TSTP Solution File: SWV394+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWV394+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% 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 : Thu Aug 31 21:38:23 EDT 2023

% Result   : Theorem 0.17s 0.59s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   43
% Syntax   : Number of formulae    :   78 (  11 unt;  34 typ;   0 def)
%            Number of atoms       :  115 (  10 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  118 (  47   ~;  42   |;  15   &)
%                                         (   4 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   46 (  26   >;  20   *;   0   +;   0  <<)
%            Number of predicates  :   12 (   9 usr;   2 prp; 0-3 aty)
%            Number of functors    :   25 (  25 usr;   8 con; 0-3 aty)
%            Number of variables   :  121 (  12 sgn;  77   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    less_than: ( $i * $i ) > $o ).

tff(decl_23,type,
    strictly_less_than: ( $i * $i ) > $o ).

tff(decl_24,type,
    bottom: $i ).

tff(decl_25,type,
    create_slb: $i ).

tff(decl_26,type,
    isnonempty_slb: $i > $o ).

tff(decl_27,type,
    pair: ( $i * $i ) > $i ).

tff(decl_28,type,
    insert_slb: ( $i * $i ) > $i ).

tff(decl_29,type,
    contains_slb: ( $i * $i ) > $o ).

tff(decl_30,type,
    pair_in_list: ( $i * $i * $i ) > $o ).

tff(decl_31,type,
    remove_slb: ( $i * $i ) > $i ).

tff(decl_32,type,
    lookup_slb: ( $i * $i ) > $i ).

tff(decl_33,type,
    update_slb: ( $i * $i ) > $i ).

tff(decl_34,type,
    succ_cpq: ( $i * $i ) > $o ).

tff(decl_35,type,
    insert_cpq: ( $i * $i ) > $i ).

tff(decl_36,type,
    remove_cpq: ( $i * $i ) > $i ).

tff(decl_37,type,
    findmin_cpq_eff: $i > $i ).

tff(decl_38,type,
    removemin_cpq_eff: $i > $i ).

tff(decl_39,type,
    triple: ( $i * $i * $i ) > $i ).

tff(decl_40,type,
    check_cpq: $i > $o ).

tff(decl_41,type,
    contains_cpq: ( $i * $i ) > $o ).

tff(decl_42,type,
    bad: $i ).

tff(decl_43,type,
    ok: $i > $o ).

tff(decl_44,type,
    insert_pqp: ( $i * $i ) > $i ).

tff(decl_45,type,
    remove_pqp: ( $i * $i ) > $i ).

tff(decl_46,type,
    findmin_pqp_res: $i > $i ).

tff(decl_47,type,
    findmin_cpq_res: $i > $i ).

tff(decl_48,type,
    removemin_cpq_res: $i > $i ).

tff(decl_49,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_50,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_51,type,
    esk3_0: $i ).

tff(decl_52,type,
    esk4_0: $i ).

tff(decl_53,type,
    esk5_0: $i ).

tff(decl_54,type,
    esk6_0: $i ).

tff(decl_55,type,
    esk7_0: $i ).

fof(ax40,axiom,
    ! [X1,X2] :
      ( ok(triple(X1,X2,bad))
    <=> ~ $true ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax40) ).

fof(l30_co,conjecture,
    ! [X1,X2,X3,X4] :
      ( ( check_cpq(remove_cpq(triple(X1,X2,X3),X4))
        & ok(remove_cpq(triple(X1,X2,X3),X4)) )
     => ! [X5] :
          ( pair_in_list(X2,X4,X5)
         => less_than(X5,X4) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l30_co) ).

fof(ax43,axiom,
    ! [X1,X2,X3,X4] :
      ( ~ contains_slb(X2,X4)
     => remove_cpq(triple(X1,X2,X3),X4) = triple(X1,X2,bad) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax43) ).

fof(ax45,axiom,
    ! [X1,X2,X3,X4] :
      ( ( contains_slb(X2,X4)
        & strictly_less_than(X4,lookup_slb(X2,X4)) )
     => remove_cpq(triple(X1,X2,X3),X4) = triple(remove_pqp(X1,X4),remove_slb(X2,X4),bad) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax45) ).

fof(stricly_smaller_definition,axiom,
    ! [X1,X2] :
      ( strictly_less_than(X1,X2)
    <=> ( less_than(X1,X2)
        & ~ less_than(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax',stricly_smaller_definition) ).

fof(totality,axiom,
    ! [X1,X2] :
      ( less_than(X1,X2)
      | less_than(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax',totality) ).

fof(l30_li4142,lemma,
    ! [X1,X2,X3] :
      ( check_cpq(triple(X1,X2,X3))
    <=> ! [X4,X5] :
          ( pair_in_list(X2,X4,X5)
         => less_than(X5,X4) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l30_li4142) ).

