TSTP Solution File: HEN009-1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : HEN009-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n022.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 01:54:23 EDT 2023

% Result   : Unsatisfiable 1.33s 1.51s
% Output   : CNFRefutation 1.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   34
%            Number of leaves      :   22
% Syntax   : Number of formulae    :  113 (  47 unt;   9 typ;   0 def)
%            Number of atoms       :  199 (  32 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :  192 (  97   ~;  95   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   3   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :  202 (  35 sgn;   0   !;   0   ?;   0   :)

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

tff(decl_23,type,
    zero: $i ).

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

tff(decl_25,type,
    identity: $i ).

tff(decl_26,type,
    divide: ( $i * $i ) > $i ).

tff(decl_27,type,
    a: $i ).

tff(decl_28,type,
    idQa: $i ).

tff(decl_29,type,
    idQ_idQa: $i ).

tff(decl_30,type,
    idQ__idQ_idQa: $i ).

cnf(divisor_existence,axiom,
    ( less_equal(X3,X1)
    | ~ quotient(X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).

cnf(closure,axiom,
    quotient(X1,X2,divide(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',closure) ).

cnf(quotient_property,axiom,
    ( less_equal(X7,X8)
    | ~ quotient(X1,X2,X3)
    | ~ quotient(X2,X4,X5)
    | ~ quotient(X1,X4,X6)
    | ~ quotient(X6,X5,X7)
    | ~ quotient(X3,X4,X8) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',quotient_property) ).

cnf(quotient_less_equal,axiom,
    ( quotient(X1,X2,zero)
    | ~ less_equal(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',quotient_less_equal) ).

cnf(less_equal_and_equal,axiom,
    ( X1 = X2
    | ~ less_equal(X1,X2)
    | ~ less_equal(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).

cnf(less_equal_quotient,axiom,
    ( less_equal(X1,X2)
    | ~ quotient(X1,X2,zero) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',less_equal_quotient) ).

cnf(zero_is_smallest,axiom,
    less_equal(zero,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',zero_is_smallest) ).

cnf(identity_is_largest,axiom,
    less_equal(X1,identity),
    file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',identity_is_largest) ).

cnf(identity_divide_idQa,hypothesis,
    quotient(identity,idQa,idQ_idQa),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_idQa) ).

cnf(identity_divide_idQ_idQa,hypothesis,
    quotient(identity,idQ_idQa,idQ__idQ_idQa),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_idQ_idQa) ).

cnf(identity_divide_a,hypothesis,
    quotient(identity,a,idQa),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_a) ).

cnf(well_defined,axiom,
    ( X3 = X4
    | ~ quotient(X1,X2,X3)
    | ~ quotient(X1,X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',well_defined) ).

cnf(prove_one_inversion_equals_three,negated_conjecture,
    idQa != idQ__idQ_idQa,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_one_inversion_equals_three) ).

cnf(c_0_13,axiom,
    ( less_equal(X3,X1)
    | ~ quotient(X1,X2,X3) ),
    divisor_existence ).

cnf(c_0_14,axiom,
    quotient(X1,X2,divide(X1,X2)),
    closure ).

cnf(c_0_15,axiom,
    ( less_equal(X7,X8)
    | ~ quotient(X1,X2,X3)
    | ~ quotient(X2,X4,X5)
    | ~ quotient(X1,X4,X6)
    | ~ quotient(X6,X5,X7)
    | ~ quotient(X3,X4,X8) ),
    quotient_property ).

cnf(c_0_16,axiom,
    ( quotient(X1,X2,zero)
    | ~ less_equal(X1,X2) ),
    quotient_less_equal ).

cnf(c_0_17,plain,
    less_equal(divide(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_18,plain,
    ( less_equal(divide(X1,X2),X3)
    | ~ quotient(X4,X5,X3)
    | ~ quotient(X6,X5,X2)
    | ~ quotient(X7,X5,X1)
    | ~ quotient(X7,X6,X4) ),
    inference(spm,[status(thm)],[c_0_15,c_0_14]) ).

cnf(c_0_19,plain,
    quotient(divide(X1,X2),X1,zero),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_20,plain,
    ( less_equal(divide(X1,X2),zero)
    | ~ quotient(X3,X4,divide(X5,X6))
    | ~ quotient(X4,X5,X2)
    | ~ quotient(X3,X5,X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_21,plain,
    ( less_equal(divide(X1,X2),zero)
    | ~ quotient(X3,X4,X2)
    | ~ quotient(X4,X4,X1) ),
    inference(spm,[status(thm)],[c_0_20,c_0_14]) ).

