TSTP Solution File: SWV398+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWV398+1 : TPTP v8.1.2. Released v3.3.0.
% 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 03:14:19 EDT 2024

% Result   : Theorem 130.00s 16.79s
% Output   : CNFRefutation 130.00s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   18
% Syntax   : Number of formulae    :  139 (  22 unt;   0 def)
%            Number of atoms       :  396 (  94 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  444 ( 187   ~; 202   |;  38   &)
%                                         (   4 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   16 (  16 usr;   5 con; 0-3 aty)
%            Number of variables   :  316 (  26 sgn 158   !;  22   ?)

% 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(f8,axiom,
    ! [X0] : ~ contains_slb(create_slb,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).

fof(f9,axiom,
    ! [X0,X1,X2,X3] :
      ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
    <=> ( X1 = X2
        | contains_slb(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).

fof(f24,axiom,
    ! [X0,X1] : check_cpq(triple(X0,create_slb,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax36) ).

fof(f35,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(f36,axiom,
    ! [X0,X1,X2,X3] :
      ( ( strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
        & 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',ax48) ).

fof(f37,axiom,
    ! [X0,X1,X2,X3] :
      ( ( less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
        & 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)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49) ).

fof(f42,axiom,
    ! [X0,X1,X2] :
      ( check_cpq(triple(X0,X1,X2))
    <=> ! [X3,X4] :
          ( pair_in_list(X1,X3,X4)
         => less_than(X4,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l26_li4142) ).

fof(f43,axiom,
    ! [X0] :
      ( ? [X1,X2] :
          ( strictly_less_than(X1,X2)
          & pair_in_list(X0,X1,X2) )
     => ! [X3] :
        ? [X4,X5] :
          ( strictly_less_than(X4,X5)
          & pair_in_list(update_slb(X0,X3),X4,X5) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l34_l35) ).

fof(f44,conjecture,
    ! [X0,X1,X2] :
      ( ~ check_cpq(triple(X0,X1,X2))
     => ~ check_cpq(findmin_cpq_eff(triple(X0,X1,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l24_co) ).

fof(f45,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ~ check_cpq(triple(X0,X1,X2))
       => ~ check_cpq(findmin_cpq_eff(triple(X0,X1,X2))) ),
    inference(negated_conjecture,[],[f44]) ).

fof(f50,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,[],[f35]) ).

fof(f51,plain,
    ! [X0,X1,X2] :
      ( ( strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
        & 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,[],[f36]) ).

fof(f52,plain,
    ! [X0,X1,X2] :
      ( ( less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
        & 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)),X2) ),
    inference(rectify,[],[f37]) ).

fof(f74,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,[],[f50]) ).

fof(f75,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,[],[f74]) ).

fof(f76,plain,
    ! [X0,X1,X2] :
      ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
      | ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
      | ~ contains_slb(X1,findmin_pqp_res(X0))
      | create_slb = X1 ),
    inference(ennf_transformation,[],[f51]) ).

fof(f77,plain,
    ! [X0,X1,X2] :
      ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
      | ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
      | ~ contains_slb(X1,findmin_pqp_res(X0))
      | create_slb = X1 ),
    inference(flattening,[],[f76]) ).

fof(f78,plain,
    ! [X0,X1,X2] :
      ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2)
      | ~ less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
      | ~ contains_slb(X1,findmin_pqp_res(X0))
      | create_slb = X1 ),
    inference(ennf_transformation,[],[f52]) ).

fof(f79,plain,
    ! [X0,X1,X2] :
      ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2)
      | ~ less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
      | ~ contains_slb(X1,findmin_pqp_res(X0))
      | create_slb = X1 ),
    inference(flattening,[],[f78]) ).

fof(f81,plain,
    ! [X0,X1,X2] :
      ( check_cpq(triple(X0,X1,X2))
    <=> ! [X3,X4] :
          ( less_than(X4,X3)
          | ~ pair_in_list(X1,X3,X4) ) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f82,plain,
    ! [X0] :
      ( ! [X3] :
        ? [X4,X5] :
          ( strictly_less_than(X4,X5)
          & pair_in_list(update_slb(X0,X3),X4,X5) )
      | ! [X1,X2] :
          ( ~ strictly_less_than(X1,X2)
          | ~ pair_in_list(X0,X1,X2) ) ),
    inference(ennf_transformation,[],[f43]) ).

fof(f83,plain,
    ? [X0,X1,X2] :
      ( check_cpq(findmin_cpq_eff(triple(X0,X1,X2)))
      & ~ check_cpq(triple(X0,X1,X2)) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( ( strictly_less_than(X0,X1)
        | less_than(X1,X0)
        | ~ less_than(X0,X1) )
      & ( ( ~ less_than(X1,X0)
          & less_than(X0,X1) )
        | ~ strictly_less_than(X0,X1) ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( ( strictly_less_than(X0,X1)
        | less_than(X1,X0)
        | ~ less_than(X0,X1) )
      & ( ( ~ less_than(X1,X0)
          & less_than(X0,X1) )
        | ~ strictly_less_than(X0,X1) ) ),
    inference(flattening,[],[f84]) ).

