%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU264+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 : n001.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 16:23:56 EDT 2023

% Result   : Theorem 0.21s 0.60s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   41 (   9 unt;  16 typ;   0 def)
%            Number of atoms       :   54 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   48 (  19   ~;  16   |;   5   &)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   21 (  12   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   4 con; 0-2 aty)
%            Number of variables   :   48 (   4 sgn;  31   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    cartesian_product2: ( $i * $i ) > $i ).

tff(decl_23,type,
    powerset: $i > $i ).

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

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

tff(decl_26,type,
    relation_of2_as_subset: ( $i * $i * $i ) > $o ).

tff(decl_27,type,
    relation_of2: ( $i * $i * $i ) > $o ).

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

tff(decl_29,type,
    relation_dom: $i > $i ).

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

tff(decl_31,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_32,type,
    esk2_1: $i > $i ).

tff(decl_33,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_34,type,
    esk4_0: $i ).

tff(decl_35,type,
    esk5_0: $i ).

tff(decl_36,type,
    esk6_0: $i ).

tff(decl_37,type,
    esk7_0: $i ).

fof(t16_relset_1,conjecture,
    ! [X1,X2,X3,X4] :
      ( relation_of2_as_subset(X4,X3,X1)
     => ( subset(X1,X2)
       => relation_of2_as_subset(X4,X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_1) ).

fof(t1_xboole_1,axiom,
    ! [X1,X2,X3] :
      ( ( subset(X1,X2)
        & subset(X2,X3) )
     => subset(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).

fof(t12_relset_1,axiom,
    ! [X1,X2,X3] :
      ( relation_of2_as_subset(X3,X1,X2)
     => ( subset(relation_dom(X3),X1)
        & subset(relation_rng(X3),X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_1) ).

fof(reflexivity_r1_tarski,axiom,
    ! [X1,X2] : subset(X1,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

fof(t14_relset_1,axiom,
    ! [X1,X2,X3,X4] :
      ( relation_of2_as_subset(X4,X3,X1)
     => ( subset(relation_rng(X4),X2)
       => relation_of2_as_subset(X4,X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relset_1) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( relation_of2_as_subset(X4,X3,X1)
       => ( subset(X1,X2)
         => relation_of2_as_subset(X4,X3,X2) ) ),
    inference(assume_negation,[status(cth)],[t16_relset_1]) ).

fof(c_0_6,plain,
    ! [X34,X35,X36] :
      ( ~ subset(X34,X35)
      | ~ subset(X35,X36)
      | subset(X34,X36) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).

fof(c_0_7,negated_conjecture,
    ( relation_of2_as_subset(esk7_0,esk6_0,esk4_0)
    & subset(esk4_0,esk5_0)
    & ~ relation_of2_as_subset(esk7_0,esk6_0,esk5_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

cnf(c_0_8,plain,
    ( subset(X1,X3)
    | ~ subset(X1,X2)
    | ~ subset(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_9,negated_conjecture,
    subset(esk4_0,esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_10,plain,
    ! [X23,X24,X25] :
      ( ( subset(relation_dom(X25),X23)
        | ~ relation_of2_as_subset(X25,X23,X24) )
      & ( subset(relation_rng(X25),X24)
        | ~ relation_of2_as_subset(X25,X23,X24) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_relset_1])])]) ).

cnf(c_0_11,negated_conjecture,
    ( subset(X1,esk5_0)
    | ~ subset(X1,esk4_0) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_12,plain,
    ( subset(relation_rng(X1),X2)
    | ~ relation_of2_as_subset(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_13,negated_conjecture,
    relation_of2_as_subset(esk7_0,esk6_0,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_14,negated_conjecture,
    ( subset(X1,esk5_0)
    | ~ subset(X2,esk4_0)
    | ~ subset(X1,X2) ),
    inference(spm,[status(thm)],[c_0_8,c_0_11]) ).

cnf(c_0_15,negated_conjecture,
    subset(relation_rng(esk7_0),esk4_0),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

fof(c_0_16,plain,
    ! [X22] : subset(X22,X22),
    inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).

fof(c_0_17,plain,
    ! [X26,X27,X28,X29] :
      ( ~ relation_of2_as_subset(X29,X28,X26)
      | ~ subset(relation_rng(X29),X27)
      | relation_of2_as_subset(X29,X28,X27) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t14_relset_1])]) ).

cnf(c_0_18,negated_conjecture,
    ( subset(X1,esk5_0)
    | ~ subset(X1,relation_rng(esk7_0)) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_19,plain,
    subset(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_20,plain,
    ( relation_of2_as_subset(X1,X2,X4)
    | ~ relation_of2_as_subset(X1,X2,X3)
    | ~ subset(relation_rng(X1),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_21,negated_conjecture,
    subset(relation_rng(esk7_0),esk5_0),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_22,negated_conjecture,
    ( relation_of2_as_subset(esk7_0,X1,esk5_0)
    | ~ relation_of2_as_subset(esk7_0,X1,X2) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_23,negated_conjecture,
    ~ relation_of2_as_subset(esk7_0,esk6_0,esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_24,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_13]),c_0_23]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU264+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n001.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Wed Aug 23 18:10:40 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.58  start to proof: theBenchmark
% 0.21/0.60  % Version  : CSE_E---1.5
% 0.21/0.60  % Problem  : theBenchmark.p
% 0.21/0.60  % Proof found
% 0.21/0.60  % SZS status Theorem for theBenchmark.p
% 0.21/0.60  % SZS output start Proof
% See solution above
% 0.21/0.60  % Total time : 0.008000 s
% 0.21/0.60  % SZS output end Proof
% 0.21/0.60  % Total time : 0.011000 s
%------------------------------------------------------------------------------