TSTP Solution File: KRS117+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : KRS117+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 : n023.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 05:40:19 EDT 2023

% Result   : Unsatisfiable 0.53s 0.58s
% Output   : CNFRefutation 0.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   32
% Syntax   : Number of formulae    :   75 (   5 unt;  21 typ;   0 def)
%            Number of atoms       :  158 (   6 equ)
%            Maximal formula atoms :   19 (   2 avg)
%            Number of connectives :  183 (  79   ~;  69   |;  24   &)
%                                         (   7 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   25 (  20   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :   16 (  14 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   1 con; 0-1 aty)
%            Number of variables   :   89 (   3 sgn;  43   !;   5   ?;   0   :)

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

tff(decl_23,type,
    ca_Vx3: $i > $o ).

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

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

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

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

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

tff(decl_29,type,
    ra_Px1: ( $i * $i ) > $o ).

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

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

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

tff(decl_33,type,
    rr: ( $i * $i ) > $o ).

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

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

tff(decl_36,type,
    i2003_11_14_17_21_37349: $i ).

tff(decl_37,type,
    esk1_1: $i > $i ).

tff(decl_38,type,
    esk2_1: $i > $i ).

tff(decl_39,type,
    esk3_1: $i > $i ).

tff(decl_40,type,
    esk4_1: $i > $i ).

tff(decl_41,type,
    esk5_1: $i > $i ).

tff(decl_42,type,
    esk6_1: $i > $i ).

fof(axiom_0,axiom,
    ! [X4] :
      ( cowlThing(X4)
      & ~ cowlNothing(X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_0) ).

fof(axiom_3,axiom,
    ! [X4] :
      ( cc(X4)
    <=> ~ ? [X5] : ra_Px1(X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).

fof(axiom_4,axiom,
    ! [X4] :
      ( ccxcomp(X4)
    <=> ? [X6] : ra_Px1(X4,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).

fof(axiom_7,axiom,
    ! [X4] :
      ( cowlThing(X4)
     => ! [X6,X7] :
          ( ( rf(X4,X6)
            & rf(X4,X7) )
         => X6 = X7 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).

fof(axiom_8,axiom,
    ! [X4,X5] :
      ( rinvF(X4,X5)
    <=> rf(X5,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).

fof(axiom_6,axiom,
    ! [X4] :
      ( ca_Vx3(X4)
    <=> ? [X5] :
          ( rinvF(X4,X5)
          & cd(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).

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

fof(axiom_12,axiom,
    ! [X4,X5] :
      ( rf(X4,X5)
     => rr(X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_12) ).

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

fof(axiom_2,axiom,
    ! [X4] :
      ( cUnsatisfiable(X4)
    <=> ( ccxcomp(X4)
        & ! [X5] :
            ( rinvR(X4,X5)
           => ca_Vx3(X5) )
        & ? [X5] :
            ( rinvF(X4,X5)
            & cd(X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

fof(axiom_11,axiom,
    cUnsatisfiable(i2003_11_14_17_21_37349),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).

fof(c_0_11,plain,
    ! [X4] :
      ( cowlThing(X4)
      & ~ cowlNothing(X4) ),
    inference(fof_simplification,[status(thm)],[axiom_0]) ).

fof(c_0_12,plain,
    ! [X65,X66,X67] :
      ( ( ~ cc(X65)
        | ~ ra_Px1(X65,X66) )
      & ( ra_Px1(X67,esk3_1(X67))
        | cc(X67) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_3])])])])]) ).

fof(c_0_13,plain,
    ! [X69,X71,X72] :
      ( ( ~ ccxcomp(X69)
        | ra_Px1(X69,esk4_1(X69)) )
      & ( ~ ra_Px1(X71,X72)
        | ccxcomp(X71) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_4])])])])]) ).

fof(c_0_14,plain,
    ! [X81,X82,X83] :
      ( ~ cowlThing(X81)
      | ~ rf(X81,X82)
      | ~ rf(X81,X83)
      | X82 = X83 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_7])])]) ).

fof(c_0_15,plain,
    ! [X57] :
      ( cowlThing(X57)
      & ~ cowlNothing(X57) ),
    inference(variable_rename,[status(thm)],[c_0_11]) ).

fof(c_0_16,plain,
    ! [X84,X85] :
      ( ( ~ rinvF(X84,X85)
        | rf(X85,X84) )
      & ( ~ rf(X85,X84)
        | rinvF(X84,X85) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_8])]) ).

fof(c_0_17,plain,
    ! [X77,X79,X80] :
      ( ( rinvF(X77,esk6_1(X77))
        | ~ ca_Vx3(X77) )
      & ( cd(esk6_1(X77))
        | ~ ca_Vx3(X77) )
      & ( ~ rinvF(X79,X80)
        | ~ cd(X80)
        | ca_Vx3(X79) ) ),
    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)],[axiom_6])])])])])]) ).

cnf(c_0_18,plain,
    ( ~ cc(X1)
    | ~ ra_Px1(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_19,plain,
    ( ra_Px1(X1,esk4_1(X1))
    | ~ ccxcomp(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_20,plain,
    ! [X73,X75,X76] :
      ( ( rf(X73,esk5_1(X73))
        | ~ cd(X73) )
      & ( ccxcomp(esk5_1(X73))
        | ~ cd(X73) )
      & ( cc(X73)
        | ~ cd(X73) )
      & ( ~ rf(X75,X76)
        | ~ ccxcomp(X76)
        | ~ cc(X75)
        | cd(X75) ) ),
    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)],[axiom_5])])])])])]) ).

