TSTP Solution File: SWV406+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWV406+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 : n004.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 21:38:26 EDT 2023

% Result   : Theorem 0.19s 0.61s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   42
% Syntax   : Number of formulae    :   88 (   8 unt;  36 typ;   0 def)
%            Number of atoms       :  151 (  17 equ)
%            Maximal formula atoms :   14 (   2 avg)
%            Number of connectives :  155 (  56   ~;  67   |;  14   &)
%                                         (   9 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   4 avg)
%            Maximal term depth    :    4 (   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    :   27 (  27 usr;  10 con; 0-3 aty)
%            Number of variables   :  137 (  17 sgn;  73   !;   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_0: $i ).

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

tff(decl_51,type,
    esk3_2: ( $i * $i ) > $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 ).

tff(decl_56,type,
    esk8_0: $i ).

tff(decl_57,type,
    esk9_0: $i ).

fof(l42_co,conjecture,
    ! [X1] :
      ( ! [X2,X3] :
          ( check_cpq(triple(X2,X1,X3))
        <=> ! [X4,X5] :
              ( pair_in_list(X1,X4,X5)
             => less_than(X5,X4) ) )
     => ! [X6,X7,X8,X9] :
          ( check_cpq(triple(X6,insert_slb(X1,pair(X8,X9)),X7))
        <=> ! [X10,X11] :
              ( pair_in_list(insert_slb(X1,pair(X8,X9)),X10,X11)
             => less_than(X11,X10) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l42_co) ).

fof(ax23,axiom,
    ! [X1,X2,X3,X4,X5] :
      ( pair_in_list(insert_slb(X1,pair(X2,X4)),X3,X5)
    <=> ( pair_in_list(X1,X3,X5)
        | ( X2 = X3
          & X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax',ax23) ).

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

fof(ax38,axiom,
    ! [X1,X2,X3,X4,X5] :
      ( strictly_less_than(X4,X5)
     => ( check_cpq(triple(X1,insert_slb(X2,pair(X4,X5)),X3))
      <=> ~ $true ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax38) ).

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

fof(ax37,axiom,
    ! [X1,X2,X3,X4,X5] :
      ( less_than(X5,X4)
     => ( check_cpq(triple(X1,insert_slb(X2,pair(X4,X5)),X3))
      <=> check_cpq(triple(X1,X2,X3)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax37) ).

fof(c_0_6,negated_conjecture,
    ~ ! [X1] :
        ( ! [X2,X3] :
            ( check_cpq(triple(X2,X1,X3))
          <=> ! [X4,X5] :
                ( pair_in_list(X1,X4,X5)
               => less_than(X5,X4) ) )
       => ! [X6,X7,X8,X9] :
            ( check_cpq(triple(X6,insert_slb(X1,pair(X8,X9)),X7))
          <=> ! [X10,X11] :
                ( pair_in_list(insert_slb(X1,pair(X8,X9)),X10,X11)
               => less_than(X11,X10) ) ) ),
    inference(assume_negation,[status(cth)],[l42_co]) ).

fof(c_0_7,plain,
    ! [X31,X32,X33,X34,X35] :
      ( ( X32 = X33
        | pair_in_list(X31,X33,X35)
        | ~ pair_in_list(insert_slb(X31,pair(X32,X34)),X33,X35) )
      & ( X34 = X35
        | pair_in_list(X31,X33,X35)
        | ~ pair_in_list(insert_slb(X31,pair(X32,X34)),X33,X35) )
      & ( ~ pair_in_list(X31,X33,X35)
        | pair_in_list(insert_slb(X31,pair(X32,X34)),X33,X35) )
      & ( X32 != X33
        | X34 != X35
        | pair_in_list(insert_slb(X31,pair(X32,X34)),X33,X35) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])]) ).

fof(c_0_8,plain,
    ! [X1,X2] :
      ( strictly_less_than(X1,X2)
    <=> ( less_than(X1,X2)
        & ~ less_than(X2,X1) ) ),
    inference(fof_simplification,[status(thm)],[stricly_smaller_definition]) ).