fof(f86,plain,
    ! [X0,X1,X2,X3] :
      ( ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
        | ( X1 != X2
          & ~ contains_slb(X0,X2) ) )
      & ( X1 = X2
        | contains_slb(X0,X2)
        | ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f87,plain,
    ! [X0,X1,X2,X3] :
      ( ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
        | ( X1 != X2
          & ~ contains_slb(X0,X2) ) )
      & ( X1 = X2
        | contains_slb(X0,X2)
        | ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ) ),
    inference(flattening,[],[f86]) ).

fof(f92,plain,
    ! [X0,X1,X2] :
      ( ( check_cpq(triple(X0,X1,X2))
        | ? [X3,X4] :
            ( ~ less_than(X4,X3)
            & pair_in_list(X1,X3,X4) ) )
      & ( ! [X3,X4] :
            ( less_than(X4,X3)
            | ~ pair_in_list(X1,X3,X4) )
        | ~ check_cpq(triple(X0,X1,X2)) ) ),
    inference(nnf_transformation,[],[f81]) ).

fof(f93,plain,
    ! [X0,X1,X2] :
      ( ( check_cpq(triple(X0,X1,X2))
        | ? [X3,X4] :
            ( ~ less_than(X4,X3)
            & pair_in_list(X1,X3,X4) ) )
      & ( ! [X5,X6] :
            ( less_than(X6,X5)
            | ~ pair_in_list(X1,X5,X6) )
        | ~ check_cpq(triple(X0,X1,X2)) ) ),
    inference(rectify,[],[f92]) ).

fof(f94,plain,
    ! [X1] :
      ( ? [X3,X4] :
          ( ~ less_than(X4,X3)
          & pair_in_list(X1,X3,X4) )
     => ( ~ less_than(sK1(X1),sK0(X1))
        & pair_in_list(X1,sK0(X1),sK1(X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f95,plain,
    ! [X0,X1,X2] :
      ( ( check_cpq(triple(X0,X1,X2))
        | ( ~ less_than(sK1(X1),sK0(X1))
          & pair_in_list(X1,sK0(X1),sK1(X1)) ) )
      & ( ! [X5,X6] :
            ( less_than(X6,X5)
            | ~ pair_in_list(X1,X5,X6) )
        | ~ check_cpq(triple(X0,X1,X2)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f93,f94]) ).

fof(f96,plain,
    ! [X0] :
      ( ! [X1] :
        ? [X2,X3] :
          ( strictly_less_than(X2,X3)
          & pair_in_list(update_slb(X0,X1),X2,X3) )
      | ! [X4,X5] :
          ( ~ strictly_less_than(X4,X5)
          | ~ pair_in_list(X0,X4,X5) ) ),
    inference(rectify,[],[f82]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( ? [X2,X3] :
          ( strictly_less_than(X2,X3)
          & pair_in_list(update_slb(X0,X1),X2,X3) )
     => ( strictly_less_than(sK2(X0,X1),sK3(X0,X1))
        & pair_in_list(update_slb(X0,X1),sK2(X0,X1),sK3(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f98,plain,
    ! [X0] :
      ( ! [X1] :
          ( strictly_less_than(sK2(X0,X1),sK3(X0,X1))
          & pair_in_list(update_slb(X0,X1),sK2(X0,X1),sK3(X0,X1)) )
      | ! [X4,X5] :
          ( ~ strictly_less_than(X4,X5)
          | ~ pair_in_list(X0,X4,X5) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f96,f97]) ).

fof(f99,plain,
    ( ? [X0,X1,X2] :
        ( check_cpq(findmin_cpq_eff(triple(X0,X1,X2)))
        & ~ check_cpq(triple(X0,X1,X2)) )
   => ( check_cpq(findmin_cpq_eff(triple(sK4,sK5,sK6)))
      & ~ check_cpq(triple(sK4,sK5,sK6)) ) ),
    introduced(choice_axiom,[]) ).

fof(f100,plain,
    ( check_cpq(findmin_cpq_eff(triple(sK4,sK5,sK6)))
    & ~ check_cpq(triple(sK4,sK5,sK6)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f83,f99]) ).

fof(f102,plain,
    ! [X0,X1] :
      ( less_than(X1,X0)
      | less_than(X0,X1) ),
    inference(cnf_transformation,[],[f2]) ).

fof(f105,plain,
    ! [X0,X1] :
      ( ~ less_than(X1,X0)
      | ~ strictly_less_than(X0,X1) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f106,plain,
    ! [X0,X1] :
      ( strictly_less_than(X0,X1)
      | less_than(X1,X0)
      | ~ less_than(X0,X1) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f110,plain,
    ! [X0] : ~ contains_slb(create_slb,X0),
    inference(cnf_transformation,[],[f8]) ).

