TSTP Solution File: SWV381+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWV381+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 : n016.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 21:38:20 EDT 2023

% Result   : Theorem 0.54s 0.61s
% Output   : CNFRefutation 0.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   62
% Syntax   : Number of formulae    :   97 (  14 unt;  52 typ;   0 def)
%            Number of atoms       :  102 (  19 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   91 (  34   ~;  37   |;  10   &)
%                                         (   4 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    4 (   1 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    :   33 (  33 usr;   7 con; 0-3 aty)
%            Number of variables   :   96 (   8 sgn;  59   !;   2   ?;   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 ).

fof(l17_l18,lemma,
    ! [X1,X2,X3] :
      ( ? [X4] :
          ( contains_cpq(triple(X1,X2,X3),X4)
          & strictly_less_than(X4,findmin_cpq_res(triple(X1,X2,X3))) )
     => ~ phi(findmin_cpq_eff(triple(X1,X2,X3))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l17_l18) ).

fof(ax51,axiom,
    ! [X1,X2,X3,X4] :
      ( X2 != create_slb
     => findmin_cpq_res(triple(X1,X2,X3)) = findmin_pqp_res(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax51) ).

fof(l17_co,conjecture,
    ! [X1,X2,X3] :
      ( phi(findmin_cpq_eff(triple(X1,X2,X3)))
     => issmallestelement_pq(i(triple(X1,X2,X3)),findmin_cpq_res(triple(X1,X2,X3))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l17_co) ).

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(l17_li56,lemma,
    ! [X1,X2,X3,X4] :
      ( contains_cpq(triple(X1,X2,X3),X4)
    <=> contains_pq(i(triple(X1,X2,X3)),X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l17_li56) ).

fof(ax10,axiom,
    ! [X1,X2] :
      ( issmallestelement_pq(X1,X2)
    <=> ! [X3] :
          ( contains_pq(X1,X3)
         => less_than(X2,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+1.ax',ax10) ).

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

fof(ax54,axiom,
    ! [X1,X2] : i(triple(X1,create_slb,X2)) = create_pq,
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+4.ax',ax54) ).

fof(ax50,axiom,
    ! [X1,X2] : findmin_cpq_res(triple(X1,create_slb,X2)) = bottom,
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax50) ).

fof(c_0_10,lemma,
    ! [X1,X2,X3] :
      ( ? [X4] :
          ( contains_cpq(triple(X1,X2,X3),X4)
          & strictly_less_than(X4,findmin_cpq_res(triple(X1,X2,X3))) )
     => ~ phi(findmin_cpq_eff(triple(X1,X2,X3))) ),
    inference(fof_simplification,[status(thm)],[l17_l18]) ).

fof(c_0_11,lemma,
    ! [X178,X179,X180,X181] :
      ( ~ contains_cpq(triple(X178,X179,X180),X181)
      | ~ strictly_less_than(X181,findmin_cpq_res(triple(X178,X179,X180)))
      | ~ phi(findmin_cpq_eff(triple(X178,X179,X180))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).

fof(c_0_12,plain,
    ! [X142,X143,X144] :
      ( X143 = create_slb
      | findmin_cpq_res(triple(X142,X143,X144)) = findmin_pqp_res(X142) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax51])])]) ).

fof(c_0_13,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( phi(findmin_cpq_eff(triple(X1,X2,X3)))
       => issmallestelement_pq(i(triple(X1,X2,X3)),findmin_cpq_res(triple(X1,X2,X3))) ),
    inference(assume_negation,[status(cth)],[l17_co]) ).

fof(c_0_14,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_15,lemma,
    ( ~ contains_cpq(triple(X1,X2,X3),X4)
    | ~ strictly_less_than(X4,findmin_cpq_res(triple(X1,X2,X3)))
    | ~ phi(findmin_cpq_eff(triple(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_16,plain,
    ( X1 = create_slb
    | findmin_cpq_res(triple(X2,X1,X3)) = findmin_pqp_res(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_17,negated_conjecture,
    ( phi(findmin_cpq_eff(triple(esk5_0,esk6_0,esk7_0)))
    & ~ issmallestelement_pq(i(triple(esk5_0,esk6_0,esk7_0)),findmin_cpq_res(triple(esk5_0,esk6_0,esk7_0))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).

fof(c_0_18,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_14])])]) ).

fof(c_0_19,plain,
    ! [X9,X10] :
      ( less_than(X9,X10)
      | less_than(X10,X9) ),
    inference(variable_rename,[status(thm)],[totality]) ).

