TSTP Solution File: HEN009-1 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : HEN009-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n009.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 : Mon May 20 21:33:58 EDT 2024

% Result   : Unsatisfiable 15.52s 2.54s
% Output   : CNFRefutation 15.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   35
%            Number of leaves      :   13
% Syntax   : Number of clauses     :  111 (  48 unt;   0 nHn;  77 RR)
%            Number of literals    :  218 (  35 equ; 110 neg)
%            Maximal clause size   :    6 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            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   :  223 (  36 sgn)

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

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

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,plain,
    ( less_equal(X3,X1)
    | ~ quotient(X1,X2,X3) ),
    inference(fof_simplification,[status(thm)],[divisor_existence]) ).

cnf(c_0_14,plain,
    ( less_equal(X7,X8)
    | ~ quotient(X1,X2,X3)
    | ~ quotient(X2,X4,X5)
    | ~ quotient(X1,X4,X6)
    | ~ quotient(X6,X5,X7)
    | ~ quotient(X3,X4,X8) ),
    inference(fof_simplification,[status(thm)],[quotient_property]) ).

cnf(c_0_15,plain,
    ( quotient(X1,X2,zero)
    | ~ less_equal(X1,X2) ),
    inference(fof_simplification,[status(thm)],[quotient_less_equal]) ).

cnf(c_0_16,plain,
    ( less_equal(X3,X1)
    | ~ quotient(X1,X2,X3) ),
    c_0_13 ).

cnf(c_0_17,axiom,
    quotient(X1,X2,divide(X1,X2)),
    closure ).

cnf(c_0_18,plain,
    ( less_equal(X7,X8)
    | ~ quotient(X1,X2,X3)
    | ~ quotient(X2,X4,X5)
    | ~ quotient(X1,X4,X6)
    | ~ quotient(X6,X5,X7)
    | ~ quotient(X3,X4,X8) ),
    c_0_14 ).

cnf(c_0_19,plain,
    ( quotient(X1,X2,zero)
    | ~ less_equal(X1,X2) ),
    c_0_15 ).

cnf(c_0_20,plain,
    less_equal(divide(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_21,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_18,c_0_17]) ).

cnf(c_0_22,plain,
    quotient(divide(X1,X2),X1,zero),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_23,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_21,c_0_22]) ).

cnf(c_0_24,plain,
    ( X1 = X2
    | ~ less_equal(X1,X2)
    | ~ less_equal(X2,X1) ),
    inference(fof_simplification,[status(thm)],[less_equal_and_equal]) ).

cnf(c_0_25,plain,
    ( less_equal(X1,X2)
    | ~ quotient(X1,X2,zero) ),
    inference(fof_simplification,[status(thm)],[less_equal_quotient]) ).

cnf(c_0_26,plain,
    ( less_equal(divide(X1,X2),zero)
    | ~ quotient(X3,X4,X2)
    | ~ quotient(X4,X4,X1) ),
    inference(spm,[status(thm)],[c_0_23,c_0_17]) ).

cnf(c_0_27,plain,
    ( X1 = X2
    | ~ less_equal(X1,X2)
    | ~ less_equal(X2,X1) ),
    c_0_24 ).

cnf(c_0_28,plain,
    ( less_equal(X1,X2)
    | ~ quotient(X1,X2,zero) ),
    c_0_25 ).

cnf(c_0_29,plain,
    ( less_equal(divide(X1,zero),zero)
    | ~ quotient(X2,X2,X1) ),
    inference(spm,[status(thm)],[c_0_26,c_0_22]) ).

cnf(c_0_30,axiom,
    less_equal(zero,X1),
    zero_is_smallest ).

cnf(c_0_31,plain,
    ( X1 = X2
    | ~ quotient(X2,X1,zero)
    | ~ less_equal(X1,X2) ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_32,plain,
    less_equal(divide(divide(X1,X1),zero),zero),
    inference(spm,[status(thm)],[c_0_29,c_0_17]) ).

cnf(c_0_33,plain,
    quotient(zero,X1,zero),
    inference(spm,[status(thm)],[c_0_19,c_0_30]) ).

cnf(c_0_34,plain,
    divide(divide(X1,X1),zero) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).

