TSTP Solution File: SWV390+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWV390+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 : n022.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 21:38:22 EDT 2023

% Result   : Theorem 0.19s 0.60s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   38
% Syntax   : Number of formulae    :   57 (  10 unt;  33 typ;   0 def)
%            Number of atoms       :   52 (   3 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   51 (  23   ~;  18   |;   4   &)
%                                         (   2 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   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  :   11 (   9 usr;   1 prp; 0-3 aty)
%            Number of functors    :   24 (  24 usr;   7 con; 0-3 aty)
%            Number of variables   :   76 (  10 sgn;  41   !;   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_2: ( $i * $i ) > $i ).

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

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

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

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

tff(decl_54,type,
    esk6_0: $i ).

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/sandbox2/benchmark/Axioms/SWV007+3.ax',ax37) ).

fof(ax42,axiom,
    ! [X1,X2,X3,X4] : insert_cpq(triple(X1,X2,X3),X4) = triple(insert_pqp(X1,X4),insert_slb(X2,pair(X4,bottom)),X3),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax42) ).

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

fof(l26_li4142,lemma,
    ! [X1,X2,X3] :
      ( check_cpq(triple(X1,X2,X3))
    <=> ! [X4,X5] :
          ( pair_in_list(X2,X4,X5)
         => less_than(X5,X4) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l26_li4142) ).

fof(l26_co,conjecture,
    ! [X1,X2,X3] :
      ( ~ check_cpq(triple(X1,X2,X3))
     => ! [X4] : ~ check_cpq(insert_cpq(triple(X1,X2,X3),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l26_co) ).

fof(c_0_5,plain,
    ! [X66,X67,X68,X69,X70] :
      ( ( ~ check_cpq(triple(X66,insert_slb(X67,pair(X69,X70)),X68))
        | check_cpq(triple(X66,X67,X68))
        | ~ less_than(X70,X69) )
      & ( ~ check_cpq(triple(X66,X67,X68))
        | check_cpq(triple(X66,insert_slb(X67,pair(X69,X70)),X68))
        | ~ less_than(X70,X69) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])]) ).

fof(c_0_6,plain,
    ! [X85,X86,X87,X88] : insert_cpq(triple(X85,X86,X87),X88) = triple(insert_pqp(X85,X88),insert_slb(X86,pair(X88,bottom)),X87),
    inference(variable_rename,[status(thm)],[ax42]) ).

fof(c_0_7,plain,
    ! [X14] : less_than(bottom,X14),
    inference(variable_rename,[status(thm)],[bottom_smallest]) ).

fof(c_0_8,lemma,
    ! [X119,X120,X121,X122,X123,X124,X125,X128] :
      ( ( ~ check_cpq(triple(X119,X120,X121))
        | ~ pair_in_list(X120,X122,X123)
        | less_than(X123,X122) )
      & ( pair_in_list(X125,esk1_2(X124,X125),esk2_2(X124,X125))
        | check_cpq(triple(X124,X125,X128)) )
      & ( ~ less_than(esk2_2(X124,X125),esk1_2(X124,X125))
        | check_cpq(triple(X124,X125,X128)) ) ),
    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)],[l26_li4142])])])])])]) ).

cnf(c_0_9,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_5]) ).

cnf(c_0_10,plain,
    insert_cpq(triple(X1,X2,X3),X4) = triple(insert_pqp(X1,X4),insert_slb(X2,pair(X4,bottom)),X3),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,plain,
    less_than(bottom,X1),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_12,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ~ check_cpq(triple(X1,X2,X3))
       => ! [X4] : ~ check_cpq(insert_cpq(triple(X1,X2,X3),X4)) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[l26_co])]) ).

cnf(c_0_13,lemma,
    ( less_than(X5,X4)
    | ~ check_cpq(triple(X1,X2,X3))
    | ~ pair_in_list(X2,X4,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,plain,
    ( check_cpq(triple(insert_pqp(X1,X2),X3,X4))
    | ~ check_cpq(insert_cpq(triple(X1,X3,X4),X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11])]) ).

fof(c_0_15,negated_conjecture,
    ( ~ check_cpq(triple(esk3_0,esk4_0,esk5_0))
    & check_cpq(insert_cpq(triple(esk3_0,esk4_0,esk5_0),esk6_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).

cnf(c_0_16,lemma,
    ( less_than(X1,X2)
    | ~ check_cpq(insert_cpq(triple(X3,X4,X5),X6))
    | ~ pair_in_list(X4,X2,X1) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_17,negated_conjecture,
    check_cpq(insert_cpq(triple(esk3_0,esk4_0,esk5_0),esk6_0)),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_18,negated_conjecture,
    ( less_than(X1,X2)
    | ~ pair_in_list(esk4_0,X2,X1) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_19,lemma,
    ( pair_in_list(X1,esk1_2(X2,X1),esk2_2(X2,X1))
    | check_cpq(triple(X2,X1,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_20,lemma,
    ( check_cpq(triple(X1,X2,X3))
    | ~ less_than(esk2_2(X1,X2),esk1_2(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_21,negated_conjecture,
    ~ check_cpq(triple(esk3_0,esk4_0,esk5_0)),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_22,lemma,
    check_cpq(triple(X1,esk4_0,X2)),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).

cnf(c_0_23,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SWV390+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n022.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 04:12:24 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.19/0.60  % Version  : CSE_E---1.5
% 0.19/0.60  % Problem  : theBenchmark.p
% 0.19/0.60  % Proof found
% 0.19/0.60  % SZS status Theorem for theBenchmark.p
% 0.19/0.60  % SZS output start Proof
% See solution above
% 0.19/0.60  % Total time : 0.017000 s
% 0.19/0.60  % SZS output end Proof
% 0.19/0.60  % Total time : 0.020000 s
%------------------------------------------------------------------------------