TSTP Solution File: HEN011-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : HEN011-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n002.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 01:54:27 EDT 2023
% Result : Unsatisfiable 19.46s 19.60s
% Output : CNFRefutation 19.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 38
% Syntax : Number of formulae : 178 ( 89 unt; 13 typ; 0 def)
% Number of atoms : 311 ( 39 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 296 ( 150 ~; 146 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 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 : 255 ( 31 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(one_inversion_equals_three,axiom,
( X2 = X4
| ~ quotient(identity,X1,X2)
| ~ quotient(identity,X2,X3)
| ~ quotient(identity,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_inversion_equals_three) ).
cnf(closure,axiom,
quotient(X1,X2,divide(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',closure) ).
cnf(identity_divide_idQa,hypothesis,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_idQa) ).
cnf(identity_divide_a,hypothesis,
quotient(identity,a,idQa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_a) ).
cnf(xLEy_implies_xQzLEyQz,axiom,
( less_equal(X4,X5)
| ~ less_equal(X1,X2)
| ~ quotient(X1,X3,X4)
| ~ quotient(X2,X3,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xLEy_implies_xQzLEyQz) ).
cnf(identity_is_largest,axiom,
less_equal(X1,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',identity_is_largest) ).
cnf(inversion_lemma,axiom,
( X2 = X4
| ~ quotient(identity,X1,X2)
| ~ quotient(identity,X2,X3)
| ~ quotient(X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inversion_lemma) ).
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(x_divide_x_is_zero,axiom,
quotient(X1,X1,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
cnf(idQb_divide_idQ_idQa,hypothesis,
quotient(idQb,idQ_idQa,idQb_Q__idQ_idQa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idQb_divide_idQ_idQa) ).
cnf(xQyLEz_implies_xQzLEy,axiom,
( less_equal(X5,X2)
| ~ quotient(X1,X2,X3)
| ~ less_equal(X3,X4)
| ~ quotient(X1,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xQyLEz_implies_xQzLEy) ).
cnf(identity_divide_idQb,hypothesis,
quotient(identity,idQb,idQ_idQb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_idQb) ).
cnf(xLEy_implies_zQyLEzQx,axiom,
( less_equal(X4,X5)
| ~ less_equal(X1,X2)
| ~ quotient(X3,X2,X4)
| ~ quotient(X3,X1,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xLEy_implies_zQyLEzQx) ).
cnf(idQa_divide_idQ_idQb,hypothesis,
quotient(idQa,idQ_idQb,idQa_Q__idQ_idQb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idQa_divide_idQ_idQb) ).
cnf(identity_divide_b,hypothesis,
quotient(identity,b,idQb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_b) ).
cnf(divisor_existence,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).
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(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(x_divde_zero_is_x,axiom,
quotient(X1,zero,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divde_zero_is_x) ).
cnf(zero_divide_anything_is_zero,axiom,
quotient(zero,X1,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
cnf(transitivity_of_less_equal,axiom,
( less_equal(X1,X3)
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_less_equal) ).
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(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(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',zero_is_smallest) ).
cnf(prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa,negated_conjecture,
idQa_Q__idQ_idQb != idQb_Q__idQ_idQa,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa) ).
cnf(c_0_25,axiom,
( X2 = X4
| ~ quotient(identity,X1,X2)
| ~ quotient(identity,X2,X3)
| ~ quotient(identity,X3,X4) ),
one_inversion_equals_three ).
cnf(c_0_26,axiom,
quotient(X1,X2,divide(X1,X2)),
closure ).
cnf(c_0_27,plain,
( X1 = divide(identity,X2)
| ~ quotient(identity,X1,X2)
| ~ quotient(identity,X3,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_28,hypothesis,
quotient(identity,idQa,idQ_idQa),
identity_divide_idQa ).
cnf(c_0_29,hypothesis,
( divide(identity,idQ_idQa) = idQa
| ~ quotient(identity,X1,idQa) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_30,hypothesis,
quotient(identity,a,idQa),
identity_divide_a ).