cnf(c_0_21,plain,
    ( X2 = X3
    | ~ cowlThing(X1)
    | ~ rf(X1,X2)
    | ~ rf(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_22,plain,
    cowlThing(X1),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_23,plain,
    ! [X91,X92] :
      ( ~ rf(X91,X92)
      | rr(X91,X92) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_12])]) ).

cnf(c_0_24,plain,
    ( rf(X2,X1)
    | ~ rinvF(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_25,plain,
    ( rinvF(X1,esk6_1(X1))
    | ~ ca_Vx3(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_26,plain,
    ( ~ ccxcomp(X1)
    | ~ cc(X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_27,plain,
    ( cc(X1)
    | ~ cd(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_28,plain,
    ( X2 = X3
    | ~ rf(X1,X3)
    | ~ rf(X1,X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]) ).

cnf(c_0_29,plain,
    ( rf(X1,esk5_1(X1))
    | ~ cd(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

fof(c_0_30,plain,
    ! [X86,X87] :
      ( ( ~ rinvR(X86,X87)
        | rr(X87,X86) )
      & ( ~ rr(X87,X86)
        | rinvR(X86,X87) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_9])]) ).

cnf(c_0_31,plain,
    ( rr(X1,X2)
    | ~ rf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_32,plain,
    ( rf(esk6_1(X1),X1)
    | ~ ca_Vx3(X1) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

fof(c_0_33,plain,
    ! [X59,X60,X62,X64] :
      ( ( ccxcomp(X59)
        | ~ cUnsatisfiable(X59) )
      & ( ~ rinvR(X59,X60)
        | ca_Vx3(X60)
        | ~ cUnsatisfiable(X59) )
      & ( rinvF(X59,esk1_1(X59))
        | ~ cUnsatisfiable(X59) )
      & ( cd(esk1_1(X59))
        | ~ cUnsatisfiable(X59) )
      & ( rinvR(X62,esk2_1(X62))
        | ~ ccxcomp(X62)
        | ~ rinvF(X62,X64)
        | ~ cd(X64)
        | cUnsatisfiable(X62) )
      & ( ~ ca_Vx3(esk2_1(X62))
        | ~ ccxcomp(X62)
        | ~ rinvF(X62,X64)
        | ~ cd(X64)
        | cUnsatisfiable(X62) ) ),
    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)],[axiom_2])])])])])]) ).

cnf(c_0_34,plain,
    ( ~ cd(X1)
    | ~ ccxcomp(X1) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_35,plain,
    ( ccxcomp(esk5_1(X1))
    | ~ cd(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_36,plain,
    ( X1 = esk5_1(X2)
    | ~ rf(X2,X1)
    | ~ cd(X2) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_37,plain,
    ( cd(esk6_1(X1))
    | ~ ca_Vx3(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_38,plain,
    ( rinvR(X2,X1)
    | ~ rr(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_39,plain,
    ( rr(esk6_1(X1),X1)
    | ~ ca_Vx3(X1) ),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_40,plain,
    ( ca_Vx3(X1)
    | ~ rinvF(X1,X2)
    | ~ cd(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_41,plain,
    ( rinvF(X1,esk1_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_42,plain,
    ( cd(esk1_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_43,plain,
    ( ~ cd(esk5_1(X1))
    | ~ cd(X1) ),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_44,plain,
    ( esk5_1(esk6_1(X1)) = X1
    | ~ ca_Vx3(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_32]),c_0_37]) ).

cnf(c_0_45,plain,
    ( ca_Vx3(X2)
    | ~ rinvR(X1,X2)
    | ~ cUnsatisfiable(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_46,plain,
    ( rinvR(X1,esk6_1(X1))
    | ~ ca_Vx3(X1) ),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_47,plain,
    ( ca_Vx3(X1)
    | ~ cUnsatisfiable(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).

cnf(c_0_48,plain,
    ( ~ cd(X1)
    | ~ ca_Vx3(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_37]) ).

cnf(c_0_49,plain,
    ( ca_Vx3(esk6_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).

cnf(c_0_50,plain,
    ( ~ cd(esk6_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_51,plain,
    cUnsatisfiable(i2003_11_14_17_21_37349),
    inference(split_conjunct,[status(thm)],[axiom_11]) ).

cnf(c_0_52,plain,
    ~ cUnsatisfiable(X1),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_37]),c_0_47]) ).

cnf(c_0_53,plain,
    $false,
    inference(sr,[status(thm)],[c_0_51,c_0_52]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : KRS117+1 : TPTP v8.1.2. Released v3.1.0.
% 0.10/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n023.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   : Mon Aug 28 01:24:55 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.53/0.58  % Version  : CSE_E---1.5
% 0.53/0.58  % Problem  : theBenchmark.p
% 0.53/0.58  % Proof found
% 0.53/0.58  % SZS status Theorem for theBenchmark.p
% 0.53/0.58  % SZS output start Proof
% See solution above
% 0.53/0.59  % Total time : 0.012000 s
% 0.53/0.59  % SZS output end Proof
% 0.53/0.59  % Total time : 0.016000 s
%------------------------------------------------------------------------------