cnf(c_0_20,lemma,
    ( X1 = create_slb
    | ~ phi(findmin_cpq_eff(triple(X2,X1,X3)))
    | ~ contains_cpq(triple(X2,X1,X3),X4)
    | ~ strictly_less_than(X4,findmin_pqp_res(X2)) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_21,negated_conjecture,
    phi(findmin_cpq_eff(triple(esk5_0,esk6_0,esk7_0))),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_22,plain,
    ( less_than(X2,X1)
    | strictly_less_than(X1,X2)
    | ~ less_than(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_23,plain,
    ( less_than(X1,X2)
    | less_than(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_24,negated_conjecture,
    ( esk6_0 = create_slb
    | ~ contains_cpq(triple(esk5_0,esk6_0,esk7_0),X1)
    | ~ strictly_less_than(X1,findmin_pqp_res(esk5_0)) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_25,plain,
    ( strictly_less_than(X1,X2)
    | less_than(X2,X1) ),
    inference(csr,[status(thm)],[c_0_22,c_0_23]) ).

fof(c_0_26,lemma,
    ! [X174,X175,X176,X177] :
      ( ( ~ contains_cpq(triple(X174,X175,X176),X177)
        | contains_pq(i(triple(X174,X175,X176)),X177) )
      & ( ~ contains_pq(i(triple(X174,X175,X176)),X177)
        | contains_cpq(triple(X174,X175,X176),X177) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l17_li56])]) ).

cnf(c_0_27,negated_conjecture,
    ( esk6_0 = create_slb
    | less_than(findmin_pqp_res(esk5_0),X1)
    | ~ contains_cpq(triple(esk5_0,esk6_0,esk7_0),X1) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_28,lemma,
    ( contains_cpq(triple(X1,X2,X3),X4)
    | ~ contains_pq(i(triple(X1,X2,X3)),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

fof(c_0_29,plain,
    ! [X21,X22,X23,X24,X25] :
      ( ( ~ issmallestelement_pq(X21,X22)
        | ~ contains_pq(X21,X23)
        | less_than(X22,X23) )
      & ( contains_pq(X24,esk1_2(X24,X25))
        | issmallestelement_pq(X24,X25) )
      & ( ~ less_than(X25,esk1_2(X24,X25))
        | issmallestelement_pq(X24,X25) ) ),
    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)],[ax10])])])])])]) ).

cnf(c_0_30,lemma,
    ( esk6_0 = create_slb
    | less_than(findmin_pqp_res(esk5_0),X1)
    | ~ contains_pq(i(triple(esk5_0,esk6_0,esk7_0)),X1) ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_31,plain,
    ( contains_pq(X1,esk1_2(X1,X2))
    | issmallestelement_pq(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_32,negated_conjecture,
    ~ issmallestelement_pq(i(triple(esk5_0,esk6_0,esk7_0)),findmin_cpq_res(triple(esk5_0,esk6_0,esk7_0))),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

fof(c_0_33,plain,
    ! [X14] : less_than(bottom,X14),
    inference(variable_rename,[status(thm)],[bottom_smallest]) ).

cnf(c_0_34,plain,
    ( issmallestelement_pq(X2,X1)
    | ~ less_than(X1,esk1_2(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_35,lemma,
    ( esk6_0 = create_slb
    | issmallestelement_pq(i(triple(esk5_0,esk6_0,esk7_0)),X1)
    | less_than(findmin_pqp_res(esk5_0),esk1_2(i(triple(esk5_0,esk6_0,esk7_0)),X1)) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_36,negated_conjecture,
    ( esk6_0 = create_slb
    | ~ issmallestelement_pq(i(triple(esk5_0,esk6_0,esk7_0)),findmin_pqp_res(esk5_0)) ),
    inference(spm,[status(thm)],[c_0_32,c_0_16]) ).

fof(c_0_37,plain,
    ! [X147,X148] : i(triple(X147,create_slb,X148)) = create_pq,
    inference(variable_rename,[status(thm)],[ax54]) ).

fof(c_0_38,plain,
    ! [X140,X141] : findmin_cpq_res(triple(X140,create_slb,X141)) = bottom,
    inference(variable_rename,[status(thm)],[ax50]) ).

cnf(c_0_39,plain,
    less_than(bottom,X1),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_40,lemma,
    esk6_0 = create_slb,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).

cnf(c_0_41,plain,
    i(triple(X1,create_slb,X2)) = create_pq,
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_42,plain,
    findmin_cpq_res(triple(X1,create_slb,X2)) = bottom,
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_43,plain,
    issmallestelement_pq(X1,bottom),
    inference(spm,[status(thm)],[c_0_34,c_0_39]) ).

cnf(c_0_44,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_40]),c_0_41]),c_0_42]),c_0_43])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SWV381+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.36  % Computer : n016.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Tue Aug 29 04:11:30 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.21/0.58  start to proof: theBenchmark
% 0.54/0.61  % Version  : CSE_E---1.5
% 0.54/0.61  % Problem  : theBenchmark.p
% 0.54/0.61  % Proof found
% 0.54/0.61  % SZS status Theorem for theBenchmark.p
% 0.54/0.61  % SZS output start Proof
% See solution above
% 0.54/0.62  % Total time : 0.026000 s
% 0.54/0.62  % SZS output end Proof
% 0.54/0.62  % Total time : 0.030000 s
%------------------------------------------------------------------------------