TSTP Solution File: HEN011-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : HEN011-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n001.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 01:54:26 EDT 2023
% Result : Unsatisfiable 19.38s 19.47s
% Output : CNFRefutation 19.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 74
% Number of leaves : 29
% Syntax : Number of formulae : 492 ( 374 unt; 13 typ; 0 def)
% Number of atoms : 637 ( 148 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 319 ( 161 ~; 158 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 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 : 11 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 478 ( 176 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,
b: $i ).
tff(decl_30,type,
idQb: $i ).
tff(decl_31,type,
idQ_idQb: $i ).
tff(decl_32,type,
idQa_Q__idQ_idQb: $i ).
tff(decl_33,type,
idQ_idQa: $i ).
tff(decl_34,type,
idQb_Q__idQ_idQa: $i ).
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/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_property) ).
cnf(closure,axiom,
quotient(X1,X2,divide(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',closure) ).
cnf(quotient_less_equal,axiom,
( quotient(X1,X2,zero)
| ~ less_equal(X1,X2) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',zero_is_smallest) ).
cnf(divisor_existence,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).
cnf(identity_is_largest,axiom,
less_equal(X1,identity),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',identity_is_largest) ).
cnf(less_equal_quotient,axiom,
( less_equal(X1,X2)
| ~ quotient(X1,X2,zero) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_quotient) ).
cnf(identity_divide_a,hypothesis,
quotient(identity,a,idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_a) ).
cnf(well_defined,axiom,
( X3 = X4
| ~ quotient(X1,X2,X3)
| ~ quotient(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',well_defined) ).
cnf(identity_divide_idQa,hypothesis,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQa) ).
cnf(identity_divide_b,hypothesis,
quotient(identity,b,idQb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_b) ).
cnf(identity_divide_idQb,hypothesis,
quotient(identity,idQb,idQ_idQb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQb) ).
cnf(idQb_divide_idQ_idQa,hypothesis,
quotient(idQb,idQ_idQa,idQb_Q__idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idQb_divide_idQ_idQa) ).
cnf(idQa_divide_idQ_idQb,hypothesis,
quotient(idQa,idQ_idQb,idQa_Q__idQ_idQb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idQa_divide_idQ_idQb) ).
cnf(prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa,negated_conjecture,
idQa_Q__idQ_idQb != idQb_Q__idQ_idQa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa) ).
cnf(c_0_16,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_17,axiom,
quotient(X1,X2,divide(X1,X2)),
closure ).
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_16,c_0_17]) ).
cnf(c_0_19,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_17]) ).
cnf(c_0_20,axiom,
( quotient(X1,X2,zero)
| ~ less_equal(X1,X2) ),
quotient_less_equal ).
cnf(c_0_21,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
less_equal_and_equal ).
cnf(c_0_22,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_23,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
divisor_existence ).
cnf(c_0_24,plain,
( less_equal(divide(X1,zero),divide(X2,X3))
| ~ quotient(X4,X3,X1)
| ~ quotient(X4,X5,X2)
| ~ less_equal(X5,X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
( X1 = zero
| ~ less_equal(X1,zero) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
less_equal(divide(X1,X2),X1),
inference(spm,[status(thm)],[c_0_23,c_0_17]) ).
cnf(c_0_27,plain,
( less_equal(divide(divide(X1,X2),zero),divide(X3,X2))
| ~ quotient(X1,X4,X3)
| ~ less_equal(X4,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_17]) ).
cnf(c_0_28,plain,
divide(zero,X1) = zero,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,plain,
( less_equal(divide(divide(X1,X2),zero),zero)
| ~ less_equal(X3,X2)
| ~ less_equal(X1,X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_20]),c_0_28]) ).
cnf(c_0_30,axiom,
less_equal(X1,identity),
identity_is_largest ).
cnf(c_0_31,plain,
( less_equal(divide(divide(X1,identity),zero),zero)
| ~ less_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_32,plain,
less_equal(divide(divide(X1,identity),zero),zero),
inference(spm,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_33,plain,
( less_equal(divide(divide(X1,X2),zero),zero)
| ~ less_equal(X1,divide(X2,X3)) ),
inference(spm,[status(thm)],[c_0_29,c_0_26]) ).
cnf(c_0_34,plain,
divide(divide(X1,identity),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_32]),c_0_22])]) ).
cnf(c_0_35,plain,
less_equal(divide(divide(divide(divide(X1,X2),X3),X1),zero),zero),
inference(spm,[status(thm)],[c_0_33,c_0_26]) ).
cnf(c_0_36,axiom,
( less_equal(X1,X2)
| ~ quotient(X1,X2,zero) ),
less_equal_quotient ).
cnf(c_0_37,plain,
quotient(divide(X1,identity),zero,zero),
inference(spm,[status(thm)],[c_0_17,c_0_34]) ).
cnf(c_0_38,plain,
divide(divide(divide(divide(X1,X2),X3),X1),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_35]),c_0_22])]) ).
cnf(c_0_39,hypothesis,
quotient(identity,a,idQa),
identity_divide_a ).
cnf(c_0_40,plain,
less_equal(divide(X1,identity),zero),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,plain,
quotient(divide(divide(divide(X1,X2),X3),X1),zero,zero),
inference(spm,[status(thm)],[c_0_17,c_0_38]) ).
cnf(c_0_42,hypothesis,
( less_equal(divide(X1,idQa),divide(X2,a))
| ~ quotient(X3,a,X1)
| ~ quotient(X3,identity,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_39]) ).
cnf(c_0_43,plain,
divide(X1,identity) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_40]),c_0_22])]) ).
cnf(c_0_44,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_19,c_0_17]) ).
cnf(c_0_45,plain,
less_equal(divide(divide(divide(X1,X2),X3),X1),zero),
inference(spm,[status(thm)],[c_0_36,c_0_41]) ).
cnf(c_0_46,hypothesis,
( less_equal(divide(idQa,idQa),divide(X1,a))
| ~ quotient(identity,identity,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_39]) ).
cnf(c_0_47,plain,
quotient(X1,identity,zero),
inference(spm,[status(thm)],[c_0_17,c_0_43]) ).
cnf(c_0_48,plain,
( less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(X4,X2))
| ~ quotient(X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_44,c_0_17]) ).
cnf(c_0_49,plain,
divide(divide(divide(X1,X2),X3),X1) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_45]),c_0_22])]) ).
cnf(c_0_50,axiom,
( X3 = X4
| ~ quotient(X1,X2,X3)
| ~ quotient(X1,X2,X4) ),
well_defined ).
cnf(c_0_51,hypothesis,
less_equal(divide(idQa,idQa),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_28]),c_0_47])]) ).
cnf(c_0_52,plain,
( less_equal(divide(divide(X1,X2),divide(X3,X2)),zero)
| ~ quotient(X1,X3,divide(divide(X2,X4),X5)) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,hypothesis,
quotient(identity,idQa,idQ_idQa),
identity_divide_idQa ).
cnf(c_0_54,plain,
( X1 = divide(X2,X3)
| ~ quotient(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_17]) ).
cnf(c_0_55,hypothesis,
divide(idQa,idQa) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_51]),c_0_22])]) ).
cnf(c_0_56,plain,
less_equal(divide(divide(divide(X1,X2),X1),divide(X3,X1)),zero),
inference(spm,[status(thm)],[c_0_52,c_0_17]) ).
cnf(c_0_57,hypothesis,
( less_equal(divide(idQ_idQa,divide(X1,idQa)),divide(X2,idQa))
| ~ quotient(identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_44,c_0_53]) ).
cnf(c_0_58,plain,
( divide(X1,X2) = zero
| ~ less_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_54,c_0_20]) ).
cnf(c_0_59,hypothesis,
quotient(idQa,idQa,zero),
inference(spm,[status(thm)],[c_0_17,c_0_55]) ).
cnf(c_0_60,hypothesis,
( less_equal(divide(X1,idQ_idQa),divide(X2,idQa))
| ~ quotient(X3,idQa,X1)
| ~ quotient(X3,identity,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_53]) ).
cnf(c_0_61,plain,
less_equal(divide(divide(divide(X1,X2),X1),zero),zero),
inference(spm,[status(thm)],[c_0_56,c_0_49]) ).
cnf(c_0_62,hypothesis,
( less_equal(divide(idQ_idQa,divide(X1,idQa)),zero)
| ~ quotient(identity,X1,X2)
| ~ less_equal(X2,idQa) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,hypothesis,
less_equal(idQa,idQa),
inference(spm,[status(thm)],[c_0_36,c_0_59]) ).
cnf(c_0_64,hypothesis,
( less_equal(divide(divide(X1,idQa),idQ_idQa),divide(X2,idQa))
| ~ quotient(X1,identity,X2) ),
inference(spm,[status(thm)],[c_0_60,c_0_17]) ).
cnf(c_0_65,plain,
divide(divide(divide(X1,X2),X1),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_61]),c_0_22])]) ).
cnf(c_0_66,hypothesis,
less_equal(divide(idQ_idQa,divide(a,idQa)),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_39]),c_0_63])]) ).
cnf(c_0_67,hypothesis,
less_equal(divide(divide(X1,idQa),idQ_idQa),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_28]),c_0_47])]) ).
cnf(c_0_68,plain,
quotient(zero,X1,zero),
inference(spm,[status(thm)],[c_0_17,c_0_28]) ).
cnf(c_0_69,plain,
quotient(divide(divide(X1,X2),X1),zero,zero),
inference(spm,[status(thm)],[c_0_17,c_0_65]) ).
cnf(c_0_70,hypothesis,
divide(idQ_idQa,divide(a,idQa)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_66]),c_0_22])]) ).
cnf(c_0_71,hypothesis,
divide(divide(X1,idQa),idQ_idQa) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_67]),c_0_22])]) ).
cnf(c_0_72,plain,
( less_equal(divide(X1,zero),divide(X2,X3))
| ~ quotient(X4,zero,X2)
| ~ quotient(X4,X3,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_68]) ).
cnf(c_0_73,plain,
less_equal(divide(divide(X1,X2),X1),zero),
inference(spm,[status(thm)],[c_0_36,c_0_69]) ).
cnf(c_0_74,hypothesis,
quotient(idQ_idQa,divide(a,idQa),zero),
inference(spm,[status(thm)],[c_0_17,c_0_70]) ).
cnf(c_0_75,hypothesis,
quotient(divide(X1,idQa),idQ_idQa,zero),
inference(spm,[status(thm)],[c_0_17,c_0_71]) ).
cnf(c_0_76,plain,
( less_equal(divide(X1,zero),divide(divide(X2,zero),X3))
| ~ quotient(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_72,c_0_17]) ).
cnf(c_0_77,plain,
divide(divide(X1,X2),X1) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_73]),c_0_22])]) ).
cnf(c_0_78,hypothesis,
less_equal(idQ_idQa,divide(a,idQa)),
inference(spm,[status(thm)],[c_0_36,c_0_74]) ).
cnf(c_0_79,hypothesis,
less_equal(divide(X1,idQa),idQ_idQa),
inference(spm,[status(thm)],[c_0_36,c_0_75]) ).
cnf(c_0_80,plain,
( less_equal(divide(X1,zero),zero)
| ~ quotient(X2,X2,X1) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_81,hypothesis,
( less_equal(divide(idQa,divide(X1,a)),divide(X2,a))
| ~ quotient(identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_44,c_0_39]) ).