cnf(c_0_35,plain,
    ( X1 = X2
    | ~ quotient(X2,X1,zero)
    | ~ quotient(X1,X2,zero) ),
    inference(spm,[status(thm)],[c_0_31,c_0_28]) ).

cnf(c_0_36,plain,
    quotient(divide(X1,X1),zero,zero),
    inference(spm,[status(thm)],[c_0_17,c_0_34]) ).

cnf(c_0_37,plain,
    divide(X1,X1) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_33])]) ).

cnf(c_0_38,plain,
    quotient(X1,X1,zero),
    inference(spm,[status(thm)],[c_0_17,c_0_37]) ).

cnf(c_0_39,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_21,c_0_38]) ).

cnf(c_0_40,plain,
    ( less_equal(divide(X1,zero),zero)
    | ~ quotient(X2,zero,X3)
    | ~ quotient(X2,X3,X1) ),
    inference(spm,[status(thm)],[c_0_39,c_0_33]) ).

cnf(c_0_41,plain,
    ( less_equal(divide(X1,zero),zero)
    | ~ quotient(X2,divide(X2,zero),X1) ),
    inference(spm,[status(thm)],[c_0_40,c_0_17]) ).

cnf(c_0_42,plain,
    less_equal(divide(divide(X1,divide(X1,zero)),zero),zero),
    inference(spm,[status(thm)],[c_0_41,c_0_17]) ).

cnf(c_0_43,axiom,
    less_equal(X1,identity),
    identity_is_largest ).

cnf(c_0_44,plain,
    divide(divide(X1,divide(X1,zero)),zero) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_42]),c_0_33])]) ).

cnf(c_0_45,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_21,c_0_33]) ).

cnf(c_0_46,plain,
    quotient(X1,identity,zero),
    inference(spm,[status(thm)],[c_0_19,c_0_43]) ).

cnf(c_0_47,plain,
    quotient(divide(X1,divide(X1,zero)),zero,zero),
    inference(spm,[status(thm)],[c_0_17,c_0_44]) ).

cnf(c_0_48,plain,
    ( less_equal(divide(X1,X2),zero)
    | ~ quotient(identity,X3,X2)
    | ~ quotient(X4,X3,X1) ),
    inference(spm,[status(thm)],[c_0_45,c_0_46]) ).

cnf(c_0_49,hypothesis,
    quotient(identity,idQa,idQ_idQa),
    identity_divide_idQa ).

cnf(c_0_50,plain,
    divide(X1,divide(X1,zero)) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_47]),c_0_33])]) ).

cnf(c_0_51,hypothesis,
    ( less_equal(divide(X1,idQ_idQa),zero)
    | ~ quotient(X2,idQa,X1) ),
    inference(spm,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_52,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_21,c_0_17]) ).

cnf(c_0_53,plain,
    quotient(X1,divide(X1,zero),zero),
    inference(spm,[status(thm)],[c_0_17,c_0_50]) ).

cnf(c_0_54,hypothesis,
    less_equal(divide(divide(X1,idQa),idQ_idQa),zero),
    inference(spm,[status(thm)],[c_0_51,c_0_17]) ).

cnf(c_0_55,plain,
    ( less_equal(divide(X1,zero),divide(X2,X3))
    | ~ quotient(X4,X3,X1)
    | ~ quotient(X4,X3,X2) ),
    inference(spm,[status(thm)],[c_0_52,c_0_38]) ).

cnf(c_0_56,plain,
    divide(X1,zero) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_53]),c_0_22])]) ).

cnf(c_0_57,hypothesis,
    divide(divide(X1,idQa),idQ_idQa) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_54]),c_0_33])]) ).

cnf(c_0_58,plain,
    ( less_equal(X1,divide(X2,X3))
    | ~ quotient(X4,X3,X1)
    | ~ quotient(X4,X3,X2) ),
    inference(rw,[status(thm)],[c_0_55,c_0_56]) ).

cnf(c_0_59,hypothesis,
    quotient(identity,idQ_idQa,idQ__idQ_idQa),
    identity_divide_idQ_idQa ).

cnf(c_0_60,hypothesis,
    quotient(divide(X1,idQa),idQ_idQa,zero),
    inference(spm,[status(thm)],[c_0_17,c_0_57]) ).

