TSTP Solution File: SEU019+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU019+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/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 16:22:09 EDT 2023

% Result   : Theorem 0.19s 0.59s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   31
% Syntax   : Number of formulae    :   57 (  11 unt;  26 typ;   0 def)
%            Number of atoms       :  111 (  31 equ)
%            Maximal formula atoms :   23 (   3 avg)
%            Number of connectives :  130 (  50   ~;  60   |;  14   &)
%                                         (   2 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   23 (  18   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;   8 con; 0-2 aty)
%            Number of variables   :   40 (   3 sgn;  18   !;   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,
    relation_dom: $i > $i ).

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

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

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

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

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

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

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

tff(decl_35,type,
    esk1_1: $i > $i ).

tff(decl_36,type,
    esk2_1: $i > $i ).

tff(decl_37,type,
    esk3_1: $i > $i ).

tff(decl_38,type,
    esk4_0: $i ).

tff(decl_39,type,
    esk5_0: $i ).

tff(decl_40,type,
    esk6_1: $i > $i ).

tff(decl_41,type,
    esk7_0: $i ).

tff(decl_42,type,
    esk8_0: $i ).

tff(decl_43,type,
    esk9_1: $i > $i ).

tff(decl_44,type,
    esk10_0: $i ).

tff(decl_45,type,
    esk11_0: $i ).

tff(decl_46,type,
    esk12_2: ( $i * $i ) > $i ).

tff(decl_47,type,
    esk13_0: $i ).

fof(t34_funct_1,axiom,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => ( X2 = identity_relation(X1)
      <=> ( relation_dom(X2) = X1
          & ! [X3] :
              ( in(X3,X1)
             => apply(X2,X3) = X3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).

fof(dt_k6_relat_1,axiom,
    ! [X1] : relation(identity_relation(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).

fof(fc2_funct_1,axiom,
    ! [X1] :
      ( relation(identity_relation(X1))
      & function(identity_relation(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).

fof(d8_funct_1,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ( one_to_one(X1)
      <=> ! [X2,X3] :
            ( ( in(X2,relation_dom(X1))
              & in(X3,relation_dom(X1))
              & apply(X1,X2) = apply(X1,X3) )
           => X2 = X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).

fof(t52_funct_1,conjecture,
    ! [X1] : one_to_one(identity_relation(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_funct_1) ).

fof(c_0_5,plain,
    ! [X35,X36,X37] :
      ( ( relation_dom(X36) = X35
        | X36 != identity_relation(X35)
        | ~ relation(X36)
        | ~ function(X36) )
      & ( ~ in(X37,X35)
        | apply(X36,X37) = X37
        | X36 != identity_relation(X35)
        | ~ relation(X36)
        | ~ function(X36) )
      & ( in(esk12_2(X35,X36),X35)
        | relation_dom(X36) != X35
        | X36 = identity_relation(X35)
        | ~ relation(X36)
        | ~ function(X36) )
      & ( apply(X36,esk12_2(X35,X36)) != esk12_2(X35,X36)
        | relation_dom(X36) != X35
        | X36 = identity_relation(X35)
        | ~ relation(X36)
        | ~ function(X36) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t34_funct_1])])])])]) ).

fof(c_0_6,plain,
    ! [X13] : relation(identity_relation(X13)),
    inference(variable_rename,[status(thm)],[dt_k6_relat_1]) ).

fof(c_0_7,plain,
    ! [X17] :
      ( relation(identity_relation(X17))
      & function(identity_relation(X17)) ),
    inference(variable_rename,[status(thm)],[fc2_funct_1]) ).

fof(c_0_8,plain,
    ! [X8,X9,X10] :
      ( ( ~ one_to_one(X8)
        | ~ in(X9,relation_dom(X8))
        | ~ in(X10,relation_dom(X8))
        | apply(X8,X9) != apply(X8,X10)
        | X9 = X10
        | ~ relation(X8)
        | ~ function(X8) )
      & ( in(esk1_1(X8),relation_dom(X8))
        | one_to_one(X8)
        | ~ relation(X8)
        | ~ function(X8) )
      & ( in(esk2_1(X8),relation_dom(X8))
        | one_to_one(X8)
        | ~ relation(X8)
        | ~ function(X8) )
      & ( apply(X8,esk1_1(X8)) = apply(X8,esk2_1(X8))
        | one_to_one(X8)
        | ~ relation(X8)
        | ~ function(X8) )
      & ( esk1_1(X8) != esk2_1(X8)
        | one_to_one(X8)
        | ~ relation(X8)
        | ~ function(X8) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_funct_1])])])])]) ).

