TSTP Solution File: KRS170+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : KRS170+1 : TPTP v8.1.2. Released v3.1.0.
% 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 05:40:43 EDT 2023

% Result   : Theorem 0.19s 0.57s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   65 (   5 unt;  12 typ;   0 def)
%            Number of atoms       :  234 (   0 equ)
%            Maximal formula atoms :   48 (   4 avg)
%            Number of connectives :  285 ( 104   ~; 152   |;  20   &)
%                                         (   5 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   6   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   6 con; 0-0 aty)
%            Number of variables   :   30 (   2 sgn;  22   !;   0   ?;   0   :)

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

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

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

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

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

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

tff(decl_28,type,
    esk1_0: $i ).

tff(decl_29,type,
    esk2_0: $i ).

tff(decl_30,type,
    esk3_0: $i ).

tff(decl_31,type,
    esk4_0: $i ).

tff(decl_32,type,
    esk5_0: $i ).

tff(decl_33,type,
    esk6_0: $i ).

fof(the_axiom,conjecture,
    ( ! [X1] :
        ( cowlThing(X1)
        & ~ cowlNothing(X1) )
    & ! [X1] :
        ( xsd_string(X1)
      <=> ~ xsd_integer(X1) )
    & ! [X1,X2] :
        ( rhasLeader(X1,X2)
       => rhasHead(X1,X2) )
    & ! [X1,X2] :
        ( rhasHead(X1,X2)
       => rhasLeader(X1,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',the_axiom) ).

fof(axiom_0,axiom,
    ! [X1] :
      ( cowlThing(X1)
      & ~ cowlNothing(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_0) ).

fof(axiom_1,axiom,
    ! [X1] :
      ( xsd_string(X1)
    <=> ~ xsd_integer(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).

fof(axiom_2,axiom,
    ! [X1,X2] :
      ( rhasLeader(X1,X2)
    <=> rhasHead(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

fof(c_0_4,negated_conjecture,
    ~ ( ! [X1] :
          ( cowlThing(X1)
          & ~ cowlNothing(X1) )
      & ! [X1] :
          ( xsd_string(X1)
        <=> ~ xsd_integer(X1) )
      & ! [X1,X2] :
          ( rhasLeader(X1,X2)
         => rhasHead(X1,X2) )
      & ! [X1,X2] :
          ( rhasHead(X1,X2)
         => rhasLeader(X1,X2) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[the_axiom])]) ).

fof(c_0_5,plain,
    ! [X1] :
      ( cowlThing(X1)
      & ~ cowlNothing(X1) ),
    inference(fof_simplification,[status(thm)],[axiom_0]) ).

fof(c_0_6,negated_conjecture,
    ( ( rhasHead(esk5_0,esk6_0)
      | rhasLeader(esk3_0,esk4_0)
      | ~ xsd_string(esk2_0)
      | xsd_integer(esk2_0)
      | ~ cowlThing(esk1_0)
      | cowlNothing(esk1_0) )
    & ( ~ rhasLeader(esk5_0,esk6_0)
      | rhasLeader(esk3_0,esk4_0)
      | ~ xsd_string(esk2_0)
      | xsd_integer(esk2_0)
      | ~ cowlThing(esk1_0)
      | cowlNothing(esk1_0) )
    & ( rhasHead(esk5_0,esk6_0)
      | ~ rhasHead(esk3_0,esk4_0)
      | ~ xsd_string(esk2_0)
      | xsd_integer(esk2_0)
      | ~ cowlThing(esk1_0)
      | cowlNothing(esk1_0) )
    & ( ~ rhasLeader(esk5_0,esk6_0)
      | ~ rhasHead(esk3_0,esk4_0)
      | ~ xsd_string(esk2_0)
      | xsd_integer(esk2_0)
      | ~ cowlThing(esk1_0)
      | cowlNothing(esk1_0) )
    & ( rhasHead(esk5_0,esk6_0)
      | rhasLeader(esk3_0,esk4_0)
      | xsd_string(esk2_0)
      | ~ xsd_integer(esk2_0)
      | ~ cowlThing(esk1_0)
      | cowlNothing(esk1_0) )
    & ( ~ rhasLeader(esk5_0,esk6_0)
      | rhasLeader(esk3_0,esk4_0)
      | xsd_string(esk2_0)
      | ~ xsd_integer(esk2_0)
      | ~ cowlThing(esk1_0)
      | cowlNothing(esk1_0) )
    & ( rhasHead(esk5_0,esk6_0)
      | ~ rhasHead(esk3_0,esk4_0)
      | xsd_string(esk2_0)
      | ~ xsd_integer(esk2_0)
      | ~ cowlThing(esk1_0)
      | cowlNothing(esk1_0) )
    & ( ~ rhasLeader(esk5_0,esk6_0)
      | ~ rhasHead(esk3_0,esk4_0)
      | xsd_string(esk2_0)
      | ~ xsd_integer(esk2_0)
      | ~ cowlThing(esk1_0)
      | cowlNothing(esk1_0) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).