cnf(c_0_61,plain,
    ( divide(X1,X2) = X1
    | ~ less_equal(X1,divide(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_27,c_0_20]) ).

cnf(c_0_62,hypothesis,
    ( less_equal(idQ__idQ_idQa,divide(X1,idQ_idQa))
    | ~ quotient(identity,idQ_idQa,X1) ),
    inference(spm,[status(thm)],[c_0_58,c_0_59]) ).

cnf(c_0_63,hypothesis,
    ( less_equal(divide(X1,idQ__idQ_idQa),zero)
    | ~ quotient(X2,idQ_idQa,X1) ),
    inference(spm,[status(thm)],[c_0_48,c_0_59]) ).

cnf(c_0_64,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_21,c_0_60]) ).

cnf(c_0_65,hypothesis,
    divide(idQ__idQ_idQa,idQ_idQa) = idQ__idQ_idQa,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_59])]) ).

cnf(c_0_66,hypothesis,
    quotient(identity,a,idQa),
    identity_divide_a ).

cnf(c_0_67,hypothesis,
    less_equal(divide(divide(X1,idQ_idQa),idQ__idQ_idQa),zero),
    inference(spm,[status(thm)],[c_0_63,c_0_17]) ).

cnf(c_0_68,hypothesis,
    ( less_equal(divide(X1,X2),zero)
    | ~ quotient(idQa,idQ_idQa,X2)
    | ~ quotient(X3,idQ_idQa,X1) ),
    inference(spm,[status(thm)],[c_0_64,c_0_17]) ).

cnf(c_0_69,hypothesis,
    quotient(idQ__idQ_idQa,idQ_idQa,idQ__idQ_idQa),
    inference(spm,[status(thm)],[c_0_17,c_0_65]) ).

cnf(c_0_70,hypothesis,
    ( less_equal(divide(X1,idQa),zero)
    | ~ quotient(X2,a,X1) ),
    inference(spm,[status(thm)],[c_0_48,c_0_66]) ).

cnf(c_0_71,hypothesis,
    divide(divide(X1,idQ_idQa),idQ__idQ_idQa) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_67]),c_0_33])]) ).

cnf(c_0_72,hypothesis,
    ( less_equal(divide(idQ__idQ_idQa,X1),zero)
    | ~ quotient(idQa,idQ_idQa,X1) ),
    inference(spm,[status(thm)],[c_0_68,c_0_69]) ).

cnf(c_0_73,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_52,c_0_17]) ).

cnf(c_0_74,hypothesis,
    less_equal(divide(divide(X1,a),idQa),zero),
    inference(spm,[status(thm)],[c_0_70,c_0_17]) ).

cnf(c_0_75,hypothesis,
    quotient(divide(X1,idQ_idQa),idQ__idQ_idQa,zero),
    inference(spm,[status(thm)],[c_0_17,c_0_71]) ).

cnf(c_0_76,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_31,c_0_72]),c_0_33])]) ).

cnf(c_0_77,hypothesis,
    ( less_equal(divide(idQ_idQa,divide(X1,idQa)),divide(X2,idQa))
    | ~ quotient(identity,X1,X2) ),
    inference(spm,[status(thm)],[c_0_73,c_0_49]) ).

cnf(c_0_78,hypothesis,
    divide(divide(X1,a),idQa) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_74]),c_0_33])]) ).

cnf(c_0_79,plain,
    ( X3 = X4
    | ~ quotient(X1,X2,X3)
    | ~ quotient(X1,X2,X4) ),
    inference(fof_simplification,[status(thm)],[well_defined]) ).

cnf(c_0_80,hypothesis,
    ( divide(X1,idQ_idQa) = idQ__idQ_idQa
    | ~ quotient(idQ__idQ_idQa,divide(X1,idQ_idQa),zero) ),
    inference(spm,[status(thm)],[c_0_35,c_0_75]) ).

cnf(c_0_81,hypothesis,
    ( quotient(idQ__idQ_idQa,X1,zero)
    | ~ quotient(idQa,idQ_idQa,X1) ),
    inference(spm,[status(thm)],[c_0_17,c_0_76]) ).

cnf(c_0_82,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_52,c_0_22]) ).

