TSTP Solution File: KRS084+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : KRS084+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 : n032.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 05:40:11 EDT 2023

% Result   : Unsatisfiable 0.13s 0.48s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   53 (   4 unt;  16 typ;   0 def)
%            Number of atoms       :  128 (   5 equ)
%            Maximal formula atoms :   23 (   3 avg)
%            Number of connectives :  156 (  65   ~;  57   |;  24   &)
%                                         (   6 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   20 (  15   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  11 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :   71 (   1 sgn;  32   !;   6   ?;   0   :)

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

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

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

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

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

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

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

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

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

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

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

tff(decl_33,type,
    i2003_11_14_17_19_35232: $i ).

tff(decl_34,type,
    esk1_1: $i > $i ).

tff(decl_35,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_36,type,
    esk3_1: $i > $i ).

tff(decl_37,type,
    esk4_1: $i > $i ).

fof(axiom_3,axiom,
    ! [X4] :
      ( cd(X4)
    <=> ( ? [X5] :
            ( rf(X4,X5)
            & ~ cc(X5) )
        & cc(X4) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).

fof(axiom_2,axiom,
    ! [X4] :
      ( cUnsatisfiable(X4)
    <=> ( ? [X5] :
            ( rinvF(X4,X5)
            & cd(X5) )
        & ! [X5] :
            ( rinvR(X4,X5)
           => ? [X6] :
                ( rinvF(X5,X6)
                & cd(X6) ) )
        & ~ cc(X4) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

fof(axiom_4,axiom,
    ! [X4,X5,X6] :
      ( ( rf(X4,X5)
        & rf(X4,X6) )
     => X5 = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).

fof(axiom_5,axiom,
    ! [X4,X5] :
      ( rinvF(X4,X5)
    <=> rf(X5,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).

fof(axiom_6,axiom,
    ! [X4,X5] :
      ( rinvR(X4,X5)
    <=> rr(X5,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).

fof(axiom_9,axiom,
    ! [X4,X5] :
      ( rf(X4,X5)
     => rr(X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).

fof(axiom_8,axiom,
    cUnsatisfiable(i2003_11_14_17_19_35232),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).

fof(c_0_7,plain,
    ! [X4] :
      ( cd(X4)
    <=> ( ? [X5] :
            ( rf(X4,X5)
            & ~ cc(X5) )
        & cc(X4) ) ),
    inference(fof_simplification,[status(thm)],[axiom_3]) ).

fof(c_0_8,plain,
    ! [X4] :
      ( cUnsatisfiable(X4)
    <=> ( ? [X5] :
            ( rinvF(X4,X5)
            & cd(X5) )
        & ! [X5] :
            ( rinvR(X4,X5)
           => ? [X6] :
                ( rinvF(X5,X6)
                & cd(X6) ) )
        & ~ cc(X4) ) ),
    inference(fof_simplification,[status(thm)],[axiom_2]) ).

fof(c_0_9,plain,
    ! [X59,X60,X61] :
      ( ~ rf(X59,X60)
      | ~ rf(X59,X61)
      | X60 = X61 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_4])]) ).

fof(c_0_10,plain,
    ! [X55,X57,X58] :
      ( ( rf(X55,esk4_1(X55))
        | ~ cd(X55) )
      & ( ~ cc(esk4_1(X55))
        | ~ cd(X55) )
      & ( cc(X55)
        | ~ cd(X55) )
      & ( ~ rf(X57,X58)
        | cc(X58)
        | ~ cc(X57)
        | cd(X57) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])])]) ).

fof(c_0_11,plain,
    ! [X62,X63] :
      ( ( ~ rinvF(X62,X63)
        | rf(X63,X62) )
      & ( ~ rf(X63,X62)
        | rinvF(X62,X63) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_5])]) ).

fof(c_0_12,plain,
    ! [X47,X49,X51,X52,X54] :
      ( ( rinvF(X47,esk1_1(X47))
        | ~ cUnsatisfiable(X47) )
      & ( cd(esk1_1(X47))
        | ~ cUnsatisfiable(X47) )
      & ( rinvF(X49,esk2_2(X47,X49))
        | ~ rinvR(X47,X49)
        | ~ cUnsatisfiable(X47) )
      & ( cd(esk2_2(X47,X49))
        | ~ rinvR(X47,X49)
        | ~ cUnsatisfiable(X47) )
      & ( ~ cc(X47)
        | ~ cUnsatisfiable(X47) )
      & ( rinvR(X51,esk3_1(X51))
        | ~ rinvF(X51,X52)
        | ~ cd(X52)
        | cc(X51)
        | cUnsatisfiable(X51) )
      & ( ~ rinvF(esk3_1(X51),X54)
        | ~ cd(X54)
        | ~ rinvF(X51,X52)
        | ~ cd(X52)
        | cc(X51)
        | cUnsatisfiable(X51) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])])]) ).