cnf(c_0_22,axiom,
    ( X1 = X2
    | ~ less_equal(X1,X2)
    | ~ less_equal(X2,X1) ),
    less_equal_and_equal ).

cnf(c_0_23,axiom,
    ( less_equal(X1,X2)
    | ~ quotient(X1,X2,zero) ),
    less_equal_quotient ).

cnf(c_0_24,plain,
    ( less_equal(divide(X1,zero),zero)
    | ~ quotient(X2,X2,X1) ),
    inference(spm,[status(thm)],[c_0_21,c_0_19]) ).

cnf(c_0_25,axiom,
    less_equal(zero,X1),
    zero_is_smallest ).

cnf(c_0_26,plain,
    ( X1 = X2
    | ~ quotient(X2,X1,zero)
    | ~ less_equal(X1,X2) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_27,plain,
    less_equal(divide(divide(X1,X1),zero),zero),
    inference(spm,[status(thm)],[c_0_24,c_0_14]) ).

cnf(c_0_28,plain,
    quotient(zero,X1,zero),
    inference(spm,[status(thm)],[c_0_16,c_0_25]) ).

cnf(c_0_29,plain,
    divide(divide(X1,X1),zero) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).

cnf(c_0_30,plain,
    ( X1 = X2
    | ~ quotient(X2,X1,zero)
    | ~ quotient(X1,X2,zero) ),
    inference(spm,[status(thm)],[c_0_26,c_0_23]) ).

cnf(c_0_31,plain,
    quotient(divide(X1,X1),zero,zero),
    inference(spm,[status(thm)],[c_0_14,c_0_29]) ).

cnf(c_0_32,plain,
    divide(X1,X1) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_28])]) ).

cnf(c_0_33,plain,
    quotient(X1,X1,zero),
    inference(spm,[status(thm)],[c_0_14,c_0_32]) ).

cnf(c_0_34,plain,
    ( less_equal(divide(X1,X2),zero)
    | ~ quotient(X3,X4,X2)
    | ~ quotient(X5,X4,X1)
    | ~ quotient(X5,X3,X4) ),
    inference(spm,[status(thm)],[c_0_18,c_0_33]) ).

cnf(c_0_35,plain,
    ( less_equal(divide(X1,zero),zero)
    | ~ quotient(X2,zero,X3)
    | ~ quotient(X2,X3,X1) ),
    inference(spm,[status(thm)],[c_0_34,c_0_28]) ).

cnf(c_0_36,plain,
    ( less_equal(divide(X1,zero),zero)
    | ~ quotient(X2,divide(X2,zero),X1) ),
    inference(spm,[status(thm)],[c_0_35,c_0_14]) ).

cnf(c_0_37,plain,
    less_equal(divide(divide(X1,divide(X1,zero)),zero),zero),
    inference(spm,[status(thm)],[c_0_36,c_0_14]) ).

cnf(c_0_38,axiom,
    less_equal(X1,identity),
    identity_is_largest ).

cnf(c_0_39,plain,
    divide(divide(X1,divide(X1,zero)),zero) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_37]),c_0_28])]) ).

cnf(c_0_40,plain,
    ( less_equal(divide(X1,X2),zero)
    | ~ quotient(X3,X4,zero)
    | ~ quotient(X4,X5,X2)
    | ~ quotient(X3,X5,X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_28]) ).

cnf(c_0_41,plain,
    quotient(X1,identity,zero),
    inference(spm,[status(thm)],[c_0_16,c_0_38]) ).

cnf(c_0_42,plain,
    quotient(divide(X1,divide(X1,zero)),zero,zero),
    inference(spm,[status(thm)],[c_0_14,c_0_39]) ).

cnf(c_0_43,plain,
    ( less_equal(divide(X1,X2),zero)
    | ~ quotient(identity,X3,X2)
    | ~ quotient(X4,X3,X1) ),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_44,hypothesis,
    quotient(identity,idQa,idQ_idQa),
    identity_divide_idQa ).

cnf(c_0_45,plain,
    divide(X1,divide(X1,zero)) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_42]),c_0_28])]) ).

