TSTP Solution File: ITP020+1 by CSE

TSTP Solution File: ITP020+1 by CSE_E---1.5

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : ITP020+1 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n007.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 03:10:54 EDT 2023

% Result   : Theorem 0.18s 0.62s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   63
% Syntax   : Number of formulae    :   71 (   8 unt;  60 typ;   0 def)
%            Number of atoms       :   16 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   11 (   6   ~;   3   |;   1   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  110 (  42   >;  68   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   58 (  58 usr;  18 con; 0-4 aty)
%            Number of variables   :   26 (   2 sgn;  15   !;   5   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    tyop_2Emin_2Efun: ( $i * $i ) > $i ).

tff(decl_23,type,
    s: ( $i * $i ) > $i ).

tff(decl_24,type,
    app_2E2: ( $i * $i ) > $i ).

tff(decl_25,type,
    tyop_2Emin_2Ebool: $i ).

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

tff(decl_27,type,
    c_2Ebool_2ET_2E0: $i ).

tff(decl_28,type,
    c_2Ebool_2EF_2E0: $i ).

tff(decl_29,type,
    combin_i_2E0: $i ).

tff(decl_30,type,
    combin_k_2E0: $i ).

tff(decl_31,type,
    combin_s_2E0: $i ).

tff(decl_32,type,
    c_2Ebool_2E_2F_5C_2E2: ( $i * $i ) > $i ).

tff(decl_33,type,
    c_2Ebool_2E_5C_2F_2E2: ( $i * $i ) > $i ).

tff(decl_34,type,
    c_2Ebool_2E_7E_2E1: $i > $i ).

tff(decl_35,type,
    c_2Emin_2E_3D_3D_3E_2E2: ( $i * $i ) > $i ).

tff(decl_36,type,
    c_2Emin_2E_3D_2E2: ( $i * $i ) > $i ).

tff(decl_37,type,
    c_2Ebool_2E_21_2E1: $i > $i ).

tff(decl_38,type,
    c_2Ebool_2E_3F_2E1: $i > $i ).

tff(decl_39,type,
    c_2Ebool_2E_2F_5C_2E0: $i ).

tff(decl_40,type,
    c_2Ebool_2E_5C_2F_2E0: $i ).

tff(decl_41,type,
    c_2Ebool_2E_7E_2E0: $i ).

tff(decl_42,type,
    c_2Emin_2E_3D_3D_3E_2E0: $i ).

tff(decl_43,type,
    c_2Emin_2E_3D_2E0: $i ).

tff(decl_44,type,
    c_2Ebool_2E_21_2E0: $i ).

tff(decl_45,type,
    c_2Ebool_2E_3F_2E0: $i ).

tff(decl_46,type,
    c_2Epred__set_2EBIJ_2E3: ( $i * $i * $i ) > $i ).

tff(decl_47,type,
    c_2Epred__set_2EBIJ_2E0: $i ).

tff(decl_48,type,
    tyop_2Enum_2Enum: $i ).

tff(decl_49,type,
    tyop_2Epair_2Eprod: ( $i * $i ) > $i ).

tff(decl_50,type,
    c_2Epred__set_2ECROSS_2E2: ( $i * $i ) > $i ).

tff(decl_51,type,
    c_2Epred__set_2ECROSS_2E0: $i ).

tff(decl_52,type,
    c_2Epred__set_2EUNIV_2E0: $i ).

tff(decl_53,type,
    epred1_3: ( $i * $i * $i ) > $o ).

tff(decl_54,type,
    esk1_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_55,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_56,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_57,type,
    esk4_2: ( $i * $i ) > $i ).

tff(decl_58,type,
    esk5_2: ( $i * $i ) > $i ).

tff(decl_59,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_60,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_61,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_62,type,
    esk9_3: ( $i * $i * $i ) > $i ).

tff(decl_63,type,
    esk10_3: ( $i * $i * $i ) > $i ).

tff(decl_64,type,
    esk11_3: ( $i * $i * $i ) > $i ).

tff(decl_65,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_66,type,
    esk13_3: ( $i * $i * $i ) > $i ).

tff(decl_67,type,
    esk14_3: ( $i * $i * $i ) > $i ).