cnf(c_0_13,plain,
    ( X2 = X3
    | ~ rf(X1,X2)
    | ~ rf(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,plain,
    ( rf(X1,esk4_1(X1))
    | ~ cd(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_15,plain,
    ( rf(X2,X1)
    | ~ rinvF(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_16,plain,
    ( rinvF(X1,esk2_2(X2,X1))
    | ~ rinvR(X2,X1)
    | ~ cUnsatisfiable(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_17,plain,
    ( X1 = esk4_1(X2)
    | ~ rf(X2,X1)
    | ~ cd(X2) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_18,plain,
    ( rf(esk2_2(X1,X2),X2)
    | ~ rinvR(X1,X2)
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_19,plain,
    ( cd(esk2_2(X1,X2))
    | ~ rinvR(X1,X2)
    | ~ cUnsatisfiable(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_20,plain,
    ( ~ cc(esk4_1(X1))
    | ~ cd(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_21,plain,
    ( esk4_1(esk2_2(X1,X2)) = X2
    | ~ rinvR(X1,X2)
    | ~ cUnsatisfiable(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).

fof(c_0_22,plain,
    ! [X64,X65] :
      ( ( ~ rinvR(X64,X65)
        | rr(X65,X64) )
      & ( ~ rr(X65,X64)
        | rinvR(X64,X65) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_6])]) ).

cnf(c_0_23,plain,
    ( ~ rinvR(X1,X2)
    | ~ cc(X2)
    | ~ cUnsatisfiable(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_19]) ).

cnf(c_0_24,plain,
    ( rinvR(X2,X1)
    | ~ rr(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

fof(c_0_25,plain,
    ! [X69,X70] :
      ( ~ rf(X69,X70)
      | rr(X69,X70) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_9])]) ).

cnf(c_0_26,plain,
    ( ~ rr(X1,X2)
    | ~ cc(X1)
    | ~ cUnsatisfiable(X2) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_27,plain,
    ( rr(X1,X2)
    | ~ rf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_28,plain,
    ( rinvF(X1,esk1_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_29,plain,
    ( ~ rf(X1,X2)
    | ~ cc(X1)
    | ~ cUnsatisfiable(X2) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_30,plain,
    ( rf(esk1_1(X1),X1)
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[c_0_15,c_0_28]) ).

cnf(c_0_31,plain,
    ( ~ cc(esk1_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_32,plain,
    ( cc(X1)
    | ~ cd(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_33,plain,
    ( cd(esk1_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_34,plain,
    cUnsatisfiable(i2003_11_14_17_19_35232),
    inference(split_conjunct,[status(thm)],[axiom_8]) ).

cnf(c_0_35,plain,
    ~ cUnsatisfiable(X1),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).

cnf(c_0_36,plain,
    $false,
    inference(sr,[status(thm)],[c_0_34,c_0_35]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : KRS084+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.09  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.28  % Computer : n032.cluster.edu
% 0.11/0.28  % Model    : x86_64 x86_64
% 0.11/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.28  % Memory   : 8042.1875MB
% 0.11/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.28  % CPULimit   : 300
% 0.11/0.28  % WCLimit    : 300
% 0.11/0.28  % DateTime   : Mon Aug 28 01:17:45 EDT 2023
% 0.11/0.29  % CPUTime  : 
% 0.13/0.47  start to proof: theBenchmark
% 0.13/0.48  % Version  : CSE_E---1.5
% 0.13/0.48  % Problem  : theBenchmark.p
% 0.13/0.48  % Proof found
% 0.13/0.48  % SZS status Theorem for theBenchmark.p
% 0.13/0.48  % SZS output start Proof
% See solution above
% 0.13/0.49  % Total time : 0.008000 s
% 0.13/0.49  % SZS output end Proof
% 0.13/0.49  % Total time : 0.010000 s
%------------------------------------------------------------------------------