TSTP Solution File: HAL001+2 by Enigma---0.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Enigma---0.5.1
% Problem  : HAL001+2 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : enigmatic-eprover.py %s %d 1

% 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  : 600s
% DateTime : Sat Jul 16 12:45:05 EDT 2022

% Result   : Theorem 18.61s 3.56s
% Output   : CNFRefutation 18.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   84 (  42 unt;   0 def)
%            Number of atoms       :  238 (  70 equ)
%            Maximal formula atoms :   24 (   2 avg)
%            Number of connectives :  280 ( 126   ~; 125   |;  19   &)
%                                         (   1 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   4 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-4 aty)
%            Number of functors    :   17 (  17 usr;  13 con; 0-6 aty)
%            Number of variables   :  138 (   0 sgn  55   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(commute_properties,axiom,
    ! [X13,X14,X15,X16,X2,X17,X18,X3] :
      ( ( commute(X13,X14,X15,X16)
        & morphism(X13,X2,X17)
        & morphism(X14,X17,X3)
        & morphism(X15,X2,X18)
        & morphism(X16,X18,X3) )
     => ! [X8] :
          ( element(X8,X2)
         => apply(X14,apply(X13,X8)) = apply(X16,apply(X15,X8)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HAL001+0.ax',commute_properties) ).

fof(beta_h_g_delta_commute,axiom,
    commute(beta,h,g,delta),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta_h_g_delta_commute) ).

fof(delta_morphism,axiom,
    morphism(delta,e,r),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',delta_morphism) ).

fof(g_injection,conjecture,
    injection(g),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',g_injection) ).

fof(alpha_g_f_gamma_commute,axiom,
    commute(alpha,g,f,gamma),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',alpha_g_f_gamma_commute) ).

fof(injection_properties_2,axiom,
    ! [X1,X2,X3] :
      ( ( injection(X1)
        & morphism(X1,X2,X3) )
     => ! [X4] :
          ( ( element(X4,X2)
            & apply(X1,X4) = zero(X3) )
         => X4 = zero(X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',injection_properties_2) ).

fof(morphism,axiom,
    ! [X1,X2,X3] :
      ( morphism(X1,X2,X3)
     => ( ! [X4] :
            ( element(X4,X2)
           => element(apply(X1,X4),X3) )
        & apply(X1,zero(X2)) = zero(X3) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HAL001+0.ax',morphism) ).

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

fof(properties_for_injection_2,axiom,
    ! [X1,X2,X3] :
      ( ( morphism(X1,X2,X3)
        & ! [X4] :
            ( ( element(X4,X2)
              & apply(X1,X4) = zero(X3) )
           => X4 = zero(X2) ) )
     => injection(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',properties_for_injection_2) ).

fof(gamma_morphism,axiom,
    morphism(gamma,d,e),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gamma_morphism) ).

fof(exact_properties,axiom,
    ! [X9,X10,X2,X11,X3] :
      ( ( exact(X9,X10)
        & morphism(X9,X2,X11)
        & morphism(X10,X11,X3) )
     => ! [X12] :
          ( ( element(X12,X11)
            & apply(X10,X12) = zero(X3) )
        <=> ? [X8] :
              ( element(X8,X2)
              & apply(X9,X8) = X12 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HAL001+0.ax',exact_properties) ).

fof(h_morphism,axiom,
    morphism(h,c,r),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_morphism) ).

fof(h_injection,hypothesis,
    injection(h),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_injection) ).

fof(beta_morphism,axiom,
    morphism(beta,b,c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta_morphism) ).

fof(f_morphism,axiom,
    morphism(f,a,d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_morphism) ).

fof(alpha_morphism,axiom,
    morphism(alpha,a,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',alpha_morphism) ).

fof(alpha_beta_exact,axiom,
    exact(alpha,beta),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',alpha_beta_exact) ).

fof(gamma_injection,axiom,
    injection(gamma),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gamma_injection) ).

fof(f_injection,hypothesis,
    injection(f),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_injection) ).

fof(c_0_19,plain,
    ! [X60,X61,X62,X63,X64,X65,X66,X67,X68] :
      ( ~ commute(X60,X61,X62,X63)
      | ~ morphism(X60,X64,X65)
      | ~ morphism(X61,X65,X67)
      | ~ morphism(X62,X64,X66)
      | ~ morphism(X63,X66,X67)
      | ~ element(X68,X64)
      | apply(X61,apply(X60,X68)) = apply(X63,apply(X62,X68)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[commute_properties])])]) ).

