TSTP Solution File: HEN011-1 by E---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : HEN011-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% 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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 17:50:54 EDT 2023
% Result : Unsatisfiable 7.12s 1.37s
% Output : CNFRefutation 7.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 16
% Syntax : Number of clauses : 176 ( 125 unt; 0 nHn; 119 RR)
% Number of literals : 258 ( 54 equ; 85 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 215 ( 48 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(divisor_existence,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
file('/export/starexec/sandbox2/tmp/tmp.luZ4rjz2Ft/E---3.1_17740.p',divisor_existence) ).
cnf(closure,axiom,
quotient(X1,X2,divide(X1,X2)),
file('/export/starexec/sandbox2/tmp/tmp.luZ4rjz2Ft/E---3.1_17740.p',closure) ).
cnf(quotient_property,axiom,
( less_equal(X7,X8)
| ~ quotient(X1,X2,X3)
| ~ quotient(X2,X4,X5)
| ~ quotient(X1,X4,X6)
| ~ quotient(X6,X5,X7)
| ~ quotient(X3,X4,X8) ),
file('/export/starexec/sandbox2/tmp/tmp.luZ4rjz2Ft/E---3.1_17740.p',quotient_property) ).
cnf(quotient_less_equal,axiom,
( quotient(X1,X2,zero)
| ~ less_equal(X1,X2) ),
file('/export/starexec/sandbox2/tmp/tmp.luZ4rjz2Ft/E---3.1_17740.p',quotient_less_equal) ).
cnf(less_equal_and_equal,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.luZ4rjz2Ft/E---3.1_17740.p',less_equal_and_equal) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox2/tmp/tmp.luZ4rjz2Ft/E---3.1_17740.p',zero_is_smallest) ).
cnf(less_equal_quotient,axiom,
( less_equal(X1,X2)
| ~ quotient(X1,X2,zero) ),
file('/export/starexec/sandbox2/tmp/tmp.luZ4rjz2Ft/E---3.1_17740.p',less_equal_quotient) ).
cnf(identity_is_largest,axiom,
less_equal(X1,identity),
file('/export/starexec/sandbox2/tmp/tmp.luZ4rjz2Ft/E---3.1_17740.p',identity_is_largest) ).
cnf(well_defined,axiom,
( X3 = X4
| ~ quotient(X1,X2,X3)
| ~ quotient(X1,X2,X4) ),
file('/export/starexec/sandbox2/tmp/tmp.luZ4rjz2Ft/E---3.1_17740.p',well_defined) ).
cnf(identity_divide_b,hypothesis,
quotient(identity,b,idQb),
file('/export/starexec/sandbox2/tmp/tmp.luZ4rjz2Ft/E---3.1_17740.p',identity_divide_b) ).
cnf(identity_divide_a,hypothesis,
quotient(identity,a,idQa),
file('/export/starexec/sandbox2/tmp/tmp.luZ4rjz2Ft/E---3.1_17740.p',identity_divide_a) ).
cnf(identity_divide_idQb,hypothesis,
quotient(identity,idQb,idQ_idQb),
file('/export/starexec/sandbox2/tmp/tmp.luZ4rjz2Ft/E---3.1_17740.p',identity_divide_idQb) ).
cnf(identity_divide_idQa,hypothesis,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox2/tmp/tmp.luZ4rjz2Ft/E---3.1_17740.p',identity_divide_idQa) ).
cnf(idQa_divide_idQ_idQb,hypothesis,
quotient(idQa,idQ_idQb,idQa_Q__idQ_idQb),
file('/export/starexec/sandbox2/tmp/tmp.luZ4rjz2Ft/E---3.1_17740.p',idQa_divide_idQ_idQb) ).
cnf(idQb_divide_idQ_idQa,hypothesis,
quotient(idQb,idQ_idQa,idQb_Q__idQ_idQa),
file('/export/starexec/sandbox2/tmp/tmp.luZ4rjz2Ft/E---3.1_17740.p',idQb_divide_idQ_idQa) ).