cnf(c_0_9,plain,
    ( relation_dom(X1) = X2
    | X1 != identity_relation(X2)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_10,plain,
    relation(identity_relation(X1)),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,plain,
    function(identity_relation(X1)),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,plain,
    ( apply(X3,X1) = X1
    | ~ in(X1,X2)
    | X3 != identity_relation(X2)
    | ~ relation(X3)
    | ~ function(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_13,plain,
    ( in(esk2_1(X1),relation_dom(X1))
    | one_to_one(X1)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,plain,
    relation_dom(identity_relation(X1)) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_9]),c_0_10]),c_0_11])]) ).

cnf(c_0_15,plain,
    ( in(esk1_1(X1),relation_dom(X1))
    | one_to_one(X1)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_16,plain,
    ( apply(X1,esk1_1(X1)) = apply(X1,esk2_1(X1))
    | one_to_one(X1)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_17,plain,
    ( apply(identity_relation(X1),X2) = X2
    | ~ in(X2,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_12]),c_0_10]),c_0_11])]) ).

cnf(c_0_18,plain,
    ( one_to_one(identity_relation(X1))
    | in(esk2_1(identity_relation(X1)),X1) ),
    inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_10]),c_0_11])]),c_0_14]) ).

fof(c_0_19,negated_conjecture,
    ~ ! [X1] : one_to_one(identity_relation(X1)),
    inference(assume_negation,[status(cth)],[t52_funct_1]) ).

cnf(c_0_20,plain,
    ( one_to_one(identity_relation(X1))
    | in(esk1_1(identity_relation(X1)),X1) ),
    inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_10]),c_0_11])]),c_0_14]) ).

cnf(c_0_21,plain,
    ( apply(identity_relation(X1),esk2_1(identity_relation(X1))) = apply(identity_relation(X1),esk1_1(identity_relation(X1)))
    | one_to_one(identity_relation(X1)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_10]),c_0_11])]) ).

cnf(c_0_22,plain,
    ( apply(identity_relation(X1),esk2_1(identity_relation(X1))) = esk2_1(identity_relation(X1))
    | one_to_one(identity_relation(X1)) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_23,plain,
    ( one_to_one(X1)
    | esk1_1(X1) != esk2_1(X1)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_24,negated_conjecture,
    ~ one_to_one(identity_relation(esk13_0)),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).

cnf(c_0_25,plain,
    ( apply(identity_relation(X1),esk1_1(identity_relation(X1))) = esk1_1(identity_relation(X1))
    | one_to_one(identity_relation(X1)) ),
    inference(spm,[status(thm)],[c_0_17,c_0_20]) ).

cnf(c_0_26,plain,
    ( apply(identity_relation(X1),esk1_1(identity_relation(X1))) = esk2_1(identity_relation(X1))
    | one_to_one(identity_relation(X1)) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_27,plain,
    ( one_to_one(identity_relation(X1))
    | esk2_1(identity_relation(X1)) != esk1_1(identity_relation(X1)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_10]),c_0_11])]) ).

cnf(c_0_28,negated_conjecture,
    ~ one_to_one(identity_relation(esk13_0)),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_29,plain,
    one_to_one(identity_relation(X1)),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).

cnf(c_0_30,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : SEU019+1 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n031.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   : Wed Aug 23 17:23:35 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.19/0.59  % Version  : CSE_E---1.5
% 0.19/0.59  % Problem  : theBenchmark.p
% 0.19/0.59  % Proof found
% 0.19/0.59  % SZS status Theorem for theBenchmark.p
% 0.19/0.59  % SZS output start Proof
% See solution above
% 0.19/0.60  % Total time : 0.012000 s
% 0.19/0.60  % SZS output end Proof
% 0.19/0.60  % Total time : 0.015000 s
%------------------------------------------------------------------------------