fof(f111,plain,
    ! [X2,X3,X0,X1] :
      ( X1 = X2
      | contains_slb(X0,X2)
      | ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ),
    inference(cnf_transformation,[],[f87]) ).

fof(f113,plain,
    ! [X2,X3,X0,X1] :
      ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
      | X1 != X2 ),
    inference(cnf_transformation,[],[f87]) ).

fof(f131,plain,
    ! [X0,X1] : check_cpq(triple(X0,create_slb,X1)),
    inference(cnf_transformation,[],[f24]) ).

fof(f144,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,[],[f75]) ).

fof(f145,plain,
    ! [X2,X0,X1] :
      ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
      | ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
      | ~ contains_slb(X1,findmin_pqp_res(X0))
      | create_slb = X1 ),
    inference(cnf_transformation,[],[f77]) ).

fof(f146,plain,
    ! [X2,X0,X1] :
      ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2)
      | ~ less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
      | ~ contains_slb(X1,findmin_pqp_res(X0))
      | create_slb = X1 ),
    inference(cnf_transformation,[],[f79]) ).

fof(f151,plain,
    ! [X2,X0,X1,X6,X5] :
      ( less_than(X6,X5)
      | ~ pair_in_list(X1,X5,X6)
      | ~ check_cpq(triple(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f152,plain,
    ! [X2,X0,X1] :
      ( check_cpq(triple(X0,X1,X2))
      | pair_in_list(X1,sK0(X1),sK1(X1)) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f153,plain,
    ! [X2,X0,X1] :
      ( check_cpq(triple(X0,X1,X2))
      | ~ less_than(sK1(X1),sK0(X1)) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f154,plain,
    ! [X0,X1,X4,X5] :
      ( pair_in_list(update_slb(X0,X1),sK2(X0,X1),sK3(X0,X1))
      | ~ strictly_less_than(X4,X5)
      | ~ pair_in_list(X0,X4,X5) ),
    inference(cnf_transformation,[],[f98]) ).

fof(f155,plain,
    ! [X0,X1,X4,X5] :
      ( strictly_less_than(sK2(X0,X1),sK3(X0,X1))
      | ~ strictly_less_than(X4,X5)
      | ~ pair_in_list(X0,X4,X5) ),
    inference(cnf_transformation,[],[f98]) ).

fof(f156,plain,
    ~ check_cpq(triple(sK4,sK5,sK6)),
    inference(cnf_transformation,[],[f100]) ).

fof(f157,plain,
    check_cpq(findmin_cpq_eff(triple(sK4,sK5,sK6))),
    inference(cnf_transformation,[],[f100]) ).

fof(f162,plain,
    ! [X2,X3,X0] : contains_slb(insert_slb(X0,pair(X2,X3)),X2),
    inference(equality_resolution,[],[f113]) ).

cnf(c_50,plain,
    ( less_than(X0,X1)
    | less_than(X1,X0) ),
    inference(cnf_transformation,[],[f102]) ).

cnf(c_52,plain,
    ( ~ less_than(X0,X1)
    | less_than(X1,X0)
    | strictly_less_than(X0,X1) ),
    inference(cnf_transformation,[],[f106]) ).

cnf(c_53,plain,
    ( ~ less_than(X0,X1)
    | ~ strictly_less_than(X1,X0) ),
    inference(cnf_transformation,[],[f105]) ).

cnf(c_58,plain,
    ~ contains_slb(create_slb,X0),
    inference(cnf_transformation,[],[f110]) ).

cnf(c_59,plain,
    contains_slb(insert_slb(X0,pair(X1,X2)),X1),
    inference(cnf_transformation,[],[f162]) ).

cnf(c_61,plain,
    ( ~ contains_slb(insert_slb(X0,pair(X1,X2)),X3)
    | X1 = X3
    | contains_slb(X0,X3) ),
    inference(cnf_transformation,[],[f111]) ).

cnf(c_79,plain,
    check_cpq(triple(X0,create_slb,X1)),
    inference(cnf_transformation,[],[f131]) ).

cnf(c_92,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,[],[f144]) ).

cnf(c_93,plain,
    ( ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
    | ~ contains_slb(X1,findmin_pqp_res(X0))
    | triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) = findmin_cpq_eff(triple(X0,X1,X2))
    | X1 = create_slb ),
    inference(cnf_transformation,[],[f145]) ).

cnf(c_94,plain,
    ( ~ less_than(lookup_slb(X0,findmin_pqp_res(X1)),findmin_pqp_res(X1))
    | ~ contains_slb(X0,findmin_pqp_res(X1))
    | triple(X1,update_slb(X0,findmin_pqp_res(X1)),X2) = findmin_cpq_eff(triple(X1,X0,X2))
    | X0 = create_slb ),
    inference(cnf_transformation,[],[f146]) ).