cnf(c_0_46,hypothesis,
    ( less_equal(divide(X1,idQ_idQa),zero)
    | ~ quotient(X2,idQa,X1) ),
    inference(spm,[status(thm)],[c_0_43,c_0_44]) ).

cnf(c_0_47,plain,
    ( less_equal(divide(X1,X2),divide(X3,X4))
    | ~ quotient(X5,X4,X2)
    | ~ quotient(X6,X4,X1)
    | ~ quotient(X6,X5,X3) ),
    inference(spm,[status(thm)],[c_0_18,c_0_14]) ).

cnf(c_0_48,plain,
    quotient(X1,divide(X1,zero),zero),
    inference(spm,[status(thm)],[c_0_14,c_0_45]) ).

cnf(c_0_49,hypothesis,
    less_equal(divide(divide(X1,idQa),idQ_idQa),zero),
    inference(spm,[status(thm)],[c_0_46,c_0_14]) ).

cnf(c_0_50,plain,
    ( less_equal(divide(X1,zero),divide(X2,X3))
    | ~ quotient(X4,X3,X1)
    | ~ quotient(X4,X3,X2) ),
    inference(spm,[status(thm)],[c_0_47,c_0_33]) ).

cnf(c_0_51,plain,
    divide(X1,zero) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_48]),c_0_19])]) ).

cnf(c_0_52,hypothesis,
    divide(divide(X1,idQa),idQ_idQa) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_49]),c_0_28])]) ).

cnf(c_0_53,plain,
    ( less_equal(X1,divide(X2,X3))
    | ~ quotient(X4,X3,X1)
    | ~ quotient(X4,X3,X2) ),
    inference(rw,[status(thm)],[c_0_50,c_0_51]) ).

cnf(c_0_54,hypothesis,
    quotient(identity,idQ_idQa,idQ__idQ_idQa),
    identity_divide_idQ_idQa ).

cnf(c_0_55,hypothesis,
    quotient(divide(X1,idQa),idQ_idQa,zero),
    inference(spm,[status(thm)],[c_0_14,c_0_52]) ).

cnf(c_0_56,plain,
    ( divide(X1,X2) = X1
    | ~ less_equal(X1,divide(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_22,c_0_17]) ).

cnf(c_0_57,hypothesis,
    ( less_equal(idQ__idQ_idQa,divide(X1,idQ_idQa))
    | ~ quotient(identity,idQ_idQa,X1) ),
    inference(spm,[status(thm)],[c_0_53,c_0_54]) ).

cnf(c_0_58,hypothesis,
    ( less_equal(divide(X1,idQ__idQ_idQa),zero)
    | ~ quotient(X2,idQ_idQa,X1) ),
    inference(spm,[status(thm)],[c_0_43,c_0_54]) ).

cnf(c_0_59,hypothesis,
    ( less_equal(divide(X1,X2),zero)
    | ~ quotient(X3,X4,divide(X5,idQa))
    | ~ quotient(X4,idQ_idQa,X2)
    | ~ quotient(X3,idQ_idQa,X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_55]) ).

cnf(c_0_60,hypothesis,
    divide(idQ__idQ_idQa,idQ_idQa) = idQ__idQ_idQa,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_54])]) ).

cnf(c_0_61,hypothesis,
    quotient(identity,a,idQa),
    identity_divide_a ).

cnf(c_0_62,hypothesis,
    less_equal(divide(divide(X1,idQ_idQa),idQ__idQ_idQa),zero),
    inference(spm,[status(thm)],[c_0_58,c_0_14]) ).

cnf(c_0_63,hypothesis,
    ( less_equal(divide(X1,X2),zero)
    | ~ quotient(idQa,idQ_idQa,X2)
    | ~ quotient(X3,idQ_idQa,X1) ),
    inference(spm,[status(thm)],[c_0_59,c_0_14]) ).

cnf(c_0_64,hypothesis,
    quotient(idQ__idQ_idQa,idQ_idQa,idQ__idQ_idQa),
    inference(spm,[status(thm)],[c_0_14,c_0_60]) ).

cnf(c_0_65,hypothesis,
    ( less_equal(divide(X1,idQa),zero)
    | ~ quotient(X2,a,X1) ),
    inference(spm,[status(thm)],[c_0_43,c_0_61]) ).

cnf(c_0_66,hypothesis,
    divide(divide(X1,idQ_idQa),idQ__idQ_idQa) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_62]),c_0_28])]) ).