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/tmp/tmp.luZ4rjz2Ft/E---3.1_17740.p',prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa) ).
cnf(c_0_16,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
divisor_existence ).
cnf(c_0_17,axiom,
quotient(X1,X2,divide(X1,X2)),
closure ).
cnf(c_0_18,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_19,axiom,
( quotient(X1,X2,zero)
| ~ less_equal(X1,X2) ),
quotient_less_equal ).
cnf(c_0_20,plain,
less_equal(divide(X1,X2),X1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
( less_equal(divide(X1,X2),X3)
| ~ quotient(X4,X5,X3)
| ~ quotient(X6,X5,X2)
| ~ quotient(X7,X5,X1)
| ~ quotient(X7,X6,X4) ),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_22,plain,
quotient(divide(X1,X2),X1,zero),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,X4,divide(X5,X6))
| ~ quotient(X4,X5,X2)
| ~ quotient(X3,X5,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_24,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,X4,X2)
| ~ quotient(X4,X4,X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_17]) ).
cnf(c_0_25,plain,
( less_equal(divide(X1,zero),zero)
| ~ quotient(X2,X2,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_26,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
less_equal_and_equal ).
cnf(c_0_27,plain,
less_equal(divide(divide(X1,X1),zero),zero),
inference(spm,[status(thm)],[c_0_25,c_0_17]) ).
cnf(c_0_28,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_29,plain,
divide(divide(X1,X1),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
cnf(c_0_30,axiom,
( less_equal(X1,X2)
| ~ quotient(X1,X2,zero) ),
less_equal_quotient ).
cnf(c_0_31,plain,
quotient(divide(X1,X1),zero,zero),
inference(spm,[status(thm)],[c_0_17,c_0_29]) ).
cnf(c_0_32,plain,
less_equal(divide(X1,X1),zero),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,plain,
divide(X1,X1) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_32]),c_0_28])]) ).
cnf(c_0_34,plain,
quotient(X1,X1,zero),
inference(spm,[status(thm)],[c_0_17,c_0_33]) ).
cnf(c_0_35,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,X4,X2)
| ~ quotient(X5,X4,X1)
| ~ quotient(X5,X3,X4) ),
inference(spm,[status(thm)],[c_0_21,c_0_34]) ).
cnf(c_0_36,plain,
quotient(zero,X1,zero),
inference(spm,[status(thm)],[c_0_19,c_0_28]) ).
cnf(c_0_37,plain,
( less_equal(divide(X1,zero),zero)
| ~ quotient(X2,zero,X3)
| ~ quotient(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,plain,
( less_equal(divide(X1,zero),zero)
| ~ quotient(X2,divide(X2,zero),X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_17]) ).
cnf(c_0_39,plain,
less_equal(divide(divide(X1,divide(X1,zero)),zero),zero),
inference(spm,[status(thm)],[c_0_38,c_0_17]) ).
cnf(c_0_40,plain,
divide(divide(X1,divide(X1,zero)),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_39]),c_0_28])]) ).
cnf(c_0_41,plain,
quotient(divide(X1,divide(X1,zero)),zero,zero),
inference(spm,[status(thm)],[c_0_17,c_0_40]) ).
cnf(c_0_42,plain,
less_equal(divide(X1,divide(X1,zero)),zero),
inference(spm,[status(thm)],[c_0_30,c_0_41]) ).
cnf(c_0_43,plain,
divide(X1,divide(X1,zero)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_42]),c_0_28])]) ).
cnf(c_0_44,plain,
quotient(X1,divide(X1,zero),zero),
inference(spm,[status(thm)],[c_0_17,c_0_43]) ).
cnf(c_0_45,plain,
less_equal(X1,divide(X1,zero)),
inference(spm,[status(thm)],[c_0_30,c_0_44]) ).
cnf(c_0_46,axiom,
less_equal(X1,identity),
identity_is_largest ).
cnf(c_0_47,plain,
( less_equal(divide(X1,X2),divide(X3,X4))
| ~ quotient(X5,X4,X2)
| ~ quotient(X6,X4,X1)
| ~ quotient(X6,X5,X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_17]) ).
cnf(c_0_48,plain,
divide(X1,zero) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_45]),c_0_20])]) ).
cnf(c_0_49,axiom,
( X3 = X4
| ~ quotient(X1,X2,X3)
| ~ quotient(X1,X2,X4) ),
well_defined ).
cnf(c_0_50,hypothesis,
quotient(identity,b,idQb),
identity_divide_b ).
cnf(c_0_51,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,X4,zero)
| ~ quotient(X4,X5,X2)
| ~ quotient(X3,X5,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_36]) ).
cnf(c_0_52,plain,
quotient(X1,identity,zero),
inference(spm,[status(thm)],[c_0_19,c_0_46]) ).
