TSTP Solution File: SEU014+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU014+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 : n005.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 16:22:08 EDT 2023

% Result   : Theorem 0.22s 0.75s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   33
% Syntax   : Number of formulae    :   72 (  17 unt;  27 typ;   0 def)
%            Number of atoms       :  169 (  27 equ)
%            Maximal formula atoms :   23 (   3 avg)
%            Number of connectives :  202 (  78   ~;  80   |;  27   &)
%                                         (   1 <=>;  16  =>;   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    :   19 (  19 usr;   9 con; 0-2 aty)
%            Number of variables   :   51 (   0 sgn;  28   !;   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,
    relation_composition: ( $i * $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,
    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_1: $i > $i ).

tff(decl_38,type,
    esk3_1: $i > $i ).

tff(decl_39,type,
    esk4_0: $i ).

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

tff(decl_41,type,
    esk6_1: $i > $i ).

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

tff(decl_43,type,
    esk8_0: $i ).

tff(decl_44,type,
    esk9_1: $i > $i ).

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

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

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

tff(decl_48,type,
    esk13_0: $i ).

fof(t47_funct_1,conjecture,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ! [X2] :
          ( ( relation(X2)
            & function(X2) )
         => ( ( one_to_one(relation_composition(X2,X1))
              & subset(relation_rng(X2),relation_dom(X1)) )
           => one_to_one(X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_funct_1) ).

fof(dt_k5_relat_1,axiom,
    ! [X1,X2] :
      ( ( relation(X1)
        & relation(X2) )
     => relation(relation_composition(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).

fof(fc1_funct_1,axiom,
    ! [X1,X2] :
      ( ( relation(X1)
        & function(X1)
        & relation(X2)
        & function(X2) )
     => ( relation(relation_composition(X1,X2))
        & function(relation_composition(X1,X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_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(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(t23_funct_1,axiom,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => ! [X3] :
          ( ( relation(X3)
            & function(X3) )
         => ( in(X1,relation_dom(X2))
           => apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).

fof(c_0_6,negated_conjecture,
    ~ ! [X1] :
        ( ( relation(X1)
          & function(X1) )
       => ! [X2] :
            ( ( relation(X2)
              & function(X2) )
           => ( ( one_to_one(relation_composition(X2,X1))
                & subset(relation_rng(X2),relation_dom(X1)) )
             => one_to_one(X2) ) ) ),
    inference(assume_negation,[status(cth)],[t47_funct_1]) ).

fof(c_0_7,plain,
    ! [X13,X14] :
      ( ~ relation(X13)
      | ~ relation(X14)
      | relation(relation_composition(X13,X14)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relat_1])]) ).

fof(c_0_8,negated_conjecture,
    ( relation(esk12_0)
    & function(esk12_0)
    & relation(esk13_0)
    & function(esk13_0)
    & one_to_one(relation_composition(esk13_0,esk12_0))
    & subset(relation_rng(esk13_0),relation_dom(esk12_0))
    & ~ one_to_one(esk13_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).

fof(c_0_9,plain,
    ! [X19,X20] :
      ( ( relation(relation_composition(X19,X20))
        | ~ relation(X19)
        | ~ function(X19)
        | ~ relation(X20)
        | ~ function(X20) )
      & ( function(relation_composition(X19,X20))
        | ~ relation(X19)
        | ~ function(X19)
        | ~ relation(X20)
        | ~ function(X20) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_funct_1])])]) ).

fof(c_0_10,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])])])])]) ).

fof(c_0_11,plain,
    ! [X48,X49] :
      ( ~ relation(X48)
      | ~ relation(X49)
      | ~ subset(relation_rng(X48),relation_dom(X49))
      | relation_dom(relation_composition(X48,X49)) = relation_dom(X48) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t46_relat_1])])]) ).

cnf(c_0_12,plain,
    ( relation(relation_composition(X1,X2))
    | ~ relation(X1)
    | ~ relation(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

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

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

cnf(c_0_15,negated_conjecture,
    function(esk12_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_16,plain,
    ! [X41,X42,X43] :
      ( ~ relation(X42)
      | ~ function(X42)
      | ~ relation(X43)
      | ~ function(X43)
      | ~ in(X41,relation_dom(X42))
      | apply(relation_composition(X42,X43),X41) = apply(X43,apply(X42,X41)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_funct_1])])]) ).

cnf(c_0_17,plain,
    ( in(esk2_1(X1),relation_dom(X1))
    | one_to_one(X1)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_18,negated_conjecture,
    relation(esk13_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_19,negated_conjecture,
    function(esk13_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_20,negated_conjecture,
    ~ one_to_one(esk13_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_21,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_10]) ).

cnf(c_0_22,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_11]) ).

cnf(c_0_23,negated_conjecture,
    subset(relation_rng(esk13_0),relation_dom(esk12_0)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_24,negated_conjecture,
    ( relation(relation_composition(X1,esk12_0))
    | ~ relation(X1) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_25,negated_conjecture,
    ( function(relation_composition(X1,esk12_0))
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_13]),c_0_15])]) ).