cnf(c_0_83,hypothesis,
    ( less_equal(divide(idQ_idQa,divide(X1,idQa)),zero)
    | ~ quotient(identity,X1,divide(X2,a)) ),
    inference(spm,[status(thm)],[c_0_77,c_0_78]) ).

cnf(c_0_84,plain,
    ( X3 = X4
    | ~ quotient(X1,X2,X3)
    | ~ quotient(X1,X2,X4) ),
    c_0_79 ).

cnf(c_0_85,plain,
    ( less_equal(divide(X1,X2),zero)
    | ~ quotient(divide(X3,X4),X5,X1)
    | ~ quotient(X3,X5,X2) ),
    inference(spm,[status(thm)],[c_0_45,c_0_22]) ).

cnf(c_0_86,plain,
    quotient(X1,zero,X1),
    inference(spm,[status(thm)],[c_0_17,c_0_56]) ).

cnf(c_0_87,hypothesis,
    ( divide(X1,idQ_idQa) = idQ__idQ_idQa
    | ~ quotient(idQa,idQ_idQa,divide(X1,idQ_idQa)) ),
    inference(spm,[status(thm)],[c_0_80,c_0_81]) ).

cnf(c_0_88,plain,
    ( less_equal(X1,divide(X2,X3))
    | ~ quotient(X4,divide(X3,X5),X2)
    | ~ quotient(X4,X3,X1) ),
    inference(rw,[status(thm)],[c_0_82,c_0_56]) ).

cnf(c_0_89,hypothesis,
    less_equal(divide(idQ_idQa,divide(a,idQa)),zero),
    inference(spm,[status(thm)],[c_0_83,c_0_17]) ).

cnf(c_0_90,plain,
    ( X1 = zero
    | ~ quotient(zero,X2,X1) ),
    inference(spm,[status(thm)],[c_0_84,c_0_33]) ).

cnf(c_0_91,plain,
    ( less_equal(divide(divide(X1,X2),X3),zero)
    | ~ quotient(X1,zero,X3) ),
    inference(spm,[status(thm)],[c_0_85,c_0_86]) ).

cnf(c_0_92,hypothesis,
    divide(idQa,idQ_idQa) = idQ__idQ_idQa,
    inference(spm,[status(thm)],[c_0_87,c_0_17]) ).

cnf(c_0_93,plain,
    ( less_equal(X1,divide(divide(X2,divide(X3,X4)),X3))
    | ~ quotient(X2,X3,X1) ),
    inference(spm,[status(thm)],[c_0_88,c_0_17]) ).

cnf(c_0_94,hypothesis,
    divide(idQ_idQa,divide(a,idQa)) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_89]),c_0_33])]) ).

cnf(c_0_95,plain,
    divide(zero,X1) = zero,
    inference(spm,[status(thm)],[c_0_90,c_0_17]) ).

cnf(c_0_96,hypothesis,
    ( less_equal(divide(idQ__idQ_idQa,X1),zero)
    | ~ quotient(idQa,zero,X1) ),
    inference(spm,[status(thm)],[c_0_91,c_0_92]) ).

cnf(c_0_97,hypothesis,
    ( less_equal(X1,zero)
    | ~ quotient(idQ_idQa,a,X1) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95]) ).

cnf(c_0_98,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_31,c_0_96]),c_0_33])]) ).

cnf(c_0_99,hypothesis,
    ( less_equal(divide(idQa,divide(X1,a)),divide(X2,a))
    | ~ quotient(identity,X1,X2) ),
    inference(spm,[status(thm)],[c_0_73,c_0_66]) ).

cnf(c_0_100,hypothesis,
    ( X1 = zero
    | ~ quotient(idQ_idQa,a,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_97]),c_0_33])]) ).

cnf(c_0_101,plain,
    ( divide(X1,X2) = X1
    | ~ quotient(X1,divide(X1,X2),zero) ),
    inference(spm,[status(thm)],[c_0_31,c_0_20]) ).

cnf(c_0_102,hypothesis,
    ( quotient(idQ__idQ_idQa,X1,zero)
    | ~ quotient(idQa,zero,X1) ),
    inference(spm,[status(thm)],[c_0_17,c_0_98]) ).