cnf(c_0_53,plain,
( less_equal(X1,divide(X2,X3))
| ~ quotient(X4,X3,X1)
| ~ quotient(X4,X3,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_34]),c_0_48]) ).
cnf(c_0_54,hypothesis,
( X1 = idQb
| ~ quotient(identity,b,X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_55,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(identity,X3,X2)
| ~ quotient(X4,X3,X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,hypothesis,
quotient(identity,a,idQa),
identity_divide_a ).
cnf(c_0_57,hypothesis,
( less_equal(idQb,divide(X1,b))
| ~ quotient(identity,b,X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_50]) ).
cnf(c_0_58,hypothesis,
divide(identity,b) = idQb,
inference(spm,[status(thm)],[c_0_54,c_0_17]) ).
cnf(c_0_59,hypothesis,
( less_equal(divide(X1,idQb),zero)
| ~ quotient(X2,b,X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_50]) ).
cnf(c_0_60,plain,
( less_equal(divide(X1,divide(X2,X3)),divide(X4,X3))
| ~ quotient(X5,X3,X1)
| ~ quotient(X5,X2,X4) ),
inference(spm,[status(thm)],[c_0_47,c_0_17]) ).
cnf(c_0_61,hypothesis,
quotient(identity,idQb,idQ_idQb),
identity_divide_idQb ).
cnf(c_0_62,hypothesis,
( X1 = idQa
| ~ quotient(identity,a,X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_56]) ).
cnf(c_0_63,hypothesis,
less_equal(idQb,divide(idQb,b)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_17]),c_0_58]) ).
cnf(c_0_64,hypothesis,
less_equal(divide(divide(X1,b),idQb),zero),
inference(spm,[status(thm)],[c_0_59,c_0_17]) ).
cnf(c_0_65,hypothesis,
( less_equal(divide(idQ_idQb,divide(X1,idQb)),divide(X2,idQb))
| ~ quotient(identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_66,hypothesis,
( less_equal(divide(X1,idQ_idQb),zero)
| ~ quotient(X2,idQb,X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_61]) ).
cnf(c_0_67,hypothesis,
( less_equal(idQa,divide(X1,a))
| ~ quotient(identity,a,X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_56]) ).
cnf(c_0_68,hypothesis,
divide(identity,a) = idQa,
inference(spm,[status(thm)],[c_0_62,c_0_17]) ).
cnf(c_0_69,hypothesis,
( less_equal(divide(X1,idQa),zero)
| ~ quotient(X2,a,X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_70,hypothesis,
quotient(identity,idQa,idQ_idQa),
identity_divide_idQa ).
cnf(c_0_71,plain,
( less_equal(X1,divide(X2,X3))
| ~ quotient(X4,divide(X3,X5),X2)
| ~ quotient(X4,X3,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_22]),c_0_48]) ).
cnf(c_0_72,hypothesis,
divide(idQb,b) = idQb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_63]),c_0_20])]) ).
cnf(c_0_73,hypothesis,
divide(divide(X1,b),idQb) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_64]),c_0_28])]) ).
cnf(c_0_74,hypothesis,
less_equal(divide(idQ_idQb,divide(b,idQb)),zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_50]),c_0_33]) ).
cnf(c_0_75,hypothesis,
less_equal(divide(divide(X1,idQb),idQ_idQb),zero),
inference(spm,[status(thm)],[c_0_66,c_0_17]) ).
cnf(c_0_76,hypothesis,
less_equal(idQa,divide(idQa,a)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_17]),c_0_68]) ).
cnf(c_0_77,hypothesis,
less_equal(divide(divide(X1,a),idQa),zero),
inference(spm,[status(thm)],[c_0_69,c_0_17]) ).
cnf(c_0_78,hypothesis,
( less_equal(divide(idQ_idQa,divide(X1,idQa)),divide(X2,idQa))
| ~ quotient(identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_60,c_0_70]) ).
cnf(c_0_79,hypothesis,
( less_equal(divide(X1,idQ_idQa),zero)
| ~ quotient(X2,idQa,X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_70]) ).
cnf(c_0_80,plain,
( less_equal(X1,divide(divide(X2,divide(X3,X4)),X3))
| ~ quotient(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_17]) ).
cnf(c_0_81,hypothesis,
quotient(idQb,b,idQb),
inference(spm,[status(thm)],[c_0_17,c_0_72]) ).