cnf(c_0_82,hypothesis,
divide(a,idQa) = idQ_idQa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_78]),c_0_79])]) ).
cnf(c_0_83,plain,
less_equal(divide(divide(X1,X1),zero),zero),
inference(spm,[status(thm)],[c_0_80,c_0_17]) ).
cnf(c_0_84,hypothesis,
( less_equal(divide(idQa,divide(X1,a)),zero)
| ~ quotient(identity,X1,X2)
| ~ less_equal(X2,a) ),
inference(spm,[status(thm)],[c_0_81,c_0_58]) ).
cnf(c_0_85,hypothesis,
less_equal(idQ_idQa,a),
inference(spm,[status(thm)],[c_0_26,c_0_82]) ).
cnf(c_0_86,plain,
divide(divide(X1,X1),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_83]),c_0_22])]) ).
cnf(c_0_87,hypothesis,
less_equal(divide(idQa,divide(idQa,a)),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_53]),c_0_85])]) ).
cnf(c_0_88,plain,
quotient(divide(X1,X1),zero,zero),
inference(spm,[status(thm)],[c_0_17,c_0_86]) ).
cnf(c_0_89,hypothesis,
quotient(identity,b,idQb),
identity_divide_b ).
cnf(c_0_90,hypothesis,
divide(idQa,divide(idQa,a)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_87]),c_0_22])]) ).
cnf(c_0_91,plain,
less_equal(divide(X1,X1),zero),
inference(spm,[status(thm)],[c_0_36,c_0_88]) ).
cnf(c_0_92,hypothesis,
( less_equal(divide(X1,idQb),divide(X2,b))
| ~ quotient(X3,b,X1)
| ~ quotient(X3,identity,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_89]) ).
cnf(c_0_93,hypothesis,
quotient(idQa,divide(idQa,a),zero),
inference(spm,[status(thm)],[c_0_17,c_0_90]) ).
cnf(c_0_94,plain,
divide(X1,X1) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_91]),c_0_22])]) ).
cnf(c_0_95,hypothesis,
( less_equal(divide(idQb,idQb),divide(X1,b))
| ~ quotient(identity,identity,X1) ),
inference(spm,[status(thm)],[c_0_92,c_0_89]) ).
cnf(c_0_96,hypothesis,
less_equal(idQa,divide(idQa,a)),
inference(spm,[status(thm)],[c_0_36,c_0_93]) ).
cnf(c_0_97,hypothesis,
( less_equal(divide(idQ_idQa,zero),divide(X1,idQa))
| ~ quotient(identity,X2,X1)
| ~ less_equal(X2,idQa) ),
inference(spm,[status(thm)],[c_0_24,c_0_53]) ).
cnf(c_0_98,plain,
quotient(X1,X1,zero),
inference(spm,[status(thm)],[c_0_17,c_0_94]) ).
cnf(c_0_99,hypothesis,
less_equal(divide(idQb,idQb),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_28]),c_0_47])]) ).
cnf(c_0_100,plain,
( divide(X1,X2) = X1
| ~ less_equal(X1,divide(X1,X2)) ),
inference(spm,[status(thm)],[c_0_21,c_0_26]) ).
cnf(c_0_101,hypothesis,
divide(idQa,a) = idQa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_96]),c_0_26])]) ).
cnf(c_0_102,plain,
( less_equal(divide(divide(X1,X2),zero),divide(divide(X1,X3),X2))
| ~ less_equal(X3,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_17]) ).
cnf(c_0_103,hypothesis,
( less_equal(divide(idQ_idQa,zero),divide(divide(identity,X1),idQa))
| ~ less_equal(X1,idQa) ),
inference(spm,[status(thm)],[c_0_97,c_0_17]) ).
cnf(c_0_104,hypothesis,
divide(identity,idQa) = idQ_idQa,
inference(spm,[status(thm)],[c_0_54,c_0_53]) ).
cnf(c_0_105,plain,
less_equal(X1,X1),
inference(spm,[status(thm)],[c_0_36,c_0_98]) ).
cnf(c_0_106,hypothesis,
quotient(identity,idQb,idQ_idQb),
identity_divide_idQb ).
cnf(c_0_107,hypothesis,
divide(idQb,idQb) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_99]),c_0_22])]) ).
cnf(c_0_108,plain,
( divide(divide(X1,zero),X2) = divide(X1,zero)
| ~ quotient(X1,X2,X1) ),
inference(spm,[status(thm)],[c_0_100,c_0_76]) ).
cnf(c_0_109,hypothesis,
quotient(idQa,a,idQa),
inference(spm,[status(thm)],[c_0_17,c_0_101]) ).
cnf(c_0_110,plain,
( less_equal(divide(divide(X1,X2),zero),zero)
| ~ less_equal(divide(X1,X3),X2)
| ~ less_equal(X3,X2) ),
inference(spm,[status(thm)],[c_0_102,c_0_58]) ).
cnf(c_0_111,hypothesis,
less_equal(divide(idQ_idQa,zero),divide(idQ_idQa,idQa)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_105])]) ).
cnf(c_0_112,hypothesis,
( less_equal(divide(idQ_idQb,divide(X1,idQb)),divide(X2,idQb))
| ~ quotient(identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_44,c_0_106]) ).
cnf(c_0_113,hypothesis,
quotient(idQb,idQb,zero),
inference(spm,[status(thm)],[c_0_17,c_0_107]) ).
cnf(c_0_114,hypothesis,
( less_equal(divide(X1,idQ_idQb),divide(X2,idQb))
| ~ quotient(X3,idQb,X1)
| ~ quotient(X3,identity,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_106]) ).
cnf(c_0_115,plain,
quotient(divide(divide(X1,X2),X3),X1,zero),
inference(spm,[status(thm)],[c_0_17,c_0_49]) ).
cnf(c_0_116,hypothesis,
divide(divide(idQa,zero),a) = divide(idQa,zero),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_117,hypothesis,
less_equal(divide(divide(idQ_idQa,divide(idQ_idQa,idQa)),zero),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_22])]) ).
cnf(c_0_118,hypothesis,
( less_equal(divide(idQ_idQb,zero),divide(X1,idQb))
| ~ quotient(identity,X2,X1)
| ~ less_equal(X2,idQb) ),
inference(spm,[status(thm)],[c_0_24,c_0_106]) ).
cnf(c_0_119,hypothesis,
( less_equal(divide(idQ_idQb,divide(X1,idQb)),zero)
| ~ quotient(identity,X1,X2)
| ~ less_equal(X2,idQb) ),
inference(spm,[status(thm)],[c_0_112,c_0_58]) ).
cnf(c_0_120,hypothesis,
less_equal(idQb,idQb),
inference(spm,[status(thm)],[c_0_36,c_0_113]) ).
cnf(c_0_121,hypothesis,
( less_equal(divide(divide(X1,idQb),idQ_idQb),divide(X2,idQb))
| ~ quotient(X1,identity,X2) ),
inference(spm,[status(thm)],[c_0_114,c_0_17]) ).
cnf(c_0_122,hypothesis,
quotient(divide(divide(idQa,zero),X1),divide(idQa,zero),zero),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_123,hypothesis,
divide(divide(idQ_idQa,divide(idQ_idQa,idQa)),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_117]),c_0_22])]) ).
cnf(c_0_124,hypothesis,
( less_equal(divide(idQ_idQb,zero),divide(idQ_idQb,idQb))
| ~ less_equal(idQb,idQb) ),
inference(spm,[status(thm)],[c_0_118,c_0_106]) ).
cnf(c_0_125,hypothesis,
less_equal(divide(idQ_idQb,divide(b,idQb)),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_89]),c_0_120])]) ).
cnf(c_0_126,hypothesis,
less_equal(divide(divide(X1,idQb),idQ_idQb),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_28]),c_0_47])]) ).
cnf(c_0_127,hypothesis,
quotient(divide(idQa,zero),divide(idQa,zero),zero),
inference(spm,[status(thm)],[c_0_122,c_0_116]) ).
cnf(c_0_128,hypothesis,
quotient(divide(idQ_idQa,divide(idQ_idQa,idQa)),zero,zero),
inference(spm,[status(thm)],[c_0_17,c_0_123]) ).
cnf(c_0_129,hypothesis,
less_equal(divide(idQ_idQb,zero),divide(idQ_idQb,idQb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_124,c_0_120])]) ).
cnf(c_0_130,hypothesis,
divide(idQ_idQb,divide(b,idQb)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_125]),c_0_22])]) ).
cnf(c_0_131,hypothesis,
divide(divide(X1,idQb),idQ_idQb) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_126]),c_0_22])]) ).
cnf(c_0_132,hypothesis,
divide(divide(idQa,zero),divide(idQa,zero)) = zero,
inference(spm,[status(thm)],[c_0_54,c_0_127]) ).
cnf(c_0_133,hypothesis,
less_equal(divide(idQ_idQa,divide(idQ_idQa,idQa)),zero),
inference(spm,[status(thm)],[c_0_36,c_0_128]) ).
cnf(c_0_134,hypothesis,
less_equal(divide(divide(idQ_idQb,divide(idQ_idQb,idQb)),zero),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_129]),c_0_22])]) ).
cnf(c_0_135,hypothesis,
quotient(idQ_idQb,divide(b,idQb),zero),
inference(spm,[status(thm)],[c_0_17,c_0_130]) ).
cnf(c_0_136,hypothesis,
quotient(divide(X1,idQb),idQ_idQb,zero),
inference(spm,[status(thm)],[c_0_17,c_0_131]) ).
cnf(c_0_137,hypothesis,
less_equal(divide(divide(idQa,divide(idQa,zero)),zero),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_132]),c_0_22])]) ).
cnf(c_0_138,hypothesis,
quotient(idQb,idQ_idQa,idQb_Q__idQ_idQa),
idQb_divide_idQ_idQa ).
cnf(c_0_139,hypothesis,
divide(idQ_idQa,divide(idQ_idQa,idQa)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_133]),c_0_22])]) ).
cnf(c_0_140,hypothesis,
divide(divide(idQ_idQb,divide(idQ_idQb,idQb)),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_134]),c_0_22])]) ).
cnf(c_0_141,hypothesis,
less_equal(idQ_idQb,divide(b,idQb)),
inference(spm,[status(thm)],[c_0_36,c_0_135]) ).
cnf(c_0_142,hypothesis,
less_equal(divide(X1,idQb),idQ_idQb),
inference(spm,[status(thm)],[c_0_36,c_0_136]) ).
cnf(c_0_143,hypothesis,
divide(divide(idQa,divide(idQa,zero)),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_137]),c_0_22])]) ).
cnf(c_0_144,plain,
( divide(X1,X2) = divide(divide(X3,X2),divide(X4,X2))
| ~ quotient(X3,X4,X1)
| ~ less_equal(divide(X1,X2),divide(divide(X3,X2),divide(X4,X2))) ),
inference(spm,[status(thm)],[c_0_21,c_0_48]) ).
cnf(c_0_145,hypothesis,
( less_equal(divide(idQb_Q__idQ_idQa,divide(X1,idQ_idQa)),divide(X2,idQ_idQa))
| ~ quotient(idQb,X1,X2) ),
inference(spm,[status(thm)],[c_0_44,c_0_138]) ).