cnf(c_0_31,axiom,
( less_equal(X4,X5)
| ~ less_equal(X1,X2)
| ~ quotient(X1,X3,X4)
| ~ quotient(X2,X3,X5) ),
xLEy_implies_xQzLEyQz ).
cnf(c_0_32,axiom,
less_equal(X1,identity),
identity_is_largest ).
cnf(c_0_33,axiom,
( X2 = X4
| ~ quotient(identity,X1,X2)
| ~ quotient(identity,X2,X3)
| ~ quotient(X2,X3,X4) ),
inversion_lemma ).
cnf(c_0_34,hypothesis,
divide(identity,idQ_idQa) = idQa,
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,axiom,
( less_equal(X1,X2)
| ~ quotient(X1,X2,zero) ),
less_equal_quotient ).
cnf(c_0_36,axiom,
quotient(X1,X1,zero),
x_divide_x_is_zero ).
cnf(c_0_37,plain,
( less_equal(X1,X2)
| ~ quotient(identity,X3,X2)
| ~ quotient(X4,X3,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,hypothesis,
quotient(idQb,idQ_idQa,idQb_Q__idQ_idQa),
idQb_divide_idQ_idQa ).
cnf(c_0_39,plain,
( divide(X1,X2) = X1
| ~ quotient(identity,X1,X2)
| ~ quotient(identity,X3,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_26]) ).
cnf(c_0_40,hypothesis,
quotient(identity,idQ_idQa,idQa),
inference(spm,[status(thm)],[c_0_26,c_0_34]) ).
cnf(c_0_41,axiom,
( less_equal(X5,X2)
| ~ quotient(X1,X2,X3)
| ~ less_equal(X3,X4)
| ~ quotient(X1,X4,X5) ),
xQyLEz_implies_xQzLEy ).
cnf(c_0_42,plain,
less_equal(X1,X1),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_43,hypothesis,
( less_equal(idQb_Q__idQ_idQa,X1)
| ~ quotient(identity,idQ_idQa,X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,hypothesis,
( divide(idQ_idQa,idQa) = idQ_idQa
| ~ quotient(identity,X1,idQ_idQa) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,plain,
( less_equal(X1,X2)
| ~ quotient(X3,X4,X1)
| ~ quotient(X3,X2,X4) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,hypothesis,
quotient(identity,idQb,idQ_idQb),
identity_divide_idQb ).
cnf(c_0_47,axiom,
( less_equal(X4,X5)
| ~ less_equal(X1,X2)
| ~ quotient(X3,X2,X4)
| ~ quotient(X3,X1,X5) ),
xLEy_implies_zQyLEzQx ).
cnf(c_0_48,hypothesis,
less_equal(idQb_Q__idQ_idQa,idQa),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_26]),c_0_34]) ).
cnf(c_0_49,hypothesis,
divide(idQ_idQa,idQa) = idQ_idQa,
inference(spm,[status(thm)],[c_0_44,c_0_28]) ).
cnf(c_0_50,plain,
( less_equal(divide(X1,X2),X3)
| ~ quotient(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_45,c_0_26]) ).
cnf(c_0_51,hypothesis,
quotient(idQa,idQ_idQb,idQa_Q__idQ_idQb),
idQa_divide_idQ_idQb ).
cnf(c_0_52,hypothesis,
( divide(idQb,idQ_idQb) = idQb
| ~ quotient(identity,X1,idQb) ),
inference(spm,[status(thm)],[c_0_39,c_0_46]) ).
cnf(c_0_53,hypothesis,
quotient(identity,b,idQb),
identity_divide_b ).
cnf(c_0_54,hypothesis,
( less_equal(X1,X2)
| ~ quotient(X3,idQa,X1)
| ~ quotient(X3,idQb_Q__idQ_idQa,X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_55,hypothesis,
quotient(idQ_idQa,idQa,idQ_idQa),
inference(spm,[status(thm)],[c_0_26,c_0_49]) ).
