%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN009-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:32:01 AM UTC 2026
% Result : Unsatisfiable 3.43s 0.91s
% Output : CNFRefutation 3.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 12
% Syntax : Number of formulae : 165 ( 93 unt; 0 def)
% Number of atoms : 313 ( 54 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 302 ( 154 ~; 148 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 282 ( 69 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(quotient_less_equal,axiom,
! [VAR_0,VAR_1] :
( quotient(VAR_0,VAR_1,zero)
| ~ less_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',quotient_less_equal) ).
cnf(c_1,plain,
( quotient(A,B,zero)
| ~ less_equal(A,B) ),
inference(clausify,[status(thm)],[quotient_less_equal]) ).
fof(less_equal_quotient,axiom,
! [VAR_0,VAR_1] :
( less_equal(VAR_0,VAR_1)
| ~ quotient(VAR_0,VAR_1,zero) ),
file('theBenchmark.p',less_equal_quotient) ).
cnf(c_2,plain,
( less_equal(A,B)
| ~ quotient(A,B,zero) ),
inference(clausify,[status(thm)],[less_equal_quotient]) ).
fof(divisor_existence,axiom,
! [VAR_0,VAR_1,VAR_2] :
( less_equal(VAR_2,VAR_0)
| ~ quotient(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',divisor_existence) ).
cnf(c_3,plain,
( less_equal(C,A)
| ~ quotient(A,B,C) ),
inference(clausify,[status(thm)],[divisor_existence]) ).
fof(quotient_property,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7] :
( less_equal(VAR_6,VAR_7)
| ~ quotient(VAR_2,VAR_3,VAR_7)
| ~ quotient(VAR_5,VAR_4,VAR_6)
| ~ quotient(VAR_0,VAR_3,VAR_5)
| ~ quotient(VAR_1,VAR_3,VAR_4)
| ~ quotient(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',quotient_property) ).
cnf(c_4,plain,
( less_equal(V6,V7)
| ~ quotient(C,D,V7)
| ~ quotient(F,E,V6)
| ~ quotient(A,D,F)
| ~ quotient(B,D,E)
| ~ quotient(A,B,C) ),
inference(clausify,[status(thm)],[quotient_property]) ).
fof(zero_is_smallest,axiom,
! [VAR_0] : less_equal(zero,VAR_0),
file('theBenchmark.p',zero_is_smallest) ).
cnf(c_5,plain,
less_equal(zero,A),
inference(clausify,[status(thm)],[zero_is_smallest]) ).
fof(less_equal_and_equal,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| ~ less_equal(VAR_1,VAR_0)
| ~ less_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',less_equal_and_equal) ).
cnf(c_6,plain,
( A = B
| ~ less_equal(B,A)
| ~ less_equal(A,B) ),
inference(clausify,[status(thm)],[less_equal_and_equal]) ).
fof(identity_is_largest,axiom,
! [VAR_0] : less_equal(VAR_0,identity),
file('theBenchmark.p',identity_is_largest) ).
cnf(c_7,plain,
less_equal(A,identity),
inference(clausify,[status(thm)],[identity_is_largest]) ).
fof(closure,axiom,
! [VAR_0,VAR_1] : quotient(VAR_0,VAR_1,divide(VAR_0,VAR_1)),
file('theBenchmark.p',closure) ).
cnf(c_8,plain,
quotient(A,B,divide(A,B)),
inference(clausify,[status(thm)],[closure]) ).
fof(identity_divide_a,axiom,
quotient(identity,a,idQa),
file('theBenchmark.p',identity_divide_a) ).
cnf(c_10,plain,
quotient(identity,a,idQa),
inference(clausify,[status(thm)],[identity_divide_a]) ).
fof(identity_divide_idQa,axiom,
quotient(identity,idQa,idQ_idQa),
file('theBenchmark.p',identity_divide_idQa) ).
cnf(c_11,plain,
quotient(identity,idQa,idQ_idQa),
inference(clausify,[status(thm)],[identity_divide_idQa]) ).
fof(identity_divide_idQ_idQa,axiom,
quotient(identity,idQ_idQa,idQ__idQ_idQa),
file('theBenchmark.p',identity_divide_idQ_idQa) ).
