TSTP Solution File: HAL002+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : HAL002+1 : TPTP v8.1.2. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n027.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 01:53:27 EDT 2023

% Result   : Theorem 0.17s 0.58s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   33
% Syntax   : Number of formulae    :   97 (  10 unt;  22 typ;   0 def)
%            Number of atoms       :  227 (  64 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  243 (  91   ~; 114   |;  21   &)
%                                         (   2 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   55 (  19   >;  36   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-4 aty)
%            Number of functors    :   15 (  15 usr;   3 con; 0-6 aty)
%            Number of variables   :  136 (   6 sgn;  67   !;   0   ?;   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,
    injection_2: $i > $o ).

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

tff(decl_33,type,
    any1: $i ).

tff(decl_34,type,
    any2: $i ).

tff(decl_35,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_36,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_37,type,
    esk3_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_38,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_39,type,
    esk5_6: ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_40,type,
    esk6_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_41,type,
    esk7_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_42,type,
    esk8_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_43,type,
    esk9_3: ( $i * $i * $i ) > $i ).

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

fof(subtract_to_0,axiom,
    ! [X2,X4] :
      ( element(X4,X2)
     => subtract(X2,X4,X4) = zero(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HAL001+0.ax',subtract_to_0) ).

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_2(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',properties_for_injection_2) ).

fof(my,conjecture,
    ( injection(x)
  <=> injection_2(x) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',my) ).

fof(x_morphism,hypothesis,
    morphism(x,any1,any2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_morphism) ).

fof(properties_for_injection,axiom,
    ! [X1,X2,X3] :
      ( ( morphism(X1,X2,X3)
        & ! [X5,X6] :
            ( ( element(X5,X2)
              & element(X6,X2)
              & apply(X1,X5) = apply(X1,X6) )
           => X5 = X6 ) )
     => injection(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HAL001+0.ax',properties_for_injection) ).

fof(subtract_distribution,axiom,
    ! [X1,X2,X3] :
      ( morphism(X1,X2,X3)
     => ! [X5,X6] :
          ( ( element(X5,X2)
            & element(X6,X2) )
         => apply(X1,subtract(X2,X5,X6)) = subtract(X3,apply(X1,X5),apply(X1,X6)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HAL001+0.ax',subtract_distribution) ).

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

fof(injection_properties_2,axiom,
    ! [X1,X2,X3] :
      ( ( injection_2(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(injection_properties,axiom,
    ! [X1,X2,X3] :
      ( ( injection(X1)
        & morphism(X1,X2,X3) )
     => ! [X5,X6] :
          ( ( element(X5,X2)
            & element(X6,X2)
            & apply(X1,X5) = apply(X1,X6) )
         => X5 = X6 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HAL001+0.ax',injection_properties) ).

fof(c_0_11,plain,
    ! [X78,X79,X80] :
      ( ~ element(X79,X78)
      | ~ element(X80,X78)
      | element(subtract(X78,X79,X80),X78) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subtract_in_domain])]) ).

fof(c_0_12,plain,
    ! [X81,X82] :
      ( ~ element(X82,X81)
      | subtract(X81,X82,X82) = zero(X81) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subtract_to_0])]) ).

fof(c_0_13,plain,
    ! [X95,X96,X97] :
      ( ( element(esk9_3(X95,X96,X97),X96)
        | ~ morphism(X95,X96,X97)
        | injection_2(X95) )
      & ( apply(X95,esk9_3(X95,X96,X97)) = zero(X97)
        | ~ morphism(X95,X96,X97)
        | injection_2(X95) )
      & ( esk9_3(X95,X96,X97) != zero(X96)
        | ~ morphism(X95,X96,X97)
        | injection_2(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_14,negated_conjecture,
    ~ ( injection(x)
    <=> injection_2(x) ),
    inference(assume_negation,[status(cth)],[my]) ).