cnf(c_0_103,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_31,c_0_99]) ).

cnf(c_0_104,hypothesis,
    divide(idQ_idQa,a) = zero,
    inference(spm,[status(thm)],[c_0_100,c_0_17]) ).

cnf(c_0_105,hypothesis,
    quotient(divide(X1,a),idQa,zero),
    inference(spm,[status(thm)],[c_0_17,c_0_78]) ).

cnf(c_0_106,negated_conjecture,
    idQa != idQ__idQ_idQa,
    inference(fof_simplification,[status(thm)],[prove_one_inversion_equals_three]) ).

cnf(c_0_107,hypothesis,
    ( divide(idQ__idQ_idQa,X1) = idQ__idQ_idQa
    | ~ quotient(idQa,zero,divide(idQ__idQ_idQa,X1)) ),
    inference(spm,[status(thm)],[c_0_101,c_0_102]) ).

cnf(c_0_108,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_103,c_0_104]),c_0_56]),c_0_56]),c_0_105])]) ).

cnf(c_0_109,negated_conjecture,
    idQa != idQ__idQ_idQa,
    c_0_106 ).

cnf(c_0_110,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_86]),c_0_59])]),c_0_109]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.15  % Problem    : HEN009-1 : TPTP v8.2.0. Released v1.0.0.
% 0.08/0.17  % Command    : run_E %s %d THM
% 0.17/0.39  % Computer : n009.cluster.edu
% 0.17/0.39  % Model    : x86_64 x86_64
% 0.17/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.39  % Memory   : 8042.1875MB
% 0.17/0.39  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.39  % CPULimit   : 300
% 0.17/0.39  % WCLimit    : 300
% 0.17/0.39  % DateTime   : Sun May 19 22:53:23 EDT 2024
% 0.17/0.40  % CPUTime    : 
% 0.26/0.56  Running first-order model finding
% 0.26/0.56  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.52/2.54  # Version: 3.1.0
% 15.52/2.54  # Preprocessing class: FSMSSMSSSSSNFFN.
% 15.52/2.54  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.52/2.54  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 15.52/2.54  # Starting new_bool_3 with 300s (1) cores
% 15.52/2.54  # Starting new_bool_1 with 300s (1) cores
% 15.52/2.54  # Starting sh5l with 300s (1) cores
% 15.52/2.54  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3004 completed with status 0
% 15.52/2.54  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 15.52/2.54  # Preprocessing class: FSMSSMSSSSSNFFN.
% 15.52/2.54  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.52/2.54  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 15.52/2.54  # No SInE strategy applied
% 15.52/2.54  # Search class: FHUSS-FFSS22-SFFFFFNN
% 15.52/2.54  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 15.52/2.54  # Starting SAT001_MinMin_p005000_rr_RG with 811s (1) cores
% 15.52/2.54  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 15.52/2.54  # Starting new_bool_3 with 136s (1) cores
% 15.52/2.54  # Starting new_bool_1 with 136s (1) cores
% 15.52/2.54  # Starting sh5l with 136s (1) cores
% 15.52/2.54  # SAT001_MinMin_p005000_rr_RG with pid 3008 completed with status 0
% 15.52/2.54  # Result found by SAT001_MinMin_p005000_rr_RG
% 15.52/2.54  # Preprocessing class: FSMSSMSSSSSNFFN.
% 15.52/2.54  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.52/2.54  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 15.52/2.54  # No SInE strategy applied
% 15.52/2.54  # Search class: FHUSS-FFSS22-SFFFFFNN
% 15.52/2.54  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 15.52/2.54  # Starting SAT001_MinMin_p005000_rr_RG with 811s (1) cores
% 15.52/2.54  # Preprocessing time       : 0.001 s
% 15.52/2.54  # Presaturation interreduction done
% 15.52/2.54  
% 15.52/2.54  # Proof found!
% 15.52/2.54  # SZS status Unsatisfiable
% 15.52/2.54  # SZS output start CNFRefutation
% See solution above
% 15.52/2.54  # Parsed axioms                        : 13
% 15.52/2.54  # Removed by relevancy pruning/SinE    : 0
% 15.52/2.54  # Initial clauses                      : 13
% 15.52/2.54  # Removed in clause preprocessing      : 0