cnf(c_12,plain,
quotient(identity,idQ_idQa,idQ__idQ_idQa),
inference(clausify,[status(thm)],[identity_divide_idQ_idQa]) ).
fof(prove_one_inversion_equals_three,axiom,
idQa != idQ__idQ_idQa,
file('theBenchmark.p',prove_one_inversion_equals_three) ).
cnf(c_13,plain,
idQa != idQ__idQ_idQa,
inference(clausify,[status(thm)],[prove_one_inversion_equals_three]) ).
cnf(c_14,plain,
idQ__idQ_idQa != idQa,
inference(copy,[status(thm)],[c_13]) ).
cnf(c_15,plain,
quotient(zero,A,zero),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_16,plain,
quotient(A,identity,zero),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_558,plain,
( less_equal(F,V6)
| ~ quotient(divide(D,A),B,V6)
| ~ quotient(E,C,F)
| ~ quotient(D,B,E)
| ~ quotient(A,B,C) ),
inference(resolve,[status(thm)],[c_4,c_8]) ).
cnf(c_559,plain,
( less_equal(E,F)
| ~ quotient(divide(A,D),B,F)
| ~ quotient(C,divide(D,B),E)
| ~ quotient(A,B,C) ),
inference(resolve,[status(thm)],[c_558,c_8]) ).
cnf(c_560,plain,
( less_equal(D,E)
| ~ quotient(divide(A,C),B,E)
| ~ quotient(divide(A,B),divide(C,B),D) ),
inference(resolve,[status(thm)],[c_559,c_8]) ).
cnf(c_561,plain,
( less_equal(divide(divide(A,C),divide(B,C)),D)
| ~ quotient(divide(A,B),C,D) ),
inference(resolve,[status(thm)],[c_560,c_8]) ).
cnf(c_17,plain,
less_equal(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),
inference(resolve,[status(thm)],[c_561,c_8]) ).
cnf(c_18,plain,
less_equal(divide(A,B),A),
inference(resolve,[status(thm)],[c_3,c_8]) ).
cnf(c_562,plain,
( less_equal(D,E)
| ~ quotient(idQa,A,E)
| ~ quotient(C,B,D)
| ~ quotient(identity,A,C)
| ~ quotient(a,A,B) ),
inference(resolve,[status(thm)],[c_4,c_10]) ).
cnf(c_563,plain,
( less_equal(C,D)
| ~ quotient(idQa,A,D)
| ~ quotient(B,divide(a,A),C)
| ~ quotient(identity,A,B) ),
inference(resolve,[status(thm)],[c_562,c_8]) ).
cnf(c_564,plain,
( less_equal(A,B)
| ~ quotient(idQa,idQa,B)
| ~ quotient(idQ_idQa,divide(a,idQa),A) ),
inference(resolve,[status(thm)],[c_563,c_11]) ).
cnf(c_565,plain,
( less_equal(divide(idQ_idQa,divide(a,idQa)),A)
| ~ quotient(idQa,idQa,A) ),
inference(resolve,[status(thm)],[c_564,c_8]) ).
cnf(c_27,plain,
less_equal(divide(idQ_idQa,divide(a,idQa)),divide(idQa,idQa)),
inference(resolve,[status(thm)],[c_565,c_8]) ).
cnf(c_566,plain,
( less_equal(D,E)
| ~ quotient(idQ_idQa,A,E)
| ~ quotient(C,B,D)
| ~ quotient(identity,A,C)
| ~ quotient(idQa,A,B) ),
inference(resolve,[status(thm)],[c_4,c_11]) ).
cnf(c_567,plain,
( less_equal(C,D)
| ~ quotient(idQ_idQa,A,D)
| ~ quotient(B,divide(idQa,A),C)
| ~ quotient(identity,A,B) ),
inference(resolve,[status(thm)],[c_566,c_8]) ).
cnf(c_568,plain,
( less_equal(A,B)
| ~ quotient(idQ_idQa,idQ_idQa,B)
| ~ quotient(idQ__idQ_idQa,divide(idQa,idQ_idQa),A) ),
inference(resolve,[status(thm)],[c_567,c_12]) ).
