TSTP Solution File: HAL003+3 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : HAL003+3 : TPTP v8.1.2. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n029.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 01:53:28 EDT 2023

% Result   : Theorem 0.20s 0.57s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   43
% Syntax   : Number of formulae    :   58 (   6 unt;  38 typ;   0 def)
%            Number of atoms       :   57 (   7 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   63 (  26   ~;  25   |;   8   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   58 (  24   >;  34   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-4 aty)
%            Number of functors    :   32 (  32 usr;  14 con; 0-6 aty)
%            Number of variables   :   38 (   0 sgn;  16   !;   3   ?;   0   :)

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

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

tff(decl_24,type,
    apply: ( $i * $i ) > $i ).

tff(decl_25,type,
    zero: $i > $i ).

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

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

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

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

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

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

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

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

tff(decl_34,type,
    beta: $i ).

tff(decl_35,type,
    c: $i ).

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

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

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

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

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

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

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

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

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

tff(decl_45,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_46,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_47,type,
    esk3_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_48,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_49,type,
    esk5_6: ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_50,type,
    esk6_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_51,type,
    esk7_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_52,type,
    esk8_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_53,type,
    esk9_1: $i > $i ).

tff(decl_54,type,
    esk10_1: $i > $i ).

tff(decl_55,type,
    esk11_1: $i > $i ).

tff(decl_56,type,
    esk12_1: $i > $i ).

tff(decl_57,type,
    esk13_1: $i > $i ).

tff(decl_58,type,
    esk14_1: $i > $i ).

tff(decl_59,type,
    esk15_1: $i > $i ).

fof(properties_for_surjection,axiom,
    ! [X1,X2,X3] :
      ( ( morphism(X1,X2,X3)
        & ! [X7] :
            ( element(X7,X3)
           => ? [X8] :
                ( element(X8,X2)
                & apply(X1,X8) = X7 ) ) )
     => surjection(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',properties_for_surjection) ).

fof(subtract_in_domain,axiom,
    ! [X2,X5,X6] :
      ( ( element(X5,X2)
        & element(X6,X2) )
     => element(subtract(X2,X5,X6),X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',subtract_in_domain) ).

fof(lemma12,axiom,
    ! [X19] :
      ( element(X19,e)
     => ? [X21,X24] :
          ( element(X21,b)
          & element(X24,b)
          & apply(g,subtract(b,X21,X24)) = X19 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma12) ).

fof(g_surjection,conjecture,
    surjection(g),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',g_surjection) ).

fof(g_morphism,axiom,
    morphism(g,b,e),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',g_morphism) ).

fof(c_0_5,plain,
    ! [X44,X45,X46,X48] :
      ( ( element(esk4_3(X44,X45,X46),X46)
        | ~ morphism(X44,X45,X46)
        | surjection(X44) )
      & ( ~ element(X48,X45)
        | apply(X44,X48) != esk4_3(X44,X45,X46)
        | ~ morphism(X44,X45,X46)
        | surjection(X44) ) ),
    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)],[properties_for_surjection])])])])])]) ).

fof(c_0_6,plain,
    ! [X84,X85,X86] :
      ( ~ element(X85,X84)
      | ~ element(X86,X84)
      | element(subtract(X84,X85,X86),X84) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subtract_in_domain])]) ).

cnf(c_0_7,plain,
    ( surjection(X3)
    | ~ element(X1,X2)
    | apply(X3,X1) != esk4_3(X3,X2,X4)
    | ~ morphism(X3,X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,plain,
    ( element(subtract(X2,X1,X3),X2)
    | ~ element(X1,X2)
    | ~ element(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_9,plain,
    ! [X104] :
      ( ( element(esk14_1(X104),b)
        | ~ element(X104,e) )
      & ( element(esk15_1(X104),b)
        | ~ element(X104,e) )
      & ( apply(g,subtract(b,esk14_1(X104),esk15_1(X104))) = X104
        | ~ element(X104,e) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[lemma12])])])]) ).

fof(c_0_10,negated_conjecture,
    ~ surjection(g),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[g_surjection])]) ).

cnf(c_0_11,plain,
    ( surjection(X1)
    | apply(X1,subtract(X2,X3,X4)) != esk4_3(X1,X2,X5)
    | ~ element(X4,X2)
    | ~ element(X3,X2)
    | ~ morphism(X1,X2,X5) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_12,plain,
    ( apply(g,subtract(b,esk14_1(X1),esk15_1(X1))) = X1
    | ~ element(X1,e) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_13,negated_conjecture,
    ~ surjection(g),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,plain,
    ( element(esk14_1(X1),b)
    | ~ element(X1,e) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_15,plain,
    ( element(esk15_1(X1),b)
    | ~ element(X1,e) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_16,plain,
    ( ~ element(esk4_3(g,b,X1),e)
    | ~ morphism(g,b,X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]),c_0_14]),c_0_15]) ).

cnf(c_0_17,plain,
    ( element(esk4_3(X1,X2,X3),X3)
    | surjection(X1)
    | ~ morphism(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_18,plain,
    morphism(g,b,e),
    inference(split_conjunct,[status(thm)],[g_morphism]) ).

cnf(c_0_19,plain,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]),c_0_13]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : HAL003+3 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n029.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon Aug 28 02:51:26 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.54  start to proof: theBenchmark
% 0.20/0.57  % Version  : CSE_E---1.5
% 0.20/0.57  % Problem  : theBenchmark.p
% 0.20/0.57  % Proof found
% 0.20/0.57  % SZS status Theorem for theBenchmark.p
% 0.20/0.57  % SZS output start Proof
% See solution above
% 0.20/0.57  % Total time : 0.023000 s
% 0.20/0.57  % SZS output end Proof
% 0.20/0.57  % Total time : 0.026000 s
%------------------------------------------------------------------------------