TSTP Solution File: HEN011-2 by E-SAT---3.1
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%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : HEN011-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n023.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 17:51:04 EDT 2023
% Result : Unsatisfiable 194.54s 24.92s
% Output : CNFRefutation 194.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 25
% Syntax : Number of clauses : 165 ( 89 unt; 0 nHn; 140 RR)
% Number of literals : 311 ( 39 equ; 150 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 3 ( 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 : 255 ( 31 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(one_inversion_equals_three,axiom,
( X2 = X4
| ~ quotient(identity,X1,X2)
| ~ quotient(identity,X2,X3)
| ~ quotient(identity,X3,X4) ),
file('/export/starexec/sandbox/tmp/tmp.BbRTY3Hhy1/E---3.1_17551.p',one_inversion_equals_three) ).
cnf(closure,axiom,
quotient(X1,X2,divide(X1,X2)),
file('/export/starexec/sandbox/tmp/tmp.BbRTY3Hhy1/E---3.1_17551.p',closure) ).
cnf(identity_divide_idQa,hypothesis,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox/tmp/tmp.BbRTY3Hhy1/E---3.1_17551.p',identity_divide_idQa) ).
cnf(identity_divide_a,hypothesis,
quotient(identity,a,idQa),
file('/export/starexec/sandbox/tmp/tmp.BbRTY3Hhy1/E---3.1_17551.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/sandbox/tmp/tmp.BbRTY3Hhy1/E---3.1_17551.p',xLEy_implies_xQzLEyQz) ).
cnf(identity_is_largest,axiom,
less_equal(X1,identity),
file('/export/starexec/sandbox/tmp/tmp.BbRTY3Hhy1/E---3.1_17551.p',identity_is_largest) ).
cnf(inversion_lemma,axiom,
( X2 = X4
| ~ quotient(identity,X1,X2)
| ~ quotient(identity,X2,X3)
| ~ quotient(X2,X3,X4) ),
file('/export/starexec/sandbox/tmp/tmp.BbRTY3Hhy1/E---3.1_17551.p',inversion_lemma) ).
cnf(less_equal_quotient,axiom,
( less_equal(X1,X2)
| ~ quotient(X1,X2,zero) ),
file('/export/starexec/sandbox/tmp/tmp.BbRTY3Hhy1/E---3.1_17551.p',less_equal_quotient) ).
cnf(x_divide_x_is_zero,axiom,
quotient(X1,X1,zero),
file('/export/starexec/sandbox/tmp/tmp.BbRTY3Hhy1/E---3.1_17551.p',x_divide_x_is_zero) ).
cnf(idQb_divide_idQ_idQa,hypothesis,
quotient(idQb,idQ_idQa,idQb_Q__idQ_idQa),
file('/export/starexec/sandbox/tmp/tmp.BbRTY3Hhy1/E---3.1_17551.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/sandbox/tmp/tmp.BbRTY3Hhy1/E---3.1_17551.p',xQyLEz_implies_xQzLEy) ).
cnf(identity_divide_idQb,hypothesis,
quotient(identity,idQb,idQ_idQb),
file('/export/starexec/sandbox/tmp/tmp.BbRTY3Hhy1/E---3.1_17551.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/sandbox/tmp/tmp.BbRTY3Hhy1/E---3.1_17551.p',xLEy_implies_zQyLEzQx) ).
cnf(idQa_divide_idQ_idQb,hypothesis,
quotient(idQa,idQ_idQb,idQa_Q__idQ_idQb),
file('/export/starexec/sandbox/tmp/tmp.BbRTY3Hhy1/E---3.1_17551.p',idQa_divide_idQ_idQb) ).
cnf(identity_divide_b,hypothesis,
quotient(identity,b,idQb),
file('/export/starexec/sandbox/tmp/tmp.BbRTY3Hhy1/E---3.1_17551.p',identity_divide_b) ).
