TSTP Solution File: SWV370+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWV370+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 : n021.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 21:38:17 EDT 2023

% Result   : Theorem 0.21s 0.66s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   60
% Syntax   : Number of formulae    :   94 (   9 unt;  55 typ;   0 def)
%            Number of atoms       :   97 (  17 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   92 (  34   ~;  41   |;   8   &)
%                                         (   7 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   76 (  45   >;  31   *;   0   +;   0  <<)
%            Number of predicates  :   21 (  19 usr;   1 prp; 0-3 aty)
%            Number of functors    :   36 (  36 usr;  10 con; 0-3 aty)
%            Number of variables   :  121 (  26 sgn;  53   !;   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_pq: $i ).

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

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

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

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

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

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

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

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

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

tff(decl_35,type,
    create_slb: $i ).

tff(decl_36,type,
    isnonempty_slb: $i > $o ).

tff(decl_37,type,
    pair: ( $i * $i ) > $i ).

tff(decl_38,type,
    insert_slb: ( $i * $i ) > $i ).

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

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

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

tff(decl_42,type,
    lookup_slb: ( $i * $i ) > $i ).

tff(decl_43,type,
    update_slb: ( $i * $i ) > $i ).

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

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

tff(decl_46,type,
    remove_cpq: ( $i * $i ) > $i ).

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

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

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

tff(decl_50,type,
    check_cpq: $i > $o ).

tff(decl_51,type,
    contains_cpq: ( $i * $i ) > $o ).

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

tff(decl_53,type,
    ok: $i > $o ).

tff(decl_54,type,
    insert_pqp: ( $i * $i ) > $i ).

tff(decl_55,type,
    remove_pqp: ( $i * $i ) > $i ).

tff(decl_56,type,
    findmin_pqp_res: $i > $i ).

tff(decl_57,type,
    findmin_cpq_res: $i > $i ).

tff(decl_58,type,
    removemin_cpq_res: $i > $i ).

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

tff(decl_60,type,
    pi_sharp_remove: ( $i * $i ) > $o ).

tff(decl_61,type,
    pi_remove: ( $i * $i ) > $o ).

tff(decl_62,type,
    pi_sharp_find_min: ( $i * $i ) > $o ).

tff(decl_63,type,
    pi_find_min: $i > $o ).

tff(decl_64,type,
    pi_sharp_removemin: ( $i * $i ) > $o ).

tff(decl_65,type,
    pi_removemin: $i > $o ).

tff(decl_66,type,
    phi: $i > $o ).

tff(decl_67,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_68,type,
    esk2_1: $i > $i ).

tff(decl_69,type,
    esk3_1: $i > $i ).

tff(decl_70,type,
    esk4_1: $i > $i ).

tff(decl_71,type,
    esk5_0: $i ).

tff(decl_72,type,
    esk6_0: $i ).

tff(decl_73,type,
    esk7_0: $i ).

tff(decl_74,type,
    esk8_0: $i ).

tff(decl_75,type,
    esk9_0: $i ).

tff(decl_76,type,
    esk10_0: $i ).

fof(l6_co,conjecture,
    ! [X1] :
      ( ! [X2,X3,X4] :
          ( contains_cpq(triple(X2,X1,X3),X4)
        <=> contains_pq(i(triple(X2,X1,X3)),X4) )
     => ! [X5,X6,X7,X8,X9] :
          ( contains_cpq(triple(X5,insert_slb(X1,pair(X7,X8)),X6),X9)
        <=> contains_pq(i(triple(X5,insert_slb(X1,pair(X7,X8)),X6)),X9) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l6_co) ).

fof(ax39,axiom,
    ! [X1,X2,X3,X4] :
      ( contains_cpq(triple(X1,X2,X3),X4)
    <=> contains_slb(X2,X4) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax39) ).

fof(ax9,axiom,
    ! [X1,X2,X3] :
      ( contains_pq(insert_pq(X1,X2),X3)
    <=> ( contains_pq(X1,X3)
        | X2 = X3 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV007+1.ax',ax9) ).

fof(ax55,axiom,
    ! [X1,X2,X3,X4,X5] : i(triple(X1,insert_slb(X2,pair(X4,X5)),X3)) = insert_pq(i(triple(X1,X2,X3)),X4),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV007+4.ax',ax55) ).