cnf(c_97,plain,
    ( ~ less_than(sK1(X0),sK0(X0))
    | check_cpq(triple(X1,X0,X2)) ),
    inference(cnf_transformation,[],[f153]) ).

cnf(c_98,plain,
    ( pair_in_list(X0,sK0(X0),sK1(X0))
    | check_cpq(triple(X1,X0,X2)) ),
    inference(cnf_transformation,[],[f152]) ).

cnf(c_99,plain,
    ( ~ check_cpq(triple(X0,X1,X2))
    | ~ pair_in_list(X1,X3,X4)
    | less_than(X4,X3) ),
    inference(cnf_transformation,[],[f151]) ).

cnf(c_100,plain,
    ( ~ pair_in_list(X0,X1,X2)
    | ~ strictly_less_than(X1,X2)
    | strictly_less_than(sK2(X0,X3),sK3(X0,X3)) ),
    inference(cnf_transformation,[],[f155]) ).

cnf(c_101,plain,
    ( ~ pair_in_list(X0,X1,X2)
    | ~ strictly_less_than(X1,X2)
    | pair_in_list(update_slb(X0,X3),sK2(X0,X3),sK3(X0,X3)) ),
    inference(cnf_transformation,[],[f154]) ).

cnf(c_102,negated_conjecture,
    check_cpq(findmin_cpq_eff(triple(sK4,sK5,sK6))),
    inference(cnf_transformation,[],[f157]) ).

cnf(c_103,negated_conjecture,
    ~ check_cpq(triple(sK4,sK5,sK6)),
    inference(cnf_transformation,[],[f156]) ).

cnf(c_107,plain,
    ~ contains_slb(create_slb,create_slb),
    inference(instantiation,[status(thm)],[c_58]) ).

cnf(c_108,plain,
    check_cpq(triple(create_slb,create_slb,create_slb)),
    inference(instantiation,[status(thm)],[c_79]) ).

cnf(c_113,plain,
    contains_slb(insert_slb(create_slb,pair(create_slb,create_slb)),create_slb),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_129,plain,
    ( ~ contains_slb(insert_slb(create_slb,pair(create_slb,create_slb)),create_slb)
    | create_slb = create_slb
    | contains_slb(create_slb,create_slb) ),
    inference(instantiation,[status(thm)],[c_61]) ).

cnf(c_138,plain,
    ( less_than(X1,X0)
    | strictly_less_than(X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_52,c_50,c_52]) ).

cnf(c_139,plain,
    ( less_than(X0,X1)
    | strictly_less_than(X1,X0) ),
    inference(renaming,[status(thm)],[c_138]) ).

cnf(c_140,plain,
    ( ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
    | triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) = findmin_cpq_eff(triple(X0,X1,X2))
    | X1 = create_slb ),
    inference(global_subsumption_just,[status(thm)],[c_93,c_92,c_93]) ).

cnf(c_186,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_195,plain,
    ( X0 != X1
    | X2 != X3
    | X4 != X5
    | ~ pair_in_list(X1,X3,X5)
    | pair_in_list(X0,X2,X4) ),
    theory(equality) ).

cnf(c_203,plain,
    ( X0 != X1
    | X2 != X3
    | X4 != X5
    | triple(X0,X2,X4) = triple(X1,X3,X5) ),
    theory(equality) ).

cnf(c_204,plain,
    ( X0 != X1
    | ~ check_cpq(X1)
    | check_cpq(X0) ),
    theory(equality) ).

cnf(c_221,plain,
    ( X0 != triple(X1,create_slb,X2)
    | ~ check_cpq(triple(X1,create_slb,X2))
    | check_cpq(X0) ),
    inference(instantiation,[status(thm)],[c_204]) ).

cnf(c_223,plain,
    ( X0 != findmin_cpq_eff(triple(sK4,sK5,sK6))
    | ~ check_cpq(findmin_cpq_eff(triple(sK4,sK5,sK6)))
    | check_cpq(X0) ),
    inference(instantiation,[status(thm)],[c_204]) ).

cnf(c_225,plain,
    ( pair_in_list(sK5,sK0(sK5),sK1(sK5))
    | check_cpq(triple(sK4,sK5,sK6)) ),
    inference(instantiation,[status(thm)],[c_98]) ).

cnf(c_239,plain,
    ( less_than(sK1(X0),sK0(X0))
    | strictly_less_than(sK0(X0),sK1(X0)) ),
    inference(instantiation,[status(thm)],[c_139]) ).

cnf(c_258,plain,
    ( ~ pair_in_list(sK5,sK0(sK5),sK1(sK5))
    | ~ check_cpq(triple(X0,sK5,X1))
    | less_than(sK1(sK5),sK0(sK5)) ),
    inference(instantiation,[status(thm)],[c_99]) ).

