TSTP Solution File: SEU025+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU025+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 : n004.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 16:22:10 EDT 2023

% Result   : Theorem 2.73s 2.84s
% Output   : CNFRefutation 2.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   32
% Syntax   : Number of formulae    :   58 (  11 unt;  26 typ;   0 def)
%            Number of atoms       :  100 (  28 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  114 (  46   ~;  42   |;  13   &)
%                                         (   0 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   20 (  16   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;  10 con; 0-2 aty)
%            Number of variables   :   29 (   1 sgn;  17   !;   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,
    function_inverse: $i > $i ).

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

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

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

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

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

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

tff(decl_34,type,
    relation_rng: $i > $i ).

tff(decl_35,type,
    subset: ( $i * $i ) > $o ).

tff(decl_36,type,
    esk1_1: $i > $i ).

tff(decl_37,type,
    esk2_0: $i ).

tff(decl_38,type,
    esk3_0: $i ).

tff(decl_39,type,
    esk4_1: $i > $i ).

tff(decl_40,type,
    esk5_0: $i ).

tff(decl_41,type,
    esk6_0: $i ).

tff(decl_42,type,
    esk7_0: $i ).

tff(decl_43,type,
    esk8_1: $i > $i ).

tff(decl_44,type,
    esk9_0: $i ).

tff(decl_45,type,
    esk10_0: $i ).

tff(decl_46,type,
    esk11_0: $i ).

tff(decl_47,type,
    esk12_0: $i ).

fof(t58_funct_1,conjecture,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ( one_to_one(X1)
       => ( relation_dom(relation_composition(X1,function_inverse(X1))) = relation_dom(X1)
          & relation_rng(relation_composition(X1,function_inverse(X1))) = relation_dom(X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_funct_1) ).

fof(t55_funct_1,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ( one_to_one(X1)
       => ( relation_rng(X1) = relation_dom(function_inverse(X1))
          & relation_dom(X1) = relation_rng(function_inverse(X1)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).

fof(t46_relat_1,axiom,
    ! [X1] :
      ( relation(X1)
     => ! [X2] :
          ( relation(X2)
         => ( subset(relation_rng(X1),relation_dom(X2))
           => relation_dom(relation_composition(X1,X2)) = relation_dom(X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_relat_1) ).

fof(dt_k2_funct_1,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ( relation(function_inverse(X1))
        & function(function_inverse(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).

fof(t47_relat_1,axiom,
    ! [X1] :
      ( relation(X1)
     => ! [X2] :
          ( relation(X2)
         => ( subset(relation_dom(X1),relation_rng(X2))
           => relation_rng(relation_composition(X2,X1)) = relation_rng(X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_relat_1) ).

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

fof(c_0_6,negated_conjecture,
    ~ ! [X1] :
        ( ( relation(X1)
          & function(X1) )
       => ( one_to_one(X1)
         => ( relation_dom(relation_composition(X1,function_inverse(X1))) = relation_dom(X1)
            & relation_rng(relation_composition(X1,function_inverse(X1))) = relation_dom(X1) ) ) ),
    inference(assume_negation,[status(cth)],[t58_funct_1]) ).

fof(c_0_7,plain,
    ! [X51] :
      ( ( relation_rng(X51) = relation_dom(function_inverse(X51))
        | ~ one_to_one(X51)
        | ~ relation(X51)
        | ~ function(X51) )
      & ( relation_dom(X51) = relation_rng(function_inverse(X51))
        | ~ one_to_one(X51)
        | ~ relation(X51)
        | ~ function(X51) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t55_funct_1])])]) ).

fof(c_0_8,negated_conjecture,
    ( relation(esk12_0)
    & function(esk12_0)
    & one_to_one(esk12_0)
    & ( relation_dom(relation_composition(esk12_0,function_inverse(esk12_0))) != relation_dom(esk12_0)
      | relation_rng(relation_composition(esk12_0,function_inverse(esk12_0))) != relation_dom(esk12_0) ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).

fof(c_0_9,plain,
    ! [X44,X45] :
      ( ~ relation(X44)
      | ~ relation(X45)
      | ~ subset(relation_rng(X44),relation_dom(X45))
      | relation_dom(relation_composition(X44,X45)) = relation_dom(X44) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t46_relat_1])])]) ).

