TSTP Solution File: SWV408+2 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWV408+2 : 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 : n002.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 21:38:27 EDT 2023

% Result   : Theorem 0.19s 0.71s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   38
% Syntax   : Number of formulae    :   61 (   4 unt;  32 typ;   0 def)
%            Number of atoms       :   79 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   80 (  30   ~;  30   |;  13   &)
%                                         (   2 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   44 (  25   >;  19   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   9 usr;   1 prp; 0-3 aty)
%            Number of functors    :   23 (  23 usr;   7 con; 0-3 aty)
%            Number of variables   :   67 (   0 sgn;  39   !;   3   ?;   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_0: $i ).

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

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

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

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(l48_li3839,lemma,
    ! [X1,X2,X3,X4] :
      ( ( pair_in_list(X1,X2,X3)
        & strictly_less_than(X3,X4) )
     => pair_in_list(update_slb(X1,X4),X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l48_li3839) ).

fof(l45_li4647,lemma,
    ! [X1,X2] :
      ( contains_slb(X1,X2)
     => ? [X3] : pair_in_list(X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_li4647) ).

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

fof(l44_co,conjecture,
    ! [X1,X2,X3,X4] :
      ( ( contains_slb(X2,X4)
        & strictly_less_than(X4,findmin_cpq_res(triple(X1,X2,X3))) )
     => ( pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X4,findmin_pqp_res(X1))
        | ? [X5] :
            ( pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X4,X5)
            & less_than(findmin_pqp_res(X1),X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l44_co) ).

fof(l49_li3637,lemma,
    ! [X1,X2,X3,X4] :
      ( ( pair_in_list(X1,X2,X3)
        & less_than(X4,X3) )
     => pair_in_list(update_slb(X1,X4),X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l49_li3637) ).

fof(c_0_6,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_7,lemma,
    ! [X122,X123,X124,X125] :
      ( ~ pair_in_list(X122,X123,X124)
      | ~ strictly_less_than(X124,X125)
      | pair_in_list(update_slb(X122,X125),X123,X125) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l48_li3839])]) ).

fof(c_0_8,lemma,
    ! [X119,X120] :
      ( ~ contains_slb(X119,X120)
      | pair_in_list(X119,X120,esk1_2(X119,X120)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l45_li4647])])]) ).

fof(c_0_9,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_6])])]) ).

fof(c_0_10,plain,
    ! [X9,X10] :
      ( less_than(X9,X10)
      | less_than(X10,X9) ),
    inference(variable_rename,[status(thm)],[totality]) ).

fof(c_0_11,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( ( contains_slb(X2,X4)
          & strictly_less_than(X4,findmin_cpq_res(triple(X1,X2,X3))) )
       => ( pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X4,findmin_pqp_res(X1))
          | ? [X5] :
              ( pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X4,X5)
              & less_than(findmin_pqp_res(X1),X5) ) ) ),
    inference(assume_negation,[status(cth)],[l44_co]) ).

cnf(c_0_12,lemma,
    ( pair_in_list(update_slb(X1,X4),X2,X4)
    | ~ pair_in_list(X1,X2,X3)
    | ~ strictly_less_than(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_13,lemma,
    ( pair_in_list(X1,X2,esk1_2(X1,X2))
    | ~ contains_slb(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,plain,
    ( less_than(X2,X1)
    | strictly_less_than(X1,X2)
    | ~ less_than(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_15,plain,
    ( less_than(X1,X2)
    | less_than(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_16,negated_conjecture,
    ! [X134] :
      ( contains_slb(esk3_0,esk5_0)
      & strictly_less_than(esk5_0,findmin_cpq_res(triple(esk2_0,esk3_0,esk4_0)))
      & ~ pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,findmin_pqp_res(esk2_0))
      & ( ~ pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,X134)
        | ~ less_than(findmin_pqp_res(esk2_0),X134) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).

fof(c_0_17,lemma,
    ! [X126,X127,X128,X129] :
      ( ~ pair_in_list(X126,X127,X128)
      | ~ less_than(X129,X128)
      | pair_in_list(update_slb(X126,X129),X127,X128) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l49_li3637])]) ).

cnf(c_0_18,lemma,
    ( pair_in_list(update_slb(X1,X2),X3,X2)
    | ~ contains_slb(X1,X3)
    | ~ strictly_less_than(esk1_2(X1,X3),X2) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_19,plain,
    ( strictly_less_than(X1,X2)
    | less_than(X2,X1) ),
    inference(csr,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_20,negated_conjecture,
    ( ~ pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,X1)
    | ~ less_than(findmin_pqp_res(esk2_0),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_21,lemma,
    ( pair_in_list(update_slb(X1,X4),X2,X3)
    | ~ pair_in_list(X1,X2,X3)
    | ~ less_than(X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_22,lemma,
    ( pair_in_list(update_slb(X1,X2),X3,X2)
    | less_than(X2,esk1_2(X1,X3))
    | ~ contains_slb(X1,X3) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_23,negated_conjecture,
    contains_slb(esk3_0,esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_24,negated_conjecture,
    ( ~ pair_in_list(esk3_0,esk5_0,X1)
    | ~ less_than(findmin_pqp_res(esk2_0),X1) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_25,negated_conjecture,
    ( pair_in_list(update_slb(esk3_0,X1),esk5_0,X1)
    | less_than(X1,esk1_2(esk3_0,esk5_0)) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_26,negated_conjecture,
    ~ pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,findmin_pqp_res(esk2_0)),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_27,negated_conjecture,
    ~ pair_in_list(esk3_0,esk5_0,esk1_2(esk3_0,esk5_0)),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).

cnf(c_0_28,lemma,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_13]),c_0_23])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWV408+2 : 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
% 0.13/0.33  % Computer : n002.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Tue Aug 29 08:15:35 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.55  start to proof: theBenchmark
% 0.19/0.71  % Version  : CSE_E---1.5
% 0.19/0.71  % Problem  : theBenchmark.p
% 0.19/0.71  % Proof found
% 0.19/0.71  % SZS status Theorem for theBenchmark.p
% 0.19/0.71  % SZS output start Proof
% See solution above
% 0.19/0.71  % Total time : 0.146000 s
% 0.19/0.71  % SZS output end Proof
% 0.19/0.71  % Total time : 0.150000 s
%------------------------------------------------------------------------------