TSTP Solution File: SEU344+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU344+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 : n031.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 16:24:37 EDT 2023

% Result   : Theorem 0.20s 0.66s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   60
% Syntax   : Number of formulae    :   92 (  13 unt;  52 typ;   0 def)
%            Number of atoms       :  112 (  19 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  114 (  42   ~;  39   |;  15   &)
%                                         (   4 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   71 (  39   >;  32   *;   0   +;   0  <<)
%            Number of predicates  :   18 (  16 usr;   1 prp; 0-3 aty)
%            Number of functors    :   36 (  36 usr;  13 con; 0-6 aty)
%            Number of variables   :   55 (   4 sgn;  36   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    latt_str: $i > $o ).

tff(decl_23,type,
    strict_latt_str: $i > $o ).

tff(decl_24,type,
    the_carrier: $i > $i ).

tff(decl_25,type,
    the_L_join: $i > $i ).

tff(decl_26,type,
    the_L_meet: $i > $i ).

tff(decl_27,type,
    latt_str_of: ( $i * $i * $i ) > $i ).

tff(decl_28,type,
    in: ( $i * $i ) > $o ).

tff(decl_29,type,
    cartesian_product2: ( $i * $i ) > $i ).

tff(decl_30,type,
    powerset: $i > $i ).

tff(decl_31,type,
    element: ( $i * $i ) > $o ).

tff(decl_32,type,
    relation: $i > $o ).

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

tff(decl_34,type,
    set_union2: ( $i * $i ) > $i ).

tff(decl_35,type,
    set_intersection2: ( $i * $i ) > $i ).

tff(decl_36,type,
    function: $i > $o ).

tff(decl_37,type,
    apply_binary: ( $i * $i * $i ) > $i ).

tff(decl_38,type,
    ordered_pair: ( $i * $i ) > $i ).

tff(decl_39,type,
    apply: ( $i * $i ) > $i ).

tff(decl_40,type,
    empty_carrier: $i > $o ).

tff(decl_41,type,
    join_semilatt_str: $i > $o ).

tff(decl_42,type,
    join: ( $i * $i * $i ) > $i ).

tff(decl_43,type,
    apply_binary_as_element: ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_44,type,
    meet_semilatt_str: $i > $o ).

tff(decl_45,type,
    meet: ( $i * $i * $i ) > $i ).

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

tff(decl_47,type,
    singleton: $i > $i ).

tff(decl_48,type,
    quasi_total: ( $i * $i * $i ) > $o ).

tff(decl_49,type,
    relation_of2: ( $i * $i * $i ) > $o ).

tff(decl_50,type,
    boole_lattice: $i > $i ).

tff(decl_51,type,
    empty: $i > $o ).

tff(decl_52,type,
    one_sorted_str: $i > $o ).

tff(decl_53,type,
    relation_of2_as_subset: ( $i * $i * $i ) > $o ).

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

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

tff(decl_56,type,
    esk1_0: $i ).

tff(decl_57,type,
    esk2_0: $i ).

tff(decl_58,type,
    esk3_0: $i ).

tff(decl_59,type,
    esk4_0: $i ).

tff(decl_60,type,
    esk5_2: ( $i * $i ) > $i ).

tff(decl_61,type,
    esk6_1: $i > $i ).

tff(decl_62,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_63,type,
    esk8_1: $i > $i ).

tff(decl_64,type,
    esk9_0: $i ).

tff(decl_65,type,
    esk10_1: $i > $i ).

tff(decl_66,type,
    esk11_0: $i ).

tff(decl_67,type,
    esk12_0: $i ).

tff(decl_68,type,
    esk13_0: $i ).

tff(decl_69,type,
    esk14_1: $i > $i ).

tff(decl_70,type,
    esk15_0: $i ).

tff(decl_71,type,
    esk16_0: $i ).

tff(decl_72,type,
    esk17_0: $i ).

tff(decl_73,type,
    esk18_0: $i ).

fof(t2_lattice3,conjecture,
    ! [X1,X2] :
      ( element(X2,the_carrier(boole_lattice(X1)))
     => ! [X3] :
          ( element(X3,the_carrier(boole_lattice(X1)))
         => ( below(boole_lattice(X1),X2,X3)
          <=> subset(X2,X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_lattice3) ).

fof(d3_lattices,axiom,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & join_semilatt_str(X1) )
     => ! [X2] :
          ( element(X2,the_carrier(X1))
         => ! [X3] :
              ( element(X3,the_carrier(X1))
             => ( below(X1,X2,X3)
              <=> join(X1,X2,X3) = X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattices) ).