fof(ax44,axiom,
    ! [X1,X2,X3,X4] :
      ( ( contains_slb(X2,X4)
        & less_than(lookup_slb(X2,X4),X4) )
     => remove_cpq(triple(X1,X2,X3),X4) = triple(remove_pqp(X1,X4),remove_slb(X2,X4),X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax44) ).

fof(l30_li3132,lemma,
    ! [X1,X2,X3,X4,X5] :
      ( ( pair_in_list(X2,X4,X5)
        & strictly_less_than(X4,X5)
        & ok(remove_cpq(triple(X1,X2,X3),X4)) )
     => pair_in_list(remove_slb(X2,X4),X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l30_li3132) ).

fof(c_0_9,plain,
    ! [X1,X2] : ~ ok(triple(X1,X2,bad)),
    inference(fof_simplification,[status(thm)],[ax40]) ).

fof(c_0_10,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( ( check_cpq(remove_cpq(triple(X1,X2,X3),X4))
          & ok(remove_cpq(triple(X1,X2,X3),X4)) )
       => ! [X5] :
            ( pair_in_list(X2,X4,X5)
           => less_than(X5,X4) ) ),
    inference(assume_negation,[status(cth)],[l30_co]) ).

fof(c_0_11,plain,
    ! [X1,X2,X3,X4] :
      ( ~ contains_slb(X2,X4)
     => remove_cpq(triple(X1,X2,X3),X4) = triple(X1,X2,bad) ),
    inference(fof_simplification,[status(thm)],[ax43]) ).

fof(c_0_12,plain,
    ! [X80,X81] : ~ ok(triple(X80,X81,bad)),
    inference(variable_rename,[status(thm)],[c_0_9]) ).

fof(c_0_13,plain,
    ! [X97,X98,X99,X100] :
      ( ~ contains_slb(X98,X100)
      | ~ strictly_less_than(X100,lookup_slb(X98,X100))
      | remove_cpq(triple(X97,X98,X99),X100) = triple(remove_pqp(X97,X100),remove_slb(X98,X100),bad) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])]) ).

fof(c_0_14,negated_conjecture,
    ( check_cpq(remove_cpq(triple(esk3_0,esk4_0,esk5_0),esk6_0))
    & ok(remove_cpq(triple(esk3_0,esk4_0,esk5_0),esk6_0))
    & pair_in_list(esk4_0,esk6_0,esk7_0)
    & ~ less_than(esk7_0,esk6_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).

fof(c_0_15,plain,
    ! [X89,X90,X91,X92] :
      ( contains_slb(X90,X92)
      | remove_cpq(triple(X89,X90,X91),X92) = triple(X89,X90,bad) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).

fof(c_0_16,plain,
    ! [X1,X2] :
      ( strictly_less_than(X1,X2)
    <=> ( less_than(X1,X2)
        & ~ less_than(X2,X1) ) ),
    inference(fof_simplification,[status(thm)],[stricly_smaller_definition]) ).

cnf(c_0_17,plain,
    ~ ok(triple(X1,X2,bad)),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_18,plain,
    ( remove_cpq(triple(X3,X1,X4),X2) = triple(remove_pqp(X3,X2),remove_slb(X1,X2),bad)
    | ~ contains_slb(X1,X2)
    | ~ strictly_less_than(X2,lookup_slb(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_19,negated_conjecture,
    ok(remove_cpq(triple(esk3_0,esk4_0,esk5_0),esk6_0)),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_20,plain,
    ( contains_slb(X1,X2)
    | remove_cpq(triple(X3,X1,X4),X2) = triple(X3,X1,bad) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_21,plain,
    ! [X12,X13] :
      ( ( less_than(X12,X13)
        | ~ strictly_less_than(X12,X13) )
      & ( ~ less_than(X13,X12)
        | ~ strictly_less_than(X12,X13) )
      & ( ~ less_than(X12,X13)
        | less_than(X13,X12)
        | strictly_less_than(X12,X13) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).

fof(c_0_22,plain,
    ! [X9,X10] :
      ( less_than(X9,X10)
      | less_than(X10,X9) ),
    inference(variable_rename,[status(thm)],[totality]) ).

fof(c_0_23,lemma,
    ! [X119,X120,X121,X122,X123,X124,X125,X128] :
      ( ( ~ check_cpq(triple(X119,X120,X121))
        | ~ pair_in_list(X120,X122,X123)
        | less_than(X123,X122) )
      & ( pair_in_list(X125,esk1_2(X124,X125),esk2_2(X124,X125))
        | check_cpq(triple(X124,X125,X128)) )
      & ( ~ less_than(esk2_2(X124,X125),esk1_2(X124,X125))
        | check_cpq(triple(X124,X125,X128)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[l30_li4142])])])])])]) ).