cnf(c_259,plain,
    ( ~ pair_in_list(sK5,sK0(sK5),sK1(sK5))
    | ~ check_cpq(triple(create_slb,sK5,create_slb))
    | less_than(sK1(sK5),sK0(sK5)) ),
    inference(instantiation,[status(thm)],[c_258]) ).

cnf(c_314,plain,
    ( triple(X0,X1,X2) != triple(X3,create_slb,X4)
    | ~ check_cpq(triple(X3,create_slb,X4))
    | check_cpq(triple(X0,X1,X2)) ),
    inference(instantiation,[status(thm)],[c_221]) ).

cnf(c_315,plain,
    ( X0 != X1
    | X2 != create_slb
    | X3 != X4
    | triple(X0,X2,X3) = triple(X1,create_slb,X4) ),
    inference(instantiation,[status(thm)],[c_203]) ).

cnf(c_333,plain,
    ( ~ less_than(sK1(sK5),sK0(sK5))
    | check_cpq(triple(sK4,sK5,sK6)) ),
    inference(instantiation,[status(thm)],[c_97]) ).

cnf(c_459,plain,
    ( less_than(sK1(sK5),sK0(sK5))
    | strictly_less_than(sK0(sK5),sK1(sK5)) ),
    inference(instantiation,[status(thm)],[c_239]) ).

cnf(c_494,plain,
    pair_in_list(sK5,sK0(sK5),sK1(sK5)),
    inference(resolution,[status(thm)],[c_103,c_98]) ).

cnf(c_781,plain,
    ( triple(X0,sK5,X1) != triple(X2,create_slb,X3)
    | ~ check_cpq(triple(X2,create_slb,X3))
    | check_cpq(triple(X0,sK5,X1)) ),
    inference(instantiation,[status(thm)],[c_314]) ).

cnf(c_782,plain,
    ( triple(create_slb,sK5,create_slb) != triple(create_slb,create_slb,create_slb)
    | ~ check_cpq(triple(create_slb,create_slb,create_slb))
    | check_cpq(triple(create_slb,sK5,create_slb)) ),
    inference(instantiation,[status(thm)],[c_781]) ).

cnf(c_1495,plain,
    ( ~ pair_in_list(X0,sK0(sK5),sK1(sK5))
    | ~ strictly_less_than(sK0(sK5),sK1(sK5))
    | strictly_less_than(sK2(X0,X1),sK3(X0,X1)) ),
    inference(instantiation,[status(thm)],[c_100]) ).

cnf(c_2426,plain,
    ( X0 != X1
    | X2 != X3
    | sK5 != create_slb
    | triple(X0,sK5,X2) = triple(X1,create_slb,X3) ),
    inference(instantiation,[status(thm)],[c_315]) ).

cnf(c_2427,plain,
    ( create_slb != create_slb
    | sK5 != create_slb
    | triple(create_slb,sK5,create_slb) = triple(create_slb,create_slb,create_slb) ),
    inference(instantiation,[status(thm)],[c_2426]) ).

cnf(c_6789,plain,
    ( ~ check_cpq(findmin_cpq_eff(triple(X0,X1,X2)))
    | X1 = create_slb
    | check_cpq(triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad))
    | contains_slb(X1,findmin_pqp_res(X0)) ),
    inference(resolution,[status(thm)],[c_92,c_204]) ).

cnf(c_7435,plain,
    ( ~ less_than(lookup_slb(sK5,findmin_pqp_res(X0)),findmin_pqp_res(X0))
    | ~ contains_slb(sK5,findmin_pqp_res(X0))
    | triple(X0,update_slb(sK5,findmin_pqp_res(X0)),X1) = findmin_cpq_eff(triple(X0,sK5,X1))
    | sK5 = create_slb ),
    inference(instantiation,[status(thm)],[c_94]) ).

cnf(c_8660,plain,
    ( ~ pair_in_list(sK5,sK0(sK5),sK1(sK5))
    | ~ strictly_less_than(sK0(sK5),sK1(sK5))
    | strictly_less_than(sK2(sK5,X0),sK3(sK5,X0)) ),
    inference(instantiation,[status(thm)],[c_1495]) ).

cnf(c_9289,plain,
    ( X0 != sK5
    | X1 != sK0(sK5)
    | X2 != sK1(sK5)
    | pair_in_list(X0,X1,X2) ),
    inference(resolution,[status(thm)],[c_195,c_494]) ).

cnf(c_10071,plain,
    ( X0 != sK5
    | X1 != sK0(sK5)
    | pair_in_list(X0,X1,sK1(sK5)) ),
    inference(resolution,[status(thm)],[c_9289,c_186]) ).

cnf(c_13482,plain,
    ( ~ strictly_less_than(sK0(sK5),sK1(sK5))
    | strictly_less_than(sK2(sK5,X0),sK3(sK5,X0)) ),
    inference(resolution,[status(thm)],[c_100,c_494]) ).