cnf(c_0_67,hypothesis,
    ( less_equal(divide(idQ__idQ_idQa,X1),zero)
    | ~ quotient(idQa,idQ_idQa,X1) ),
    inference(spm,[status(thm)],[c_0_63,c_0_64]) ).

cnf(c_0_68,plain,
    ( less_equal(divide(X1,divide(X2,X3)),divide(X4,X3))
    | ~ quotient(X5,X3,X1)
    | ~ quotient(X5,X2,X4) ),
    inference(spm,[status(thm)],[c_0_47,c_0_14]) ).

cnf(c_0_69,hypothesis,
    less_equal(divide(divide(X1,a),idQa),zero),
    inference(spm,[status(thm)],[c_0_65,c_0_14]) ).

cnf(c_0_70,hypothesis,
    quotient(divide(X1,idQ_idQa),idQ__idQ_idQa,zero),
    inference(spm,[status(thm)],[c_0_14,c_0_66]) ).

cnf(c_0_71,hypothesis,
    ( divide(idQ__idQ_idQa,X1) = zero
    | ~ quotient(idQa,idQ_idQa,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_67]),c_0_28])]) ).

cnf(c_0_72,hypothesis,
    ( less_equal(divide(idQ_idQa,divide(X1,idQa)),divide(X2,idQa))
    | ~ quotient(identity,X1,X2) ),
    inference(spm,[status(thm)],[c_0_68,c_0_44]) ).

cnf(c_0_73,hypothesis,
    divide(divide(X1,a),idQa) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_69]),c_0_28])]) ).

cnf(c_0_74,hypothesis,
    ( divide(X1,idQ_idQa) = idQ__idQ_idQa
    | ~ quotient(idQ__idQ_idQa,divide(X1,idQ_idQa),zero) ),
    inference(spm,[status(thm)],[c_0_30,c_0_70]) ).

cnf(c_0_75,hypothesis,
    ( quotient(idQ__idQ_idQa,X1,zero)
    | ~ quotient(idQa,idQ_idQa,X1) ),
    inference(spm,[status(thm)],[c_0_14,c_0_71]) ).

cnf(c_0_76,plain,
    ( less_equal(divide(X1,zero),divide(X2,X3))
    | ~ quotient(X4,divide(X3,X5),X2)
    | ~ quotient(X4,X3,X1) ),
    inference(spm,[status(thm)],[c_0_47,c_0_19]) ).

cnf(c_0_77,hypothesis,
    ( less_equal(divide(idQ_idQa,divide(X1,idQa)),zero)
    | ~ quotient(identity,X1,divide(X2,a)) ),
    inference(spm,[status(thm)],[c_0_72,c_0_73]) ).

cnf(c_0_78,axiom,
    ( X3 = X4
    | ~ quotient(X1,X2,X3)
    | ~ quotient(X1,X2,X4) ),
    well_defined ).

cnf(c_0_79,plain,
    ( less_equal(divide(X1,X2),zero)
    | ~ quotient(divide(X3,X4),X5,X1)
    | ~ quotient(X3,X5,X2) ),
    inference(spm,[status(thm)],[c_0_40,c_0_19]) ).

cnf(c_0_80,plain,
    quotient(X1,zero,X1),
    inference(spm,[status(thm)],[c_0_14,c_0_51]) ).

cnf(c_0_81,hypothesis,
    ( divide(X1,idQ_idQa) = idQ__idQ_idQa
    | ~ quotient(idQa,idQ_idQa,divide(X1,idQ_idQa)) ),
    inference(spm,[status(thm)],[c_0_74,c_0_75]) ).

cnf(c_0_82,plain,
    ( less_equal(X1,divide(X2,X3))
    | ~ quotient(X4,divide(X3,X5),X2)
    | ~ quotient(X4,X3,X1) ),
    inference(rw,[status(thm)],[c_0_76,c_0_51]) ).

cnf(c_0_83,hypothesis,
    less_equal(divide(idQ_idQa,divide(a,idQa)),zero),
    inference(spm,[status(thm)],[c_0_77,c_0_14]) ).

cnf(c_0_84,plain,
    ( X1 = zero
    | ~ quotient(zero,X2,X1) ),
    inference(spm,[status(thm)],[c_0_78,c_0_28]) ).