cnf(divisor_existence,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
file('/export/starexec/sandbox/tmp/tmp.BbRTY3Hhy1/E---3.1_17551.p',divisor_existence) ).
cnf(less_equal_and_equal,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
file('/export/starexec/sandbox/tmp/tmp.BbRTY3Hhy1/E---3.1_17551.p',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/sandbox/tmp/tmp.BbRTY3Hhy1/E---3.1_17551.p',quotient_property) ).
cnf(x_divde_zero_is_x,axiom,
quotient(X1,zero,X1),
file('/export/starexec/sandbox/tmp/tmp.BbRTY3Hhy1/E---3.1_17551.p',x_divde_zero_is_x) ).
cnf(zero_divide_anything_is_zero,axiom,
quotient(zero,X1,zero),
file('/export/starexec/sandbox/tmp/tmp.BbRTY3Hhy1/E---3.1_17551.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/sandbox/tmp/tmp.BbRTY3Hhy1/E---3.1_17551.p',transitivity_of_less_equal) ).
cnf(quotient_less_equal,axiom,
( quotient(X1,X2,zero)
| ~ less_equal(X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.BbRTY3Hhy1/E---3.1_17551.p',quotient_less_equal) ).
cnf(well_defined,axiom,
( X3 = X4
| ~ quotient(X1,X2,X3)
| ~ quotient(X1,X2,X4) ),
file('/export/starexec/sandbox/tmp/tmp.BbRTY3Hhy1/E---3.1_17551.p',well_defined) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox/tmp/tmp.BbRTY3Hhy1/E---3.1_17551.p',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/sandbox/tmp/tmp.BbRTY3Hhy1/E---3.1_17551.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
% 0.11/0.11 % Problem : HEN011-2 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n023.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 : 2400
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Oct 2 11:36:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Running first-order model finding
% 0.19/0.46 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.BbRTY3Hhy1/E---3.1_17551.p
% 194.54/24.92 # Version: 3.1pre001
% 194.54/24.92 # Preprocessing class: FSMSSMSMSSSNFFN.
% 194.54/24.92 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 194.54/24.92 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 194.54/24.92 # Starting new_bool_3 with 300s (1) cores
% 194.54/24.92 # Starting new_bool_1 with 300s (1) cores
% 194.54/24.92 # Starting sh5l with 300s (1) cores
% 194.54/24.92 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 17629 completed with status 0
% 194.54/24.92 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 194.54/24.92 # Preprocessing class: FSMSSMSMSSSNFFN.
% 194.54/24.92 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 194.54/24.92 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 194.54/24.92 # No SInE strategy applied
% 194.54/24.92 # Search class: FHUSM-FFMM22-SFFFFFNN
% 194.54/24.92 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 194.54/24.92 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 811s (1) cores
% 194.54/24.92 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 194.54/24.92 # Starting new_bool_3 with 136s (1) cores
% 194.54/24.92 # Starting new_bool_1 with 136s (1) cores
% 194.54/24.92 # Starting sh5l with 136s (1) cores
% 194.54/24.92 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with pid 17633 completed with status 0
% 194.54/24.92 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d
% 194.54/24.92 # Preprocessing class: FSMSSMSMSSSNFFN.
% 194.54/24.92 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 194.54/24.92 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 194.54/24.92 # No SInE strategy applied
% 194.54/24.92 # Search class: FHUSM-FFMM22-SFFFFFNN
% 194.54/24.92 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 194.54/24.92 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 811s (1) cores
% 194.54/24.92 # Preprocessing time : 0.001 s
% 194.54/24.92 # Presaturation interreduction done
% 194.54/24.92
% 194.54/24.92 # Proof found!