cnf(c_0_82,hypothesis,
quotient(divide(X1,b),idQb,zero),
inference(spm,[status(thm)],[c_0_17,c_0_73]) ).
cnf(c_0_83,hypothesis,
divide(idQ_idQb,divide(b,idQb)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_74]),c_0_28])]) ).
cnf(c_0_84,hypothesis,
divide(divide(X1,idQb),idQ_idQb) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_75]),c_0_28])]) ).
cnf(c_0_85,hypothesis,
divide(idQa,a) = idQa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_76]),c_0_20])]) ).
cnf(c_0_86,hypothesis,
divide(divide(X1,a),idQa) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_77]),c_0_28])]) ).
cnf(c_0_87,hypothesis,
less_equal(divide(idQ_idQa,divide(a,idQa)),zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_56]),c_0_33]) ).
cnf(c_0_88,hypothesis,
less_equal(divide(divide(X1,idQa),idQ_idQa),zero),
inference(spm,[status(thm)],[c_0_79,c_0_17]) ).
cnf(c_0_89,hypothesis,
less_equal(idQb,divide(divide(idQb,divide(b,X1)),b)),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_90,hypothesis,
less_equal(divide(X1,b),idQb),
inference(spm,[status(thm)],[c_0_30,c_0_82]) ).
cnf(c_0_91,hypothesis,
quotient(idQ_idQb,divide(b,idQb),zero),
inference(spm,[status(thm)],[c_0_17,c_0_83]) ).
cnf(c_0_92,hypothesis,
quotient(divide(X1,idQb),idQ_idQb,zero),
inference(spm,[status(thm)],[c_0_17,c_0_84]) ).
cnf(c_0_93,hypothesis,
quotient(idQa,a,idQa),
inference(spm,[status(thm)],[c_0_17,c_0_85]) ).
cnf(c_0_94,hypothesis,
quotient(divide(X1,a),idQa,zero),
inference(spm,[status(thm)],[c_0_17,c_0_86]) ).
cnf(c_0_95,hypothesis,
divide(idQ_idQa,divide(a,idQa)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_87]),c_0_28])]) ).
cnf(c_0_96,hypothesis,
divide(divide(X1,idQa),idQ_idQa) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_88]),c_0_28])]) ).
cnf(c_0_97,plain,
( less_equal(divide(X1,divide(identity,X2)),zero)
| ~ quotient(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_17]) ).
cnf(c_0_98,plain,
( divide(X1,X2) = X1
| ~ less_equal(X1,divide(X1,X2)) ),
inference(spm,[status(thm)],[c_0_26,c_0_20]) ).
cnf(c_0_99,hypothesis,
divide(divide(idQb,divide(b,X1)),b) = idQb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_89]),c_0_90])]) ).
cnf(c_0_100,hypothesis,
less_equal(idQ_idQb,divide(b,idQb)),
inference(spm,[status(thm)],[c_0_30,c_0_91]) ).
cnf(c_0_101,hypothesis,
less_equal(divide(X1,idQb),idQ_idQb),
inference(spm,[status(thm)],[c_0_30,c_0_92]) ).
cnf(c_0_102,hypothesis,
less_equal(idQa,divide(divide(idQa,divide(a,X1)),a)),
inference(spm,[status(thm)],[c_0_80,c_0_93]) ).
cnf(c_0_103,hypothesis,
less_equal(divide(X1,a),idQa),
inference(spm,[status(thm)],[c_0_30,c_0_94]) ).
cnf(c_0_104,hypothesis,
quotient(idQ_idQa,divide(a,idQa),zero),
inference(spm,[status(thm)],[c_0_17,c_0_95]) ).
cnf(c_0_105,hypothesis,
quotient(divide(X1,idQa),idQ_idQa,zero),
inference(spm,[status(thm)],[c_0_17,c_0_96]) ).
cnf(c_0_106,plain,
less_equal(divide(divide(X1,X2),divide(identity,X2)),zero),
inference(spm,[status(thm)],[c_0_97,c_0_17]) ).
cnf(c_0_107,plain,
( less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(X4,X2))
| ~ quotient(X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_60,c_0_17]) ).
cnf(c_0_108,hypothesis,
divide(idQb,divide(b,X1)) = idQb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_20])]) ).
cnf(c_0_109,hypothesis,
divide(b,idQb) = idQ_idQb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_100]),c_0_101])]) ).