cnf(c_0_15,plain,
    ( element(subtract(X2,X1,X3),X2)
    | ~ element(X1,X2)
    | ~ element(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_16,plain,
    ( subtract(X2,X1,X1) = zero(X2)
    | ~ element(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_17,plain,
    ( element(esk9_3(X1,X2,X3),X2)
    | injection_2(X1)
    | ~ morphism(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_18,hypothesis,
    morphism(x,any1,any2),
    inference(split_conjunct,[status(thm)],[x_morphism]) ).

fof(c_0_19,plain,
    ! [X28,X29,X30] :
      ( ( element(esk1_2(X28,X29),X29)
        | ~ morphism(X28,X29,X30)
        | injection(X28) )
      & ( element(esk2_2(X28,X29),X29)
        | ~ morphism(X28,X29,X30)
        | injection(X28) )
      & ( apply(X28,esk1_2(X28,X29)) = apply(X28,esk2_2(X28,X29))
        | ~ morphism(X28,X29,X30)
        | injection(X28) )
      & ( esk1_2(X28,X29) != esk2_2(X28,X29)
        | ~ morphism(X28,X29,X30)
        | injection(X28) ) ),
    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])])])])])]) ).

fof(c_0_20,negated_conjecture,
    ( ( ~ injection(x)
      | ~ injection_2(x) )
    & ( injection(x)
      | injection_2(x) ) ),
    inference(fof_nnf,[status(thm)],[c_0_14]) ).

cnf(c_0_21,plain,
    ( element(zero(X1),X1)
    | ~ element(X2,X1) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_22,hypothesis,
    ( injection_2(x)
    | element(esk9_3(x,any1,any2),any1) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

fof(c_0_23,plain,
    ! [X86,X87,X88,X89,X90] :
      ( ~ morphism(X86,X87,X88)
      | ~ element(X89,X87)
      | ~ element(X90,X87)
      | apply(X86,subtract(X87,X89,X90)) = subtract(X88,apply(X86,X89),apply(X86,X90)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subtract_distribution])])]) ).

fof(c_0_24,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_25,plain,
    ( element(esk1_2(X1,X2),X2)
    | injection(X1)
    | ~ morphism(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_26,negated_conjecture,
    ( ~ injection(x)
    | ~ injection_2(x) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_27,hypothesis,
    ( injection_2(x)
    | element(zero(any1),any1) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_28,plain,
    ( apply(X1,subtract(X2,X4,X5)) = subtract(X3,apply(X1,X4),apply(X1,X5))
    | ~ morphism(X1,X2,X3)
    | ~ element(X4,X2)
    | ~ element(X5,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_29,plain,
    ( apply(X1,zero(X2)) = zero(X3)
    | ~ morphism(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_30,hypothesis,
    ( injection(x)
    | element(esk1_2(x,any1),any1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_18]) ).

cnf(c_0_31,negated_conjecture,
    ( element(zero(any1),any1)
    | ~ injection(x) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

fof(c_0_32,plain,
    ! [X83,X84,X85] :
      ( ~ element(X84,X83)
      | ~ element(X85,X83)
      | subtract(X83,X84,subtract(X83,X84,X85)) = X85 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subtract_cancellation])]) ).

cnf(c_0_33,hypothesis,
    ( subtract(any2,apply(x,X1),apply(x,X2)) = apply(x,subtract(any1,X1,X2))
    | ~ element(X2,any1)
    | ~ element(X1,any1) ),
    inference(spm,[status(thm)],[c_0_28,c_0_18]) ).

cnf(c_0_34,hypothesis,
    apply(x,zero(any1)) = zero(any2),
    inference(spm,[status(thm)],[c_0_29,c_0_18]) ).

cnf(c_0_35,hypothesis,
    element(zero(any1),any1),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_30]),c_0_31]) ).

cnf(c_0_36,plain,
    ( apply(X1,esk1_2(X1,X2)) = apply(X1,esk2_2(X1,X2))
    | injection(X1)
    | ~ morphism(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_37,plain,
    ( element(esk2_2(X1,X2),X2)
    | injection(X1)
    | ~ morphism(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_38,plain,
    ( element(apply(X3,X1),X4)
    | ~ element(X1,X2)
    | ~ morphism(X3,X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

fof(c_0_39,plain,
    ! [X91,X92,X93,X94] :
      ( ~ injection_2(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])])]) ).

