb(sK3,removemin_cpq_res(triple(sK2,sK3,sK4))),
    inference(superposition,[status(thm)],[c_96,c_9007]) ).

cnf(c_9078,plain,
    ( ~ contains_slb(sK3,findmin_pqp_res(sK2))
    | create_slb = sK3 ),
    inference(superposition,[status(thm)],[c_109,c_9075]) ).

cnf(c_9097,plain,
    ~ ok(findmin_cpq_eff(triple(sK2,sK3,sK4))),
    inference(superposition,[status(thm)],[c_118,c_9007]) ).

cnf(c_11106,plain,
    ( triple(sK2,update_slb(sK3,findmin_pqp_res(sK2)),bad) = findmin_cpq_eff(triple(sK2,sK3,X0))
    | create_slb = sK3 ),
    inference(superposition,[status(thm)],[c_105,c_9078]) ).

cnf(c_11897,plain,
    ( ~ phi(findmin_cpq_eff(triple(sK2,sK3,X0)))
    | create_slb = sK3
    | ok(triple(sK2,update_slb(sK3,findmin_pqp_res(sK2)),bad)) ),
    inference(superposition,[status(thm)],[c_11106,c_119]) ).

cnf(c_11902,plain,
    ( ~ ok(findmin_cpq_eff(triple(sK2,sK3,X0)))
    | create_slb = sK3 ),
    inference(superposition,[status(thm)],[c_11106,c_98]) ).

cnf(c_11905,plain,
    ( findmin_cpq_eff(triple(sK2,sK3,X0)) = findmin_cpq_eff(triple(sK2,sK3,X1))
    | create_slb = sK3 ),
    inference(superposition,[status(thm)],[c_11106,c_11106]) ).

cnf(c_11915,plain,
    ( ~ phi(findmin_cpq_eff(triple(sK2,sK3,create_slb)))
    | create_slb = sK3
    | ok(triple(sK2,update_slb(sK3,findmin_pqp_res(sK2)),bad)) ),
    inference(instantiation,[status(thm)],[c_11897]) ).

cnf(c_12171,plain,
    ( ~ ok(triple(sK2,update_slb(sK3,findmin_pqp_res(sK2)),bad))
    | create_slb = sK3 ),
    inference(superposition,[status(thm)],[c_11106,c_11902]) ).

cnf(c_12249,plain,
    ( create_slb = sK3
    | phi(findmin_cpq_eff(triple(sK2,sK3,X0))) ),
    inference(superposition,[status(thm)],[c_11905,c_121]) ).

cnf(c_12257,plain,
    ( create_slb = sK3
    | phi(findmin_cpq_eff(triple(sK2,sK3,create_slb))) ),
    inference(instantiation,[status(thm)],[c_12249]) ).

cnf(c_13147,plain,
    create_slb = sK3,
    inference(global_subsumption_just,[status(thm)],[c_12249,c_11915,c_12171,c_12257]) ).

cnf(c_13160,plain,
    ~ ok(findmin_cpq_eff(triple(sK2,create_slb,sK4))),
    inference(superposition,[status(thm)],[c_13147,c_9097]) ).

cnf(c_13171,plain,
    phi(findmin_cpq_eff(triple(sK2,create_slb,sK4))),
    inference(superposition,[status(thm)],[c_13147,c_121]) ).

cnf(c_13392,plain,
    phi(triple(sK2,create_slb,bad)),
    inference(superposition,[status(thm)],[c_104,c_13171]) ).

cnf(c_13663,plain,
    ok(triple(sK2,create_slb,bad)),
    inference(superposition,[status(thm)],[c_13392,c_119]) ).

cnf(c_13664,plain,
    ~ ok(triple(sK2,create_slb,bad)),
    inference(superposition,[status(thm)],[c_104,c_13160]) ).

cnf(c_13665,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_13664,c_13663]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SWV372+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.12  % Command  : run_iprover %s %d THM
% 0.11/0.33  % Computer : n006.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Fri May  3 00:00:34 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.17/0.45  Running first-order theorem proving
% 0.17/0.45  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
% 10.13/2.13  % SZS status Started for theBenchmark.p
% 10.13/2.13  % SZS status Theorem for theBenchmark.p
% 10.13/2.13  
% 10.13/2.13  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 10.13/2.13  
% 10.13/2.13  ------  iProver source info
% 10.13/2.13  
% 10.13/2.13  git: date: 2024-05-02 19:28:25 +0000
% 10.13/2.13  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 10.13/2.13  git: non_committed_changes: false
% 10.13/2.13  
% 10.13/2.13  ------ Parsing...
% 10.13/2.13  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 10.13/2.13  
% 10.13/2.13  ------ 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 
% 10.13/2.13  
% 10.13/2.13  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 10.13/2.13  
% 10.13/2.13  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 10.13/2.13  ------ Proving...
% 10.13/2.13  ------ Problem Properties 
% 10.13/2.13  
% 10.13/2.13  
% 10.13/2.13  clauses                                 70
% 10.13/2.13  conjectures                             2
% 10.13/2.13  EPR                                     9
% 10.13/2.13  Horn                                    53
% 10.13/2.13  unary                                   25
% 10.13/2.13  binary                                  26
% 10.13/2.13  lits                                    136
% 10.13/2.13  lits eq                                 40
% 10.13/2.13  fd_pure                                 0
% 10.13/2.13  fd_pseudo                               0
% 10.13/2.13  fd_cond                                 5
% 10.13/2.13  fd_pseudo_cond                          7
% 10.13/2.13  AC symbols                              0
% 10.13/2.13  
% 10.13/2.13  ------ Input Options Time Limit: Unbounded
% 10.13/2.13  
% 10.13/2.13  
% 10.13/2.13  ------ 
% 10.13/2.13  Current options:
% 10.13/2.13  ------ 
% 10.13/2.13  
% 10.13/2.13  
% 10.13/2.13  
% 10.13/2.13  
% 10.13/2.13  ------ Proving...
% 10.13/2.13  
% 10.13/2.13  
% 10.13/2.13  % SZS status Theorem for theBenchmark.p
% 10.13/2.13  
% 10.13/2.13  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.13/2.13  
% 10.13/2.14  
%------------------------------------------------------------------------------