cnf(c_0_20,plain,
    ( apply(X2,apply(X1,X9)) = apply(X4,apply(X3,X9))
    | ~ commute(X1,X2,X3,X4)
    | ~ morphism(X1,X5,X6)
    | ~ morphism(X2,X6,X7)
    | ~ morphism(X3,X5,X8)
    | ~ morphism(X4,X8,X7)
    | ~ element(X9,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_21,plain,
    commute(beta,h,g,delta),
    inference(split_conjunct,[status(thm)],[beta_h_g_delta_commute]) ).

cnf(c_0_22,plain,
    ( apply(h,apply(beta,X1)) = apply(delta,apply(g,X1))
    | ~ element(X1,X2)
    | ~ morphism(delta,X3,X4)
    | ~ morphism(g,X2,X3)
    | ~ morphism(h,X5,X4)
    | ~ morphism(beta,X2,X5) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_23,plain,
    morphism(delta,e,r),
    inference(split_conjunct,[status(thm)],[delta_morphism]) ).

fof(c_0_24,negated_conjecture,
    ~ injection(g),
    inference(assume_negation,[status(cth)],[g_injection]) ).

cnf(c_0_25,plain,
    commute(alpha,g,f,gamma),
    inference(split_conjunct,[status(thm)],[alpha_g_f_gamma_commute]) ).

fof(c_0_26,plain,
    ! [X91,X92,X93,X94] :
      ( ~ injection(X91)
      | ~ morphism(X91,X92,X93)
      | ~ element(X94,X92)
      | apply(X91,X94) != zero(X93)
      | X94 = zero(X92) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[injection_properties_2])])]) ).

fof(c_0_27,plain,
    ! [X19,X20,X21,X22] :
      ( ( ~ element(X22,X20)
        | element(apply(X19,X22),X21)
        | ~ morphism(X19,X20,X21) )
      & ( apply(X19,zero(X20)) = zero(X21)
        | ~ morphism(X19,X20,X21) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[morphism])])])]) ).

cnf(c_0_28,plain,
    ( apply(h,apply(beta,X1)) = apply(delta,apply(g,X1))
    | ~ element(X1,X2)
    | ~ morphism(g,X2,e)
    | ~ morphism(h,X3,r)
    | ~ morphism(beta,X2,X3) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_29,plain,
    morphism(g,b,e),
    inference(split_conjunct,[status(thm)],[g_morphism]) ).

fof(c_0_30,plain,
    ! [X95,X96,X97] :
      ( ( element(esk9_3(X95,X96,X97),X96)
        | ~ morphism(X95,X96,X97)
        | injection(X95) )
      & ( apply(X95,esk9_3(X95,X96,X97)) = zero(X97)
        | ~ morphism(X95,X96,X97)
        | injection(X95) )
      & ( esk9_3(X95,X96,X97) != zero(X96)
        | ~ morphism(X95,X96,X97)
        | injection(X95) ) ),
    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_injection_2])])])])])]) ).

fof(c_0_31,negated_conjecture,
    ~ injection(g),
    inference(fof_simplification,[status(thm)],[c_0_24]) ).

cnf(c_0_32,plain,
    ( apply(gamma,apply(f,X1)) = apply(g,apply(alpha,X1))
    | ~ element(X1,X2)
    | ~ morphism(gamma,X3,X4)
    | ~ morphism(f,X2,X3)
    | ~ morphism(g,X5,X4)
    | ~ morphism(alpha,X2,X5) ),
    inference(spm,[status(thm)],[c_0_20,c_0_25]) ).

cnf(c_0_33,plain,
    morphism(gamma,d,e),
    inference(split_conjunct,[status(thm)],[gamma_morphism]) ).