% 194.54/24.92 # SZS status Unsatisfiable
% 194.54/24.92 # SZS output start CNFRefutation
% See solution above
% 194.54/24.92 # Parsed axioms : 26
% 194.54/24.92 # Removed by relevancy pruning/SinE : 0
% 194.54/24.92 # Initial clauses : 26
% 194.54/24.92 # Removed in clause preprocessing : 0
% 194.54/24.92 # Initial clauses in saturation : 26
% 194.54/24.92 # Processed clauses : 207526
% 194.54/24.92 # ...of these trivial : 1894
% 194.54/24.92 # ...subsumed : 186043
% 194.54/24.92 # ...remaining for further processing : 19589
% 194.54/24.92 # Other redundant clauses eliminated : 0
% 194.54/24.92 # Clauses deleted for lack of memory : 0
% 194.54/24.92 # Backward-subsumed : 1366
% 194.54/24.92 # Backward-rewritten : 963
% 194.54/24.92 # Generated clauses : 749352
% 194.54/24.92 # ...of the previous two non-redundant : 426229
% 194.54/24.92 # ...aggressively subsumed : 0
% 194.54/24.92 # Contextual simplify-reflections : 0
% 194.54/24.92 # Paramodulations : 749352
% 194.54/24.92 # Factorizations : 0
% 194.54/24.92 # NegExts : 0
% 194.54/24.92 # Equation resolutions : 0
% 194.54/24.92 # Total rewrite steps : 733585
% 194.54/24.92 # Propositional unsat checks : 3
% 194.54/24.92 # Propositional check models : 0
% 194.54/24.92 # Propositional check unsatisfiable : 0
% 194.54/24.92 # Propositional clauses : 0
% 194.54/24.92 # Propositional clauses after purity: 0
% 194.54/24.92 # Propositional unsat core size : 0
% 194.54/24.92 # Propositional preprocessing time : 0.000
% 194.54/24.92 # Propositional encoding time : 0.225
% 194.54/24.92 # Propositional solver time : 0.168
% 194.54/24.92 # Success case prop preproc time : 0.000
% 194.54/24.92 # Success case prop encoding time : 0.000
% 194.54/24.92 # Success case prop solver time : 0.000
% 194.54/24.92 # Current number of processed clauses : 17234
% 194.54/24.92 # Positive orientable unit clauses : 2442
% 194.54/24.92 # Positive unorientable unit clauses: 0
% 194.54/24.92 # Negative unit clauses : 9
% 194.54/24.92 # Non-unit-clauses : 14783
% 194.54/24.92 # Current number of unprocessed clauses: 215959
% 194.54/24.92 # ...number of literals in the above : 537879
% 194.54/24.92 # Current number of archived formulas : 0
% 194.54/24.92 # Current number of archived clauses : 2355
% 194.54/24.92 # Clause-clause subsumption calls (NU) : 133810936
% 194.54/24.92 # Rec. Clause-clause subsumption calls : 84925507
% 194.54/24.92 # Non-unit clause-clause subsumptions : 187366
% 194.54/24.92 # Unit Clause-clause subsumption calls : 107534
% 194.54/24.92 # Rewrite failures with RHS unbound : 0
% 194.54/24.92 # BW rewrite match attempts : 38206
% 194.54/24.92 # BW rewrite match successes : 284
% 194.54/24.92 # Condensation attempts : 0
% 194.54/24.92 # Condensation successes : 0
% 194.54/24.92 # Termbank termtop insertions : 10738722
% 194.54/24.92
% 194.54/24.92 # -------------------------------------------------
% 194.54/24.92 # User time : 24.114 s
% 194.54/24.92 # System time : 0.201 s
% 194.54/24.92 # Total time : 24.315 s
% 194.54/24.92 # Maximum resident set size: 1644 pages
% 194.54/24.92
% 194.54/24.92 # -------------------------------------------------
% 194.54/24.92 # User time : 120.670 s
% 194.54/24.92 # System time : 0.730 s
% 194.54/24.92 # Total time : 121.400 s
% 194.54/24.92 # Maximum resident set size: 1692 pages
% 194.54/24.92 % E---3.1 exiting
%------------------------------------------------------------------------------