TSTP Solution File: SWV376+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWV376+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n025.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 21:38:19 EDT 2023

% Result   : Theorem 0.19s 0.57s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   45
% Syntax   : Number of formulae    :   69 (  11 unt;  40 typ;   0 def)
%            Number of atoms       :   74 (   6 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :   87 (  42   ~;  22   |;   4   &)
%                                         (   1 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   43 (  25   >;  18   *;   0   +;   0  <<)
%            Number of predicates  :   12 (   9 usr;   2 prp; 0-3 aty)
%            Number of functors    :   31 (  31 usr;  15 con; 0-3 aty)
%            Number of variables   :   92 (   4 sgn;  66   !;   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,
    im_succ_cpq: $i > $i ).

tff(decl_50,type,
    esk1_0: $i ).

tff(decl_51,type,
    esk2_0: $i ).

tff(decl_52,type,
    esk3_0: $i ).

tff(decl_53,type,
    esk4_0: $i ).

tff(decl_54,type,
    esk5_0: $i ).

tff(decl_55,type,
    esk6_0: $i ).

tff(decl_56,type,
    esk7_0: $i ).

tff(decl_57,type,
    esk8_0: $i ).

tff(decl_58,type,
    esk9_0: $i ).

tff(decl_59,type,
    esk10_0: $i ).

tff(decl_60,type,
    esk11_0: $i ).

tff(decl_61,type,
    esk12_0: $i ).

fof(l12_co,conjecture,
    ! [X1,X2,X3] :
      ( ~ ok(triple(X1,X2,X3))
     => ! [X4,X5,X6] :
          ( succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6))
         => ~ ok(triple(X4,X5,X6)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_co) ).

fof(ax41,axiom,
    ! [X1,X2,X3] :
      ( ~ ok(triple(X1,X2,X3))
     => X3 = bad ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax41) ).

fof(l12_induction,axiom,
    ( ! [X1,X2,X3,X4,X5,X6] :
        ( succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6))
       => ( ~ ok(triple(X4,X5,X6))
         => ~ ok(im_succ_cpq(triple(X4,X5,X6))) ) )
   => ! [X7,X8,X9] :
        ( ~ ok(triple(X7,X8,X9))
       => ! [X10,X11,X12] :
            ( succ_cpq(triple(X7,X8,X9),triple(X10,X11,X12))
           => ~ ok(triple(X10,X11,X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_induction) ).

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

fof(l12_l13,lemma,
    ! [X1,X2,X3] :
      ( ~ ok(triple(X1,X2,X3))
     => ~ ok(im_succ_cpq(triple(X1,X2,X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_l13) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ~ ok(triple(X1,X2,X3))
       => ! [X4,X5,X6] :
            ( succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6))
           => ~ ok(triple(X4,X5,X6)) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[l12_co])]) ).

fof(c_0_6,plain,
    ! [X1,X2,X3] :
      ( ~ ok(triple(X1,X2,X3))
     => X3 = bad ),
    inference(fof_simplification,[status(thm)],[ax41]) ).

fof(c_0_7,plain,
    ( ! [X1,X2,X3,X4,X5,X6] :
        ( succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6))
       => ( ~ ok(triple(X4,X5,X6))
         => ~ ok(im_succ_cpq(triple(X4,X5,X6))) ) )
   => ! [X7,X8,X9] :
        ( ~ ok(triple(X7,X8,X9))
       => ! [X10,X11,X12] :
            ( succ_cpq(triple(X7,X8,X9),triple(X10,X11,X12))
           => ~ ok(triple(X10,X11,X12)) ) ) ),
    inference(fof_simplification,[status(thm)],[l12_induction]) ).

fof(c_0_8,negated_conjecture,
    ( ~ ok(triple(esk7_0,esk8_0,esk9_0))
    & succ_cpq(triple(esk7_0,esk8_0,esk9_0),triple(esk10_0,esk11_0,esk12_0))
    & ok(triple(esk10_0,esk11_0,esk12_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

fof(c_0_9,plain,
    ! [X89,X90,X91] :
      ( ok(triple(X89,X90,X91))
      | X91 = bad ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])]) ).

fof(c_0_10,plain,
    ! [X1,X2] : ~ ok(triple(X1,X2,bad)),
    inference(fof_simplification,[status(thm)],[ax40]) ).