cnf(c_13941,plain,
    ( X0 != sK5
    | X1 != sK0(sK5)
    | ~ strictly_less_than(X1,sK1(sK5))
    | pair_in_list(update_slb(X0,X2),sK2(X0,X2),sK3(X0,X2)) ),
    inference(resolution,[status(thm)],[c_101,c_10071]) ).

cnf(c_13944,plain,
    strictly_less_than(sK2(sK5,X0),sK3(sK5,X0)),
    inference(global_subsumption_just,[status(thm)],[c_13482,c_103,c_225,c_333,c_459,c_8660]) ).

cnf(c_13951,plain,
    ~ less_than(sK3(sK5,X0),sK2(sK5,X0)),
    inference(resolution,[status(thm)],[c_13944,c_53]) ).

cnf(c_14792,plain,
    ( ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
    | ~ check_cpq(findmin_cpq_eff(triple(X0,X1,X2)))
    | X1 = create_slb
    | check_cpq(triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)) ),
    inference(resolution,[status(thm)],[c_140,c_204]) ).

cnf(c_17022,plain,
    ( X0 != sK5
    | ~ strictly_less_than(sK0(sK5),sK1(sK5))
    | pair_in_list(update_slb(X0,X1),sK2(X0,X1),sK3(X0,X1)) ),
    inference(resolution,[status(thm)],[c_13941,c_186]) ).

cnf(c_31415,plain,
    ( ~ less_than(lookup_slb(sK5,findmin_pqp_res(sK4)),findmin_pqp_res(sK4))
    | ~ contains_slb(sK5,findmin_pqp_res(sK4))
    | triple(sK4,update_slb(sK5,findmin_pqp_res(sK4)),X0) = findmin_cpq_eff(triple(sK4,sK5,X0))
    | sK5 = create_slb ),
    inference(instantiation,[status(thm)],[c_7435]) ).

cnf(c_35299,plain,
    ( X0 != sK5
    | pair_in_list(update_slb(X0,X1),sK2(X0,X1),sK3(X0,X1)) ),
    inference(global_subsumption_just,[status(thm)],[c_17022,c_103,c_333,c_459,c_17022]) ).

cnf(c_40447,plain,
    ( less_than(lookup_slb(sK5,findmin_pqp_res(sK4)),findmin_pqp_res(sK4))
    | strictly_less_than(findmin_pqp_res(sK4),lookup_slb(sK5,findmin_pqp_res(sK4))) ),
    inference(instantiation,[status(thm)],[c_139]) ).

cnf(c_50887,plain,
    ( ~ less_than(lookup_slb(sK5,findmin_pqp_res(sK4)),findmin_pqp_res(sK4))
    | ~ contains_slb(sK5,findmin_pqp_res(sK4))
    | triple(sK4,update_slb(sK5,findmin_pqp_res(sK4)),sK6) = findmin_cpq_eff(triple(sK4,sK5,sK6))
    | sK5 = create_slb ),
    inference(instantiation,[status(thm)],[c_31415]) ).

cnf(c_50888,plain,
    ( triple(sK4,update_slb(sK5,findmin_pqp_res(sK4)),sK6) != findmin_cpq_eff(triple(sK4,sK5,sK6))
    | ~ check_cpq(findmin_cpq_eff(triple(sK4,sK5,sK6)))
    | check_cpq(triple(sK4,update_slb(sK5,findmin_pqp_res(sK4)),sK6)) ),
    inference(instantiation,[status(thm)],[c_223]) ).

cnf(c_153992,plain,
    ( sK5 = create_slb
    | check_cpq(triple(sK4,update_slb(sK5,findmin_pqp_res(sK4)),bad))
    | contains_slb(sK5,findmin_pqp_res(sK4)) ),
    inference(resolution,[status(thm)],[c_6789,c_102]) ).

cnf(c_154214,plain,
    ( check_cpq(triple(sK4,update_slb(sK5,findmin_pqp_res(sK4)),bad))
    | contains_slb(sK5,findmin_pqp_res(sK4)) ),
    inference(global_subsumption_just,[status(thm)],[c_153992,c_107,c_108,c_103,c_113,c_129,c_225,c_259,c_333,c_782,c_2427,c_153992]) ).

cnf(c_154271,plain,
    ( ~ pair_in_list(update_slb(sK5,findmin_pqp_res(sK4)),X0,X1)
    | contains_slb(sK5,findmin_pqp_res(sK4))
    | less_than(X1,X0) ),
    inference(resolution,[status(thm)],[c_154214,c_99]) ).

cnf(c_154366,plain,
    ( sK5 != sK5
    | less_than(sK3(sK5,findmin_pqp_res(sK4)),sK2(sK5,findmin_pqp_res(sK4)))
    | contains_slb(sK5,findmin_pqp_res(sK4)) ),
    inference(resolution,[status(thm)],[c_154271,c_35299]) ).