cnf(c_0_26,plain,
    ( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
    | ~ relation(X1)
    | ~ function(X1)
    | ~ relation(X2)
    | ~ function(X2)
    | ~ in(X3,relation_dom(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_27,negated_conjecture,
    in(esk2_1(esk13_0),relation_dom(esk13_0)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]),c_0_20]) ).

cnf(c_0_28,negated_conjecture,
    apply(esk13_0,esk2_1(esk13_0)) = apply(esk13_0,esk1_1(esk13_0)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_18]),c_0_19])]),c_0_20]) ).

cnf(c_0_29,plain,
    ( in(esk1_1(X1),relation_dom(X1))
    | one_to_one(X1)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_30,plain,
    ( X2 = X3
    | ~ one_to_one(X1)
    | ~ in(X2,relation_dom(X1))
    | ~ in(X3,relation_dom(X1))
    | apply(X1,X2) != apply(X1,X3)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_31,negated_conjecture,
    relation_dom(relation_composition(esk13_0,esk12_0)) = relation_dom(esk13_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_13]),c_0_18])]) ).

cnf(c_0_32,negated_conjecture,
    one_to_one(relation_composition(esk13_0,esk12_0)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_33,negated_conjecture,
    relation(relation_composition(esk13_0,esk12_0)),
    inference(spm,[status(thm)],[c_0_24,c_0_18]) ).

cnf(c_0_34,negated_conjecture,
    function(relation_composition(esk13_0,esk12_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_18]),c_0_19])]) ).

cnf(c_0_35,negated_conjecture,
    ( apply(relation_composition(esk13_0,X1),esk2_1(esk13_0)) = apply(X1,apply(esk13_0,esk1_1(esk13_0)))
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_18]),c_0_19])]),c_0_28]) ).

cnf(c_0_36,negated_conjecture,
    in(esk1_1(esk13_0),relation_dom(esk13_0)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_18]),c_0_19])]),c_0_20]) ).

cnf(c_0_37,negated_conjecture,
    ( X1 = X2
    | apply(relation_composition(esk13_0,esk12_0),X1) != apply(relation_composition(esk13_0,esk12_0),X2)
    | ~ in(X2,relation_dom(esk13_0))
    | ~ in(X1,relation_dom(esk13_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]),c_0_33]),c_0_34])]) ).

cnf(c_0_38,negated_conjecture,
    apply(relation_composition(esk13_0,esk12_0),esk2_1(esk13_0)) = apply(esk12_0,apply(esk13_0,esk1_1(esk13_0))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_13]),c_0_15])]) ).

cnf(c_0_39,negated_conjecture,
    ( apply(relation_composition(esk13_0,X1),esk1_1(esk13_0)) = apply(X1,apply(esk13_0,esk1_1(esk13_0)))
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_36]),c_0_18]),c_0_19])]) ).

cnf(c_0_40,plain,
    ( one_to_one(X1)
    | esk1_1(X1) != esk2_1(X1)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_41,negated_conjecture,
    ( X1 = esk2_1(esk13_0)
    | apply(relation_composition(esk13_0,esk12_0),X1) != apply(esk12_0,apply(esk13_0,esk1_1(esk13_0)))
    | ~ in(X1,relation_dom(esk13_0)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_27]),c_0_38]) ).

cnf(c_0_42,negated_conjecture,
    apply(relation_composition(esk13_0,esk12_0),esk1_1(esk13_0)) = apply(esk12_0,apply(esk13_0,esk1_1(esk13_0))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_13]),c_0_15])]) ).

cnf(c_0_43,negated_conjecture,
    esk2_1(esk13_0) != esk1_1(esk13_0),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_18]),c_0_19])]),c_0_20]) ).

cnf(c_0_44,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_36]),c_0_42])]),c_0_43]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : SEU014+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.15  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.37  % Computer : n005.cluster.edu
% 0.14/0.37  % Model    : x86_64 x86_64
% 0.14/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37  % Memory   : 8042.1875MB
% 0.14/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37  % CPULimit   : 300
% 0.14/0.37  % WCLimit    : 300
% 0.14/0.37  % DateTime   : Wed Aug 23 13:26:54 EDT 2023
% 0.14/0.37  % CPUTime  : 
% 0.22/0.64  start to proof: theBenchmark
% 0.22/0.75  % Version  : CSE_E---1.5
% 0.22/0.75  % Problem  : theBenchmark.p
% 0.22/0.75  % Proof found
% 0.22/0.75  % SZS status Theorem for theBenchmark.p
% 0.22/0.75  % SZS output start Proof
% See solution above
% 0.22/0.75  % Total time : 0.100000 s
% 0.22/0.75  % SZS output end Proof
% 0.22/0.75  % Total time : 0.103000 s
%------------------------------------------------------------------------------