fof(c_0_34,plain,
    ! [X43,X44,X45,X46,X47,X48,X50,X51] :
      ( ( element(esk5_6(X43,X44,X45,X46,X47,X48),X45)
        | ~ element(X48,X46)
        | apply(X44,X48) != zero(X47)
        | ~ exact(X43,X44)
        | ~ morphism(X43,X45,X46)
        | ~ morphism(X44,X46,X47) )
      & ( apply(X43,esk5_6(X43,X44,X45,X46,X47,X48)) = X48
        | ~ element(X48,X46)
        | apply(X44,X48) != zero(X47)
        | ~ exact(X43,X44)
        | ~ morphism(X43,X45,X46)
        | ~ morphism(X44,X46,X47) )
      & ( element(X50,X46)
        | ~ element(X51,X45)
        | apply(X43,X51) != X50
        | ~ exact(X43,X44)
        | ~ morphism(X43,X45,X46)
        | ~ morphism(X44,X46,X47) )
      & ( apply(X44,X50) = zero(X47)
        | ~ element(X51,X45)
        | apply(X43,X51) != X50
        | ~ exact(X43,X44)
        | ~ morphism(X43,X45,X46)
        | ~ morphism(X44,X46,X47) ) ),
    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)],[exact_properties])])])])])]) ).

cnf(c_0_35,plain,
    ( X4 = zero(X2)
    | ~ injection(X1)
    | ~ morphism(X1,X2,X3)
    | ~ element(X4,X2)
    | apply(X1,X4) != zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_36,plain,
    morphism(h,c,r),
    inference(split_conjunct,[status(thm)],[h_morphism]) ).

cnf(c_0_37,hypothesis,
    injection(h),
    inference(split_conjunct,[status(thm)],[h_injection]) ).

cnf(c_0_38,plain,
    ( element(apply(X3,X1),X4)
    | ~ element(X1,X2)
    | ~ morphism(X3,X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_39,plain,
    morphism(beta,b,c),
    inference(split_conjunct,[status(thm)],[beta_morphism]) ).

cnf(c_0_40,plain,
    ( apply(h,apply(beta,X1)) = apply(delta,apply(g,X1))
    | ~ element(X1,b)
    | ~ morphism(h,X2,r)
    | ~ morphism(beta,b,X2) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_41,plain,
    ( element(esk9_3(X1,X2,X3),X2)
    | injection(X1)
    | ~ morphism(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_42,negated_conjecture,
    ~ injection(g),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_43,plain,
    ( apply(X1,esk9_3(X1,X2,X3)) = zero(X3)
    | injection(X1)
    | ~ morphism(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_44,plain,
    ( apply(X1,zero(X2)) = zero(X3)
    | ~ morphism(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_45,plain,
    ( apply(gamma,apply(f,X1)) = apply(g,apply(alpha,X1))
    | ~ element(X1,X2)
    | ~ morphism(f,X2,d)
    | ~ morphism(g,X3,e)
    | ~ morphism(alpha,X2,X3) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_46,plain,
    morphism(f,a,d),
    inference(split_conjunct,[status(thm)],[f_morphism]) ).

cnf(c_0_47,plain,
    ( element(esk5_6(X1,X2,X3,X4,X5,X6),X3)
    | ~ element(X6,X4)
    | apply(X2,X6) != zero(X5)
    | ~ exact(X1,X2)
    | ~ morphism(X1,X3,X4)
    | ~ morphism(X2,X4,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_48,plain,
    ( apply(X1,esk5_6(X1,X2,X3,X4,X5,X6)) = X6
    | ~ element(X6,X4)
    | apply(X2,X6) != zero(X5)
    | ~ exact(X1,X2)
    | ~ morphism(X1,X3,X4)
    | ~ morphism(X2,X4,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_49,plain,
    ( X1 = zero(c)
    | apply(h,X1) != zero(r)
    | ~ element(X1,c) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).

cnf(c_0_50,plain,
    ( element(apply(beta,X1),c)
    | ~ element(X1,b) ),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_51,plain,
    ( apply(h,apply(beta,X1)) = apply(delta,apply(g,X1))
    | ~ element(X1,b) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_36]),c_0_39])]) ).

cnf(c_0_52,plain,
    element(esk9_3(g,b,e),b),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_29]),c_0_42]) ).

cnf(c_0_53,plain,
    apply(g,esk9_3(g,b,e)) = zero(e),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_29]),c_0_42]) ).

cnf(c_0_54,plain,
    apply(delta,zero(e)) = zero(r),
    inference(spm,[status(thm)],[c_0_44,c_0_23]) ).