tff(decl_68,type,
    esk15_3: ( $i * $i * $i ) > $i ).

tff(decl_69,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_70,type,
    esk17_3: ( $i * $i * $i ) > $i ).

tff(decl_71,type,
    esk18_3: ( $i * $i * $i ) > $i ).

tff(decl_72,type,
    esk19_3: ( $i * $i * $i ) > $i ).

tff(decl_73,type,
    esk20_3: ( $i * $i * $i ) > $i ).

tff(decl_74,type,
    esk21_3: ( $i * $i * $i ) > $i ).

tff(decl_75,type,
    esk22_3: ( $i * $i * $i ) > $i ).

tff(decl_76,type,
    esk23_3: ( $i * $i * $i ) > $i ).

tff(decl_77,type,
    esk24_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_78,type,
    esk25_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_79,type,
    esk26_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_80,type,
    esk27_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_81,type,
    esk28_0: $i ).

fof(thm_2Eutil__prob_2ENUM__2D__BIJ__INV,conjecture,
    ? [X3] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X3),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eutil__prob_2ENUM__2D__BIJ__INV) ).

fof(thm_2Epred__set_2EBIJ__SYM,axiom,
    ! [X1,X2,X28,X29] :
      ( ? [X30] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(X1,X2),X30),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X28),s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X29))))
    <=> ? [X31] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(X2,X1),X31),s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X29),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X28)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EBIJ__SYM) ).

fof(thm_2Eutil__prob_2ENUM__2D__BIJ,axiom,
    ? [X3] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),X3),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eutil__prob_2ENUM__2D__BIJ) ).

fof(c_0_3,negated_conjecture,
    ~ ? [X3] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X3),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))),
    inference(assume_negation,[status(cth)],[thm_2Eutil__prob_2ENUM__2D__BIJ__INV]) ).

fof(c_0_4,plain,
    ! [X226,X227,X228,X229,X230,X232,X233,X234,X235,X236] :
      ( ( ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(X226,X227),X230),s(tyop_2Emin_2Efun(X226,tyop_2Emin_2Ebool),X228),s(tyop_2Emin_2Efun(X227,tyop_2Emin_2Ebool),X229))))
        | p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(X227,X226),esk26_4(X226,X227,X228,X229)),s(tyop_2Emin_2Efun(X227,tyop_2Emin_2Ebool),X229),s(tyop_2Emin_2Efun(X226,tyop_2Emin_2Ebool),X228)))) )
      & ( ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(X233,X232),X236),s(tyop_2Emin_2Efun(X233,tyop_2Emin_2Ebool),X235),s(tyop_2Emin_2Efun(X232,tyop_2Emin_2Ebool),X234))))
        | p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(X232,X233),esk27_4(X232,X233,X234,X235)),s(tyop_2Emin_2Efun(X232,tyop_2Emin_2Ebool),X234),s(tyop_2Emin_2Efun(X233,tyop_2Emin_2Ebool),X235)))) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Epred__set_2EBIJ__SYM])])])])]) ).

fof(c_0_5,plain,
    p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),esk28_0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[thm_2Eutil__prob_2ENUM__2D__BIJ])]) ).

fof(c_0_6,negated_conjecture,
    ! [X259] : ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X259),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])]) ).

cnf(c_0_7,plain,
    ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(X2,X1),esk26_4(X1,X2,X4,X5)),s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X5),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X4))))
    | ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(X1,X2),X3),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X4),s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X5)))) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_8,plain,
    p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),esk28_0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,negated_conjecture,
    ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X1),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,plain,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem    : ITP020+1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.10/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.33  % Computer : n007.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Sun Aug 27 15:47:27 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 0.18/0.54  start to proof: theBenchmark
% 0.18/0.62  % Version  : CSE_E---1.5
% 0.18/0.62  % Problem  : theBenchmark.p
% 0.18/0.62  % Proof found
% 0.18/0.62  % SZS status Theorem for theBenchmark.p
% 0.18/0.62  % SZS output start Proof
% See solution above
% 0.18/0.63  % Total time : 0.069000 s
% 0.18/0.63  % SZS output end Proof
% 0.18/0.63  % Total time : 0.073000 s
%------------------------------------------------------------------------------