fof(c_0_11,plain,
    ! [X132,X133,X134,X135,X136,X137] :
      ( ( succ_cpq(triple(esk1_0,esk2_0,esk3_0),triple(esk4_0,esk5_0,esk6_0))
        | ok(triple(X132,X133,X134))
        | ~ succ_cpq(triple(X132,X133,X134),triple(X135,X136,X137))
        | ~ ok(triple(X135,X136,X137)) )
      & ( ~ ok(triple(esk4_0,esk5_0,esk6_0))
        | ok(triple(X132,X133,X134))
        | ~ succ_cpq(triple(X132,X133,X134),triple(X135,X136,X137))
        | ~ ok(triple(X135,X136,X137)) )
      & ( ok(im_succ_cpq(triple(esk4_0,esk5_0,esk6_0)))
        | ok(triple(X132,X133,X134))
        | ~ succ_cpq(triple(X132,X133,X134),triple(X135,X136,X137))
        | ~ ok(triple(X135,X136,X137)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).

cnf(c_0_12,negated_conjecture,
    ~ ok(triple(esk7_0,esk8_0,esk9_0)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,plain,
    ( ok(triple(X1,X2,X3))
    | X3 = bad ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

fof(c_0_14,plain,
    ! [X87,X88] : ~ ok(triple(X87,X88,bad)),
    inference(variable_rename,[status(thm)],[c_0_10]) ).

cnf(c_0_15,plain,
    ( ok(triple(X1,X2,X3))
    | ~ ok(triple(esk4_0,esk5_0,esk6_0))
    | ~ succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6))
    | ~ ok(triple(X4,X5,X6)) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_16,negated_conjecture,
    succ_cpq(triple(esk7_0,esk8_0,esk9_0),triple(esk10_0,esk11_0,esk12_0)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_17,negated_conjecture,
    esk9_0 = bad,
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_18,negated_conjecture,
    ok(triple(esk10_0,esk11_0,esk12_0)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_19,plain,
    ~ ok(triple(X1,X2,bad)),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_20,negated_conjecture,
    ~ ok(triple(esk4_0,esk5_0,esk6_0)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18])]),c_0_19]) ).

fof(c_0_21,lemma,
    ! [X1,X2,X3] :
      ( ~ ok(triple(X1,X2,X3))
     => ~ ok(im_succ_cpq(triple(X1,X2,X3))) ),
    inference(fof_simplification,[status(thm)],[l12_l13]) ).

cnf(c_0_22,plain,
    ( ok(im_succ_cpq(triple(esk4_0,esk5_0,esk6_0)))
    | ok(triple(X1,X2,X3))
    | ~ succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6))
    | ~ ok(triple(X4,X5,X6)) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_23,negated_conjecture,
    esk6_0 = bad,
    inference(spm,[status(thm)],[c_0_20,c_0_13]) ).

fof(c_0_24,lemma,
    ! [X138,X139,X140] :
      ( ok(triple(X138,X139,X140))
      | ~ ok(im_succ_cpq(triple(X138,X139,X140))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])]) ).

cnf(c_0_25,plain,
    ( ok(im_succ_cpq(triple(esk4_0,esk5_0,bad)))
    | ok(triple(X1,X2,X3))
    | ~ ok(triple(X4,X5,X6))
    | ~ succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6)) ),
    inference(rw,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_26,lemma,
    ( ok(triple(X1,X2,X3))
    | ~ ok(im_succ_cpq(triple(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_27,negated_conjecture,
    ok(im_succ_cpq(triple(esk4_0,esk5_0,bad))),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_16]),c_0_17]),c_0_18])]),c_0_19]) ).

cnf(c_0_28,lemma,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_19]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWV376+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n025.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 29 09:03:10 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.55  start to proof: theBenchmark
% 0.19/0.57  % Version  : CSE_E---1.5
% 0.19/0.57  % Problem  : theBenchmark.p
% 0.19/0.57  % Proof found
% 0.19/0.57  % SZS status Theorem for theBenchmark.p
% 0.19/0.57  % SZS output start Proof
% See solution above
% 0.19/0.57  % Total time : 0.014000 s
% 0.19/0.57  % SZS output end Proof
% 0.19/0.57  % Total time : 0.018000 s
%------------------------------------------------------------------------------