cnf(c_0_146,hypothesis,
quotient(idQ_idQa,divide(idQ_idQa,idQa),zero),
inference(spm,[status(thm)],[c_0_17,c_0_139]) ).
cnf(c_0_147,hypothesis,
quotient(divide(idQ_idQb,divide(idQ_idQb,idQb)),zero,zero),
inference(spm,[status(thm)],[c_0_17,c_0_140]) ).
cnf(c_0_148,hypothesis,
( less_equal(divide(idQb,divide(X1,b)),divide(X2,b))
| ~ quotient(identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_44,c_0_89]) ).
cnf(c_0_149,hypothesis,
divide(b,idQb) = idQ_idQb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_141]),c_0_142])]) ).
cnf(c_0_150,hypothesis,
( less_equal(divide(idQ_idQb,idQ_idQb),divide(X1,idQb))
| ~ quotient(identity,identity,X1) ),
inference(spm,[status(thm)],[c_0_114,c_0_106]) ).
cnf(c_0_151,hypothesis,
quotient(divide(idQa,divide(idQa,zero)),zero,zero),
inference(spm,[status(thm)],[c_0_17,c_0_143]) ).
cnf(c_0_152,plain,
( divide(divide(X1,X2),divide(X3,X2)) = zero
| ~ quotient(X1,X3,X4)
| ~ less_equal(X4,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_58]),c_0_22])]) ).
cnf(c_0_153,hypothesis,
( less_equal(divide(idQb_Q__idQ_idQa,zero),divide(X1,idQ_idQa))
| ~ quotient(idQb,divide(divide(idQ_idQa,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_145,c_0_49]) ).
cnf(c_0_154,hypothesis,
less_equal(idQ_idQa,divide(idQ_idQa,idQa)),
inference(spm,[status(thm)],[c_0_36,c_0_146]) ).
cnf(c_0_155,hypothesis,
less_equal(divide(idQ_idQb,divide(idQ_idQb,idQb)),zero),
inference(spm,[status(thm)],[c_0_36,c_0_147]) ).
cnf(c_0_156,hypothesis,
( less_equal(divide(idQb,divide(X1,b)),zero)
| ~ quotient(identity,X1,X2)
| ~ less_equal(X2,b) ),
inference(spm,[status(thm)],[c_0_148,c_0_58]) ).
cnf(c_0_157,hypothesis,
less_equal(idQ_idQb,b),
inference(spm,[status(thm)],[c_0_26,c_0_149]) ).
cnf(c_0_158,hypothesis,
( less_equal(divide(idQ_idQb,idQ_idQb),zero)
| ~ quotient(identity,identity,zero) ),
inference(spm,[status(thm)],[c_0_150,c_0_28]) ).
cnf(c_0_159,hypothesis,
less_equal(divide(idQa,divide(idQa,zero)),zero),
inference(spm,[status(thm)],[c_0_36,c_0_151]) ).
cnf(c_0_160,plain,
( divide(divide(X1,X2),divide(X3,X2)) = zero
| ~ less_equal(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_20]),c_0_22])]) ).
cnf(c_0_161,hypothesis,
less_equal(divide(idQb_Q__idQ_idQa,zero),divide(divide(idQb,divide(divide(idQ_idQa,X1),X2)),idQ_idQa)),
inference(spm,[status(thm)],[c_0_153,c_0_17]) ).
cnf(c_0_162,hypothesis,
divide(idQ_idQa,idQa) = idQ_idQa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_154]),c_0_26])]) ).
cnf(c_0_163,hypothesis,
quotient(idQa,idQ_idQb,idQa_Q__idQ_idQb),
idQa_divide_idQ_idQb ).
cnf(c_0_164,hypothesis,
divide(idQ_idQb,divide(idQ_idQb,idQb)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_155]),c_0_22])]) ).
cnf(c_0_165,hypothesis,
less_equal(divide(idQb,divide(idQb,b)),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_106]),c_0_157])]) ).
cnf(c_0_166,hypothesis,
( divide(idQ_idQb,idQ_idQb) = zero
| ~ quotient(identity,identity,zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_158]),c_0_22])]) ).
cnf(c_0_167,hypothesis,
divide(idQa,divide(idQa,zero)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_159]),c_0_22])]) ).
cnf(c_0_168,plain,
( divide(divide(X1,X2),zero) = zero
| ~ less_equal(X1,divide(X2,X3)) ),
inference(spm,[status(thm)],[c_0_160,c_0_77]) ).
cnf(c_0_169,hypothesis,
less_equal(divide(idQb_Q__idQ_idQa,zero),divide(divide(idQb,divide(idQ_idQa,X1)),idQ_idQa)),
inference(spm,[status(thm)],[c_0_161,c_0_162]) ).
cnf(c_0_170,hypothesis,
( less_equal(divide(idQa_Q__idQ_idQb,divide(X1,idQ_idQb)),divide(X2,idQ_idQb))
| ~ quotient(idQa,X1,X2) ),
inference(spm,[status(thm)],[c_0_44,c_0_163]) ).
cnf(c_0_171,hypothesis,
quotient(idQ_idQb,divide(idQ_idQb,idQb),zero),
inference(spm,[status(thm)],[c_0_17,c_0_164]) ).
cnf(c_0_172,hypothesis,
divide(idQb,divide(idQb,b)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_165]),c_0_22])]) ).
cnf(c_0_173,hypothesis,
divide(idQ_idQb,idQ_idQb) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_20]),c_0_30])]) ).
cnf(c_0_174,hypothesis,
( less_equal(divide(idQ_idQa,idQ_idQa),divide(X1,idQa))
| ~ quotient(identity,identity,X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_53]) ).
cnf(c_0_175,hypothesis,
quotient(idQa,divide(idQa,zero),zero),
inference(spm,[status(thm)],[c_0_17,c_0_167]) ).
cnf(c_0_176,hypothesis,
divide(divide(divide(idQb_Q__idQ_idQa,zero),divide(idQb,divide(idQ_idQa,X1))),zero) = zero,
inference(spm,[status(thm)],[c_0_168,c_0_169]) ).
cnf(c_0_177,hypothesis,
( less_equal(divide(idQa_Q__idQ_idQb,zero),divide(X1,idQ_idQb))
| ~ quotient(idQa,divide(divide(idQ_idQb,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_170,c_0_49]) ).
cnf(c_0_178,hypothesis,
less_equal(idQ_idQb,divide(idQ_idQb,idQb)),
inference(spm,[status(thm)],[c_0_36,c_0_171]) ).
cnf(c_0_179,hypothesis,
quotient(idQb,divide(idQb,b),zero),
inference(spm,[status(thm)],[c_0_17,c_0_172]) ).
cnf(c_0_180,hypothesis,
quotient(idQ_idQb,idQ_idQb,zero),
inference(spm,[status(thm)],[c_0_17,c_0_173]) ).
cnf(c_0_181,hypothesis,
less_equal(divide(idQ_idQa,idQ_idQa),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_28]),c_0_47])]) ).
cnf(c_0_182,hypothesis,
less_equal(idQa,divide(idQa,zero)),
inference(spm,[status(thm)],[c_0_36,c_0_175]) ).
cnf(c_0_183,hypothesis,
( less_equal(divide(divide(X1,a),idQa),divide(X2,a))
| ~ quotient(X1,identity,X2) ),
inference(spm,[status(thm)],[c_0_42,c_0_17]) ).
cnf(c_0_184,hypothesis,
quotient(divide(divide(idQb_Q__idQ_idQa,zero),divide(idQb,divide(idQ_idQa,X1))),zero,zero),
inference(spm,[status(thm)],[c_0_17,c_0_176]) ).
cnf(c_0_185,hypothesis,
( less_equal(divide(idQa_Q__idQ_idQb,divide(X1,idQ_idQb)),zero)
| ~ quotient(idQa,X1,divide(X2,idQb)) ),
inference(spm,[status(thm)],[c_0_170,c_0_131]) ).
cnf(c_0_186,hypothesis,
less_equal(divide(idQa_Q__idQ_idQb,zero),divide(divide(idQa,divide(divide(idQ_idQb,X1),X2)),idQ_idQb)),
inference(spm,[status(thm)],[c_0_177,c_0_17]) ).
cnf(c_0_187,hypothesis,
divide(idQ_idQb,idQb) = idQ_idQb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_178]),c_0_26])]) ).
cnf(c_0_188,hypothesis,
less_equal(idQb,divide(idQb,b)),
inference(spm,[status(thm)],[c_0_36,c_0_179]) ).
cnf(c_0_189,hypothesis,
( less_equal(divide(idQa_Q__idQ_idQb,zero),divide(X1,idQ_idQb))
| ~ quotient(idQa,X2,X1)
| ~ less_equal(X2,idQ_idQb) ),
inference(spm,[status(thm)],[c_0_24,c_0_163]) ).
cnf(c_0_190,hypothesis,
less_equal(idQ_idQb,idQ_idQb),
inference(spm,[status(thm)],[c_0_36,c_0_180]) ).
cnf(c_0_191,hypothesis,
divide(idQ_idQa,idQ_idQa) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_181]),c_0_22])]) ).
cnf(c_0_192,hypothesis,
( less_equal(divide(idQa,zero),divide(X1,a))
| ~ quotient(identity,divide(divide(a,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_81,c_0_49]) ).
cnf(c_0_193,hypothesis,
divide(idQa,zero) = idQa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_182]),c_0_26])]) ).
cnf(c_0_194,hypothesis,
less_equal(divide(divide(X1,a),idQa),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_28]),c_0_47])]) ).
cnf(c_0_195,hypothesis,
less_equal(divide(divide(idQb_Q__idQ_idQa,zero),divide(idQb,divide(idQ_idQa,X1))),zero),
inference(spm,[status(thm)],[c_0_36,c_0_184]) ).
cnf(c_0_196,hypothesis,
less_equal(divide(idQa_Q__idQ_idQb,divide(idQb,idQ_idQb)),zero),
inference(spm,[status(thm)],[c_0_185,c_0_17]) ).
cnf(c_0_197,hypothesis,
less_equal(divide(idQa_Q__idQ_idQb,zero),divide(divide(idQa,divide(idQ_idQb,X1)),idQ_idQb)),
inference(spm,[status(thm)],[c_0_186,c_0_187]) ).
cnf(c_0_198,hypothesis,
divide(idQb,b) = idQb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_188]),c_0_26])]) ).
cnf(c_0_199,hypothesis,
( X1 = idQb_Q__idQ_idQa
| ~ quotient(idQb,idQ_idQa,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_138]) ).
cnf(c_0_200,hypothesis,
less_equal(divide(idQa_Q__idQ_idQb,zero),divide(idQa_Q__idQ_idQb,idQ_idQb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_163]),c_0_190])]) ).
cnf(c_0_201,hypothesis,
( less_equal(divide(idQb_Q__idQ_idQa,zero),divide(X1,idQ_idQa))
| ~ quotient(idQb,X2,X1)
| ~ less_equal(X2,idQ_idQa) ),
inference(spm,[status(thm)],[c_0_24,c_0_138]) ).
