TSTP Solution File: SEU125+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU125+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 : n010.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 16:22:34 EDT 2023

% Result   : Theorem 0.21s 0.63s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   48 (  13 unt;  12 typ;   0 def)
%            Number of atoms       :   94 (  16 equ)
%            Maximal formula atoms :   20 (   2 avg)
%            Number of connectives :   89 (  31   ~;  41   |;  11   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (   6   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-3 aty)
%            Number of variables   :   73 (   4 sgn;  32   !;   0   ?;   0   :)

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

tff(decl_23,type,
    set_union2: ( $i * $i ) > $i ).

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

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

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

tff(decl_27,type,
    esk1_3: ( $i * $i * $i ) > $i ).

tff(decl_28,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_29,type,
    esk3_0: $i ).

tff(decl_30,type,
    esk4_0: $i ).

tff(decl_31,type,
    esk5_0: $i ).

tff(decl_32,type,
    esk6_0: $i ).

tff(decl_33,type,
    esk7_0: $i ).

fof(t8_xboole_1,conjecture,
    ! [X1,X2,X3] :
      ( ( subset(X1,X2)
        & subset(X3,X2) )
     => subset(set_union2(X1,X3),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).

fof(d2_xboole_0,axiom,
    ! [X1,X2,X3] :
      ( X3 = set_union2(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            | in(X4,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).

fof(d3_tarski,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( in(X3,X1)
         => in(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(t1_boole,axiom,
    ! [X1] : set_union2(X1,empty_set) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).

fof(commutativity_k2_xboole_0,axiom,
    ! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( subset(X1,X2)
          & subset(X3,X2) )
       => subset(set_union2(X1,X3),X2) ),
    inference(assume_negation,[status(cth)],[t8_xboole_1]) ).

fof(c_0_6,plain,
    ! [X9,X10,X11,X12,X13,X14,X15,X16] :
      ( ( ~ in(X12,X11)
        | in(X12,X9)
        | in(X12,X10)
        | X11 != set_union2(X9,X10) )
      & ( ~ in(X13,X9)
        | in(X13,X11)
        | X11 != set_union2(X9,X10) )
      & ( ~ in(X13,X10)
        | in(X13,X11)
        | X11 != set_union2(X9,X10) )
      & ( ~ in(esk1_3(X14,X15,X16),X14)
        | ~ in(esk1_3(X14,X15,X16),X16)
        | X16 = set_union2(X14,X15) )
      & ( ~ in(esk1_3(X14,X15,X16),X15)
        | ~ in(esk1_3(X14,X15,X16),X16)
        | X16 = set_union2(X14,X15) )
      & ( in(esk1_3(X14,X15,X16),X16)
        | in(esk1_3(X14,X15,X16),X14)
        | in(esk1_3(X14,X15,X16),X15)
        | X16 = set_union2(X14,X15) ) ),
    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)],[d2_xboole_0])])])])])]) ).

fof(c_0_7,plain,
    ! [X18,X19,X20,X21,X22] :
      ( ( ~ subset(X18,X19)
        | ~ in(X20,X18)
        | in(X20,X19) )
      & ( in(esk2_2(X21,X22),X21)
        | subset(X21,X22) )
      & ( ~ in(esk2_2(X21,X22),X22)
        | subset(X21,X22) ) ),
    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)],[d3_tarski])])])])])]) ).

fof(c_0_8,negated_conjecture,
    ( subset(esk5_0,esk6_0)
    & subset(esk7_0,esk6_0)
    & ~ subset(set_union2(esk5_0,esk7_0),esk6_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

cnf(c_0_9,plain,
    ( in(X1,X3)
    | ~ in(X1,X2)
    | X3 != set_union2(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,plain,
    ( in(X3,X2)
    | ~ subset(X1,X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,negated_conjecture,
    subset(esk7_0,esk6_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12,plain,
    ( subset(X1,X2)
    | ~ in(esk2_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_13,plain,
    ( in(X1,set_union2(X2,X3))
    | ~ in(X1,X3) ),
    inference(er,[status(thm)],[c_0_9]) ).