cnf(c_0_40,plain,
    ( subtract(X2,X1,subtract(X2,X1,X3)) = X3
    | ~ element(X1,X2)
    | ~ element(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_41,hypothesis,
    ( subtract(any2,apply(x,X1),zero(any2)) = apply(x,subtract(any1,X1,zero(any1)))
    | ~ element(X1,any1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).

cnf(c_0_42,hypothesis,
    ( apply(x,esk2_2(x,any1)) = apply(x,esk1_2(x,any1))
    | injection(x) ),
    inference(spm,[status(thm)],[c_0_36,c_0_18]) ).

cnf(c_0_43,hypothesis,
    ( injection(x)
    | element(esk2_2(x,any1),any1) ),
    inference(spm,[status(thm)],[c_0_37,c_0_18]) ).

cnf(c_0_44,hypothesis,
    ( element(apply(x,X1),any2)
    | ~ element(X1,any1) ),
    inference(spm,[status(thm)],[c_0_38,c_0_18]) ).

cnf(c_0_45,plain,
    ( X4 = zero(X2)
    | ~ injection_2(X1)
    | ~ morphism(X1,X2,X3)
    | ~ element(X4,X2)
    | apply(X1,X4) != zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_46,plain,
    ( subtract(X1,X2,zero(X1)) = X2
    | ~ element(X2,X1) ),
    inference(spm,[status(thm)],[c_0_40,c_0_16]) ).

cnf(c_0_47,hypothesis,
    ( subtract(any2,apply(x,esk1_2(x,any1)),zero(any2)) = apply(x,subtract(any1,esk2_2(x,any1),zero(any1)))
    | injection(x) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).

cnf(c_0_48,hypothesis,
    ( injection(x)
    | element(apply(x,esk1_2(x,any1)),any2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_42]),c_0_43]) ).

cnf(c_0_49,hypothesis,
    ( X1 = zero(any1)
    | apply(x,X1) != zero(any2)
    | ~ injection_2(x)
    | ~ element(X1,any1) ),
    inference(spm,[status(thm)],[c_0_45,c_0_18]) ).

cnf(c_0_50,negated_conjecture,
    ( injection(x)
    | injection_2(x) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_51,hypothesis,
    ( subtract(any2,apply(x,X1),apply(x,subtract(any1,X1,X2))) = apply(x,X2)
    | ~ element(X2,any1)
    | ~ element(X1,any1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_33]),c_0_44]),c_0_44]) ).

cnf(c_0_52,hypothesis,
    ( apply(x,subtract(any1,esk2_2(x,any1),zero(any1))) = apply(x,esk1_2(x,any1))
    | injection(x) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).

cnf(c_0_53,negated_conjecture,
    ( X1 = zero(any1)
    | injection(x)
    | apply(x,X1) != zero(any2)
    | ~ element(X1,any1) ),
    inference(spm,[status(thm)],[c_0_49,c_0_50]) ).

cnf(c_0_54,hypothesis,
    ( subtract(any2,apply(x,esk2_2(x,any1)),apply(x,esk1_2(x,any1))) = zero(any2)
    | injection(x) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_34]),c_0_35])]),c_0_43]) ).

cnf(c_0_55,negated_conjecture,
    ( subtract(any1,X1,X2) = zero(any1)
    | injection(x)
    | apply(x,subtract(any1,X1,X2)) != zero(any2)
    | ~ element(X2,any1)
    | ~ element(X1,any1) ),
    inference(spm,[status(thm)],[c_0_53,c_0_15]) ).

cnf(c_0_56,hypothesis,
    ( apply(x,subtract(any1,esk2_2(x,any1),esk1_2(x,any1))) = zero(any2)
    | injection(x) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_54]),c_0_43]),c_0_30]) ).