fof(fc1_lattice3,axiom,
    ! [X1] :
      ( ~ empty_carrier(boole_lattice(X1))
      & strict_latt_str(boole_lattice(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_lattice3) ).

fof(dt_l3_lattices,axiom,
    ! [X1] :
      ( latt_str(X1)
     => ( meet_semilatt_str(X1)
        & join_semilatt_str(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).

fof(dt_k1_lattice3,axiom,
    ! [X1] :
      ( strict_latt_str(boole_lattice(X1))
      & latt_str(boole_lattice(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattice3) ).

fof(t1_lattice3,axiom,
    ! [X1,X2] :
      ( element(X2,the_carrier(boole_lattice(X1)))
     => ! [X3] :
          ( element(X3,the_carrier(boole_lattice(X1)))
         => ( join(boole_lattice(X1),X2,X3) = set_union2(X2,X3)
            & meet(boole_lattice(X1),X2,X3) = set_intersection2(X2,X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_lattice3) ).

fof(t12_xboole_1,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
     => set_union2(X1,X2) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).

fof(t7_xboole_1,axiom,
    ! [X1,X2] : subset(X1,set_union2(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).

fof(c_0_8,negated_conjecture,
    ~ ! [X1,X2] :
        ( element(X2,the_carrier(boole_lattice(X1)))
       => ! [X3] :
            ( element(X3,the_carrier(boole_lattice(X1)))
           => ( below(boole_lattice(X1),X2,X3)
            <=> subset(X2,X3) ) ) ),
    inference(assume_negation,[status(cth)],[t2_lattice3]) ).

fof(c_0_9,plain,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & join_semilatt_str(X1) )
     => ! [X2] :
          ( element(X2,the_carrier(X1))
         => ! [X3] :
              ( element(X3,the_carrier(X1))
             => ( below(X1,X2,X3)
              <=> join(X1,X2,X3) = X3 ) ) ) ),
    inference(fof_simplification,[status(thm)],[d3_lattices]) ).

fof(c_0_10,plain,
    ! [X1] :
      ( ~ empty_carrier(boole_lattice(X1))
      & strict_latt_str(boole_lattice(X1)) ),
    inference(fof_simplification,[status(thm)],[fc1_lattice3]) ).

fof(c_0_11,plain,
    ! [X51] :
      ( ( meet_semilatt_str(X51)
        | ~ latt_str(X51) )
      & ( join_semilatt_str(X51)
        | ~ latt_str(X51) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).

fof(c_0_12,plain,
    ! [X36] :
      ( strict_latt_str(boole_lattice(X36))
      & latt_str(boole_lattice(X36)) ),
    inference(variable_rename,[status(thm)],[dt_k1_lattice3]) ).

fof(c_0_13,plain,
    ! [X116,X117,X118] :
      ( ( join(boole_lattice(X116),X117,X118) = set_union2(X117,X118)
        | ~ element(X118,the_carrier(boole_lattice(X116)))
        | ~ element(X117,the_carrier(boole_lattice(X116))) )
      & ( meet(boole_lattice(X116),X117,X118) = set_intersection2(X117,X118)
        | ~ element(X118,the_carrier(boole_lattice(X116)))
        | ~ element(X117,the_carrier(boole_lattice(X116))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_lattice3])])])]) ).

fof(c_0_14,negated_conjecture,
    ( element(esk17_0,the_carrier(boole_lattice(esk16_0)))
    & element(esk18_0,the_carrier(boole_lattice(esk16_0)))
    & ( ~ below(boole_lattice(esk16_0),esk17_0,esk18_0)
      | ~ subset(esk17_0,esk18_0) )
    & ( below(boole_lattice(esk16_0),esk17_0,esk18_0)
      | subset(esk17_0,esk18_0) ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).

fof(c_0_15,plain,
    ! [X28,X29,X30] :
      ( ( ~ below(X28,X29,X30)
        | join(X28,X29,X30) = X30
        | ~ element(X30,the_carrier(X28))
        | ~ element(X29,the_carrier(X28))
        | empty_carrier(X28)
        | ~ join_semilatt_str(X28) )
      & ( join(X28,X29,X30) != X30
        | below(X28,X29,X30)
        | ~ element(X30,the_carrier(X28))
        | ~ element(X29,the_carrier(X28))
        | empty_carrier(X28)
        | ~ join_semilatt_str(X28) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).