cnf(c_0_202,hypothesis,
quotient(idQ_idQa,idQ_idQa,zero),
inference(spm,[status(thm)],[c_0_17,c_0_191]) ).
cnf(c_0_203,plain,
quotient(divide(X1,X2),X1,zero),
inference(spm,[status(thm)],[c_0_17,c_0_77]) ).
cnf(c_0_204,hypothesis,
( less_equal(idQa,divide(X1,a))
| ~ quotient(identity,divide(divide(a,X2),X3),X1) ),
inference(rw,[status(thm)],[c_0_192,c_0_193]) ).
cnf(c_0_205,hypothesis,
divide(divide(X1,a),idQa) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_194]),c_0_22])]) ).
cnf(c_0_206,plain,
( divide(divide(X1,X2),X3) = divide(divide(X1,X3),zero)
| ~ less_equal(divide(divide(X1,X2),X3),divide(divide(X1,X3),zero))
| ~ less_equal(X2,X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_102]) ).
cnf(c_0_207,hypothesis,
divide(divide(idQb_Q__idQ_idQa,zero),divide(idQb,divide(idQ_idQa,X1))) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_195]),c_0_22])]) ).
cnf(c_0_208,hypothesis,
divide(idQa_Q__idQ_idQb,divide(idQb,idQ_idQb)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_196]),c_0_22])]) ).
cnf(c_0_209,hypothesis,
divide(divide(divide(idQa_Q__idQ_idQb,zero),divide(idQa,divide(idQ_idQb,X1))),zero) = zero,
inference(spm,[status(thm)],[c_0_168,c_0_197]) ).
cnf(c_0_210,hypothesis,
quotient(divide(idQb,X1),idQb,zero),
inference(spm,[status(thm)],[c_0_115,c_0_198]) ).
cnf(c_0_211,hypothesis,
divide(idQb,idQ_idQa) = idQb_Q__idQ_idQa,
inference(spm,[status(thm)],[c_0_199,c_0_17]) ).
cnf(c_0_212,hypothesis,
less_equal(divide(divide(idQa_Q__idQ_idQb,divide(idQa_Q__idQ_idQb,idQ_idQb)),zero),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_200]),c_0_22])]) ).
cnf(c_0_213,hypothesis,
( less_equal(divide(idQb_Q__idQ_idQa,zero),divide(idQb_Q__idQ_idQa,idQ_idQa))
| ~ less_equal(idQ_idQa,idQ_idQa) ),
inference(spm,[status(thm)],[c_0_201,c_0_138]) ).
cnf(c_0_214,hypothesis,
less_equal(idQ_idQa,idQ_idQa),
inference(spm,[status(thm)],[c_0_36,c_0_202]) ).
cnf(c_0_215,plain,
divide(divide(divide(X1,X2),X3),divide(X1,X3)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_203]),c_0_22])]) ).
cnf(c_0_216,hypothesis,
less_equal(idQa,divide(divide(identity,divide(divide(a,X1),X2)),a)),
inference(spm,[status(thm)],[c_0_204,c_0_17]) ).
cnf(c_0_217,hypothesis,
quotient(divide(X1,a),idQa,zero),
inference(spm,[status(thm)],[c_0_17,c_0_205]) ).
cnf(c_0_218,hypothesis,
divide(divide(idQb_Q__idQ_idQa,divide(idQb,divide(idQ_idQa,X1))),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_207]),c_0_22]),c_0_22])]) ).
cnf(c_0_219,hypothesis,
quotient(idQa_Q__idQ_idQb,divide(idQb,idQ_idQb),zero),
inference(spm,[status(thm)],[c_0_17,c_0_208]) ).
cnf(c_0_220,hypothesis,
quotient(divide(divide(idQa_Q__idQ_idQb,zero),divide(idQa,divide(idQ_idQb,X1))),zero,zero),
inference(spm,[status(thm)],[c_0_17,c_0_209]) ).
cnf(c_0_221,plain,
( less_equal(divide(divide(X1,X2),divide(X3,X2)),zero)
| ~ quotient(X1,X3,X4)
| ~ less_equal(X4,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_58]) ).
cnf(c_0_222,hypothesis,
quotient(idQb_Q__idQ_idQa,idQb,zero),
inference(spm,[status(thm)],[c_0_210,c_0_211]) ).
cnf(c_0_223,hypothesis,
divide(divide(idQa_Q__idQ_idQb,divide(idQa_Q__idQ_idQb,idQ_idQb)),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_212]),c_0_22])]) ).
cnf(c_0_224,hypothesis,
less_equal(divide(idQb_Q__idQ_idQa,zero),divide(idQb_Q__idQ_idQa,idQ_idQa)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_213,c_0_214])]) ).
cnf(c_0_225,plain,
quotient(divide(divide(X1,X2),X3),divide(X1,X3),zero),
inference(spm,[status(thm)],[c_0_17,c_0_215]) ).
cnf(c_0_226,hypothesis,
less_equal(idQa,divide(divide(identity,divide(idQ_idQa,X1)),a)),
inference(spm,[status(thm)],[c_0_216,c_0_82]) ).
cnf(c_0_227,hypothesis,
less_equal(divide(X1,a),idQa),
inference(spm,[status(thm)],[c_0_36,c_0_217]) ).
cnf(c_0_228,hypothesis,
quotient(divide(idQb_Q__idQ_idQa,divide(idQb,divide(idQ_idQa,X1))),zero,zero),
inference(spm,[status(thm)],[c_0_17,c_0_218]) ).
cnf(c_0_229,hypothesis,
less_equal(idQa_Q__idQ_idQb,divide(idQb,idQ_idQb)),
inference(spm,[status(thm)],[c_0_36,c_0_219]) ).
cnf(c_0_230,hypothesis,
less_equal(divide(divide(idQa_Q__idQ_idQb,zero),divide(idQa,divide(idQ_idQb,X1))),zero),
inference(spm,[status(thm)],[c_0_36,c_0_220]) ).
cnf(c_0_231,hypothesis,
less_equal(divide(divide(idQb_Q__idQ_idQa,X1),divide(idQb,X1)),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_222]),c_0_22])]) ).
cnf(c_0_232,hypothesis,
quotient(divide(idQa_Q__idQ_idQb,divide(idQa_Q__idQ_idQb,idQ_idQb)),zero,zero),
inference(spm,[status(thm)],[c_0_17,c_0_223]) ).
cnf(c_0_233,hypothesis,
less_equal(divide(divide(idQb_Q__idQ_idQa,divide(idQb_Q__idQ_idQa,idQ_idQa)),zero),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_224]),c_0_22])]) ).
cnf(c_0_234,plain,
less_equal(divide(divide(X1,X2),X3),divide(X1,X3)),
inference(spm,[status(thm)],[c_0_36,c_0_225]) ).
cnf(c_0_235,hypothesis,
divide(divide(identity,divide(idQ_idQa,X1)),a) = idQa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_226]),c_0_227])]) ).
cnf(c_0_236,hypothesis,
( less_equal(divide(divide(X1,idQ_idQa),divide(X2,idQ_idQa)),zero)
| ~ quotient(X1,X2,divide(X3,idQa)) ),
inference(spm,[status(thm)],[c_0_48,c_0_71]) ).
cnf(c_0_237,hypothesis,
less_equal(divide(idQb_Q__idQ_idQa,divide(idQb,divide(idQ_idQa,X1))),zero),
inference(spm,[status(thm)],[c_0_36,c_0_228]) ).
cnf(c_0_238,hypothesis,
less_equal(divide(divide(idQa_Q__idQ_idQb,idQb),zero),zero),
inference(spm,[status(thm)],[c_0_33,c_0_229]) ).
cnf(c_0_239,hypothesis,
divide(divide(idQa_Q__idQ_idQb,zero),divide(idQa,divide(idQ_idQb,X1))) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_230]),c_0_22])]) ).
cnf(c_0_240,hypothesis,
divide(divide(idQb_Q__idQ_idQa,X1),divide(idQb,X1)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_231]),c_0_22])]) ).
cnf(c_0_241,hypothesis,
less_equal(divide(idQa_Q__idQ_idQb,divide(idQa_Q__idQ_idQb,idQ_idQb)),zero),
inference(spm,[status(thm)],[c_0_36,c_0_232]) ).
cnf(c_0_242,hypothesis,
divide(divide(idQb_Q__idQ_idQa,divide(idQb_Q__idQ_idQa,idQ_idQa)),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_233]),c_0_22])]) ).
cnf(c_0_243,hypothesis,
divide(divide(idQ_idQa,X1),a) = zero,
inference(spm,[status(thm)],[c_0_49,c_0_82]) ).
cnf(c_0_244,hypothesis,
less_equal(divide(idQa,X1),divide(divide(identity,divide(idQ_idQa,X2)),X1)),
inference(spm,[status(thm)],[c_0_234,c_0_235]) ).
cnf(c_0_245,hypothesis,
less_equal(divide(divide(X1,idQ_idQa),divide(idQa,idQ_idQa)),zero),
inference(spm,[status(thm)],[c_0_236,c_0_17]) ).
cnf(c_0_246,hypothesis,
divide(idQb_Q__idQ_idQa,divide(idQb,divide(idQ_idQa,X1))) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_237]),c_0_22])]) ).
cnf(c_0_247,hypothesis,
divide(divide(idQa_Q__idQ_idQb,idQb),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_238]),c_0_22])]) ).
cnf(c_0_248,hypothesis,
divide(divide(idQa_Q__idQ_idQb,divide(idQa,divide(idQ_idQb,X1))),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_239]),c_0_22]),c_0_22])]) ).
cnf(c_0_249,hypothesis,
quotient(divide(idQb_Q__idQ_idQa,X1),divide(idQb,X1),zero),
inference(spm,[status(thm)],[c_0_17,c_0_240]) ).
cnf(c_0_250,hypothesis,
divide(idQa_Q__idQ_idQb,divide(idQa_Q__idQ_idQb,idQ_idQb)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_241]),c_0_22])]) ).
cnf(c_0_251,hypothesis,
quotient(divide(idQb_Q__idQ_idQa,divide(idQb_Q__idQ_idQa,idQ_idQa)),zero,zero),
inference(spm,[status(thm)],[c_0_17,c_0_242]) ).
cnf(c_0_252,hypothesis,
less_equal(divide(divide(divide(a,X1),a),zero),zero),
inference(spm,[status(thm)],[c_0_56,c_0_243]) ).
cnf(c_0_253,hypothesis,
less_equal(divide(idQa,X1),divide(divide(identity,idQ_idQa),X1)),
inference(spm,[status(thm)],[c_0_244,c_0_162]) ).
cnf(c_0_254,hypothesis,
divide(divide(X1,idQ_idQa),divide(idQa,idQ_idQa)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_245]),c_0_22])]) ).
cnf(c_0_255,hypothesis,
less_equal(divide(divide(idQb_Q__idQ_idQa,X1),divide(idQb,divide(idQ_idQa,X2))),zero),
inference(spm,[status(thm)],[c_0_234,c_0_246]) ).
cnf(c_0_256,hypothesis,
quotient(divide(idQa_Q__idQ_idQb,idQb),zero,zero),
inference(spm,[status(thm)],[c_0_17,c_0_247]) ).