cnf(c_0_56,hypothesis,
less_equal(divide(idQa,idQa_Q__idQ_idQb),idQ_idQb),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_57,hypothesis,
divide(idQb,idQ_idQb) = idQb,
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_58,hypothesis,
( less_equal(idQ_idQa,X1)
| ~ quotient(idQ_idQa,idQb_Q__idQ_idQa,X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_59,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
divisor_existence ).
cnf(c_0_60,hypothesis,
( less_equal(X1,X2)
| ~ quotient(X3,divide(idQa,idQa_Q__idQ_idQb),X2)
| ~ quotient(X3,idQ_idQb,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_56]) ).
cnf(c_0_61,hypothesis,
quotient(idQb,idQ_idQb,idQb),
inference(spm,[status(thm)],[c_0_26,c_0_57]) ).
cnf(c_0_62,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
less_equal_and_equal ).
cnf(c_0_63,hypothesis,
less_equal(idQ_idQa,divide(idQ_idQa,idQb_Q__idQ_idQa)),
inference(spm,[status(thm)],[c_0_58,c_0_26]) ).
cnf(c_0_64,plain,
less_equal(divide(X1,X2),X1),
inference(spm,[status(thm)],[c_0_59,c_0_26]) ).
cnf(c_0_65,hypothesis,
( less_equal(X1,X2)
| ~ quotient(idQa,X3,X2)
| ~ quotient(idQb_Q__idQ_idQa,X3,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_48]) ).
cnf(c_0_66,hypothesis,
( less_equal(idQb,X1)
| ~ quotient(idQb,divide(idQa,idQa_Q__idQ_idQb),X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_67,hypothesis,
divide(idQ_idQa,idQb_Q__idQ_idQa) = idQ_idQa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64])]) ).
cnf(c_0_68,hypothesis,
( less_equal(X1,divide(idQa,X2))
| ~ quotient(idQb_Q__idQ_idQa,X2,X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_26]) ).
cnf(c_0_69,hypothesis,
less_equal(idQb,divide(idQb,divide(idQa,idQa_Q__idQ_idQb))),
inference(spm,[status(thm)],[c_0_66,c_0_26]) ).
cnf(c_0_70,plain,
( less_equal(X1,X2)
| ~ quotient(X3,divide(X4,X5),X2)
| ~ quotient(X3,X4,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_64]) ).
cnf(c_0_71,hypothesis,
quotient(idQ_idQa,idQb_Q__idQ_idQa,idQ_idQa),
inference(spm,[status(thm)],[c_0_26,c_0_67]) ).
cnf(c_0_72,hypothesis,
less_equal(divide(idQb_Q__idQ_idQa,X1),divide(idQa,X1)),
inference(spm,[status(thm)],[c_0_68,c_0_26]) ).
cnf(c_0_73,hypothesis,
divide(idQb,divide(idQa,idQa_Q__idQ_idQb)) = idQb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_69]),c_0_64])]) ).
cnf(c_0_74,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_75,axiom,
quotient(X1,zero,X1),
x_divde_zero_is_x ).
cnf(c_0_76,hypothesis,
( less_equal(idQ_idQa,X1)
| ~ quotient(idQ_idQa,divide(idQb_Q__idQ_idQa,X2),X1) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_77,hypothesis,
( less_equal(X1,X2)
| ~ quotient(X3,divide(idQa,X4),X1)
| ~ quotient(X3,divide(idQb_Q__idQ_idQa,X4),X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_72]) ).
cnf(c_0_78,hypothesis,
quotient(idQb,divide(idQa,idQa_Q__idQ_idQb),idQb),
inference(spm,[status(thm)],[c_0_26,c_0_73]) ).
cnf(c_0_79,hypothesis,
( divide(identity,idQ_idQb) = idQb
| ~ quotient(identity,X1,idQb) ),
inference(spm,[status(thm)],[c_0_27,c_0_46]) ).
cnf(c_0_80,plain,
( less_equal(X1,X2)
| ~ quotient(X3,X4,zero)
| ~ quotient(X5,X4,X2)
| ~ quotient(X6,X4,X1)
| ~ quotient(X6,X3,X5) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_81,hypothesis,
( less_equal(idQb_Q__idQ_idQa,X1)
| ~ quotient(X2,X3,idQ_idQa)
| ~ quotient(X4,X3,idQb)
| ~ quotient(X5,X3,X1)
| ~ quotient(X4,X2,X5) ),
inference(spm,[status(thm)],[c_0_74,c_0_38]) ).