% 15.52/2.54  # Initial clauses in saturation        : 13
% 15.52/2.54  # Processed clauses                    : 21578
% 15.52/2.54  # ...of these trivial                  : 21
% 15.52/2.54  # ...subsumed                          : 19038
% 15.52/2.54  # ...remaining for further processing  : 2519
% 15.52/2.54  # Other redundant clauses eliminated   : 0
% 15.52/2.54  # Clauses deleted for lack of memory   : 0
% 15.52/2.54  # Backward-subsumed                    : 476
% 15.52/2.54  # Backward-rewritten                   : 157
% 15.52/2.54  # Generated clauses                    : 82670
% 15.52/2.54  # ...of the previous two non-redundant : 61415
% 15.52/2.54  # ...aggressively subsumed             : 0
% 15.52/2.54  # Contextual simplify-reflections      : 5
% 15.52/2.54  # Paramodulations                      : 82670
% 15.52/2.54  # Factorizations                       : 0
% 15.52/2.54  # NegExts                              : 0
% 15.52/2.54  # Equation resolutions                 : 0
% 15.52/2.54  # Disequality decompositions           : 0
% 15.52/2.54  # Total rewrite steps                  : 47565
% 15.52/2.54  # ...of those cached                   : 47063
% 15.52/2.54  # Propositional unsat checks           : 0
% 15.52/2.54  #    Propositional check models        : 0
% 15.52/2.54  #    Propositional check unsatisfiable : 0
% 15.52/2.54  #    Propositional clauses             : 0
% 15.52/2.54  #    Propositional clauses after purity: 0
% 15.52/2.54  #    Propositional unsat core size     : 0
% 15.52/2.54  #    Propositional preprocessing time  : 0.000
% 15.52/2.54  #    Propositional encoding time       : 0.000
% 15.52/2.54  #    Propositional solver time         : 0.000
% 15.52/2.54  #    Success case prop preproc time    : 0.000
% 15.52/2.54  #    Success case prop encoding time   : 0.000
% 15.52/2.54  #    Success case prop solver time     : 0.000
% 15.52/2.54  # Current number of processed clauses  : 1873
% 15.52/2.54  #    Positive orientable unit clauses  : 55
% 15.52/2.54  #    Positive unorientable unit clauses: 0
% 15.52/2.54  #    Negative unit clauses             : 13
% 15.52/2.54  #    Non-unit-clauses                  : 1805
% 15.52/2.54  # Current number of unprocessed clauses: 37663
% 15.52/2.54  # ...number of literals in the above   : 139455
% 15.52/2.54  # Current number of archived formulas  : 0
% 15.52/2.54  # Current number of archived clauses   : 646
% 15.52/2.54  # Clause-clause subsumption calls (NU) : 1350244
% 15.52/2.54  # Rec. Clause-clause subsumption calls : 1113575
% 15.52/2.54  # Non-unit clause-clause subsumptions  : 17981
% 15.52/2.54  # Unit Clause-clause subsumption calls : 4407
% 15.52/2.54  # Rewrite failures with RHS unbound    : 0
% 15.52/2.54  # BW rewrite match attempts            : 223
% 15.52/2.54  # BW rewrite match successes           : 30
% 15.52/2.54  # Condensation attempts                : 0
% 15.52/2.54  # Condensation successes               : 0
% 15.52/2.54  # Termbank termtop insertions          : 989616
% 15.52/2.54  # Search garbage collected termcells   : 30
% 15.52/2.54  
% 15.52/2.54  # -------------------------------------------------
% 15.52/2.54  # User time                : 1.894 s
% 15.52/2.54  # System time              : 0.038 s
% 15.52/2.54  # Total time               : 1.932 s
% 15.52/2.54  # Maximum resident set size: 1660 pages
% 15.52/2.54  
% 15.52/2.54  # -------------------------------------------------
% 15.52/2.54  # User time                : 9.569 s
% 15.52/2.54  # System time              : 0.087 s
% 15.52/2.54  # Total time               : 9.656 s
% 15.52/2.54  # Maximum resident set size: 1708 pages
% 15.52/2.54  % E---3.1 exiting
%------------------------------------------------------------------------------