cnf(c_0_257,hypothesis,
quotient(divide(idQa_Q__idQ_idQb,divide(idQa,divide(idQ_idQb,X1))),zero,zero),
inference(spm,[status(thm)],[c_0_17,c_0_248]) ).
cnf(c_0_258,hypothesis,
less_equal(divide(idQb_Q__idQ_idQa,X1),divide(idQb,X1)),
inference(spm,[status(thm)],[c_0_36,c_0_249]) ).
cnf(c_0_259,hypothesis,
quotient(idQa_Q__idQ_idQb,divide(idQa_Q__idQ_idQb,idQ_idQb),zero),
inference(spm,[status(thm)],[c_0_17,c_0_250]) ).
cnf(c_0_260,hypothesis,
less_equal(divide(idQb_Q__idQ_idQa,divide(idQb_Q__idQ_idQa,idQ_idQa)),zero),
inference(spm,[status(thm)],[c_0_36,c_0_251]) ).
cnf(c_0_261,hypothesis,
less_equal(divide(divide(idQ_idQa,a),zero),zero),
inference(spm,[status(thm)],[c_0_252,c_0_82]) ).
cnf(c_0_262,hypothesis,
less_equal(divide(idQa,divide(idQa,idQ_idQa)),zero),
inference(spm,[status(thm)],[c_0_253,c_0_254]) ).
cnf(c_0_263,hypothesis,
divide(divide(idQb_Q__idQ_idQa,X1),divide(idQb,divide(idQ_idQa,X2))) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_255]),c_0_22])]) ).
cnf(c_0_264,hypothesis,
less_equal(divide(idQa_Q__idQ_idQb,idQb),zero),
inference(spm,[status(thm)],[c_0_36,c_0_256]) ).
cnf(c_0_265,hypothesis,
less_equal(divide(idQa_Q__idQ_idQb,divide(idQa,divide(idQ_idQb,X1))),zero),
inference(spm,[status(thm)],[c_0_36,c_0_257]) ).
cnf(c_0_266,hypothesis,
( less_equal(divide(divide(X1,idQ_idQb),zero),divide(X2,idQ_idQb))
| ~ quotient(X1,divide(X3,idQb),X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_131]) ).
cnf(c_0_267,hypothesis,
( less_equal(divide(idQb_Q__idQ_idQa,X1),zero)
| ~ less_equal(idQb,X1) ),
inference(spm,[status(thm)],[c_0_258,c_0_58]) ).
cnf(c_0_268,hypothesis,
less_equal(idQa_Q__idQ_idQb,divide(idQa_Q__idQ_idQb,idQ_idQb)),
inference(spm,[status(thm)],[c_0_36,c_0_259]) ).
cnf(c_0_269,hypothesis,
divide(idQb_Q__idQ_idQa,divide(idQb_Q__idQ_idQa,idQ_idQa)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_260]),c_0_22])]) ).
cnf(c_0_270,hypothesis,
divide(divide(idQ_idQa,a),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_261]),c_0_22])]) ).
cnf(c_0_271,hypothesis,
divide(idQa,divide(idQa,idQ_idQa)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_262]),c_0_22])]) ).
cnf(c_0_272,hypothesis,
quotient(divide(idQb_Q__idQ_idQa,X1),divide(idQb,divide(idQ_idQa,X2)),zero),
inference(spm,[status(thm)],[c_0_17,c_0_263]) ).
cnf(c_0_273,hypothesis,
divide(idQa_Q__idQ_idQb,idQb) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_264]),c_0_22])]) ).
cnf(c_0_274,hypothesis,
divide(idQa_Q__idQ_idQb,divide(idQa,divide(idQ_idQb,X1))) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_265]),c_0_22])]) ).
cnf(c_0_275,hypothesis,
less_equal(divide(divide(X1,idQ_idQb),zero),divide(divide(X1,divide(X2,idQb)),idQ_idQb)),
inference(spm,[status(thm)],[c_0_266,c_0_17]) ).
cnf(c_0_276,hypothesis,
( divide(idQb_Q__idQ_idQa,X1) = zero
| ~ less_equal(idQb,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_267]),c_0_22])]) ).
cnf(c_0_277,hypothesis,
divide(idQa_Q__idQ_idQb,idQ_idQb) = idQa_Q__idQ_idQb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_268]),c_0_26])]) ).
cnf(c_0_278,hypothesis,
quotient(idQb_Q__idQ_idQa,divide(idQb_Q__idQ_idQa,idQ_idQa),zero),
inference(spm,[status(thm)],[c_0_17,c_0_269]) ).
cnf(c_0_279,hypothesis,
quotient(divide(idQ_idQa,a),zero,zero),
inference(spm,[status(thm)],[c_0_17,c_0_270]) ).
cnf(c_0_280,hypothesis,
quotient(idQa,divide(idQa,idQ_idQa),zero),
inference(spm,[status(thm)],[c_0_17,c_0_271]) ).
cnf(c_0_281,hypothesis,
quotient(idQb_Q__idQ_idQa,divide(idQb,divide(idQ_idQa,X1)),zero),
inference(spm,[status(thm)],[c_0_17,c_0_246]) ).
cnf(c_0_282,hypothesis,
( divide(X1,b) = divide(idQb,divide(X2,b))
| ~ quotient(idQb,X2,X1)
| ~ less_equal(divide(X1,b),divide(idQb,divide(X2,b))) ),
inference(spm,[status(thm)],[c_0_144,c_0_198]) ).
cnf(c_0_283,hypothesis,
less_equal(divide(idQb_Q__idQ_idQa,X1),divide(idQb,divide(idQ_idQa,X2))),
inference(spm,[status(thm)],[c_0_36,c_0_272]) ).
cnf(c_0_284,hypothesis,
quotient(idQa_Q__idQ_idQb,idQb,zero),
inference(spm,[status(thm)],[c_0_17,c_0_273]) ).
cnf(c_0_285,hypothesis,
less_equal(divide(divide(idQa_Q__idQ_idQb,X1),divide(idQa,divide(idQ_idQb,X2))),zero),
inference(spm,[status(thm)],[c_0_234,c_0_274]) ).
cnf(c_0_286,hypothesis,
less_equal(divide(divide(X1,idQ_idQb),zero),divide(divide(X1,zero),idQ_idQb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_275,c_0_276]),c_0_105])]) ).
cnf(c_0_287,hypothesis,
quotient(idQa_Q__idQ_idQb,idQ_idQb,idQa_Q__idQ_idQb),
inference(spm,[status(thm)],[c_0_17,c_0_277]) ).
cnf(c_0_288,hypothesis,
less_equal(idQb_Q__idQ_idQa,divide(idQb_Q__idQ_idQa,idQ_idQa)),
inference(spm,[status(thm)],[c_0_36,c_0_278]) ).
cnf(c_0_289,plain,
( less_equal(divide(divide(X1,X2),zero),zero)
| ~ less_equal(X1,zero) ),
inference(spm,[status(thm)],[c_0_29,c_0_22]) ).
cnf(c_0_290,hypothesis,
less_equal(divide(idQ_idQa,a),zero),
inference(spm,[status(thm)],[c_0_36,c_0_279]) ).
cnf(c_0_291,hypothesis,
( less_equal(divide(idQb_Q__idQ_idQa,divide(X1,idQ_idQa)),zero)
| ~ quotient(idQb,X1,X2)
| ~ less_equal(X2,idQ_idQa) ),
inference(spm,[status(thm)],[c_0_145,c_0_58]) ).
cnf(c_0_292,hypothesis,
less_equal(idQa,divide(idQa,idQ_idQa)),
inference(spm,[status(thm)],[c_0_36,c_0_280]) ).
cnf(c_0_293,hypothesis,
less_equal(idQb_Q__idQ_idQa,divide(idQb,divide(idQ_idQa,X1))),
inference(spm,[status(thm)],[c_0_36,c_0_281]) ).
cnf(c_0_294,hypothesis,
divide(idQb,divide(idQ_idQa,b)) = divide(idQb_Q__idQ_idQa,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_282,c_0_283]),c_0_138])]) ).
cnf(c_0_295,hypothesis,
less_equal(divide(divide(idQa_Q__idQ_idQb,X1),divide(idQb,X1)),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_284]),c_0_22])]) ).
cnf(c_0_296,hypothesis,
divide(divide(idQa_Q__idQ_idQb,X1),divide(idQa,divide(idQ_idQb,X2))) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_285]),c_0_22])]) ).
cnf(c_0_297,hypothesis,
less_equal(divide(divide(divide(X1,idQ_idQb),divide(divide(X1,zero),idQ_idQb)),zero),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_286]),c_0_22])]) ).
cnf(c_0_298,hypothesis,
divide(divide(idQa_Q__idQ_idQb,zero),idQ_idQb) = divide(idQa_Q__idQ_idQb,zero),
inference(spm,[status(thm)],[c_0_108,c_0_287]) ).
cnf(c_0_299,hypothesis,
divide(idQb_Q__idQ_idQa,idQ_idQa) = idQb_Q__idQ_idQa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_288]),c_0_26])]) ).
cnf(c_0_300,plain,
( divide(divide(X1,X2),zero) = zero
| ~ less_equal(X1,zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_289]),c_0_22])]) ).
cnf(c_0_301,hypothesis,
divide(idQ_idQa,a) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_290]),c_0_22])]) ).
cnf(c_0_302,hypothesis,
less_equal(divide(idQb_Q__idQ_idQa,divide(identity,idQ_idQa)),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_291,c_0_47]),c_0_22])]) ).
cnf(c_0_303,hypothesis,
divide(idQa,idQ_idQa) = idQa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_292]),c_0_26])]) ).
cnf(c_0_304,hypothesis,
less_equal(idQb_Q__idQ_idQa,divide(idQb_Q__idQ_idQa,b)),
inference(spm,[status(thm)],[c_0_293,c_0_294]) ).
cnf(c_0_305,hypothesis,
divide(divide(idQa_Q__idQ_idQb,X1),divide(idQb,X1)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_295]),c_0_22])]) ).
cnf(c_0_306,hypothesis,
quotient(divide(idQa_Q__idQ_idQb,X1),divide(idQa,divide(idQ_idQb,X2)),zero),
inference(spm,[status(thm)],[c_0_17,c_0_296]) ).
cnf(c_0_307,hypothesis,
less_equal(divide(divide(idQa_Q__idQ_idQb,divide(idQa_Q__idQ_idQb,zero)),zero),zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_297,c_0_298]),c_0_277]) ).
cnf(c_0_308,hypothesis,
less_equal(divide(idQb_Q__idQ_idQa,divide(idQa,idQ_idQa)),zero),
inference(spm,[status(thm)],[c_0_245,c_0_299]) ).
cnf(c_0_309,plain,
( quotient(divide(X1,X2),zero,zero)
| ~ less_equal(X1,zero) ),
inference(spm,[status(thm)],[c_0_17,c_0_300]) ).
cnf(c_0_310,hypothesis,
quotient(idQ_idQa,a,zero),
inference(spm,[status(thm)],[c_0_17,c_0_301]) ).
cnf(c_0_311,hypothesis,
divide(idQb_Q__idQ_idQa,divide(identity,idQ_idQa)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_302]),c_0_22])]) ).
cnf(c_0_312,hypothesis,
divide(divide(X1,idQ_idQa),idQa) = zero,
inference(rw,[status(thm)],[c_0_254,c_0_303]) ).