fof(c_0_57,plain,
    ! [X23,X24,X25,X26,X27] :
      ( ~ injection(X23)
      | ~ morphism(X23,X24,X25)
      | ~ element(X26,X24)
      | ~ element(X27,X24)
      | apply(X23,X26) != apply(X23,X27)
      | X26 = X27 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[injection_properties])])]) ).

cnf(c_0_58,negated_conjecture,
    ( subtract(any1,esk2_2(x,any1),esk1_2(x,any1)) = zero(any1)
    | injection(x) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_43]),c_0_30]) ).

cnf(c_0_59,plain,
    ( injection(X1)
    | esk1_2(X1,X2) != esk2_2(X1,X2)
    | ~ morphism(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_60,plain,
    ( X4 = X5
    | ~ injection(X1)
    | ~ morphism(X1,X2,X3)
    | ~ element(X4,X2)
    | ~ element(X5,X2)
    | apply(X1,X4) != apply(X1,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

cnf(c_0_61,negated_conjecture,
    ( subtract(any1,esk2_2(x,any1),zero(any1)) = esk1_2(x,any1)
    | injection(x) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_58]),c_0_43]),c_0_30]) ).

cnf(c_0_62,hypothesis,
    ( injection(x)
    | esk2_2(x,any1) != esk1_2(x,any1) ),
    inference(spm,[status(thm)],[c_0_59,c_0_18]) ).

cnf(c_0_63,hypothesis,
    ( X1 = X2
    | apply(x,X1) != apply(x,X2)
    | ~ injection(x)
    | ~ element(X2,any1)
    | ~ element(X1,any1) ),
    inference(spm,[status(thm)],[c_0_60,c_0_18]) ).

cnf(c_0_64,negated_conjecture,
    injection(x),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_61]),c_0_43]),c_0_62]) ).

cnf(c_0_65,plain,
    ( apply(X1,esk9_3(X1,X2,X3)) = zero(X3)
    | injection_2(X1)
    | ~ morphism(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_66,hypothesis,
    ( X1 = X2
    | apply(x,X1) != apply(x,X2)
    | ~ element(X2,any1)
    | ~ element(X1,any1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64])]) ).

cnf(c_0_67,hypothesis,
    ( apply(x,esk9_3(x,any1,any2)) = zero(any2)
    | injection_2(x) ),
    inference(spm,[status(thm)],[c_0_65,c_0_18]) ).

cnf(c_0_68,negated_conjecture,
    ~ injection_2(x),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_64])]) ).

cnf(c_0_69,hypothesis,
    ( X1 = zero(any1)
    | apply(x,X1) != zero(any2)
    | ~ element(X1,any1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_34]),c_0_35])]) ).

cnf(c_0_70,hypothesis,
    apply(x,esk9_3(x,any1,any2)) = zero(any2),
    inference(sr,[status(thm)],[c_0_67,c_0_68]) ).

cnf(c_0_71,hypothesis,
    element(esk9_3(x,any1,any2),any1),
    inference(sr,[status(thm)],[c_0_22,c_0_68]) ).

cnf(c_0_72,plain,
    ( injection_2(X1)
    | esk9_3(X1,X2,X3) != zero(X2)
    | ~ morphism(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_73,hypothesis,
    esk9_3(x,any1,any2) = zero(any1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71])]) ).

cnf(c_0_74,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_18])]),c_0_68]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : HAL002+1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.33  % Computer : n027.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit   : 300
% 0.14/0.33  % WCLimit    : 300
% 0.14/0.33  % DateTime   : Mon Aug 28 02:54:51 EDT 2023
% 0.14/0.33  % CPUTime  : 
% 0.17/0.54  start to proof: theBenchmark
% 0.17/0.58  % Version  : CSE_E---1.5
% 0.17/0.58  % Problem  : theBenchmark.p
% 0.17/0.58  % Proof found
% 0.17/0.58  % SZS status Theorem for theBenchmark.p
% 0.17/0.58  % SZS output start Proof
% See solution above
% 0.17/0.58  % Total time : 0.033000 s
% 0.17/0.58  % SZS output end Proof
% 0.17/0.58  % Total time : 0.036000 s
%------------------------------------------------------------------------------