fof(c_0_7,plain,
    ! [X3] :
      ( cowlThing(X3)
      & ~ cowlNothing(X3) ),
    inference(variable_rename,[status(thm)],[c_0_5]) ).

cnf(c_0_8,negated_conjecture,
    ( xsd_string(esk2_0)
    | cowlNothing(esk1_0)
    | ~ rhasLeader(esk5_0,esk6_0)
    | ~ rhasHead(esk3_0,esk4_0)
    | ~ xsd_integer(esk2_0)
    | ~ cowlThing(esk1_0) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_9,plain,
    cowlThing(X1),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_10,plain,
    ! [X1] :
      ( xsd_string(X1)
    <=> ~ xsd_integer(X1) ),
    inference(fof_simplification,[status(thm)],[axiom_1]) ).

cnf(c_0_11,negated_conjecture,
    ( rhasHead(esk5_0,esk6_0)
    | xsd_string(esk2_0)
    | cowlNothing(esk1_0)
    | ~ rhasHead(esk3_0,esk4_0)
    | ~ xsd_integer(esk2_0)
    | ~ cowlThing(esk1_0) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_12,negated_conjecture,
    ( rhasLeader(esk3_0,esk4_0)
    | xsd_string(esk2_0)
    | cowlNothing(esk1_0)
    | ~ rhasLeader(esk5_0,esk6_0)
    | ~ xsd_integer(esk2_0)
    | ~ cowlThing(esk1_0) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_13,negated_conjecture,
    ( cowlNothing(esk1_0)
    | xsd_string(esk2_0)
    | ~ xsd_integer(esk2_0)
    | ~ rhasLeader(esk5_0,esk6_0)
    | ~ rhasHead(esk3_0,esk4_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9])]) ).

cnf(c_0_14,plain,
    ~ cowlNothing(X1),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_15,plain,
    ! [X5,X6] :
      ( ( ~ rhasLeader(X5,X6)
        | rhasHead(X5,X6) )
      & ( ~ rhasHead(X5,X6)
        | rhasLeader(X5,X6) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_2])]) ).

fof(c_0_16,plain,
    ! [X4] :
      ( ( ~ xsd_string(X4)
        | ~ xsd_integer(X4) )
      & ( xsd_integer(X4)
        | xsd_string(X4) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])]) ).

cnf(c_0_17,negated_conjecture,
    ( rhasHead(esk5_0,esk6_0)
    | xsd_integer(esk2_0)
    | cowlNothing(esk1_0)
    | ~ rhasHead(esk3_0,esk4_0)
    | ~ xsd_string(esk2_0)
    | ~ cowlThing(esk1_0) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_18,negated_conjecture,
    ( xsd_integer(esk2_0)
    | cowlNothing(esk1_0)
    | ~ rhasLeader(esk5_0,esk6_0)
    | ~ rhasHead(esk3_0,esk4_0)
    | ~ xsd_string(esk2_0)
    | ~ cowlThing(esk1_0) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_19,negated_conjecture,
    ( rhasLeader(esk3_0,esk4_0)
    | xsd_integer(esk2_0)
    | cowlNothing(esk1_0)
    | ~ rhasLeader(esk5_0,esk6_0)
    | ~ xsd_string(esk2_0)
    | ~ cowlThing(esk1_0) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_20,negated_conjecture,
    ( cowlNothing(esk1_0)
    | xsd_string(esk2_0)
    | rhasHead(esk5_0,esk6_0)
    | ~ xsd_integer(esk2_0)
    | ~ rhasHead(esk3_0,esk4_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_9])]) ).