cnf(c_0_82,hypothesis,
less_equal(idQ_idQa,divide(idQ_idQa,divide(idQb_Q__idQ_idQa,X1))),
inference(spm,[status(thm)],[c_0_76,c_0_26]) ).
cnf(c_0_83,hypothesis,
( less_equal(idQb,X1)
| ~ quotient(idQb,divide(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb),X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_84,hypothesis,
( less_equal(idQa_Q__idQ_idQb,X1)
| ~ quotient(identity,idQ_idQb,X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_51]) ).
cnf(c_0_85,hypothesis,
divide(identity,idQ_idQb) = idQb,
inference(spm,[status(thm)],[c_0_79,c_0_53]) ).
cnf(c_0_86,plain,
( less_equal(X1,divide(X2,X3))
| ~ quotient(X4,X3,zero)
| ~ quotient(X5,X3,X1)
| ~ quotient(X5,X4,X2) ),
inference(spm,[status(thm)],[c_0_80,c_0_26]) ).
cnf(c_0_87,hypothesis,
( less_equal(idQb_Q__idQ_idQa,divide(X1,X2))
| ~ quotient(X3,X2,idQ_idQa)
| ~ quotient(X4,X2,idQb)
| ~ quotient(X4,X3,X1) ),
inference(spm,[status(thm)],[c_0_81,c_0_26]) ).
cnf(c_0_88,hypothesis,
divide(idQ_idQa,divide(idQb_Q__idQ_idQa,X1)) = idQ_idQa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_82]),c_0_64])]) ).
cnf(c_0_89,hypothesis,
less_equal(idQb,divide(idQb,divide(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb))),
inference(spm,[status(thm)],[c_0_83,c_0_26]) ).
cnf(c_0_90,hypothesis,
less_equal(idQa_Q__idQ_idQb,idQb),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_26]),c_0_85]) ).
cnf(c_0_91,hypothesis,
( less_equal(idQb_Q__idQ_idQa,divide(X1,idQ_idQa))
| ~ quotient(X2,idQ_idQa,zero)
| ~ quotient(idQb,X2,X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_38]) ).
cnf(c_0_92,hypothesis,
( less_equal(idQb_Q__idQ_idQa,divide(idQb_Q__idQ_idQa,X1))
| ~ quotient(idQ_idQa,X1,idQ_idQa)
| ~ quotient(idQb,X1,idQb) ),
inference(spm,[status(thm)],[c_0_87,c_0_38]) ).
cnf(c_0_93,hypothesis,
quotient(idQ_idQa,divide(idQb_Q__idQ_idQa,X1),idQ_idQa),
inference(spm,[status(thm)],[c_0_26,c_0_88]) ).
cnf(c_0_94,hypothesis,
divide(idQb,divide(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb)) = idQb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_89]),c_0_64])]) ).
cnf(c_0_95,hypothesis,
quotient(identity,idQ_idQb,idQb),
inference(spm,[status(thm)],[c_0_26,c_0_85]) ).
cnf(c_0_96,hypothesis,
( less_equal(X1,X2)
| ~ quotient(idQb,X3,X2)
| ~ quotient(idQa_Q__idQ_idQb,X3,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_90]) ).
cnf(c_0_97,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_74,c_0_26]) ).
cnf(c_0_98,axiom,
quotient(zero,X1,zero),
zero_divide_anything_is_zero ).
cnf(c_0_99,hypothesis,
less_equal(idQb_Q__idQ_idQa,divide(idQb_Q__idQ_idQa,idQ_idQa)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_38]),c_0_36])]) ).
cnf(c_0_100,axiom,
( less_equal(X1,X3)
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X3) ),
transitivity_of_less_equal ).
cnf(c_0_101,plain,
less_equal(divide(X1,divide(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_50,c_0_26]) ).