cnf(c_0_110,hypothesis,
divide(divide(idQa,divide(a,X1)),a) = idQa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_102]),c_0_103])]) ).
cnf(c_0_111,hypothesis,
less_equal(idQ_idQa,divide(a,idQa)),
inference(spm,[status(thm)],[c_0_30,c_0_104]) ).
cnf(c_0_112,hypothesis,
less_equal(divide(X1,idQa),idQ_idQa),
inference(spm,[status(thm)],[c_0_30,c_0_105]) ).
cnf(c_0_113,plain,
divide(divide(X1,X2),divide(identity,X2)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_106]),c_0_28])]) ).
cnf(c_0_114,hypothesis,
less_equal(divide(divide(identity,X1),divide(idQb,X1)),divide(idQ_idQb,X1)),
inference(spm,[status(thm)],[c_0_107,c_0_61]) ).
cnf(c_0_115,hypothesis,
divide(idQb,idQ_idQb) = idQb,
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_116,hypothesis,
divide(idQa,divide(a,X1)) = idQa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_110]),c_0_20])]) ).
cnf(c_0_117,hypothesis,
divide(a,idQa) = idQ_idQa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_111]),c_0_112])]) ).
cnf(c_0_118,hypothesis,
quotient(idQa,idQ_idQb,idQa_Q__idQ_idQb),
idQa_divide_idQ_idQb ).
cnf(c_0_119,plain,
quotient(divide(X1,X2),divide(identity,X2),zero),
inference(spm,[status(thm)],[c_0_17,c_0_113]) ).
cnf(c_0_120,hypothesis,
less_equal(divide(divide(identity,idQ_idQb),idQb),zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_33]),c_0_115]) ).
cnf(c_0_121,hypothesis,
less_equal(divide(divide(identity,X1),divide(idQa,X1)),divide(idQ_idQa,X1)),
inference(spm,[status(thm)],[c_0_107,c_0_70]) ).
cnf(c_0_122,hypothesis,
divide(idQa,idQ_idQa) = idQa,
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_123,hypothesis,
( less_equal(divide(X1,idQa_Q__idQ_idQb),divide(X2,idQ_idQb))
| ~ quotient(X3,idQ_idQb,X1)
| ~ quotient(X3,idQa,X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_118]) ).
cnf(c_0_124,plain,
less_equal(divide(X1,X2),divide(identity,X2)),
inference(spm,[status(thm)],[c_0_30,c_0_119]) ).
cnf(c_0_125,hypothesis,
divide(divide(identity,idQ_idQb),idQb) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_120]),c_0_28])]) ).
cnf(c_0_126,hypothesis,
quotient(idQb,idQ_idQa,idQb_Q__idQ_idQa),
idQb_divide_idQ_idQa ).
cnf(c_0_127,hypothesis,
less_equal(divide(divide(identity,idQ_idQa),idQa),zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_33]),c_0_122]) ).
cnf(c_0_128,hypothesis,
( less_equal(divide(divide(X1,idQ_idQb),idQa_Q__idQ_idQb),divide(X2,idQ_idQb))
| ~ quotient(X1,idQa,X2) ),
inference(spm,[status(thm)],[c_0_123,c_0_17]) ).
cnf(c_0_129,plain,
( divide(identity,X1) = divide(X2,X1)
| ~ less_equal(divide(identity,X1),divide(X2,X1)) ),
inference(spm,[status(thm)],[c_0_26,c_0_124]) ).
cnf(c_0_130,hypothesis,
quotient(divide(identity,idQ_idQb),idQb,zero),
inference(spm,[status(thm)],[c_0_17,c_0_125]) ).
cnf(c_0_131,hypothesis,
( less_equal(divide(X1,idQb_Q__idQ_idQa),divide(X2,idQ_idQa))
| ~ quotient(X3,idQ_idQa,X1)
| ~ quotient(X3,idQb,X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_126]) ).
cnf(c_0_132,hypothesis,
divide(divide(identity,idQ_idQa),idQa) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_127]),c_0_28])]) ).
cnf(c_0_133,hypothesis,
less_equal(divide(divide(identity,idQ_idQb),idQa_Q__idQ_idQb),divide(idQ_idQa,idQ_idQb)),
inference(spm,[status(thm)],[c_0_128,c_0_70]) ).
cnf(c_0_134,hypothesis,
( divide(identity,idQ_idQb) = idQb
| ~ less_equal(divide(identity,idQ_idQb),idQb) ),
inference(spm,[status(thm)],[c_0_129,c_0_115]) ).