cnf(c_0_313,hypothesis,
divide(idQb_Q__idQ_idQa,b) = idQb_Q__idQ_idQa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_304]),c_0_26])]) ).
cnf(c_0_314,hypothesis,
quotient(divide(idQa_Q__idQ_idQb,X1),divide(idQb,X1),zero),
inference(spm,[status(thm)],[c_0_17,c_0_305]) ).
cnf(c_0_315,hypothesis,
quotient(idQa_Q__idQ_idQb,divide(idQa,divide(idQ_idQb,X1)),zero),
inference(spm,[status(thm)],[c_0_17,c_0_274]) ).
cnf(c_0_316,hypothesis,
( divide(X1,a) = divide(idQa,divide(X2,a))
| ~ quotient(idQa,X2,X1)
| ~ less_equal(divide(X1,a),divide(idQa,divide(X2,a))) ),
inference(spm,[status(thm)],[c_0_144,c_0_101]) ).
cnf(c_0_317,hypothesis,
less_equal(divide(idQa_Q__idQ_idQb,X1),divide(idQa,divide(idQ_idQb,X2))),
inference(spm,[status(thm)],[c_0_36,c_0_306]) ).
cnf(c_0_318,hypothesis,
( X1 = idQa_Q__idQ_idQb
| ~ quotient(idQa,idQ_idQb,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_163]) ).
cnf(c_0_319,hypothesis,
divide(divide(idQa_Q__idQ_idQb,divide(idQa_Q__idQ_idQb,zero)),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_307]),c_0_22])]) ).
cnf(c_0_320,hypothesis,
divide(idQb_Q__idQ_idQa,divide(idQa,idQ_idQa)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_308]),c_0_22])]) ).
cnf(c_0_321,hypothesis,
quotient(idQb,b,idQb),
inference(spm,[status(thm)],[c_0_17,c_0_198]) ).
cnf(c_0_322,plain,
( less_equal(divide(X1,X2),zero)
| ~ less_equal(X1,zero) ),
inference(spm,[status(thm)],[c_0_36,c_0_309]) ).
cnf(c_0_323,hypothesis,
less_equal(divide(divide(idQ_idQa,X1),divide(a,X1)),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_310]),c_0_22])]) ).
cnf(c_0_324,hypothesis,
quotient(idQb_Q__idQ_idQa,divide(identity,idQ_idQa),zero),
inference(spm,[status(thm)],[c_0_17,c_0_311]) ).
cnf(c_0_325,hypothesis,
quotient(divide(X1,idQ_idQa),idQa,zero),
inference(spm,[status(thm)],[c_0_17,c_0_312]) ).
cnf(c_0_326,hypothesis,
divide(idQb,divide(idQ_idQa,b)) = idQb_Q__idQ_idQa,
inference(rw,[status(thm)],[c_0_294,c_0_313]) ).
cnf(c_0_327,hypothesis,
divide(divide(divide(idQa_Q__idQ_idQb,X1),X2),divide(divide(idQb,X1),X2)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_314]),c_0_22])]) ).
cnf(c_0_328,hypothesis,
less_equal(idQa_Q__idQ_idQb,divide(idQa,divide(idQ_idQb,X1))),
inference(spm,[status(thm)],[c_0_36,c_0_315]) ).
cnf(c_0_329,hypothesis,
divide(idQa,divide(idQ_idQb,a)) = divide(idQa_Q__idQ_idQb,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_316,c_0_317]),c_0_163])]) ).
cnf(c_0_330,hypothesis,
less_equal(divide(divide(divide(X1,a),X2),divide(idQa,X2)),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_217]),c_0_22])]) ).
cnf(c_0_331,hypothesis,
divide(idQa,idQ_idQb) = idQa_Q__idQ_idQb,
inference(spm,[status(thm)],[c_0_318,c_0_17]) ).
cnf(c_0_332,hypothesis,
quotient(divide(idQa_Q__idQ_idQb,divide(idQa_Q__idQ_idQb,zero)),zero,zero),
inference(spm,[status(thm)],[c_0_17,c_0_319]) ).
cnf(c_0_333,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,X4,X2)
| ~ quotient(X5,X4,X1)
| ~ quotient(X5,X3,X6)
| ~ less_equal(X6,X4) ),
inference(spm,[status(thm)],[c_0_18,c_0_20]) ).
cnf(c_0_334,hypothesis,
less_equal(divide(divide(divide(X1,a),X2),idQa),zero),
inference(spm,[status(thm)],[c_0_234,c_0_205]) ).
cnf(c_0_335,hypothesis,
quotient(idQb_Q__idQ_idQa,divide(idQa,idQ_idQa),zero),
inference(spm,[status(thm)],[c_0_17,c_0_320]) ).
cnf(c_0_336,hypothesis,
divide(divide(idQb,zero),b) = divide(idQb,zero),
inference(spm,[status(thm)],[c_0_108,c_0_321]) ).
cnf(c_0_337,plain,
( divide(X1,X2) = zero
| ~ less_equal(X1,zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_322]),c_0_22])]) ).
cnf(c_0_338,hypothesis,
divide(divide(idQ_idQa,X1),divide(a,X1)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_323]),c_0_22])]) ).
cnf(c_0_339,hypothesis,
less_equal(divide(divide(idQb_Q__idQ_idQa,X1),divide(divide(identity,idQ_idQa),X1)),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_324]),c_0_22])]) ).
cnf(c_0_340,hypothesis,
less_equal(idQa,divide(divide(identity,idQ_idQa),idQ_idQa)),
inference(spm,[status(thm)],[c_0_253,c_0_303]) ).
cnf(c_0_341,hypothesis,
less_equal(divide(X1,idQ_idQa),idQa),
inference(spm,[status(thm)],[c_0_36,c_0_325]) ).
cnf(c_0_342,hypothesis,
( less_equal(divide(divide(X1,b),idQb),divide(X2,b))
| ~ quotient(X1,identity,X2) ),
inference(spm,[status(thm)],[c_0_92,c_0_17]) ).
cnf(c_0_343,hypothesis,
( less_equal(divide(divide(X1,a),zero),divide(X2,a))
| ~ quotient(X1,divide(idQ_idQa,X3),X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_243]) ).
cnf(c_0_344,hypothesis,
quotient(idQb,divide(idQ_idQa,b),idQb_Q__idQ_idQa),
inference(spm,[status(thm)],[c_0_17,c_0_326]) ).
cnf(c_0_345,hypothesis,
quotient(divide(divide(idQa_Q__idQ_idQb,X1),X2),divide(divide(idQb,X1),X2),zero),
inference(spm,[status(thm)],[c_0_17,c_0_327]) ).
cnf(c_0_346,hypothesis,
less_equal(idQa_Q__idQ_idQb,divide(idQa_Q__idQ_idQb,a)),
inference(spm,[status(thm)],[c_0_328,c_0_329]) ).
cnf(c_0_347,hypothesis,
less_equal(divide(divide(divide(X1,a),idQ_idQb),idQa_Q__idQ_idQb),zero),
inference(spm,[status(thm)],[c_0_330,c_0_331]) ).
cnf(c_0_348,hypothesis,
less_equal(divide(idQa_Q__idQ_idQb,divide(idQa_Q__idQ_idQb,zero)),zero),
inference(spm,[status(thm)],[c_0_36,c_0_332]) ).
cnf(c_0_349,hypothesis,
( less_equal(divide(X1,idQa_Q__idQ_idQb),zero)
| ~ quotient(X2,idQ_idQb,X1)
| ~ quotient(X2,idQa,X3)
| ~ less_equal(X3,idQ_idQb) ),
inference(spm,[status(thm)],[c_0_333,c_0_163]) ).
cnf(c_0_350,hypothesis,
divide(divide(divide(X1,a),X2),idQa) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_334]),c_0_22])]) ).
cnf(c_0_351,hypothesis,
less_equal(idQb_Q__idQ_idQa,divide(idQa,idQ_idQa)),
inference(spm,[status(thm)],[c_0_36,c_0_335]) ).
cnf(c_0_352,hypothesis,
quotient(divide(divide(idQb,zero),X1),divide(idQb,zero),zero),
inference(spm,[status(thm)],[c_0_115,c_0_336]) ).
cnf(c_0_353,plain,
( less_equal(divide(divide(X1,X2),divide(X3,X2)),zero)
| ~ quotient(X1,X3,X4)
| ~ less_equal(X4,zero) ),
inference(spm,[status(thm)],[c_0_48,c_0_337]) ).
cnf(c_0_354,hypothesis,
quotient(divide(idQ_idQa,X1),divide(a,X1),zero),
inference(spm,[status(thm)],[c_0_17,c_0_338]) ).
cnf(c_0_355,hypothesis,
quotient(idQ_idQa,idQa,idQ_idQa),
inference(spm,[status(thm)],[c_0_17,c_0_162]) ).
cnf(c_0_356,hypothesis,
divide(divide(idQb_Q__idQ_idQa,X1),divide(divide(identity,idQ_idQa),X1)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_339]),c_0_22])]) ).
cnf(c_0_357,hypothesis,
divide(divide(identity,idQ_idQa),idQ_idQa) = idQa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_340]),c_0_341])]) ).
cnf(c_0_358,hypothesis,
less_equal(divide(divide(X1,b),idQb),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_342,c_0_28]),c_0_47])]) ).
cnf(c_0_359,hypothesis,
( less_equal(divide(divide(X1,idQ_idQb),zero),zero)
| ~ less_equal(X1,idQ_idQb) ),
inference(spm,[status(thm)],[c_0_29,c_0_190]) ).
cnf(c_0_360,hypothesis,
less_equal(divide(divide(idQb,a),zero),divide(idQb_Q__idQ_idQa,a)),
inference(spm,[status(thm)],[c_0_343,c_0_344]) ).
cnf(c_0_361,hypothesis,
less_equal(divide(divide(idQa_Q__idQ_idQb,X1),X2),divide(divide(idQb,X1),X2)),
inference(spm,[status(thm)],[c_0_36,c_0_345]) ).
cnf(c_0_362,hypothesis,
divide(idQa_Q__idQ_idQb,a) = idQa_Q__idQ_idQb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_346]),c_0_26])]) ).
cnf(c_0_363,hypothesis,
divide(divide(divide(X1,a),idQ_idQb),idQa_Q__idQ_idQb) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_347]),c_0_22])]) ).
cnf(c_0_364,hypothesis,
divide(idQa_Q__idQ_idQb,divide(idQa_Q__idQ_idQb,zero)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_348]),c_0_22])]) ).
cnf(c_0_365,hypothesis,
( less_equal(divide(divide(X1,idQ_idQb),idQa_Q__idQ_idQb),zero)
| ~ quotient(X1,idQa,X2)
| ~ less_equal(X2,idQ_idQb) ),
inference(spm,[status(thm)],[c_0_349,c_0_17]) ).
cnf(c_0_366,hypothesis,
quotient(divide(divide(X1,a),X2),idQa,zero),
inference(spm,[status(thm)],[c_0_17,c_0_350]) ).
cnf(c_0_367,hypothesis,
divide(divide(idQb_Q__idQ_idQa,idQa),zero) = zero,
inference(spm,[status(thm)],[c_0_168,c_0_351]) ).