cnf(c_0_102,hypothesis,
( less_equal(idQb_Q__idQ_idQa,divide(idQb_Q__idQ_idQa,divide(idQb_Q__idQ_idQa,X1)))
| ~ quotient(idQb,divide(idQb_Q__idQ_idQa,X1),idQb) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_103,hypothesis,
quotient(idQb,divide(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb),idQb),
inference(spm,[status(thm)],[c_0_26,c_0_94]) ).
cnf(c_0_104,hypothesis,
( divide(idQ_idQb,idQb) = idQ_idQb
| ~ quotient(identity,X1,idQ_idQb) ),
inference(spm,[status(thm)],[c_0_39,c_0_95]) ).
cnf(c_0_105,hypothesis,
( divide(idQa,idQ_idQa) = idQa
| ~ quotient(identity,X1,idQa) ),
inference(spm,[status(thm)],[c_0_39,c_0_28]) ).
cnf(c_0_106,hypothesis,
less_equal(divide(idQb,idQb_Q__idQ_idQa),idQ_idQa),
inference(spm,[status(thm)],[c_0_50,c_0_38]) ).
cnf(c_0_107,hypothesis,
( less_equal(X1,divide(idQb,X2))
| ~ quotient(idQa_Q__idQ_idQb,X2,X1) ),
inference(spm,[status(thm)],[c_0_96,c_0_26]) ).
cnf(c_0_108,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_97,c_0_98]) ).
cnf(c_0_109,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_62,c_0_99]),c_0_64])]) ).
cnf(c_0_110,plain,
( less_equal(X1,X2)
| ~ less_equal(X1,divide(X3,divide(X3,X2))) ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_111,hypothesis,
less_equal(idQb_Q__idQ_idQa,divide(idQb_Q__idQ_idQa,divide(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb))),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_112,hypothesis,
divide(idQ_idQb,idQb) = idQ_idQb,
inference(spm,[status(thm)],[c_0_104,c_0_46]) ).
cnf(c_0_113,hypothesis,
divide(idQa,idQ_idQa) = idQa,
inference(spm,[status(thm)],[c_0_105,c_0_30]) ).
cnf(c_0_114,hypothesis,
( less_equal(X1,idQ_idQa)
| ~ less_equal(X1,divide(idQb,idQb_Q__idQ_idQa)) ),
inference(spm,[status(thm)],[c_0_100,c_0_106]) ).
cnf(c_0_115,hypothesis,
less_equal(divide(idQa_Q__idQ_idQb,X1),divide(idQb,X1)),
inference(spm,[status(thm)],[c_0_107,c_0_26]) ).
cnf(c_0_116,plain,
( less_equal(divide(X1,divide(X2,X3)),zero)
| ~ quotient(X4,X2,zero)
| ~ quotient(X4,X3,X1) ),
inference(spm,[status(thm)],[c_0_108,c_0_26]) ).
cnf(c_0_117,hypothesis,
quotient(idQb_Q__idQ_idQa,idQ_idQa,idQb_Q__idQ_idQa),
inference(spm,[status(thm)],[c_0_26,c_0_109]) ).
cnf(c_0_118,axiom,
( quotient(X1,X2,zero)
| ~ less_equal(X1,X2) ),
quotient_less_equal ).
cnf(c_0_119,hypothesis,
less_equal(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_120,hypothesis,
( less_equal(X1,X2)
| ~ quotient(X3,idQb,X1)
| ~ quotient(X3,idQa_Q__idQ_idQb,X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_90]) ).
cnf(c_0_121,hypothesis,
quotient(idQ_idQb,idQb,idQ_idQb),
inference(spm,[status(thm)],[c_0_26,c_0_112]) ).
cnf(c_0_122,hypothesis,
( less_equal(X1,X2)
| ~ quotient(X3,divide(idQb,idQb_Q__idQ_idQa),X2)
| ~ quotient(X3,idQ_idQa,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_106]) ).
cnf(c_0_123,hypothesis,
quotient(idQa,idQ_idQa,idQa),
inference(spm,[status(thm)],[c_0_26,c_0_113]) ).