cnf(c_0_135,hypothesis,
less_equal(divide(identity,idQ_idQb),idQb),
inference(spm,[status(thm)],[c_0_30,c_0_130]) ).
cnf(c_0_136,hypothesis,
( less_equal(divide(divide(X1,idQ_idQa),idQb_Q__idQ_idQa),divide(X2,idQ_idQa))
| ~ quotient(X1,idQb,X2) ),
inference(spm,[status(thm)],[c_0_131,c_0_17]) ).
cnf(c_0_137,hypothesis,
quotient(divide(identity,idQ_idQa),idQa,zero),
inference(spm,[status(thm)],[c_0_17,c_0_132]) ).
cnf(c_0_138,hypothesis,
quotient(divide(divide(identity,idQ_idQb),idQa_Q__idQ_idQb),divide(idQ_idQa,idQ_idQb),zero),
inference(spm,[status(thm)],[c_0_19,c_0_133]) ).
cnf(c_0_139,hypothesis,
divide(identity,idQ_idQb) = idQb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_135])]) ).
cnf(c_0_140,plain,
( X1 = zero
| ~ less_equal(X1,zero) ),
inference(spm,[status(thm)],[c_0_26,c_0_28]) ).
cnf(c_0_141,hypothesis,
less_equal(divide(divide(identity,idQ_idQa),idQb_Q__idQ_idQa),divide(idQ_idQb,idQ_idQa)),
inference(spm,[status(thm)],[c_0_136,c_0_61]) ).
cnf(c_0_142,hypothesis,
( divide(identity,idQ_idQa) = idQa
| ~ less_equal(divide(identity,idQ_idQa),idQa) ),
inference(spm,[status(thm)],[c_0_129,c_0_122]) ).
cnf(c_0_143,hypothesis,
less_equal(divide(identity,idQ_idQa),idQa),
inference(spm,[status(thm)],[c_0_30,c_0_137]) ).
cnf(c_0_144,hypothesis,
quotient(divide(idQb,idQa_Q__idQ_idQb),divide(idQ_idQa,idQ_idQb),zero),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_145,plain,
divide(zero,X1) = zero,
inference(spm,[status(thm)],[c_0_140,c_0_20]) ).
cnf(c_0_146,hypothesis,
quotient(divide(divide(identity,idQ_idQa),idQb_Q__idQ_idQa),divide(idQ_idQb,idQ_idQa),zero),
inference(spm,[status(thm)],[c_0_19,c_0_141]) ).
cnf(c_0_147,hypothesis,
divide(identity,idQ_idQa) = idQa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_142,c_0_143])]) ).
cnf(c_0_148,hypothesis,
( less_equal(X1,zero)
| ~ quotient(divide(idQb,idQa_Q__idQ_idQb),idQ_idQa,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_144]),c_0_145]) ).
cnf(c_0_149,plain,
( X1 = divide(X2,X3)
| ~ quotient(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_17]) ).
cnf(c_0_150,hypothesis,
quotient(divide(idQa,idQb_Q__idQ_idQa),divide(idQ_idQb,idQ_idQa),zero),
inference(spm,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_151,hypothesis,
less_equal(divide(divide(idQb,idQa_Q__idQ_idQb),idQ_idQa),zero),
inference(spm,[status(thm)],[c_0_148,c_0_17]) ).
cnf(c_0_152,hypothesis,
( X1 = idQb_Q__idQ_idQa
| ~ quotient(idQb,idQ_idQa,X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_126]) ).
cnf(c_0_153,plain,
less_equal(divide(X1,X2),divide(divide(X1,divide(X2,X3)),X2)),
inference(spm,[status(thm)],[c_0_80,c_0_17]) ).
cnf(c_0_154,hypothesis,
divide(divide(idQa,idQb_Q__idQ_idQa),divide(idQ_idQb,idQ_idQa)) = zero,
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_155,plain,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
inference(spm,[status(thm)],[c_0_107,c_0_17]) ).
cnf(c_0_156,hypothesis,
divide(divide(idQb,idQa_Q__idQ_idQb),idQ_idQa) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_151]),c_0_28])]) ).
cnf(c_0_157,hypothesis,
divide(idQb,idQ_idQa) = idQb_Q__idQ_idQa,
inference(spm,[status(thm)],[c_0_152,c_0_17]) ).