cnf(c_0_368,hypothesis,
quotient(divide(idQb,zero),divide(idQb,zero),zero),
inference(spm,[status(thm)],[c_0_352,c_0_336]) ).
cnf(c_0_369,hypothesis,
less_equal(divide(divide(divide(idQ_idQa,X1),X2),divide(divide(a,X1),X2)),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_353,c_0_354]),c_0_22])]) ).
cnf(c_0_370,hypothesis,
divide(divide(idQ_idQa,zero),idQa) = divide(idQ_idQa,zero),
inference(spm,[status(thm)],[c_0_108,c_0_355]) ).
cnf(c_0_371,hypothesis,
quotient(divide(idQb_Q__idQ_idQa,X1),divide(divide(identity,idQ_idQa),X1),zero),
inference(spm,[status(thm)],[c_0_17,c_0_356]) ).
cnf(c_0_372,hypothesis,
divide(identity,idQ_idQa) = idQa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_357]),c_0_341])]) ).
cnf(c_0_373,hypothesis,
divide(divide(X1,b),idQb) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_358]),c_0_22])]) ).
cnf(c_0_374,hypothesis,
( divide(divide(X1,idQ_idQb),zero) = zero
| ~ less_equal(X1,idQ_idQb) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_359]),c_0_22])]) ).
cnf(c_0_375,hypothesis,
divide(divide(divide(divide(idQb,a),zero),idQb_Q__idQ_idQa),zero) = zero,
inference(spm,[status(thm)],[c_0_168,c_0_360]) ).
cnf(c_0_376,hypothesis,
less_equal(divide(idQa_Q__idQ_idQb,X1),divide(divide(idQb,a),X1)),
inference(spm,[status(thm)],[c_0_361,c_0_362]) ).
cnf(c_0_377,hypothesis,
quotient(divide(divide(X1,a),idQ_idQb),idQa_Q__idQ_idQb,zero),
inference(spm,[status(thm)],[c_0_17,c_0_363]) ).
cnf(c_0_378,hypothesis,
quotient(idQa_Q__idQ_idQb,divide(idQa_Q__idQ_idQb,zero),zero),
inference(spm,[status(thm)],[c_0_17,c_0_364]) ).
cnf(c_0_379,hypothesis,
less_equal(divide(divide(divide(divide(X1,a),X2),idQ_idQb),idQa_Q__idQ_idQb),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_365,c_0_366]),c_0_22])]) ).
cnf(c_0_380,hypothesis,
quotient(divide(idQb_Q__idQ_idQa,idQa),zero,zero),
inference(spm,[status(thm)],[c_0_17,c_0_367]) ).
cnf(c_0_381,hypothesis,
divide(divide(idQb,zero),divide(idQb,zero)) = zero,
inference(spm,[status(thm)],[c_0_54,c_0_368]) ).
cnf(c_0_382,hypothesis,
less_equal(divide(divide(idQ_idQa,zero),divide(divide(a,zero),idQa)),zero),
inference(spm,[status(thm)],[c_0_369,c_0_370]) ).
cnf(c_0_383,hypothesis,
quotient(idQb_Q__idQ_idQa,divide(idQa,b),zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_371,c_0_313]),c_0_372]) ).
cnf(c_0_384,hypothesis,
quotient(divide(X1,b),idQb,zero),
inference(spm,[status(thm)],[c_0_17,c_0_373]) ).
cnf(c_0_385,plain,
( quotient(X1,X2,zero)
| ~ less_equal(X1,zero) ),
inference(spm,[status(thm)],[c_0_17,c_0_337]) ).
cnf(c_0_386,hypothesis,
( quotient(divide(X1,idQ_idQb),zero,zero)
| ~ less_equal(X1,idQ_idQb) ),
inference(spm,[status(thm)],[c_0_17,c_0_374]) ).
cnf(c_0_387,hypothesis,
quotient(divide(divide(divide(idQb,a),zero),idQb_Q__idQ_idQa),zero,zero),
inference(spm,[status(thm)],[c_0_17,c_0_375]) ).
cnf(c_0_388,hypothesis,
less_equal(idQa_Q__idQ_idQb,divide(divide(idQb,a),idQ_idQb)),
inference(spm,[status(thm)],[c_0_376,c_0_277]) ).
cnf(c_0_389,hypothesis,
less_equal(divide(divide(X1,a),idQ_idQb),idQa_Q__idQ_idQb),
inference(spm,[status(thm)],[c_0_36,c_0_377]) ).
cnf(c_0_390,hypothesis,
less_equal(idQa_Q__idQ_idQb,divide(idQa_Q__idQ_idQb,zero)),
inference(spm,[status(thm)],[c_0_36,c_0_378]) ).
cnf(c_0_391,hypothesis,
divide(divide(divide(divide(X1,a),X2),idQ_idQb),idQa_Q__idQ_idQb) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_379]),c_0_22])]) ).
cnf(c_0_392,hypothesis,
less_equal(divide(idQb_Q__idQ_idQa,idQa),zero),
inference(spm,[status(thm)],[c_0_36,c_0_380]) ).
cnf(c_0_393,hypothesis,
less_equal(divide(divide(idQb,divide(idQb,zero)),zero),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_381]),c_0_22])]) ).
cnf(c_0_394,hypothesis,
divide(divide(idQ_idQa,zero),divide(divide(a,zero),idQa)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_382]),c_0_22])]) ).
cnf(c_0_395,hypothesis,
less_equal(divide(divide(idQb_Q__idQ_idQa,X1),divide(divide(idQa,b),X1)),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_353,c_0_383]),c_0_22])]) ).
cnf(c_0_396,hypothesis,
less_equal(divide(divide(divide(X1,b),X2),divide(idQb,X2)),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_384]),c_0_22])]) ).
cnf(c_0_397,plain,
( less_equal(X1,X2)
| ~ less_equal(X1,zero) ),
inference(spm,[status(thm)],[c_0_36,c_0_385]) ).
cnf(c_0_398,hypothesis,
( less_equal(divide(X1,idQ_idQb),zero)
| ~ less_equal(X1,idQ_idQb) ),
inference(spm,[status(thm)],[c_0_36,c_0_386]) ).
cnf(c_0_399,hypothesis,
less_equal(divide(divide(divide(idQb,a),zero),idQb_Q__idQ_idQa),zero),
inference(spm,[status(thm)],[c_0_36,c_0_387]) ).
cnf(c_0_400,hypothesis,
divide(divide(idQb,a),idQ_idQb) = idQa_Q__idQ_idQb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_388]),c_0_389])]) ).
cnf(c_0_401,hypothesis,
divide(idQa_Q__idQ_idQb,zero) = idQa_Q__idQ_idQb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_390]),c_0_26])]) ).
cnf(c_0_402,hypothesis,
quotient(divide(divide(divide(X1,a),X2),idQ_idQb),idQa_Q__idQ_idQb,zero),
inference(spm,[status(thm)],[c_0_17,c_0_391]) ).
cnf(c_0_403,hypothesis,
divide(idQb_Q__idQ_idQa,idQa) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_392]),c_0_22])]) ).
cnf(c_0_404,hypothesis,
divide(divide(idQb,divide(idQb,zero)),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_393]),c_0_22])]) ).
cnf(c_0_405,hypothesis,
divide(divide(idQ_idQa,divide(divide(a,zero),idQa)),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_394]),c_0_22]),c_0_22])]) ).
cnf(c_0_406,hypothesis,
less_equal(divide(idQb_Q__idQ_idQa,divide(divide(idQa,b),idQ_idQa)),zero),
inference(spm,[status(thm)],[c_0_395,c_0_299]) ).
cnf(c_0_407,hypothesis,
less_equal(divide(divide(divide(X1,b),idQ_idQa),idQb_Q__idQ_idQa),zero),
inference(spm,[status(thm)],[c_0_396,c_0_211]) ).
cnf(c_0_408,hypothesis,
( less_equal(divide(X1,idQ_idQb),X2)
| ~ less_equal(X1,idQ_idQb) ),
inference(spm,[status(thm)],[c_0_397,c_0_398]) ).
cnf(c_0_409,hypothesis,
divide(divide(divide(idQb,a),zero),idQb_Q__idQ_idQa) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_399]),c_0_22])]) ).
cnf(c_0_410,hypothesis,
less_equal(idQa_Q__idQ_idQb,divide(divide(divide(idQb,a),zero),idQ_idQb)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_286,c_0_400]),c_0_401]) ).
cnf(c_0_411,hypothesis,
less_equal(divide(divide(divide(X1,a),X2),idQ_idQb),idQa_Q__idQ_idQb),
inference(spm,[status(thm)],[c_0_36,c_0_402]) ).
cnf(c_0_412,hypothesis,
quotient(idQb_Q__idQ_idQa,idQa,zero),
inference(spm,[status(thm)],[c_0_17,c_0_403]) ).
cnf(c_0_413,hypothesis,
quotient(divide(idQb,divide(idQb,zero)),zero,zero),
inference(spm,[status(thm)],[c_0_17,c_0_404]) ).
cnf(c_0_414,hypothesis,
quotient(divide(idQ_idQa,divide(divide(a,zero),idQa)),zero,zero),
inference(spm,[status(thm)],[c_0_17,c_0_405]) ).
cnf(c_0_415,hypothesis,
divide(idQb_Q__idQ_idQa,divide(divide(idQa,b),idQ_idQa)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_406]),c_0_22])]) ).
cnf(c_0_416,hypothesis,
divide(divide(divide(X1,b),idQ_idQa),idQb_Q__idQ_idQa) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_407]),c_0_22])]) ).
cnf(c_0_417,hypothesis,
( divide(X1,idQ_idQb) = divide(divide(X2,idQ_idQb),divide(X3,idQ_idQb))
| ~ quotient(X2,X3,X1)
| ~ less_equal(X1,idQ_idQb) ),
inference(spm,[status(thm)],[c_0_144,c_0_408]) ).
cnf(c_0_418,hypothesis,
quotient(divide(divide(idQb,a),zero),idQb_Q__idQ_idQa,zero),
inference(spm,[status(thm)],[c_0_17,c_0_409]) ).
cnf(c_0_419,hypothesis,
divide(divide(divide(idQb,a),zero),idQ_idQb) = idQa_Q__idQ_idQb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_410]),c_0_411])]) ).
cnf(c_0_420,hypothesis,
less_equal(divide(divide(idQb_Q__idQ_idQa,idQ_idQb),idQa_Q__idQ_idQb),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_365,c_0_412]),c_0_22])]) ).
cnf(c_0_421,hypothesis,
less_equal(divide(idQb,divide(idQb,zero)),zero),
inference(spm,[status(thm)],[c_0_36,c_0_413]) ).
cnf(c_0_422,hypothesis,
less_equal(divide(idQ_idQa,divide(divide(a,zero),idQa)),zero),
inference(spm,[status(thm)],[c_0_36,c_0_414]) ).
cnf(c_0_423,hypothesis,
quotient(idQb_Q__idQ_idQa,divide(divide(idQa,b),idQ_idQa),zero),
inference(spm,[status(thm)],[c_0_17,c_0_415]) ).
cnf(c_0_424,hypothesis,
quotient(divide(divide(X1,b),idQ_idQa),idQb_Q__idQ_idQa,zero),
inference(spm,[status(thm)],[c_0_17,c_0_416]) ).