cnf(c_569,plain,
( less_equal(divide(idQ__idQ_idQa,divide(idQa,idQ_idQa)),A)
| ~ quotient(idQ_idQa,idQ_idQa,A) ),
inference(resolve,[status(thm)],[c_568,c_8]) ).
cnf(c_35,plain,
less_equal(divide(idQ__idQ_idQa,divide(idQa,idQ_idQa)),divide(idQ_idQa,idQ_idQa)),
inference(resolve,[status(thm)],[c_569,c_8]) ).
cnf(c_570,plain,
( less_equal(E,F)
| ~ quotient(zero,A,F)
| ~ quotient(D,B,E)
| ~ quotient(C,A,D)
| ~ quotient(identity,A,B) ),
inference(resolve,[status(thm)],[c_4,c_16]) ).
cnf(c_571,plain,
( less_equal(C,D)
| ~ quotient(zero,idQ_idQa,D)
| ~ quotient(B,idQ__idQ_idQa,C)
| ~ quotient(A,idQ_idQa,B) ),
inference(resolve,[status(thm)],[c_570,c_12]) ).
cnf(c_572,plain,
( less_equal(B,C)
| ~ quotient(zero,idQ_idQa,C)
| ~ quotient(divide(A,idQ_idQa),idQ__idQ_idQa,B) ),
inference(resolve,[status(thm)],[c_571,c_8]) ).
cnf(c_573,plain,
( less_equal(divide(divide(B,idQ_idQa),idQ__idQ_idQa),A)
| ~ quotient(zero,idQ_idQa,A) ),
inference(resolve,[status(thm)],[c_572,c_8]) ).
cnf(c_52,plain,
less_equal(divide(divide(A,idQ_idQa),idQ__idQ_idQa),zero),
inference(resolve,[status(thm)],[c_573,c_15]) ).
cnf(c_574,plain,
( less_equal(E,F)
| ~ quotient(zero,A,F)
| ~ quotient(D,B,E)
| ~ quotient(C,A,D)
| ~ quotient(identity,A,B) ),
inference(resolve,[status(thm)],[c_4,c_16]) ).
cnf(c_575,plain,
( less_equal(C,D)
| ~ quotient(zero,idQa,D)
| ~ quotient(B,idQ_idQa,C)
| ~ quotient(A,idQa,B) ),
inference(resolve,[status(thm)],[c_574,c_11]) ).
cnf(c_576,plain,
( less_equal(A,B)
| ~ quotient(zero,idQa,B)
| ~ quotient(idQ_idQa,idQ_idQa,A) ),
inference(resolve,[status(thm)],[c_575,c_11]) ).
cnf(c_577,plain,
( less_equal(divide(idQ_idQa,idQ_idQa),A)
| ~ quotient(zero,idQa,A) ),
inference(resolve,[status(thm)],[c_576,c_8]) ).
cnf(c_53,plain,
less_equal(divide(idQ_idQa,idQ_idQa),zero),
inference(resolve,[status(thm)],[c_577,c_15]) ).
cnf(c_578,plain,
( less_equal(E,F)
| ~ quotient(zero,A,F)
| ~ quotient(D,B,E)
| ~ quotient(C,A,D)
| ~ quotient(identity,A,B) ),
inference(resolve,[status(thm)],[c_4,c_16]) ).
cnf(c_579,plain,
( less_equal(C,D)
| ~ quotient(zero,idQa,D)
| ~ quotient(B,idQ_idQa,C)
| ~ quotient(A,idQa,B) ),
inference(resolve,[status(thm)],[c_578,c_11]) ).
cnf(c_580,plain,
( less_equal(B,C)
| ~ quotient(zero,idQa,C)
| ~ quotient(divide(A,idQa),idQ_idQa,B) ),
inference(resolve,[status(thm)],[c_579,c_8]) ).
cnf(c_581,plain,
( less_equal(divide(divide(B,idQa),idQ_idQa),A)
| ~ quotient(zero,idQa,A) ),
inference(resolve,[status(thm)],[c_580,c_8]) ).