cnf(c_0_124,hypothesis,
less_equal(divide(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa),idQ_idQa),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_125,hypothesis,
( less_equal(divide(idQb_Q__idQ_idQa,divide(X1,idQ_idQa)),zero)
| ~ quotient(idQb_Q__idQ_idQa,X1,zero) ),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_126,hypothesis,
quotient(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb,zero),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_127,axiom,
( X3 = X4
| ~ quotient(X1,X2,X3)
| ~ quotient(X1,X2,X4) ),
well_defined ).
cnf(c_0_128,hypothesis,
( less_equal(idQ_idQb,X1)
| ~ quotient(idQ_idQb,idQa_Q__idQ_idQb,X1) ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_129,hypothesis,
( less_equal(idQa,X1)
| ~ quotient(idQa,divide(idQb,idQb_Q__idQ_idQa),X1) ),
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_130,hypothesis,
( less_equal(X1,X2)
| ~ quotient(X3,divide(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa),X2)
| ~ quotient(X3,idQ_idQa,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_124]) ).
cnf(c_0_131,hypothesis,
less_equal(divide(idQb_Q__idQ_idQa,divide(idQa_Q__idQ_idQb,idQ_idQa)),zero),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_132,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_133,plain,
( X1 = X2
| ~ quotient(X2,zero,X1) ),
inference(spm,[status(thm)],[c_0_127,c_0_75]) ).
cnf(c_0_134,hypothesis,
( less_equal(X1,idQb_Q__idQ_idQa)
| ~ quotient(idQa_Q__idQ_idQb,idQ_idQa,X1) ),
inference(spm,[status(thm)],[c_0_96,c_0_38]) ).
cnf(c_0_135,hypothesis,
less_equal(idQ_idQb,divide(idQ_idQb,idQa_Q__idQ_idQb)),
inference(spm,[status(thm)],[c_0_128,c_0_26]) ).
cnf(c_0_136,hypothesis,
less_equal(idQa,divide(idQa,divide(idQb,idQb_Q__idQ_idQa))),
inference(spm,[status(thm)],[c_0_129,c_0_26]) ).
cnf(c_0_137,hypothesis,
( less_equal(divide(X1,idQ_idQa),X2)
| ~ quotient(X1,divide(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa),X2) ),
inference(spm,[status(thm)],[c_0_130,c_0_26]) ).
cnf(c_0_138,plain,
( divide(X1,divide(X1,X2)) = X2
| ~ less_equal(X2,divide(X1,divide(X1,X2))) ),
inference(spm,[status(thm)],[c_0_62,c_0_101]) ).
cnf(c_0_139,hypothesis,
divide(idQb_Q__idQ_idQa,divide(idQa_Q__idQ_idQb,idQ_idQa)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_131]),c_0_132])]) ).
cnf(c_0_140,plain,
divide(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_133,c_0_26]) ).
cnf(c_0_141,hypothesis,
less_equal(divide(idQa_Q__idQ_idQb,idQ_idQa),idQb_Q__idQ_idQa),
inference(spm,[status(thm)],[c_0_134,c_0_26]) ).
cnf(c_0_142,hypothesis,
divide(idQ_idQb,idQa_Q__idQ_idQb) = idQ_idQb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_135]),c_0_64])]) ).
cnf(c_0_143,hypothesis,
divide(idQa,divide(idQb,idQb_Q__idQ_idQa)) = idQa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_136]),c_0_64])]) ).
cnf(c_0_144,hypothesis,
less_equal(divide(X1,idQ_idQa),divide(X1,divide(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa))),
inference(spm,[status(thm)],[c_0_137,c_0_26]) ).
cnf(c_0_145,hypothesis,
divide(idQa_Q__idQ_idQb,idQ_idQa) = 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_138,c_0_139]),c_0_140]),c_0_140]),c_0_141])]) ).
cnf(c_0_146,hypothesis,
quotient(idQ_idQb,idQa_Q__idQ_idQb,idQ_idQb),
inference(spm,[status(thm)],[c_0_26,c_0_142]) ).