cnf(c_0_425,hypothesis,
divide(idQa_Q__idQ_idQb,divide(idQb_Q__idQ_idQa,idQ_idQb)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_417,c_0_418]),c_0_28]),c_0_419]),c_0_22])]) ).
cnf(c_0_426,hypothesis,
divide(divide(idQb_Q__idQ_idQa,idQ_idQb),idQa_Q__idQ_idQb) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_420]),c_0_22])]) ).
cnf(c_0_427,plain,
less_equal(divide(divide(divide(X1,X2),X3),divide(X1,X3)),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_203]),c_0_22])]) ).
cnf(c_0_428,hypothesis,
divide(idQb,divide(idQb,zero)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_421]),c_0_22])]) ).
cnf(c_0_429,hypothesis,
divide(idQ_idQa,divide(divide(a,zero),idQa)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_422]),c_0_22])]) ).
cnf(c_0_430,hypothesis,
less_equal(idQb_Q__idQ_idQa,divide(divide(idQa,b),idQ_idQa)),
inference(spm,[status(thm)],[c_0_36,c_0_423]) ).
cnf(c_0_431,hypothesis,
less_equal(divide(divide(X1,b),idQ_idQa),idQb_Q__idQ_idQa),
inference(spm,[status(thm)],[c_0_36,c_0_424]) ).
cnf(c_0_432,hypothesis,
quotient(idQa_Q__idQ_idQb,divide(idQb_Q__idQ_idQa,idQ_idQb),zero),
inference(spm,[status(thm)],[c_0_17,c_0_425]) ).
cnf(c_0_433,hypothesis,
quotient(divide(idQb_Q__idQ_idQa,idQ_idQb),idQa_Q__idQ_idQb,zero),
inference(spm,[status(thm)],[c_0_17,c_0_426]) ).
cnf(c_0_434,hypothesis,
less_equal(divide(divide(divide(idQa,X1),idQ_idQb),idQa_Q__idQ_idQb),zero),
inference(spm,[status(thm)],[c_0_427,c_0_331]) ).
cnf(c_0_435,hypothesis,
quotient(idQb,divide(idQb,zero),zero),
inference(spm,[status(thm)],[c_0_17,c_0_428]) ).
cnf(c_0_436,hypothesis,
quotient(idQ_idQa,divide(divide(a,zero),idQa),zero),
inference(spm,[status(thm)],[c_0_17,c_0_429]) ).
cnf(c_0_437,hypothesis,
divide(divide(idQa,b),idQ_idQa) = idQb_Q__idQ_idQa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_430]),c_0_431])]) ).
cnf(c_0_438,hypothesis,
less_equal(idQa_Q__idQ_idQb,divide(idQb_Q__idQ_idQa,idQ_idQb)),
inference(spm,[status(thm)],[c_0_36,c_0_432]) ).
cnf(c_0_439,hypothesis,
less_equal(divide(idQb_Q__idQ_idQa,idQ_idQb),idQa_Q__idQ_idQb),
inference(spm,[status(thm)],[c_0_36,c_0_433]) ).
cnf(c_0_440,hypothesis,
divide(divide(divide(idQa,X1),idQ_idQb),idQa_Q__idQ_idQb) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_434]),c_0_22])]) ).
cnf(c_0_441,hypothesis,
less_equal(idQb,divide(idQb,zero)),
inference(spm,[status(thm)],[c_0_36,c_0_435]) ).
cnf(c_0_442,hypothesis,
( less_equal(divide(divide(X1,zero),idQa),divide(X2,zero))
| ~ quotient(X1,idQa,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_193]) ).
cnf(c_0_443,hypothesis,
less_equal(idQ_idQa,divide(divide(a,zero),idQa)),
inference(spm,[status(thm)],[c_0_36,c_0_436]) ).
cnf(c_0_444,hypothesis,
less_equal(divide(idQb_Q__idQ_idQa,X1),divide(divide(idQa,b),X1)),
inference(spm,[status(thm)],[c_0_234,c_0_437]) ).
cnf(c_0_445,hypothesis,
divide(idQb_Q__idQ_idQa,idQ_idQb) = idQa_Q__idQ_idQb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_438]),c_0_439])]) ).
cnf(c_0_446,hypothesis,
quotient(divide(divide(idQa,X1),idQ_idQb),idQa_Q__idQ_idQb,zero),
inference(spm,[status(thm)],[c_0_17,c_0_440]) ).
cnf(c_0_447,hypothesis,
less_equal(divide(divide(divide(divide(idQa,X1),X2),idQ_idQb),idQa_Q__idQ_idQb),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_365,c_0_115]),c_0_22])]) ).
cnf(c_0_448,hypothesis,
divide(idQb,zero) = idQb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_441]),c_0_26])]) ).
cnf(c_0_449,hypothesis,
divide(divide(X1,idQa),zero) = divide(divide(X1,zero),idQa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_442]),c_0_22]),c_0_17])]) ).
cnf(c_0_450,hypothesis,
divide(divide(a,zero),idQa) = idQ_idQa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_443]),c_0_79])]) ).
cnf(c_0_451,hypothesis,
less_equal(idQa_Q__idQ_idQb,divide(divide(idQa,b),idQ_idQb)),
inference(spm,[status(thm)],[c_0_444,c_0_445]) ).
cnf(c_0_452,hypothesis,
less_equal(divide(divide(idQa,X1),idQ_idQb),idQa_Q__idQ_idQb),
inference(spm,[status(thm)],[c_0_36,c_0_446]) ).
cnf(c_0_453,hypothesis,
divide(divide(divide(divide(idQa,X1),X2),idQ_idQb),idQa_Q__idQ_idQb) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_447]),c_0_22])]) ).
cnf(c_0_454,hypothesis,
( divide(X1,zero) = divide(idQb,divide(X2,zero))
| ~ quotient(idQb,X2,X1)
| ~ less_equal(divide(X1,zero),divide(idQb,divide(X2,zero))) ),
inference(spm,[status(thm)],[c_0_144,c_0_448]) ).
cnf(c_0_455,hypothesis,
divide(idQ_idQa,zero) = idQ_idQa,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_449,c_0_82]),c_0_450]) ).
cnf(c_0_456,hypothesis,
divide(divide(idQa,b),idQ_idQb) = idQa_Q__idQ_idQb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_451]),c_0_452])]) ).
cnf(c_0_457,hypothesis,
quotient(divide(divide(divide(idQa,X1),X2),idQ_idQb),idQa_Q__idQ_idQb,zero),
inference(spm,[status(thm)],[c_0_17,c_0_453]) ).
cnf(c_0_458,hypothesis,
divide(idQb_Q__idQ_idQa,zero) = idQb_Q__idQ_idQa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_454,c_0_283]),c_0_455]),c_0_211]),c_0_138])]) ).
cnf(c_0_459,hypothesis,
less_equal(idQa_Q__idQ_idQb,divide(divide(divide(idQa,b),zero),idQ_idQb)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_286,c_0_456]),c_0_401]) ).
cnf(c_0_460,hypothesis,
less_equal(divide(divide(divide(idQa,X1),X2),idQ_idQb),idQa_Q__idQ_idQb),
inference(spm,[status(thm)],[c_0_36,c_0_457]) ).
cnf(c_0_461,hypothesis,
less_equal(divide(idQb_Q__idQ_idQa,divide(divide(idQa,b),zero)),zero),
inference(spm,[status(thm)],[c_0_395,c_0_458]) ).
cnf(c_0_462,hypothesis,
( less_equal(divide(divide(idQa,X1),zero),divide(idQa_Q__idQ_idQb,X1))
| ~ less_equal(idQ_idQb,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_163]) ).
cnf(c_0_463,plain,
less_equal(divide(divide(X1,X2),X3),X1),
inference(spm,[status(thm)],[c_0_36,c_0_115]) ).
cnf(c_0_464,hypothesis,
divide(divide(divide(idQa,b),zero),idQ_idQb) = idQa_Q__idQ_idQb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_459]),c_0_460])]) ).
cnf(c_0_465,hypothesis,
divide(idQb_Q__idQ_idQa,divide(divide(idQa,b),zero)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_461]),c_0_22])]) ).
cnf(c_0_466,hypothesis,
less_equal(divide(idQa_Q__idQ_idQb,X1),divide(divide(idQa,b),X1)),
inference(spm,[status(thm)],[c_0_234,c_0_456]) ).
cnf(c_0_467,hypothesis,
( divide(divide(idQa,X1),zero) = divide(idQa_Q__idQ_idQb,X1)
| ~ less_equal(divide(idQa_Q__idQ_idQb,X1),divide(divide(idQa,X1),zero))
| ~ less_equal(idQ_idQb,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_462]) ).
cnf(c_0_468,hypothesis,
less_equal(divide(idQa_Q__idQ_idQb,X1),divide(divide(idQa,b),zero)),
inference(spm,[status(thm)],[c_0_463,c_0_464]) ).
cnf(c_0_469,hypothesis,
quotient(idQb_Q__idQ_idQa,divide(divide(idQa,b),zero),zero),
inference(spm,[status(thm)],[c_0_17,c_0_465]) ).
cnf(c_0_470,hypothesis,
less_equal(idQa_Q__idQ_idQb,divide(divide(idQa,b),zero)),
inference(spm,[status(thm)],[c_0_466,c_0_401]) ).
cnf(c_0_471,hypothesis,
divide(divide(idQa,b),zero) = divide(idQa_Q__idQ_idQb,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_467,c_0_468]),c_0_157])]) ).
cnf(c_0_472,hypothesis,
less_equal(idQb_Q__idQ_idQa,divide(divide(idQa,b),zero)),
inference(spm,[status(thm)],[c_0_36,c_0_469]) ).
cnf(c_0_473,hypothesis,
less_equal(idQa_Q__idQ_idQb,divide(idQa_Q__idQ_idQb,b)),
inference(rw,[status(thm)],[c_0_470,c_0_471]) ).
cnf(c_0_474,negated_conjecture,
idQa_Q__idQ_idQb != idQb_Q__idQ_idQa,
prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa ).
cnf(c_0_475,hypothesis,
less_equal(idQb_Q__idQ_idQa,divide(idQa_Q__idQ_idQb,b)),
inference(rw,[status(thm)],[c_0_472,c_0_471]) ).
cnf(c_0_476,hypothesis,
divide(idQa_Q__idQ_idQb,b) = idQa_Q__idQ_idQb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_473]),c_0_26])]) ).
cnf(c_0_477,hypothesis,
~ less_equal(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_445]),c_0_474]) ).
cnf(c_0_478,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_475,c_0_476]),c_0_477]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN011-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n001.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 : Thu Aug 24 14:07:11 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 19.38/19.47 % Version : CSE_E---1.5
% 19.38/19.47 % Problem : theBenchmark.p
% 19.38/19.47 % Proof found
% 19.38/19.47 % SZS status Theorem for theBenchmark.p
% 19.38/19.47 % SZS output start Proof
% See solution above
% 19.38/19.50 % Total time : 18.895000 s
% 19.38/19.50 % SZS output end Proof
% 19.38/19.50 % Total time : 18.899000 s
%------------------------------------------------------------------------------