cnf(c_0_55,plain,
    ( apply(gamma,apply(f,X1)) = apply(g,apply(alpha,X1))
    | ~ element(X1,a)
    | ~ morphism(g,X2,e)
    | ~ morphism(alpha,a,X2) ),
    inference(spm,[status(thm)],[c_0_45,c_0_46]) ).

cnf(c_0_56,plain,
    morphism(alpha,a,b),
    inference(split_conjunct,[status(thm)],[alpha_morphism]) ).

cnf(c_0_57,plain,
    ( element(esk5_6(X1,beta,X2,b,c,X3),X2)
    | apply(beta,X3) != zero(c)
    | ~ exact(X1,beta)
    | ~ element(X3,b)
    | ~ morphism(X1,X2,b) ),
    inference(spm,[status(thm)],[c_0_47,c_0_39]) ).

cnf(c_0_58,plain,
    exact(alpha,beta),
    inference(split_conjunct,[status(thm)],[alpha_beta_exact]) ).

cnf(c_0_59,plain,
    ( apply(X1,esk5_6(X1,beta,X2,b,c,X3)) = X3
    | apply(beta,X3) != zero(c)
    | ~ exact(X1,beta)
    | ~ element(X3,b)
    | ~ morphism(X1,X2,b) ),
    inference(spm,[status(thm)],[c_0_48,c_0_39]) ).

cnf(c_0_60,plain,
    ( apply(beta,X1) = zero(c)
    | apply(h,apply(beta,X1)) != zero(r)
    | ~ element(X1,b) ),
    inference(spm,[status(thm)],[c_0_49,c_0_50]) ).

cnf(c_0_61,plain,
    apply(h,apply(beta,esk9_3(g,b,e))) = zero(r),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_54]) ).

cnf(c_0_62,plain,
    injection(gamma),
    inference(split_conjunct,[status(thm)],[gamma_injection]) ).

cnf(c_0_63,plain,
    ( apply(gamma,apply(f,X1)) = apply(g,apply(alpha,X1))
    | ~ element(X1,a) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_29]),c_0_56])]) ).

cnf(c_0_64,plain,
    ( element(esk5_6(alpha,beta,a,b,c,X1),a)
    | apply(beta,X1) != zero(c)
    | ~ element(X1,b) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_56]),c_0_58])]) ).

cnf(c_0_65,plain,
    ( apply(alpha,esk5_6(alpha,beta,a,b,c,X1)) = X1
    | apply(beta,X1) != zero(c)
    | ~ element(X1,b) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_56]),c_0_58])]) ).

cnf(c_0_66,plain,
    apply(beta,esk9_3(g,b,e)) = zero(c),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_52])]) ).

cnf(c_0_67,plain,
    ( X1 = zero(d)
    | apply(gamma,X1) != zero(e)
    | ~ element(X1,d) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_33]),c_0_62])]) ).

cnf(c_0_68,plain,
    ( element(apply(f,X1),d)
    | ~ element(X1,a) ),
    inference(spm,[status(thm)],[c_0_38,c_0_46]) ).

cnf(c_0_69,plain,
    ( apply(gamma,apply(f,esk5_6(alpha,beta,a,b,c,X1))) = apply(g,apply(alpha,esk5_6(alpha,beta,a,b,c,X1)))
    | apply(beta,X1) != zero(c)
    | ~ element(X1,b) ),
    inference(spm,[status(thm)],[c_0_63,c_0_64]) ).

cnf(c_0_70,plain,
    apply(alpha,esk5_6(alpha,beta,a,b,c,esk9_3(g,b,e))) = esk9_3(g,b,e),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_52]),c_0_66])]) ).

cnf(c_0_71,hypothesis,
    injection(f),
    inference(split_conjunct,[status(thm)],[f_injection]) ).

cnf(c_0_72,plain,
    ( apply(f,X1) = zero(d)
    | apply(gamma,apply(f,X1)) != zero(e)
    | ~ element(X1,a) ),
    inference(spm,[status(thm)],[c_0_67,c_0_68]) ).

cnf(c_0_73,plain,
    apply(gamma,apply(f,esk5_6(alpha,beta,a,b,c,esk9_3(g,b,e)))) = zero(e),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_52]),c_0_70]),c_0_53]),c_0_66])]) ).