cnf(c_0_147,hypothesis,
( less_equal(X1,X2)
| ~ quotient(X3,divide(idQb,X4),X1)
| ~ quotient(X3,divide(idQa_Q__idQ_idQb,X4),X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_115]) ).
cnf(c_0_148,hypothesis,
quotient(idQa,divide(idQb,idQb_Q__idQ_idQa),idQa),
inference(spm,[status(thm)],[c_0_26,c_0_143]) ).
cnf(c_0_149,hypothesis,
less_equal(idQb_Q__idQ_idQa,divide(idQa_Q__idQ_idQb,divide(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa))),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_150,hypothesis,
( less_equal(idQ_idQb,X1)
| ~ quotient(idQ_idQb,divide(idQa_Q__idQ_idQb,X2),X1) ),
inference(spm,[status(thm)],[c_0_70,c_0_146]) ).
cnf(c_0_151,hypothesis,
( less_equal(idQa,X1)
| ~ quotient(idQa,divide(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa),X1) ),
inference(spm,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_152,hypothesis,
divide(idQa_Q__idQ_idQb,divide(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa)) = idQb_Q__idQ_idQa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_149]),c_0_101])]) ).
cnf(c_0_153,negated_conjecture,
idQa_Q__idQ_idQb != idQb_Q__idQ_idQa,
prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa ).
cnf(c_0_154,hypothesis,
less_equal(idQ_idQb,divide(idQ_idQb,divide(idQa_Q__idQ_idQb,X1))),
inference(spm,[status(thm)],[c_0_150,c_0_26]) ).
cnf(c_0_155,hypothesis,
less_equal(idQa,divide(idQa,divide(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa))),
inference(spm,[status(thm)],[c_0_151,c_0_26]) ).
cnf(c_0_156,hypothesis,
( less_equal(idQa_Q__idQ_idQb,X1)
| ~ quotient(X2,X3,idQ_idQb)
| ~ quotient(X4,X3,idQa)
| ~ quotient(X5,X3,X1)
| ~ quotient(X4,X2,X5) ),
inference(spm,[status(thm)],[c_0_74,c_0_51]) ).
cnf(c_0_157,hypothesis,
quotient(idQa_Q__idQ_idQb,divide(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa),idQb_Q__idQ_idQa),
inference(spm,[status(thm)],[c_0_26,c_0_152]) ).
cnf(c_0_158,hypothesis,
~ less_equal(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_119]),c_0_153]) ).
cnf(c_0_159,hypothesis,
divide(idQ_idQb,divide(idQa_Q__idQ_idQb,X1)) = idQ_idQb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_154]),c_0_64])]) ).
cnf(c_0_160,hypothesis,
divide(idQa,divide(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa)) = idQa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_155]),c_0_64])]) ).
cnf(c_0_161,hypothesis,
( ~ quotient(X1,divide(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa),idQ_idQb)
| ~ quotient(X2,divide(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa),idQa)
| ~ quotient(X2,X1,idQa_Q__idQ_idQb) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_158]) ).
cnf(c_0_162,hypothesis,
quotient(idQ_idQb,divide(idQa_Q__idQ_idQb,X1),idQ_idQb),
inference(spm,[status(thm)],[c_0_26,c_0_159]) ).
cnf(c_0_163,hypothesis,
quotient(idQa,divide(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa),idQa),
inference(spm,[status(thm)],[c_0_26,c_0_160]) ).
cnf(c_0_164,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_51]),c_0_162]),c_0_163])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN011-2 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n002.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Aug 24 13:52:01 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.54 start to proof: theBenchmark
% 19.46/19.60 % Version : CSE_E---1.5
% 19.46/19.60 % Problem : theBenchmark.p
% 19.46/19.60 % Proof found
% 19.46/19.60 % SZS status Theorem for theBenchmark.p
% 19.46/19.60 % SZS output start Proof
% See solution above
% 19.46/19.61 % Total time : 19.052000 s
% 19.46/19.61 % SZS output end Proof
% 19.46/19.61 % Total time : 19.056000 s
%------------------------------------------------------------------------------