cnf(c_0_21,negated_conjecture,
    ( cowlNothing(esk1_0)
    | xsd_string(esk2_0)
    | rhasLeader(esk3_0,esk4_0)
    | ~ xsd_integer(esk2_0)
    | ~ rhasLeader(esk5_0,esk6_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_9])]) ).

cnf(c_0_22,negated_conjecture,
    ( xsd_string(esk2_0)
    | ~ rhasHead(esk3_0,esk4_0)
    | ~ rhasLeader(esk5_0,esk6_0)
    | ~ xsd_integer(esk2_0) ),
    inference(sr,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_23,plain,
    ( rhasHead(X1,X2)
    | ~ rhasLeader(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_24,plain,
    ( xsd_integer(X1)
    | xsd_string(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_25,negated_conjecture,
    ( cowlNothing(esk1_0)
    | xsd_integer(esk2_0)
    | rhasHead(esk5_0,esk6_0)
    | ~ xsd_string(esk2_0)
    | ~ rhasHead(esk3_0,esk4_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_9])]) ).

cnf(c_0_26,negated_conjecture,
    ( cowlNothing(esk1_0)
    | xsd_integer(esk2_0)
    | ~ xsd_string(esk2_0)
    | ~ rhasLeader(esk5_0,esk6_0)
    | ~ rhasHead(esk3_0,esk4_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_9])]) ).

cnf(c_0_27,negated_conjecture,
    ( cowlNothing(esk1_0)
    | xsd_integer(esk2_0)
    | rhasLeader(esk3_0,esk4_0)
    | ~ xsd_string(esk2_0)
    | ~ rhasLeader(esk5_0,esk6_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_9])]) ).

cnf(c_0_28,negated_conjecture,
    ( rhasHead(esk5_0,esk6_0)
    | xsd_string(esk2_0)
    | ~ rhasHead(esk3_0,esk4_0)
    | ~ xsd_integer(esk2_0) ),
    inference(sr,[status(thm)],[c_0_20,c_0_14]) ).

cnf(c_0_29,negated_conjecture,
    ( rhasLeader(esk3_0,esk4_0)
    | xsd_string(esk2_0)
    | ~ rhasLeader(esk5_0,esk6_0)
    | ~ xsd_integer(esk2_0) ),
    inference(sr,[status(thm)],[c_0_21,c_0_14]) ).

cnf(c_0_30,negated_conjecture,
    ( xsd_string(esk2_0)
    | ~ rhasLeader(esk5_0,esk6_0)
    | ~ rhasLeader(esk3_0,esk4_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).

cnf(c_0_31,negated_conjecture,
    ( rhasHead(esk5_0,esk6_0)
    | rhasLeader(esk3_0,esk4_0)
    | xsd_integer(esk2_0)
    | cowlNothing(esk1_0)
    | ~ xsd_string(esk2_0)
    | ~ cowlThing(esk1_0) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_32,plain,
    ( rhasLeader(X1,X2)
    | ~ rhasHead(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_33,negated_conjecture,
    ( rhasHead(esk5_0,esk6_0)
    | xsd_integer(esk2_0)
    | ~ rhasHead(esk3_0,esk4_0) ),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[c_0_25,c_0_14]),c_0_24]) ).

cnf(c_0_34,negated_conjecture,
    ( xsd_integer(esk2_0)
    | ~ rhasHead(esk3_0,esk4_0)
    | ~ rhasLeader(esk5_0,esk6_0)
    | ~ xsd_string(esk2_0) ),
    inference(sr,[status(thm)],[c_0_26,c_0_14]) ).

cnf(c_0_35,negated_conjecture,
    ( rhasLeader(esk3_0,esk4_0)
    | xsd_integer(esk2_0)
    | ~ rhasLeader(esk5_0,esk6_0) ),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[c_0_27,c_0_14]),c_0_24]) ).

