TSTP Solution File: NUM383+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM383+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n032.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 10:37:09 EDT 2023

% Result   : Theorem 0.11s 0.48s
% Output   : CNFRefutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   30
% Syntax   : Number of formulae    :   53 (   5 unt;  24 typ;   0 def)
%            Number of atoms       :   66 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   72 (  35   ~;  25   |;   7   &)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (  11   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   9 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;  13 con; 0-1 aty)
%            Number of variables   :   51 (   3 sgn;  30   !;   0   ?;   0   :)

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

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

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

tff(decl_25,type,
    relation: $i > $o ).

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

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

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

tff(decl_29,type,
    relation_empty_yielding: $i > $o ).

tff(decl_30,type,
    relation_non_empty: $i > $o ).

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

tff(decl_32,type,
    powerset: $i > $i ).

tff(decl_33,type,
    esk1_1: $i > $i ).

tff(decl_34,type,
    esk2_0: $i ).

tff(decl_35,type,
    esk3_0: $i ).

tff(decl_36,type,
    esk4_0: $i ).

tff(decl_37,type,
    esk5_0: $i ).

tff(decl_38,type,
    esk6_0: $i ).

tff(decl_39,type,
    esk7_0: $i ).

tff(decl_40,type,
    esk8_0: $i ).

tff(decl_41,type,
    esk9_0: $i ).

tff(decl_42,type,
    esk10_0: $i ).

tff(decl_43,type,
    esk11_0: $i ).

tff(decl_44,type,
    esk12_0: $i ).

tff(decl_45,type,
    esk13_0: $i ).

fof(t5_subset,axiom,
    ! [X1,X2,X3] :
      ~ ( in(X1,X2)
        & element(X2,powerset(X3))
        & empty(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).

fof(t3_subset,axiom,
    ! [X1,X2] :
      ( element(X1,powerset(X2))
    <=> subset(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).

fof(t7_ordinal1,conjecture,
    ! [X1,X2] :
      ~ ( in(X1,X2)
        & subset(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ordinal1) ).

fof(t4_subset,axiom,
    ! [X1,X2,X3] :
      ( ( in(X1,X2)
        & element(X2,powerset(X3)) )
     => element(X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).

fof(t2_subset,axiom,
    ! [X1,X2] :
      ( element(X1,X2)
     => ( empty(X2)
        | in(X1,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).

fof(antisymmetry_r2_hidden,axiom,
    ! [X1,X2] :
      ( in(X1,X2)
     => ~ in(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

fof(c_0_6,plain,
    ! [X31,X32,X33] :
      ( ~ in(X31,X32)
      | ~ element(X32,powerset(X33))
      | ~ empty(X33) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).

fof(c_0_7,plain,
    ! [X26,X27] :
      ( ( ~ element(X26,powerset(X27))
        | subset(X26,X27) )
      & ( ~ subset(X26,X27)
        | element(X26,powerset(X27)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).

fof(c_0_8,negated_conjecture,
    ~ ! [X1,X2] :
        ~ ( in(X1,X2)
          & subset(X2,X1) ),
    inference(assume_negation,[status(cth)],[t7_ordinal1]) ).

fof(c_0_9,plain,
    ! [X28,X29,X30] :
      ( ~ in(X28,X29)
      | ~ element(X29,powerset(X30))
      | element(X28,X30) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).

cnf(c_0_10,plain,
    ( ~ in(X1,X2)
    | ~ element(X2,powerset(X3))
    | ~ empty(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,plain,
    ( element(X1,powerset(X2))
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_12,negated_conjecture,
    ( in(esk12_0,esk13_0)
    & subset(esk13_0,esk12_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).

cnf(c_0_13,plain,
    ( element(X1,X3)
    | ~ in(X1,X2)
    | ~ element(X2,powerset(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,plain,
    ( ~ subset(X1,X2)
    | ~ empty(X2)
    | ~ in(X3,X1) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_15,negated_conjecture,
    subset(esk13_0,esk12_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_16,plain,
    ! [X24,X25] :
      ( ~ element(X24,X25)
      | empty(X25)
      | in(X24,X25) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).

cnf(c_0_17,plain,
    ( element(X1,X2)
    | ~ subset(X3,X2)
    | ~ in(X1,X3) ),
    inference(spm,[status(thm)],[c_0_13,c_0_11]) ).

cnf(c_0_18,negated_conjecture,
    ( ~ empty(esk12_0)
    | ~ in(X1,esk13_0) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_19,negated_conjecture,
    in(esk12_0,esk13_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_20,plain,
    ! [X1,X2] :
      ( in(X1,X2)
     => ~ in(X2,X1) ),
    inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).

cnf(c_0_21,plain,
    ( empty(X2)
    | in(X1,X2)
    | ~ element(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_22,negated_conjecture,
    ( element(X1,esk12_0)
    | ~ in(X1,esk13_0) ),
    inference(spm,[status(thm)],[c_0_17,c_0_15]) ).

cnf(c_0_23,negated_conjecture,
    ~ empty(esk12_0),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

fof(c_0_24,plain,
    ! [X4,X5] :
      ( ~ in(X4,X5)
      | ~ in(X5,X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])]) ).

cnf(c_0_25,negated_conjecture,
    ( in(X1,esk12_0)
    | ~ in(X1,esk13_0) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).

cnf(c_0_26,plain,
    ( ~ in(X1,X2)
    | ~ in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_27,negated_conjecture,
    in(esk12_0,esk12_0),
    inference(spm,[status(thm)],[c_0_25,c_0_19]) ).

cnf(c_0_28,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_27])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem    : NUM383+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.08  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.07/0.27  % Computer : n032.cluster.edu
% 0.07/0.27  % Model    : x86_64 x86_64
% 0.07/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27  % Memory   : 8042.1875MB
% 0.07/0.27  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27  % CPULimit   : 300
% 0.07/0.27  % WCLimit    : 300
% 0.07/0.27  % DateTime   : Fri Aug 25 14:18:27 EDT 2023
% 0.07/0.27  % CPUTime  : 
% 0.11/0.46  start to proof: theBenchmark
% 0.11/0.48  % Version  : CSE_E---1.5
% 0.11/0.48  % Problem  : theBenchmark.p
% 0.11/0.48  % Proof found
% 0.11/0.48  % SZS status Theorem for theBenchmark.p
% 0.11/0.48  % SZS output start Proof
% See solution above
% 0.11/0.48  % Total time : 0.009000 s
% 0.11/0.48  % SZS output end Proof
% 0.11/0.48  % Total time : 0.012000 s
%------------------------------------------------------------------------------