fof(ax21,axiom,
    ! [X1,X2,X3,X4] :
      ( contains_slb(insert_slb(X1,pair(X2,X4)),X3)
    <=> ( contains_slb(X1,X3)
        | X2 = X3 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax',ax21) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X1] :
        ( ! [X2,X3,X4] :
            ( contains_cpq(triple(X2,X1,X3),X4)
          <=> contains_pq(i(triple(X2,X1,X3)),X4) )
       => ! [X5,X6,X7,X8,X9] :
            ( contains_cpq(triple(X5,insert_slb(X1,pair(X7,X8)),X6),X9)
          <=> contains_pq(i(triple(X5,insert_slb(X1,pair(X7,X8)),X6)),X9) ) ),
    inference(assume_negation,[status(cth)],[l6_co]) ).

fof(c_0_6,negated_conjecture,
    ! [X179,X180,X181] :
      ( ( ~ contains_cpq(triple(X179,esk5_0,X180),X181)
        | contains_pq(i(triple(X179,esk5_0,X180)),X181) )
      & ( ~ contains_pq(i(triple(X179,esk5_0,X180)),X181)
        | contains_cpq(triple(X179,esk5_0,X180),X181) )
      & ( ~ contains_cpq(triple(esk6_0,insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk7_0),esk10_0)
        | ~ contains_pq(i(triple(esk6_0,insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk7_0)),esk10_0) )
      & ( contains_cpq(triple(esk6_0,insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk7_0),esk10_0)
        | contains_pq(i(triple(esk6_0,insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk7_0)),esk10_0) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).

fof(c_0_7,plain,
    ! [X108,X109,X110,X111] :
      ( ( ~ contains_cpq(triple(X108,X109,X110),X111)
        | contains_slb(X109,X111) )
      & ( ~ contains_slb(X109,X111)
        | contains_cpq(triple(X108,X109,X110),X111) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax39])]) ).

fof(c_0_8,plain,
    ! [X22,X23,X24] :
      ( ( ~ contains_pq(insert_pq(X22,X23),X24)
        | contains_pq(X22,X24)
        | X23 = X24 )
      & ( ~ contains_pq(X22,X24)
        | contains_pq(insert_pq(X22,X23),X24) )
      & ( X23 != X24
        | contains_pq(insert_pq(X22,X23),X24) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax9])])]) ).

fof(c_0_9,plain,
    ! [X153,X154,X155,X156,X157] : i(triple(X153,insert_slb(X154,pair(X156,X157)),X155)) = insert_pq(i(triple(X153,X154,X155)),X156),
    inference(variable_rename,[status(thm)],[ax55]) ).

cnf(c_0_10,negated_conjecture,
    ( ~ contains_cpq(triple(esk6_0,insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk7_0),esk10_0)
    | ~ contains_pq(i(triple(esk6_0,insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk7_0)),esk10_0) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,plain,
    ( contains_cpq(triple(X3,X1,X4),X2)
    | ~ contains_slb(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,plain,
    ( contains_pq(insert_pq(X1,X3),X2)
    | ~ contains_pq(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,plain,
    i(triple(X1,insert_slb(X2,pair(X3,X4)),X5)) = insert_pq(i(triple(X1,X2,X5)),X3),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,plain,
    ( contains_pq(X1,X3)
    | X2 = X3
    | ~ contains_pq(insert_pq(X1,X2),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_15,plain,
    ( contains_slb(X2,X4)
    | ~ contains_cpq(triple(X1,X2,X3),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_16,negated_conjecture,
    ( contains_cpq(triple(esk6_0,insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk7_0),esk10_0)
    | contains_pq(i(triple(esk6_0,insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk7_0)),esk10_0) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_17,negated_conjecture,
    ( ~ contains_slb(insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk10_0)
    | ~ contains_pq(i(triple(esk6_0,insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk7_0)),esk10_0) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_18,plain,
    ( contains_pq(i(triple(X1,insert_slb(X2,pair(X3,X4)),X5)),X6)
    | ~ contains_pq(i(triple(X1,X2,X5)),X6) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_19,negated_conjecture,
    ( contains_pq(i(triple(X1,esk5_0,X2)),X3)
    | ~ contains_cpq(triple(X1,esk5_0,X2),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_20,plain,
    ! [X51,X52,X53,X54] :
      ( ( ~ contains_slb(insert_slb(X51,pair(X52,X54)),X53)
        | contains_slb(X51,X53)
        | X52 = X53 )
      & ( ~ contains_slb(X51,X53)
        | contains_slb(insert_slb(X51,pair(X52,X54)),X53) )
      & ( X52 != X53
        | contains_slb(insert_slb(X51,pair(X52,X54)),X53) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).