cnf(c_154369,plain,
    ( less_than(sK3(sK5,findmin_pqp_res(sK4)),sK2(sK5,findmin_pqp_res(sK4)))
    | contains_slb(sK5,findmin_pqp_res(sK4)) ),
    inference(equality_resolution_simp,[status(thm)],[c_154366]) ).

cnf(c_192020,plain,
    contains_slb(sK5,findmin_pqp_res(sK4)),
    inference(forward_subsumption_resolution,[status(thm)],[c_154369,c_13951]) ).

cnf(c_208582,plain,
    ( ~ strictly_less_than(findmin_pqp_res(sK4),lookup_slb(sK5,findmin_pqp_res(sK4)))
    | sK5 = create_slb
    | check_cpq(triple(sK4,update_slb(sK5,findmin_pqp_res(sK4)),bad)) ),
    inference(resolution,[status(thm)],[c_14792,c_102]) ).

cnf(c_208887,plain,
    ( ~ strictly_less_than(findmin_pqp_res(sK4),lookup_slb(sK5,findmin_pqp_res(sK4)))
    | check_cpq(triple(sK4,update_slb(sK5,findmin_pqp_res(sK4)),bad)) ),
    inference(global_subsumption_just,[status(thm)],[c_208582,c_107,c_108,c_103,c_113,c_129,c_225,c_259,c_333,c_782,c_2427,c_208582]) ).

cnf(c_208897,plain,
    ( ~ pair_in_list(update_slb(sK5,findmin_pqp_res(sK4)),X0,X1)
    | ~ strictly_less_than(findmin_pqp_res(sK4),lookup_slb(sK5,findmin_pqp_res(sK4)))
    | less_than(X1,X0) ),
    inference(resolution,[status(thm)],[c_208887,c_99]) ).

cnf(c_208910,plain,
    ( sK5 != sK5
    | ~ strictly_less_than(findmin_pqp_res(sK4),lookup_slb(sK5,findmin_pqp_res(sK4)))
    | less_than(sK3(sK5,findmin_pqp_res(sK4)),sK2(sK5,findmin_pqp_res(sK4))) ),
    inference(resolution,[status(thm)],[c_208897,c_35299]) ).

cnf(c_208913,plain,
    ( ~ strictly_less_than(findmin_pqp_res(sK4),lookup_slb(sK5,findmin_pqp_res(sK4)))
    | less_than(sK3(sK5,findmin_pqp_res(sK4)),sK2(sK5,findmin_pqp_res(sK4))) ),
    inference(equality_resolution_simp,[status(thm)],[c_208910]) ).

cnf(c_210299,plain,
    ( ~ pair_in_list(X0,sK0(sK5),sK1(sK5))
    | ~ strictly_less_than(sK0(sK5),sK1(sK5))
    | pair_in_list(update_slb(X0,X1),sK2(X0,X1),sK3(X0,X1)) ),
    inference(instantiation,[status(thm)],[c_101]) ).

cnf(c_210300,plain,
    ( ~ pair_in_list(X0,sK0(sK5),sK1(sK5))
    | ~ strictly_less_than(sK0(sK5),sK1(sK5))
    | strictly_less_than(sK2(X0,X1),sK3(X0,X1)) ),
    inference(instantiation,[status(thm)],[c_100]) ).

cnf(c_211107,plain,
    ( ~ pair_in_list(sK5,sK0(sK5),sK1(sK5))
    | ~ strictly_less_than(sK0(sK5),sK1(sK5))
    | strictly_less_than(sK2(sK5,X0),sK3(sK5,X0)) ),
    inference(instantiation,[status(thm)],[c_210300]) ).

cnf(c_211190,plain,
    ( ~ pair_in_list(sK5,sK0(sK5),sK1(sK5))
    | ~ strictly_less_than(sK0(sK5),sK1(sK5))
    | pair_in_list(update_slb(sK5,X0),sK2(sK5,X0),sK3(sK5,X0)) ),
    inference(instantiation,[status(thm)],[c_210299]) ).

cnf(c_216217,plain,
    ( ~ less_than(sK3(sK5,X0),sK2(sK5,X0))
    | ~ strictly_less_than(sK2(sK5,X0),sK3(sK5,X0)) ),
    inference(instantiation,[status(thm)],[c_53]) ).

cnf(c_222986,plain,
    ( ~ pair_in_list(X0,sK2(sK5,X1),sK3(sK5,X1))
    | ~ check_cpq(triple(X2,X0,X3))
    | less_than(sK3(sK5,X1),sK2(sK5,X1)) ),
    inference(instantiation,[status(thm)],[c_99]) ).

cnf(c_245717,plain,
    ~ strictly_less_than(findmin_pqp_res(sK4),lookup_slb(sK5,findmin_pqp_res(sK4))),
    inference(forward_subsumption_resolution,[status(thm)],[c_208913,c_13951]) ).