cnf(c_0_36,negated_conjecture,
    ( rhasHead(esk5_0,esk6_0)
    | rhasLeader(esk3_0,esk4_0)
    | xsd_string(esk2_0)
    | cowlNothing(esk1_0)
    | ~ xsd_integer(esk2_0)
    | ~ cowlThing(esk1_0) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_37,negated_conjecture,
    ( rhasHead(esk5_0,esk6_0)
    | xsd_string(esk2_0)
    | ~ rhasHead(esk3_0,esk4_0) ),
    inference(csr,[status(thm)],[c_0_28,c_0_24]) ).

cnf(c_0_38,negated_conjecture,
    ( xsd_string(esk2_0)
    | ~ rhasLeader(esk5_0,esk6_0) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_29,c_0_24]),c_0_30]) ).

cnf(c_0_39,negated_conjecture,
    ( cowlNothing(esk1_0)
    | xsd_integer(esk2_0)
    | rhasLeader(esk3_0,esk4_0)
    | rhasHead(esk5_0,esk6_0)
    | ~ xsd_string(esk2_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_9])]) ).

cnf(c_0_40,negated_conjecture,
    ( rhasLeader(esk5_0,esk6_0)
    | xsd_integer(esk2_0)
    | ~ rhasHead(esk3_0,esk4_0) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_41,negated_conjecture,
    ( xsd_integer(esk2_0)
    | ~ rhasLeader(esk5_0,esk6_0) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_23]),c_0_24]),c_0_35]) ).

cnf(c_0_42,negated_conjecture,
    ( cowlNothing(esk1_0)
    | xsd_string(esk2_0)
    | rhasLeader(esk3_0,esk4_0)
    | rhasHead(esk5_0,esk6_0)
    | ~ xsd_integer(esk2_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_9])]) ).

cnf(c_0_43,negated_conjecture,
    ( xsd_string(esk2_0)
    | ~ rhasHead(esk3_0,esk4_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_37]),c_0_38]) ).

cnf(c_0_44,negated_conjecture,
    ( rhasHead(esk5_0,esk6_0)
    | rhasLeader(esk3_0,esk4_0)
    | xsd_integer(esk2_0) ),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[c_0_39,c_0_14]),c_0_24]) ).

cnf(c_0_45,negated_conjecture,
    ( xsd_integer(esk2_0)
    | ~ rhasLeader(esk3_0,esk4_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_23]),c_0_41]) ).

cnf(c_0_46,negated_conjecture,
    ( rhasHead(esk5_0,esk6_0)
    | rhasLeader(esk3_0,esk4_0)
    | xsd_string(esk2_0) ),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[c_0_42,c_0_14]),c_0_24]) ).

cnf(c_0_47,negated_conjecture,
    ( xsd_string(esk2_0)
    | ~ rhasLeader(esk3_0,esk4_0) ),
    inference(spm,[status(thm)],[c_0_43,c_0_23]) ).

cnf(c_0_48,negated_conjecture,
    ( rhasHead(esk5_0,esk6_0)
    | xsd_integer(esk2_0) ),
    inference(csr,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_49,plain,
    ( ~ xsd_string(X1)
    | ~ xsd_integer(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_50,negated_conjecture,
    xsd_string(esk2_0),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_46]),c_0_47]),c_0_38]) ).

cnf(c_0_51,negated_conjecture,
    xsd_integer(esk2_0),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_48]),c_0_41]) ).

cnf(c_0_52,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : KRS170+1 : TPTP v8.1.2. Released v3.1.0.
% 0.07/0.12  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33  % Computer : n004.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Mon Aug 28 01:52:22 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.19/0.57  % Version  : CSE_E---1.5
% 0.19/0.57  % Problem  : theBenchmark.p
% 0.19/0.57  % Proof found
% 0.19/0.57  % SZS status Theorem for theBenchmark.p
% 0.19/0.57  % SZS output start Proof
% See solution above
% 0.19/0.57  % Total time : 0.006000 s
% 0.19/0.57  % SZS output end Proof
% 0.19/0.57  % Total time : 0.008000 s
%------------------------------------------------------------------------------