cnf(c_0_14,negated_conjecture,
    ( in(X1,esk6_0)
    | ~ in(X1,esk7_0) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_15,plain,
    ( in(esk2_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_16,plain,
    ( subset(X1,set_union2(X2,X3))
    | ~ in(esk2_2(X1,set_union2(X2,X3)),X3) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_17,negated_conjecture,
    ( subset(esk7_0,X1)
    | in(esk2_2(esk7_0,X1),esk6_0) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_18,negated_conjecture,
    subset(esk7_0,set_union2(X1,esk6_0)),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

fof(c_0_19,plain,
    ! [X32] : set_union2(X32,empty_set) = X32,
    inference(variable_rename,[status(thm)],[t1_boole]) ).

fof(c_0_20,plain,
    ! [X7,X8] : set_union2(X7,X8) = set_union2(X8,X7),
    inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).

cnf(c_0_21,negated_conjecture,
    ( in(X1,set_union2(X2,esk6_0))
    | ~ in(X1,esk7_0) ),
    inference(spm,[status(thm)],[c_0_10,c_0_18]) ).

cnf(c_0_22,plain,
    set_union2(X1,empty_set) = X1,
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_23,plain,
    set_union2(X1,X2) = set_union2(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_24,plain,
    ( in(X1,X3)
    | in(X1,X4)
    | ~ in(X1,X2)
    | X2 != set_union2(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_25,negated_conjecture,
    ( subset(X1,set_union2(X2,esk6_0))
    | ~ in(esk2_2(X1,set_union2(X2,esk6_0)),esk7_0) ),
    inference(spm,[status(thm)],[c_0_12,c_0_21]) ).

cnf(c_0_26,plain,
    set_union2(empty_set,X1) = X1,
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_27,plain,
    ( in(X1,X2)
    | in(X1,X3)
    | ~ in(X1,set_union2(X3,X2)) ),
    inference(er,[status(thm)],[c_0_24]) ).

cnf(c_0_28,negated_conjecture,
    subset(esk5_0,esk6_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_29,negated_conjecture,
    ( subset(X1,esk6_0)
    | ~ in(esk2_2(X1,esk6_0),esk7_0) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_30,plain,
    ( subset(set_union2(X1,X2),X3)
    | in(esk2_2(set_union2(X1,X2),X3),X2)
    | in(esk2_2(set_union2(X1,X2),X3),X1) ),
    inference(spm,[status(thm)],[c_0_27,c_0_15]) ).

cnf(c_0_31,negated_conjecture,
    ( in(X1,esk6_0)
    | ~ in(X1,esk5_0) ),
    inference(spm,[status(thm)],[c_0_10,c_0_28]) ).

cnf(c_0_32,negated_conjecture,
    ( subset(set_union2(esk7_0,X1),esk6_0)
    | in(esk2_2(set_union2(esk7_0,X1),esk6_0),X1) ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_33,negated_conjecture,
    ~ subset(set_union2(esk5_0,esk7_0),esk6_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_34,negated_conjecture,
    in(esk2_2(set_union2(esk5_0,esk7_0),esk6_0),esk6_0),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_23]),c_0_23]),c_0_33]) ).

cnf(c_0_35,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_34]),c_0_33]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SEU125+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.35  % Computer : n010.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Wed Aug 23 18:00:36 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.21/0.57  start to proof: theBenchmark
% 0.21/0.63  % Version  : CSE_E---1.5
% 0.21/0.63  % Problem  : theBenchmark.p
% 0.21/0.63  % Proof found
% 0.21/0.63  % SZS status Theorem for theBenchmark.p
% 0.21/0.63  % SZS output start Proof
% See solution above
% 0.21/0.63  % Total time : 0.049000 s
% 0.21/0.63  % SZS output end Proof
% 0.21/0.63  % Total time : 0.051000 s
%------------------------------------------------------------------------------