cnf(c_278348,plain,
    ( ~ pair_in_list(update_slb(sK5,X0),sK2(sK5,X0),sK3(sK5,X0))
    | ~ check_cpq(triple(X1,update_slb(sK5,X0),X2))
    | less_than(sK3(sK5,X0),sK2(sK5,X0)) ),
    inference(instantiation,[status(thm)],[c_222986]) ).

cnf(c_280649,plain,
    ( ~ pair_in_list(update_slb(sK5,findmin_pqp_res(sK4)),sK2(sK5,findmin_pqp_res(sK4)),sK3(sK5,findmin_pqp_res(sK4)))
    | ~ check_cpq(triple(sK4,update_slb(sK5,findmin_pqp_res(sK4)),sK6))
    | less_than(sK3(sK5,findmin_pqp_res(sK4)),sK2(sK5,findmin_pqp_res(sK4))) ),
    inference(instantiation,[status(thm)],[c_278348]) ).

cnf(c_288829,plain,
    ( ~ less_than(sK3(sK5,findmin_pqp_res(sK4)),sK2(sK5,findmin_pqp_res(sK4)))
    | ~ strictly_less_than(sK2(sK5,findmin_pqp_res(sK4)),sK3(sK5,findmin_pqp_res(sK4))) ),
    inference(instantiation,[status(thm)],[c_216217]) ).

cnf(c_299736,plain,
    ( ~ pair_in_list(sK5,sK0(sK5),sK1(sK5))
    | ~ strictly_less_than(sK0(sK5),sK1(sK5))
    | strictly_less_than(sK2(sK5,findmin_pqp_res(sK4)),sK3(sK5,findmin_pqp_res(sK4))) ),
    inference(instantiation,[status(thm)],[c_211107]) ).

cnf(c_303762,plain,
    ( ~ pair_in_list(sK5,sK0(sK5),sK1(sK5))
    | ~ strictly_less_than(sK0(sK5),sK1(sK5))
    | pair_in_list(update_slb(sK5,findmin_pqp_res(sK4)),sK2(sK5,findmin_pqp_res(sK4)),sK3(sK5,findmin_pqp_res(sK4))) ),
    inference(instantiation,[status(thm)],[c_211190]) ).

cnf(c_303763,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_303762,c_299736,c_288829,c_280649,c_245717,c_192020,c_50888,c_50887,c_40447,c_2427,c_782,c_459,c_333,c_259,c_225,c_129,c_113,c_102,c_103,c_108,c_107]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWV398+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n023.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Fri May  3 00:38:54 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  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
% 130.00/16.79  % SZS status Started for theBenchmark.p
% 130.00/16.79  % SZS status Theorem for theBenchmark.p
% 130.00/16.79  
% 130.00/16.79  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 130.00/16.79  
% 130.00/16.79  ------  iProver source info
% 130.00/16.79  
% 130.00/16.79  git: date: 2024-05-02 19:28:25 +0000
% 130.00/16.79  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 130.00/16.79  git: non_committed_changes: false
% 130.00/16.79  
% 130.00/16.79  ------ Parsing...
% 130.00/16.79  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 130.00/16.79  
% 130.00/16.79  ------ Preprocessing... sf_s  rm: 7 0s  sf_e  sf_s  rm: 2 0s  sf_e 
% 130.00/16.79  
% 130.00/16.79  ------ Preprocessing...
% 130.00/16.79  
% 130.00/16.79  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 130.00/16.79  ------ Proving...
% 130.00/16.79  ------ Problem Properties 
% 130.00/16.79  
% 130.00/16.79  
% 130.00/16.79  clauses                                 50
% 130.00/16.79  conjectures                             2
% 130.00/16.79  EPR                                     10
% 130.00/16.79  Horn                                    36
% 130.00/16.79  unary                                   18
% 130.00/16.79  binary                                  16
% 130.00/16.79  lits                                    99
% 130.00/16.79  lits eq                                 27
% 130.00/16.79  fd_pure                                 0
% 130.00/16.79  fd_pseudo                               0
% 130.00/16.79  fd_cond                                 5
% 130.00/16.79  fd_pseudo_cond                          5
% 130.00/16.79  AC symbols                              0
% 130.00/16.79  
% 130.00/16.79  ------ Input Options Time Limit: Unbounded
% 130.00/16.79  
% 130.00/16.79  
% 130.00/16.79  ------ 
% 130.00/16.79  Current options:
% 130.00/16.79  ------ 
% 130.00/16.79  
% 130.00/16.79  
% 130.00/16.79  
% 130.00/16.79  
% 130.00/16.79  ------ Proving...
% 130.00/16.79  
% 130.00/16.79  
% 130.00/16.79  % SZS status Theorem for theBenchmark.p
% 130.00/16.79  
% 130.00/16.79  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 130.00/16.79  
% 130.00/16.80  
%------------------------------------------------------------------------------