cnf(c_0_158,hypothesis,
less_equal(divide(divide(idQa,idQb_Q__idQ_idQa),idQ_idQb),zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_154]),c_0_145]) ).
cnf(c_0_159,hypothesis,
( X1 = idQa_Q__idQ_idQb
| ~ quotient(idQa,idQ_idQb,X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_118]) ).
cnf(c_0_160,hypothesis,
less_equal(divide(idQb_Q__idQ_idQa,divide(idQa_Q__idQ_idQb,idQ_idQa)),zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_157]) ).
cnf(c_0_161,hypothesis,
divide(divide(idQa,idQb_Q__idQ_idQa),idQ_idQb) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_158]),c_0_28])]) ).
cnf(c_0_162,hypothesis,
divide(idQa,idQ_idQb) = idQa_Q__idQ_idQb,
inference(spm,[status(thm)],[c_0_159,c_0_17]) ).
cnf(c_0_163,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_26,c_0_160]),c_0_28])]) ).
cnf(c_0_164,hypothesis,
less_equal(divide(idQa_Q__idQ_idQb,divide(idQb_Q__idQ_idQa,idQ_idQb)),zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_161]),c_0_162]) ).
cnf(c_0_165,hypothesis,
less_equal(divide(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb),zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_163]),c_0_145]) ).
cnf(c_0_166,hypothesis,
divide(idQa_Q__idQ_idQb,divide(idQb_Q__idQ_idQa,idQ_idQb)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_164]),c_0_28])]) ).
cnf(c_0_167,hypothesis,
divide(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_165]),c_0_28])]) ).
cnf(c_0_168,hypothesis,
less_equal(divide(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa),zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_166]),c_0_145]) ).
cnf(c_0_169,hypothesis,
quotient(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb,zero),
inference(spm,[status(thm)],[c_0_17,c_0_167]) ).
cnf(c_0_170,hypothesis,
divide(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_168]),c_0_28])]) ).
cnf(c_0_171,hypothesis,
less_equal(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb),
inference(spm,[status(thm)],[c_0_30,c_0_169]) ).
cnf(c_0_172,negated_conjecture,
idQa_Q__idQ_idQb != idQb_Q__idQ_idQa,
prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa ).
cnf(c_0_173,hypothesis,
quotient(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa,zero),
inference(spm,[status(thm)],[c_0_17,c_0_170]) ).
cnf(c_0_174,hypothesis,
~ less_equal(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_171]),c_0_172]) ).
cnf(c_0_175,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_173]),c_0_174]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN011-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.15/0.35 % Computer : n001.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 2400
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Oct 2 11:54:06 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.luZ4rjz2Ft/E---3.1_17740.p
% 7.12/1.37 # Version: 3.1pre001
% 7.12/1.37 # Preprocessing class: FSMSSMSMSSSNFFN.
% 7.12/1.37 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.12/1.37 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 7.12/1.37 # Starting new_bool_3 with 300s (1) cores
% 7.12/1.37 # Starting new_bool_1 with 300s (1) cores
% 7.12/1.37 # Starting sh5l with 300s (1) cores
% 7.12/1.37 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 17819 completed with status 0
% 7.12/1.37 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 7.12/1.37 # Preprocessing class: FSMSSMSMSSSNFFN.
% 7.12/1.37 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.12/1.37 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 7.12/1.37 # No SInE strategy applied
% 7.12/1.37 # Search class: FHUSS-FFSM22-SFFFFFNN
% 7.12/1.37 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 7.12/1.37 # Starting G-E--_300_C01_F1_SE_CS_SP_S0Y with 811s (1) cores
% 7.12/1.37 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 7.12/1.37 # Starting new_bool_3 with 136s (1) cores
% 7.12/1.37 # Starting new_bool_1 with 136s (1) cores
% 7.12/1.37 # Starting sh5l with 136s (1) cores
% 7.12/1.37 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 17824 completed with status 0
% 7.12/1.37 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 7.12/1.37 # Preprocessing class: FSMSSMSMSSSNFFN.
% 7.12/1.37 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.12/1.37 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 7.12/1.37 # No SInE strategy applied
% 7.12/1.37 # Search class: FHUSS-FFSM22-SFFFFFNN
% 7.12/1.37 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 7.12/1.37 # Starting G-E--_300_C01_F1_SE_CS_SP_S0Y with 811s (1) cores
% 7.12/1.37 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 7.12/1.37 # Preprocessing time : 0.001 s
% 7.12/1.37 # Presaturation interreduction done
% 7.12/1.37
% 7.12/1.37 # Proof found!