fof(c_0_16,plain,
    ! [X69] :
      ( ~ empty_carrier(boole_lattice(X69))
      & strict_latt_str(boole_lattice(X69)) ),
    inference(variable_rename,[status(thm)],[c_0_10]) ).

cnf(c_0_17,plain,
    ( join_semilatt_str(X1)
    | ~ latt_str(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_18,plain,
    latt_str(boole_lattice(X1)),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_19,plain,
    ( join(boole_lattice(X1),X2,X3) = set_union2(X2,X3)
    | ~ element(X3,the_carrier(boole_lattice(X1)))
    | ~ element(X2,the_carrier(boole_lattice(X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_20,negated_conjecture,
    element(esk18_0,the_carrier(boole_lattice(esk16_0))),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_21,plain,
    ( join(X1,X2,X3) = X3
    | empty_carrier(X1)
    | ~ below(X1,X2,X3)
    | ~ element(X3,the_carrier(X1))
    | ~ element(X2,the_carrier(X1))
    | ~ join_semilatt_str(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_22,plain,
    ~ empty_carrier(boole_lattice(X1)),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_23,plain,
    join_semilatt_str(boole_lattice(X1)),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_24,negated_conjecture,
    ( join(boole_lattice(esk16_0),X1,esk18_0) = set_union2(X1,esk18_0)
    | ~ element(X1,the_carrier(boole_lattice(esk16_0))) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_25,negated_conjecture,
    element(esk17_0,the_carrier(boole_lattice(esk16_0))),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_26,plain,
    ! [X113,X114] :
      ( ~ subset(X113,X114)
      | set_union2(X113,X114) = X114 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).

fof(c_0_27,plain,
    ! [X138,X139] : subset(X138,set_union2(X138,X139)),
    inference(variable_rename,[status(thm)],[t7_xboole_1]) ).

cnf(c_0_28,negated_conjecture,
    ( join(boole_lattice(esk16_0),X1,esk18_0) = esk18_0
    | ~ below(boole_lattice(esk16_0),X1,esk18_0)
    | ~ element(X1,the_carrier(boole_lattice(esk16_0))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_20]),c_0_22]),c_0_23])]) ).

cnf(c_0_29,negated_conjecture,
    ( below(boole_lattice(esk16_0),esk17_0,esk18_0)
    | subset(esk17_0,esk18_0) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_30,negated_conjecture,
    join(boole_lattice(esk16_0),esk17_0,esk18_0) = set_union2(esk17_0,esk18_0),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_31,plain,
    ( set_union2(X1,X2) = X2
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_32,plain,
    ( below(X1,X2,X3)
    | empty_carrier(X1)
    | join(X1,X2,X3) != X3
    | ~ element(X3,the_carrier(X1))
    | ~ element(X2,the_carrier(X1))
    | ~ join_semilatt_str(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_33,plain,
    subset(X1,set_union2(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_34,negated_conjecture,
    set_union2(esk17_0,esk18_0) = esk18_0,
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_25])]),c_0_31]) ).

cnf(c_0_35,negated_conjecture,
    ( below(boole_lattice(esk16_0),esk17_0,esk18_0)
    | set_union2(esk17_0,esk18_0) != esk18_0 ),
    inference(sr,[status(thm)],[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_30]),c_0_23]),c_0_20]),c_0_25])]),c_0_22]) ).

cnf(c_0_36,negated_conjecture,
    ( ~ below(boole_lattice(esk16_0),esk17_0,esk18_0)
    | ~ subset(esk17_0,esk18_0) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_37,negated_conjecture,
    subset(esk17_0,esk18_0),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_38,negated_conjecture,
    below(boole_lattice(esk16_0),esk17_0,esk18_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_34])]) ).

cnf(c_0_39,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]),c_0_38])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SEU344+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n031.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Thu Aug 24 01:11:50 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 0.20/0.66  % Version  : CSE_E---1.5
% 0.20/0.66  % Problem  : theBenchmark.p
% 0.20/0.66  % Proof found
% 0.20/0.66  % SZS status Theorem for theBenchmark.p
% 0.20/0.66  % SZS output start Proof
% See solution above
% 0.20/0.67  % Total time : 0.071000 s
% 0.20/0.67  % SZS output end Proof
% 0.20/0.67  % Total time : 0.073000 s
%------------------------------------------------------------------------------