cnf(c_0_85,plain,
    ( less_equal(divide(divide(X1,X2),X3),zero)
    | ~ quotient(X1,zero,X3) ),
    inference(spm,[status(thm)],[c_0_79,c_0_80]) ).

cnf(c_0_86,hypothesis,
    divide(idQa,idQ_idQa) = idQ__idQ_idQa,
    inference(spm,[status(thm)],[c_0_81,c_0_14]) ).

cnf(c_0_87,plain,
    ( less_equal(X1,divide(divide(X2,divide(X3,X4)),X3))
    | ~ quotient(X2,X3,X1) ),
    inference(spm,[status(thm)],[c_0_82,c_0_14]) ).

cnf(c_0_88,hypothesis,
    divide(idQ_idQa,divide(a,idQa)) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_83]),c_0_28])]) ).

cnf(c_0_89,plain,
    divide(zero,X1) = zero,
    inference(spm,[status(thm)],[c_0_84,c_0_14]) ).

cnf(c_0_90,hypothesis,
    ( less_equal(divide(idQ__idQ_idQa,X1),zero)
    | ~ quotient(idQa,zero,X1) ),
    inference(spm,[status(thm)],[c_0_85,c_0_86]) ).

cnf(c_0_91,hypothesis,
    ( less_equal(X1,zero)
    | ~ quotient(idQ_idQa,a,X1) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89]) ).

cnf(c_0_92,hypothesis,
    ( divide(idQ__idQ_idQa,X1) = zero
    | ~ quotient(idQa,zero,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_90]),c_0_28])]) ).

cnf(c_0_93,hypothesis,
    ( less_equal(divide(idQa,divide(X1,a)),divide(X2,a))
    | ~ quotient(identity,X1,X2) ),
    inference(spm,[status(thm)],[c_0_68,c_0_61]) ).

cnf(c_0_94,hypothesis,
    ( X1 = zero
    | ~ quotient(idQ_idQa,a,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_91]),c_0_28])]) ).

cnf(c_0_95,plain,
    ( divide(X1,X2) = X1
    | ~ quotient(X1,divide(X1,X2),zero) ),
    inference(spm,[status(thm)],[c_0_26,c_0_17]) ).

cnf(c_0_96,hypothesis,
    ( quotient(idQ__idQ_idQa,X1,zero)
    | ~ quotient(idQa,zero,X1) ),
    inference(spm,[status(thm)],[c_0_14,c_0_92]) ).

cnf(c_0_97,hypothesis,
    ( divide(idQa,divide(X1,a)) = divide(X2,a)
    | ~ quotient(divide(X2,a),divide(idQa,divide(X1,a)),zero)
    | ~ quotient(identity,X1,X2) ),
    inference(spm,[status(thm)],[c_0_26,c_0_93]) ).

cnf(c_0_98,hypothesis,
    divide(idQ_idQa,a) = zero,
    inference(spm,[status(thm)],[c_0_94,c_0_14]) ).

cnf(c_0_99,hypothesis,
    quotient(divide(X1,a),idQa,zero),
    inference(spm,[status(thm)],[c_0_14,c_0_73]) ).

cnf(c_0_100,hypothesis,
    ( divide(idQ__idQ_idQa,X1) = idQ__idQ_idQa
    | ~ quotient(idQa,zero,divide(idQ__idQ_idQa,X1)) ),
    inference(spm,[status(thm)],[c_0_95,c_0_96]) ).

cnf(c_0_101,hypothesis,
    ( divide(X1,a) = idQa
    | ~ quotient(identity,idQ_idQa,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_51]),c_0_51]),c_0_99])]) ).

cnf(c_0_102,negated_conjecture,
    idQa != idQ__idQ_idQa,
    prove_one_inversion_equals_three ).

cnf(c_0_103,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_80]),c_0_54])]),c_0_102]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : HEN009-1 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34  % Computer : n022.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Thu Aug 24 13:28:41 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.58  start to proof: theBenchmark
% 1.33/1.51  % Version  : CSE_E---1.5
% 1.33/1.51  % Problem  : theBenchmark.p
% 1.33/1.51  % Proof found
% 1.33/1.51  % SZS status Theorem for theBenchmark.p
% 1.33/1.51  % SZS output start Proof
% See solution above
% 1.33/1.51  % Total time : 0.919000 s
% 1.33/1.51  % SZS output end Proof
% 1.33/1.51  % Total time : 0.922000 s
%------------------------------------------------------------------------------