% 7.12/1.37 # SZS status Unsatisfiable
% 7.12/1.37 # SZS output start CNFRefutation
% See solution above
% 7.12/1.37 # Parsed axioms : 16
% 7.12/1.37 # Removed by relevancy pruning/SinE : 0
% 7.12/1.37 # Initial clauses : 16
% 7.12/1.37 # Removed in clause preprocessing : 0
% 7.12/1.37 # Initial clauses in saturation : 16
% 7.12/1.37 # Processed clauses : 20269
% 7.12/1.37 # ...of these trivial : 256
% 7.12/1.37 # ...subsumed : 16594
% 7.12/1.37 # ...remaining for further processing : 3419
% 7.12/1.37 # Other redundant clauses eliminated : 0
% 7.12/1.37 # Clauses deleted for lack of memory : 0
% 7.12/1.37 # Backward-subsumed : 65
% 7.12/1.37 # Backward-rewritten : 733
% 7.12/1.37 # Generated clauses : 70308
% 7.12/1.37 # ...of the previous two non-redundant : 36506
% 7.12/1.37 # ...aggressively subsumed : 0
% 7.12/1.37 # Contextual simplify-reflections : 0
% 7.12/1.37 # Paramodulations : 70308
% 7.12/1.37 # Factorizations : 0
% 7.12/1.37 # NegExts : 0
% 7.12/1.37 # Equation resolutions : 0
% 7.12/1.37 # Total rewrite steps : 72681
% 7.12/1.37 # Propositional unsat checks : 0
% 7.12/1.37 # Propositional check models : 0
% 7.12/1.37 # Propositional check unsatisfiable : 0
% 7.12/1.37 # Propositional clauses : 0
% 7.12/1.37 # Propositional clauses after purity: 0
% 7.12/1.37 # Propositional unsat core size : 0
% 7.12/1.37 # Propositional preprocessing time : 0.000
% 7.12/1.37 # Propositional encoding time : 0.000
% 7.12/1.37 # Propositional solver time : 0.000
% 7.12/1.37 # Success case prop preproc time : 0.000
% 7.12/1.37 # Success case prop encoding time : 0.000
% 7.12/1.37 # Success case prop solver time : 0.000
% 7.12/1.37 # Current number of processed clauses : 2605
% 7.12/1.37 # Positive orientable unit clauses : 651
% 7.12/1.37 # Positive unorientable unit clauses: 0
% 7.12/1.37 # Negative unit clauses : 2
% 7.12/1.37 # Non-unit-clauses : 1952
% 7.12/1.37 # Current number of unprocessed clauses: 14876
% 7.12/1.37 # ...number of literals in the above : 32603
% 7.12/1.37 # Current number of archived formulas : 0
% 7.12/1.37 # Current number of archived clauses : 814
% 7.12/1.37 # Clause-clause subsumption calls (NU) : 2920422
% 7.12/1.37 # Rec. Clause-clause subsumption calls : 1851808
% 7.12/1.37 # Non-unit clause-clause subsumptions : 16653
% 7.12/1.37 # Unit Clause-clause subsumption calls : 3515
% 7.12/1.37 # Rewrite failures with RHS unbound : 0
% 7.12/1.37 # BW rewrite match attempts : 3729
% 7.12/1.37 # BW rewrite match successes : 252
% 7.12/1.37 # Condensation attempts : 0
% 7.12/1.37 # Condensation successes : 0
% 7.12/1.37 # Termbank termtop insertions : 809736
% 7.12/1.37
% 7.12/1.37 # -------------------------------------------------
% 7.12/1.37 # User time : 0.835 s
% 7.12/1.37 # System time : 0.023 s
% 7.12/1.37 # Total time : 0.858 s
% 7.12/1.37 # Maximum resident set size: 1648 pages
% 7.12/1.37
% 7.12/1.37 # -------------------------------------------------
% 7.12/1.37 # User time : 4.239 s
% 7.12/1.37 # System time : 0.059 s
% 7.12/1.37 # Total time : 4.298 s
% 7.12/1.37 # Maximum resident set size: 1684 pages
% 7.12/1.37 % E---3.1 exiting
% 7.12/1.37 % E---3.1 exiting
%------------------------------------------------------------------------------