TSTP Solution File: SWW469+5 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWW469+5 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n008.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 : Fri Sep  1 00:17:52 EDT 2023

% Result   : Theorem 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   40
% Syntax   : Number of formulae    :   48 (   8 unt;  37 typ;   0 def)
%            Number of atoms       :   16 (   8 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   14 (   9   ~;   3   |;   1   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   67 (  28   >;  39   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   34 (  34 usr;   9 con; 0-7 aty)
%            Number of variables   :   10 (   1 sgn;   7   !;   2   ?;   0   :)

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

tff(decl_23,type,
    bool: $i ).

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

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

tff(decl_26,type,
    ti: ( $i * $i ) > $i ).

tff(decl_27,type,
    induct_equal: $i > $i ).

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

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

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

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

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

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

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

tff(decl_35,type,
    hoare_509422987triple: $i > $i ).

tff(decl_36,type,
    hoare_244953527triple: $i > $i ).

tff(decl_37,type,
    hoare_2037801986triple: $i > $i ).

tff(decl_38,type,
    hoare_1883395792gleton: $i ).

tff(decl_39,type,
    hoare_1580379338ep_set: $i > $i ).

tff(decl_40,type,
    collect: $i > $i ).

tff(decl_41,type,
    type_definition: ( $i * $i ) > $i ).

tff(decl_42,type,
    fequal: $i > $i ).

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

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

tff(decl_45,type,
    member: $i > $i ).

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

tff(decl_47,type,
    esk1_0: $i ).

tff(decl_48,type,
    esk2_0: $i ).

tff(decl_49,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_50,type,
    esk4_2: ( $i * $i ) > $i ).

tff(decl_51,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_52,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_53,type,
    esk7_6: ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_54,type,
    esk8_6: ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_55,type,
    esk9_7: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_56,type,
    esk10_7: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_57,type,
    esk11_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_58,type,
    esk12_0: $i ).

fof(conj_1,conjecture,
    ! [X6] :
      ~ ! [X5] : ti(state,X5) = ti(state,X6),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

fof(fact_0_state__not__singleton__def,axiom,
    ( hBOOL(hoare_1883395792gleton)
  <=> ? [X5,X6] : ti(state,X5) != ti(state,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_state__not__singleton__def) ).

fof(conj_0,hypothesis,
    hBOOL(hoare_1883395792gleton),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X6] :
        ~ ! [X5] : ti(state,X5) = ti(state,X6),
    inference(assume_negation,[status(cth)],[conj_1]) ).

fof(c_0_4,plain,
    ! [X49,X50] :
      ( ( ~ hBOOL(hoare_1883395792gleton)
        | ti(state,esk1_0) != ti(state,esk2_0) )
      & ( ti(state,X49) = ti(state,X50)
        | hBOOL(hoare_1883395792gleton) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_0_state__not__singleton__def])])])]) ).

fof(c_0_5,negated_conjecture,
    ! [X181] : ti(state,X181) = ti(state,esk12_0),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

cnf(c_0_6,plain,
    ( ~ hBOOL(hoare_1883395792gleton)
    | ti(state,esk1_0) != ti(state,esk2_0) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_7,negated_conjecture,
    ti(state,X1) = ti(state,esk12_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,hypothesis,
    hBOOL(hoare_1883395792gleton),
    inference(split_conjunct,[status(thm)],[conj_0]) ).

cnf(c_0_9,plain,
    ~ hBOOL(hoare_1883395792gleton),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7]),c_0_7])]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWW469+5 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n008.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Sun Aug 27 19:07:17 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.59  % Version  : CSE_E---1.5
% 0.20/0.59  % Problem  : theBenchmark.p
% 0.20/0.59  % Proof found
% 0.20/0.59  % SZS status Theorem for theBenchmark.p
% 0.20/0.59  % SZS output start Proof
% See solution above
% 0.20/0.59  % Total time : 0.008000 s
% 0.20/0.59  % SZS output end Proof
% 0.20/0.59  % Total time : 0.014000 s
%------------------------------------------------------------------------------