cnf(c_0_10,plain,
    ( relation_rng(X1) = relation_dom(function_inverse(X1))
    | ~ one_to_one(X1)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,negated_conjecture,
    relation(esk12_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12,negated_conjecture,
    one_to_one(esk12_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,negated_conjecture,
    function(esk12_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,plain,
    ( relation_dom(relation_composition(X1,X2)) = relation_dom(X1)
    | ~ relation(X1)
    | ~ relation(X2)
    | ~ subset(relation_rng(X1),relation_dom(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_15,negated_conjecture,
    relation_dom(function_inverse(esk12_0)) = relation_rng(esk12_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13])]) ).

fof(c_0_16,plain,
    ! [X9] :
      ( ( relation(function_inverse(X9))
        | ~ relation(X9)
        | ~ function(X9) )
      & ( function(function_inverse(X9))
        | ~ relation(X9)
        | ~ function(X9) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_funct_1])])]) ).

fof(c_0_17,plain,
    ! [X46,X47] :
      ( ~ relation(X46)
      | ~ relation(X47)
      | ~ subset(relation_dom(X46),relation_rng(X47))
      | relation_rng(relation_composition(X47,X46)) = relation_rng(X46) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t47_relat_1])])]) ).

cnf(c_0_18,plain,
    ( relation_dom(X1) = relation_rng(function_inverse(X1))
    | ~ one_to_one(X1)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_19,negated_conjecture,
    ( relation_dom(relation_composition(X1,function_inverse(esk12_0))) = relation_dom(X1)
    | ~ subset(relation_rng(X1),relation_rng(esk12_0))
    | ~ relation(function_inverse(esk12_0))
    | ~ relation(X1) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_20,plain,
    ( relation(function_inverse(X1))
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_21,plain,
    ! [X37] : subset(X37,X37),
    inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).

cnf(c_0_22,plain,
    ( relation_rng(relation_composition(X2,X1)) = relation_rng(X1)
    | ~ relation(X1)
    | ~ relation(X2)
    | ~ subset(relation_dom(X1),relation_rng(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_23,negated_conjecture,
    relation_rng(function_inverse(esk12_0)) = relation_dom(esk12_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_11]),c_0_12]),c_0_13])]) ).

cnf(c_0_24,negated_conjecture,
    ( relation_dom(relation_composition(X1,function_inverse(esk12_0))) = relation_dom(X1)
    | ~ subset(relation_rng(X1),relation_rng(esk12_0))
    | ~ relation(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_11]),c_0_13])]) ).

cnf(c_0_25,plain,
    subset(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_26,negated_conjecture,
    ( relation_rng(relation_composition(X1,function_inverse(esk12_0))) = relation_dom(esk12_0)
    | ~ subset(relation_rng(esk12_0),relation_rng(X1))
    | ~ relation(function_inverse(esk12_0))
    | ~ relation(X1) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_15]),c_0_23]) ).

cnf(c_0_27,negated_conjecture,
    ( relation_dom(relation_composition(esk12_0,function_inverse(esk12_0))) != relation_dom(esk12_0)
    | relation_rng(relation_composition(esk12_0,function_inverse(esk12_0))) != relation_dom(esk12_0) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_28,negated_conjecture,
    relation_dom(relation_composition(esk12_0,function_inverse(esk12_0))) = relation_dom(esk12_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_11])]) ).

cnf(c_0_29,negated_conjecture,
    ( relation_rng(relation_composition(X1,function_inverse(esk12_0))) = relation_dom(esk12_0)
    | ~ subset(relation_rng(esk12_0),relation_rng(X1))
    | ~ relation(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_20]),c_0_11]),c_0_13])]) ).

cnf(c_0_30,negated_conjecture,
    relation_rng(relation_composition(esk12_0,function_inverse(esk12_0))) != relation_dom(esk12_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).

cnf(c_0_31,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_25]),c_0_11])]),c_0_30]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SEU025+1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.12  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n004.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 17:19:08 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 2.73/2.84  % Version  : CSE_E---1.5
% 2.73/2.84  % Problem  : theBenchmark.p
% 2.73/2.84  % Proof found
% 2.73/2.84  % SZS status Theorem for theBenchmark.p
% 2.73/2.84  % SZS output start Proof
% See solution above
% 2.73/2.84  % Total time : 2.268000 s
% 2.73/2.84  % SZS output end Proof
% 2.73/2.84  % Total time : 2.271000 s
%------------------------------------------------------------------------------