cnf(c_0_21,negated_conjecture,
    ( contains_cpq(triple(X1,esk5_0,X2),X3)
    | ~ contains_pq(i(triple(X1,esk5_0,X2)),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_22,plain,
    ( X1 = X2
    | contains_pq(i(triple(X3,X4,X5)),X2)
    | ~ contains_pq(i(triple(X3,insert_slb(X4,pair(X1,X6)),X5)),X2) ),
    inference(spm,[status(thm)],[c_0_14,c_0_13]) ).

cnf(c_0_23,negated_conjecture,
    ( contains_slb(insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk10_0)
    | contains_pq(i(triple(esk6_0,insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk7_0)),esk10_0) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_24,negated_conjecture,
    ( ~ contains_slb(insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk10_0)
    | ~ contains_pq(i(triple(esk6_0,esk5_0,esk7_0)),esk10_0) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_25,negated_conjecture,
    ( contains_pq(i(triple(X1,esk5_0,X2)),X3)
    | ~ contains_slb(esk5_0,X3) ),
    inference(spm,[status(thm)],[c_0_19,c_0_11]) ).

cnf(c_0_26,plain,
    ( contains_slb(insert_slb(X1,pair(X3,X4)),X2)
    | ~ contains_slb(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_27,negated_conjecture,
    ( contains_slb(esk5_0,X1)
    | ~ contains_pq(i(triple(X2,esk5_0,X3)),X1) ),
    inference(spm,[status(thm)],[c_0_15,c_0_21]) ).

cnf(c_0_28,negated_conjecture,
    ( esk10_0 = esk8_0
    | contains_slb(insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk10_0)
    | contains_pq(i(triple(esk6_0,esk5_0,esk7_0)),esk10_0) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_29,negated_conjecture,
    ~ contains_slb(esk5_0,esk10_0),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).

cnf(c_0_30,plain,
    ( contains_pq(insert_pq(X3,X1),X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_31,plain,
    ( contains_slb(X1,X4)
    | X2 = X4
    | ~ contains_slb(insert_slb(X1,pair(X2,X3)),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_32,negated_conjecture,
    ( esk10_0 = esk8_0
    | contains_slb(insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk10_0) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).

cnf(c_0_33,plain,
    ( contains_slb(insert_slb(X3,pair(X1,X4)),X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_34,plain,
    contains_pq(insert_pq(X1,X2),X2),
    inference(er,[status(thm)],[c_0_30]) ).

cnf(c_0_35,negated_conjecture,
    esk10_0 = esk8_0,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_29]) ).

cnf(c_0_36,plain,
    contains_slb(insert_slb(X1,pair(X2,X3)),X2),
    inference(er,[status(thm)],[c_0_33]) ).

cnf(c_0_37,plain,
    contains_pq(i(triple(X1,insert_slb(X2,pair(X3,X4)),X5)),X3),
    inference(spm,[status(thm)],[c_0_34,c_0_13]) ).

cnf(c_0_38,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_35]),c_0_36]),c_0_35]),c_0_37])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SWV370+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n021.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % 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   : Tue Aug 29 04:52:14 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.21/0.59  start to proof: theBenchmark
% 0.21/0.66  % Version  : CSE_E---1.5
% 0.21/0.66  % Problem  : theBenchmark.p
% 0.21/0.66  % Proof found
% 0.21/0.66  % SZS status Theorem for theBenchmark.p
% 0.21/0.66  % SZS output start Proof
% See solution above
% 0.21/0.67  % Total time : 0.067000 s
% 0.21/0.67  % SZS output end Proof
% 0.21/0.67  % Total time : 0.072000 s
%------------------------------------------------------------------------------