fof(c_0_9,negated_conjecture,
    ! [X126,X127,X128,X129,X138,X139] :
      ( ( ~ check_cpq(triple(X126,esk1_0,X127))
        | ~ pair_in_list(esk1_0,X128,X129)
        | less_than(X129,X128) )
      & ( pair_in_list(esk1_0,esk2_2(X126,X127),esk3_2(X126,X127))
        | check_cpq(triple(X126,esk1_0,X127)) )
      & ( ~ less_than(esk3_2(X126,X127),esk2_2(X126,X127))
        | check_cpq(triple(X126,esk1_0,X127)) )
      & ( pair_in_list(insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk8_0,esk9_0)
        | ~ check_cpq(triple(esk4_0,insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk5_0)) )
      & ( ~ less_than(esk9_0,esk8_0)
        | ~ check_cpq(triple(esk4_0,insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk5_0)) )
      & ( check_cpq(triple(esk4_0,insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk5_0))
        | ~ pair_in_list(insert_slb(esk1_0,pair(esk6_0,esk7_0)),X138,X139)
        | less_than(X139,X138) ) ),
    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_6])])])])]) ).

fof(c_0_10,plain,
    ! [X1,X2,X3,X4,X5] :
      ( strictly_less_than(X4,X5)
     => ~ check_cpq(triple(X1,insert_slb(X2,pair(X4,X5)),X3)) ),
    inference(fof_simplification,[status(thm)],[ax38]) ).

cnf(c_0_11,plain,
    ( pair_in_list(insert_slb(X5,pair(X1,X3)),X2,X4)
    | X1 != X2
    | X3 != X4 ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_12,plain,
    ! [X18,X19] :
      ( ( less_than(X18,X19)
        | ~ strictly_less_than(X18,X19) )
      & ( ~ less_than(X19,X18)
        | ~ strictly_less_than(X18,X19) )
      & ( ~ less_than(X18,X19)
        | less_than(X19,X18)
        | strictly_less_than(X18,X19) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).

fof(c_0_13,plain,
    ! [X15,X16] :
      ( less_than(X15,X16)
      | less_than(X16,X15) ),
    inference(variable_rename,[status(thm)],[totality]) ).

cnf(c_0_14,negated_conjecture,
    ( check_cpq(triple(esk4_0,insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk5_0))
    | less_than(X2,X1)
    | ~ pair_in_list(insert_slb(esk1_0,pair(esk6_0,esk7_0)),X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_15,plain,
    ( pair_in_list(insert_slb(X1,pair(X4,X5)),X2,X3)
    | ~ pair_in_list(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_16,plain,
    ! [X77,X78,X79,X80,X81] :
      ( ~ strictly_less_than(X80,X81)
      | ~ check_cpq(triple(X77,insert_slb(X78,pair(X80,X81)),X79)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])]) ).

cnf(c_0_17,plain,
    pair_in_list(insert_slb(X1,pair(X2,X3)),X2,X3),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_11])]) ).

cnf(c_0_18,plain,
    ( less_than(X2,X1)
    | strictly_less_than(X1,X2)
    | ~ less_than(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_19,plain,
    ( less_than(X1,X2)
    | less_than(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_20,plain,
    ! [X72,X73,X74,X75,X76] :
      ( ( ~ check_cpq(triple(X72,insert_slb(X73,pair(X75,X76)),X74))
        | check_cpq(triple(X72,X73,X74))
        | ~ less_than(X76,X75) )
      & ( ~ check_cpq(triple(X72,X73,X74))
        | check_cpq(triple(X72,insert_slb(X73,pair(X75,X76)),X74))
        | ~ less_than(X76,X75) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])]) ).

cnf(c_0_21,negated_conjecture,
    ( check_cpq(triple(esk4_0,insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk5_0))
    | less_than(X1,X2)
    | ~ pair_in_list(esk1_0,X2,X1) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_22,negated_conjecture,
    ( pair_in_list(esk1_0,esk2_2(X1,X2),esk3_2(X1,X2))
    | check_cpq(triple(X1,esk1_0,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_23,negated_conjecture,
    ( check_cpq(triple(X1,esk1_0,X2))
    | ~ less_than(esk3_2(X1,X2),esk2_2(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_24,plain,
    ( ~ strictly_less_than(X1,X2)
    | ~ check_cpq(triple(X3,insert_slb(X4,pair(X1,X2)),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_25,negated_conjecture,
    ( check_cpq(triple(esk4_0,insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk5_0))
    | less_than(esk7_0,esk6_0) ),
    inference(spm,[status(thm)],[c_0_14,c_0_17]) ).

cnf(c_0_26,plain,
    ( strictly_less_than(X1,X2)
    | less_than(X2,X1) ),
    inference(csr,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_27,plain,
    ( check_cpq(triple(X1,X2,X5))
    | ~ check_cpq(triple(X1,insert_slb(X2,pair(X3,X4)),X5))
    | ~ less_than(X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_28,negated_conjecture,
    ( check_cpq(triple(esk4_0,insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk5_0))
    | check_cpq(triple(X1,esk1_0,X2)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).