cnf(c_0_74,plain,
    ( X1 = zero(a)
    | apply(f,X1) != zero(d)
    | ~ element(X1,a) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_46]),c_0_71])]) ).

cnf(c_0_75,plain,
    ( apply(f,esk5_6(alpha,beta,a,b,c,esk9_3(g,b,e))) = zero(d)
    | ~ element(esk5_6(alpha,beta,a,b,c,esk9_3(g,b,e)),a) ),
    inference(spm,[status(thm)],[c_0_72,c_0_73]) ).

cnf(c_0_76,plain,
    ( injection(X1)
    | esk9_3(X1,X2,X3) != zero(X2)
    | ~ morphism(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_77,plain,
    ( esk5_6(alpha,beta,a,b,c,X1) = zero(a)
    | apply(f,esk5_6(alpha,beta,a,b,c,X1)) != zero(d)
    | apply(beta,X1) != zero(c)
    | ~ element(X1,b) ),
    inference(spm,[status(thm)],[c_0_74,c_0_64]) ).

cnf(c_0_78,plain,
    apply(f,esk5_6(alpha,beta,a,b,c,esk9_3(g,b,e))) = zero(d),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_64]),c_0_66]),c_0_52])]) ).

cnf(c_0_79,negated_conjecture,
    ( esk9_3(g,X1,X2) != zero(X1)
    | ~ morphism(g,X1,X2) ),
    inference(spm,[status(thm)],[c_0_42,c_0_76]) ).

cnf(c_0_80,plain,
    esk5_6(alpha,beta,a,b,c,esk9_3(g,b,e)) = zero(a),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_66]),c_0_52])]) ).

cnf(c_0_81,plain,
    apply(alpha,zero(a)) = zero(b),
    inference(spm,[status(thm)],[c_0_44,c_0_56]) ).

cnf(c_0_82,negated_conjecture,
    esk9_3(g,b,e) != zero(b),
    inference(spm,[status(thm)],[c_0_79,c_0_29]) ).

cnf(c_0_83,plain,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_80]),c_0_81]),c_0_82]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.09  % Problem  : HAL001+2 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.10  % Command  : enigmatic-eprover.py %s %d 1
% 0.10/0.29  % Computer : n032.cluster.edu
% 0.10/0.29  % Model    : x86_64 x86_64
% 0.10/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29  % Memory   : 8042.1875MB
% 0.10/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29  % CPULimit : 300
% 0.10/0.29  % WCLimit  : 600
% 0.10/0.29  % DateTime : Tue Jun  7 20:55:07 EDT 2022
% 0.10/0.29  % CPUTime  : 
% 0.14/0.36  # ENIGMATIC: Selected SinE mode:
% 0.14/0.37  # Parsing /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.37  # Filter: axfilter_auto   0 goes into file theBenchmark_axfilter_auto   0.p
% 0.14/0.37  # Filter: axfilter_auto   1 goes into file theBenchmark_axfilter_auto   1.p
% 0.14/0.37  # Filter: axfilter_auto   2 goes into file theBenchmark_axfilter_auto   2.p
% 18.61/3.56  # ENIGMATIC: Solved by autoschedule:
% 18.61/3.56  # No SInE strategy applied
% 18.61/3.56  # Trying AutoSched0 for 150 seconds
% 18.61/3.56  # AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S059I
% 18.61/3.56  # and selection function SelectComplexExceptUniqMaxPosHorn.
% 18.61/3.56  #
% 18.61/3.56  # Preprocessing time       : 0.016 s
% 18.61/3.56  # Presaturation interreduction done
% 18.61/3.56  
% 18.61/3.56  # Proof found!
% 18.61/3.56  # SZS status Theorem
% 18.61/3.56  # SZS output start CNFRefutation
% See solution above
% 18.61/3.56  # Training examples: 0 positive, 0 negative
% 18.61/3.56  
% 18.61/3.56  # -------------------------------------------------
% 18.61/3.56  # User time                : 1.332 s
% 18.61/3.56  # System time              : 0.046 s
% 18.61/3.56  # Total time               : 1.378 s
% 18.61/3.56  # Maximum resident set size: 7124 pages
% 18.61/3.56  
%------------------------------------------------------------------------------