fof(c_0_24,plain,
    ! [X93,X94,X95,X96] :
      ( ~ contains_slb(X94,X96)
      | ~ less_than(lookup_slb(X94,X96),X96)
      | remove_cpq(triple(X93,X94,X95),X96) = triple(remove_pqp(X93,X96),remove_slb(X94,X96),X95) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])]) ).

cnf(c_0_25,plain,
    ( ~ ok(remove_cpq(triple(X1,X2,X3),X4))
    | ~ contains_slb(X2,X4)
    | ~ strictly_less_than(X4,lookup_slb(X2,X4)) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_26,negated_conjecture,
    contains_slb(esk4_0,esk6_0),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_17]) ).

cnf(c_0_27,plain,
    ( less_than(X2,X1)
    | strictly_less_than(X1,X2)
    | ~ less_than(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_28,plain,
    ( less_than(X1,X2)
    | less_than(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_29,lemma,
    ( less_than(X5,X4)
    | ~ check_cpq(triple(X1,X2,X3))
    | ~ pair_in_list(X2,X4,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_30,plain,
    ( remove_cpq(triple(X3,X1,X4),X2) = triple(remove_pqp(X3,X2),remove_slb(X1,X2),X4)
    | ~ contains_slb(X1,X2)
    | ~ less_than(lookup_slb(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_31,negated_conjecture,
    ~ strictly_less_than(esk6_0,lookup_slb(esk4_0,esk6_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_19]),c_0_26])]) ).

cnf(c_0_32,plain,
    ( strictly_less_than(X1,X2)
    | less_than(X2,X1) ),
    inference(csr,[status(thm)],[c_0_27,c_0_28]) ).

fof(c_0_33,lemma,
    ! [X129,X130,X131,X132,X133] :
      ( ~ pair_in_list(X130,X132,X133)
      | ~ strictly_less_than(X132,X133)
      | ~ ok(remove_cpq(triple(X129,X130,X131),X132))
      | pair_in_list(remove_slb(X130,X132),X132,X133) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l30_li3132])]) ).

cnf(c_0_34,lemma,
    ( less_than(X1,X2)
    | ~ check_cpq(remove_cpq(triple(X3,X4,X5),X6))
    | ~ pair_in_list(remove_slb(X4,X6),X2,X1)
    | ~ contains_slb(X4,X6)
    | ~ less_than(lookup_slb(X4,X6),X6) ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_35,negated_conjecture,
    check_cpq(remove_cpq(triple(esk3_0,esk4_0,esk5_0),esk6_0)),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_36,negated_conjecture,
    less_than(lookup_slb(esk4_0,esk6_0),esk6_0),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_37,lemma,
    ( pair_in_list(remove_slb(X1,X2),X2,X3)
    | ~ pair_in_list(X1,X2,X3)
    | ~ strictly_less_than(X2,X3)
    | ~ ok(remove_cpq(triple(X4,X1,X5),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_38,negated_conjecture,
    ( less_than(X1,X2)
    | ~ pair_in_list(remove_slb(esk4_0,esk6_0),X2,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_26]),c_0_36])]) ).

cnf(c_0_39,negated_conjecture,
    ( pair_in_list(remove_slb(esk4_0,esk6_0),esk6_0,X1)
    | ~ pair_in_list(esk4_0,esk6_0,X1)
    | ~ strictly_less_than(esk6_0,X1) ),
    inference(spm,[status(thm)],[c_0_37,c_0_19]) ).

cnf(c_0_40,negated_conjecture,
    ( less_than(X1,esk6_0)
    | ~ pair_in_list(esk4_0,esk6_0,X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_32]) ).

cnf(c_0_41,negated_conjecture,
    pair_in_list(esk4_0,esk6_0,esk7_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_42,negated_conjecture,
    ~ less_than(esk7_0,esk6_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_43,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWV394+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.32  % Computer : n012.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32  % CPULimit   : 300
% 0.13/0.32  % WCLimit    : 300
% 0.13/0.32  % DateTime   : Tue Aug 29 06:47:24 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.17/0.55  start to proof: theBenchmark
% 0.17/0.59  % Version  : CSE_E---1.5
% 0.17/0.59  % Problem  : theBenchmark.p
% 0.17/0.59  % Proof found
% 0.17/0.59  % SZS status Theorem for theBenchmark.p
% 0.17/0.59  % SZS output start Proof
% See solution above
% 0.17/0.60  % Total time : 0.032000 s
% 0.17/0.60  % SZS output end Proof
% 0.17/0.60  % Total time : 0.035000 s
%------------------------------------------------------------------------------