cnf(c_0_29,negated_conjecture,
    less_than(esk7_0,esk6_0),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).

cnf(c_0_30,negated_conjecture,
    ( pair_in_list(insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk8_0,esk9_0)
    | ~ check_cpq(triple(esk4_0,insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk5_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_31,plain,
    ( check_cpq(triple(X1,insert_slb(X2,pair(X4,X5)),X3))
    | ~ check_cpq(triple(X1,X2,X3))
    | ~ less_than(X5,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_32,negated_conjecture,
    ( check_cpq(triple(esk4_0,esk1_0,esk5_0))
    | check_cpq(triple(X1,esk1_0,X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).

cnf(c_0_33,plain,
    ( X1 = X2
    | pair_in_list(X3,X4,X2)
    | ~ pair_in_list(insert_slb(X3,pair(X5,X1)),X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_34,negated_conjecture,
    ( pair_in_list(insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk8_0,esk9_0)
    | ~ check_cpq(triple(esk4_0,esk1_0,esk5_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_29])]) ).

cnf(c_0_35,negated_conjecture,
    ( ~ less_than(esk9_0,esk8_0)
    | ~ check_cpq(triple(esk4_0,insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk5_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_36,plain,
    ( X1 = X2
    | pair_in_list(X3,X2,X4)
    | ~ pair_in_list(insert_slb(X3,pair(X1,X5)),X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_37,negated_conjecture,
    ( less_than(X4,X3)
    | ~ check_cpq(triple(X1,esk1_0,X2))
    | ~ pair_in_list(esk1_0,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_38,negated_conjecture,
    check_cpq(triple(esk4_0,esk1_0,esk5_0)),
    inference(ef,[status(thm)],[c_0_32]) ).

cnf(c_0_39,negated_conjecture,
    ( esk9_0 = esk7_0
    | pair_in_list(esk1_0,esk8_0,esk9_0)
    | ~ check_cpq(triple(esk4_0,esk1_0,esk5_0)) ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_40,negated_conjecture,
    ( ~ check_cpq(triple(esk4_0,esk1_0,esk5_0))
    | ~ less_than(esk9_0,esk8_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_31]),c_0_29])]) ).

cnf(c_0_41,negated_conjecture,
    ( check_cpq(triple(X1,esk1_0,X2))
    | ~ less_than(esk9_0,esk8_0) ),
    inference(spm,[status(thm)],[c_0_35,c_0_28]) ).

cnf(c_0_42,negated_conjecture,
    ( esk8_0 = esk6_0
    | pair_in_list(esk1_0,esk8_0,esk9_0)
    | ~ check_cpq(triple(esk4_0,esk1_0,esk5_0)) ),
    inference(spm,[status(thm)],[c_0_36,c_0_34]) ).

cnf(c_0_43,negated_conjecture,
    ( less_than(X1,X2)
    | ~ pair_in_list(esk1_0,X2,X1) ),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_44,negated_conjecture,
    ( esk9_0 = esk7_0
    | pair_in_list(esk1_0,esk8_0,esk9_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_38])]) ).

cnf(c_0_45,negated_conjecture,
    ~ less_than(esk9_0,esk8_0),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_46,negated_conjecture,
    ( esk8_0 = esk6_0
    | pair_in_list(esk1_0,esk8_0,esk9_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_38])]) ).

cnf(c_0_47,negated_conjecture,
    esk9_0 = esk7_0,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).

cnf(c_0_48,negated_conjecture,
    ( esk8_0 = esk6_0
    | pair_in_list(esk1_0,esk8_0,esk7_0) ),
    inference(rw,[status(thm)],[c_0_46,c_0_47]) ).

cnf(c_0_49,negated_conjecture,
    ~ less_than(esk7_0,esk8_0),
    inference(rw,[status(thm)],[c_0_45,c_0_47]) ).

cnf(c_0_50,negated_conjecture,
    esk8_0 = esk6_0,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_48]),c_0_49]) ).

cnf(c_0_51,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50]),c_0_29])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWV406+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n004.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
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 29 06:29:52 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.19/0.61  % Version  : CSE_E---1.5
% 0.19/0.61  % Problem  : theBenchmark.p
% 0.19/0.61  % Proof found
% 0.19/0.61  % SZS status Theorem for theBenchmark.p
% 0.19/0.61  % SZS output start Proof
% See solution above
% 0.19/0.61  % Total time : 0.028000 s
% 0.19/0.61  % SZS output end Proof
% 0.19/0.61  % Total time : 0.032000 s
%------------------------------------------------------------------------------