cnf(c_54,plain,
less_equal(divide(divide(A,idQa),idQ_idQa),zero),
inference(resolve,[status(thm)],[c_581,c_15]) ).
cnf(c_582,plain,
( less_equal(E,F)
| ~ quotient(zero,A,F)
| ~ quotient(D,B,E)
| ~ quotient(C,A,D)
| ~ quotient(identity,A,B) ),
inference(resolve,[status(thm)],[c_4,c_16]) ).
cnf(c_583,plain,
( less_equal(C,D)
| ~ quotient(zero,a,D)
| ~ quotient(B,idQa,C)
| ~ quotient(A,a,B) ),
inference(resolve,[status(thm)],[c_582,c_10]) ).
cnf(c_584,plain,
( less_equal(A,B)
| ~ quotient(zero,a,B)
| ~ quotient(idQa,idQa,A) ),
inference(resolve,[status(thm)],[c_583,c_10]) ).
cnf(c_585,plain,
( less_equal(divide(idQa,idQa),A)
| ~ quotient(zero,a,A) ),
inference(resolve,[status(thm)],[c_584,c_8]) ).
cnf(c_55,plain,
less_equal(divide(idQa,idQa),zero),
inference(resolve,[status(thm)],[c_585,c_15]) ).
cnf(c_586,plain,
( less_equal(E,F)
| ~ quotient(zero,A,F)
| ~ quotient(D,B,E)
| ~ quotient(C,A,D)
| ~ quotient(identity,A,B) ),
inference(resolve,[status(thm)],[c_4,c_16]) ).
cnf(c_587,plain,
( less_equal(D,E)
| ~ quotient(zero,B,E)
| ~ quotient(C,divide(identity,B),D)
| ~ quotient(A,B,C) ),
inference(resolve,[status(thm)],[c_586,c_8]) ).
cnf(c_588,plain,
( less_equal(C,D)
| ~ quotient(zero,B,D)
| ~ quotient(divide(A,B),divide(identity,B),C) ),
inference(resolve,[status(thm)],[c_587,c_8]) ).
cnf(c_589,plain,
( less_equal(divide(divide(C,A),divide(identity,A)),B)
| ~ quotient(zero,A,B) ),
inference(resolve,[status(thm)],[c_588,c_8]) ).
cnf(c_57,plain,
less_equal(divide(divide(A,B),divide(identity,B)),zero),
inference(resolve,[status(thm)],[c_589,c_15]) ).
cnf(c_58,plain,
quotient(divide(A,B),A,zero),
inference(resolve,[status(thm)],[c_1,c_18]) ).
cnf(c_590,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_591,plain,
zero = divide(idQ_idQa,idQ_idQa),
inference(resolve,[status(thm)],[c_590,c_53]) ).
cnf(c_62,plain,
divide(idQ_idQa,idQ_idQa) = zero,
inference(copy,[status(thm)],[c_591]) ).
cnf(c_63,plain,
less_equal(divide(idQ__idQ_idQa,divide(idQa,idQ_idQa)),zero),
inference(paramod,[status(thm)],[c_62,c_35]) ).
cnf(c_592,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_593,plain,
zero = divide(idQa,idQa),
inference(resolve,[status(thm)],[c_592,c_55]) ).
cnf(c_65,plain,
divide(idQa,idQa) = zero,
inference(copy,[status(thm)],[c_593]) ).
cnf(c_66,plain,
less_equal(divide(idQ_idQa,divide(a,idQa)),zero),
inference(paramod,[status(thm)],[c_65,c_27]) ).
cnf(c_594,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_595,plain,
zero = divide(divide(A,idQ_idQa),idQ__idQ_idQa),
inference(resolve,[status(thm)],[c_594,c_52]) ).
cnf(c_93,plain,
divide(divide(A,idQ_idQa),idQ__idQ_idQa) = zero,
inference(copy,[status(thm)],[c_595]) ).
cnf(c_596,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_597,plain,
zero = divide(divide(A,idQa),idQ_idQa),
inference(resolve,[status(thm)],[c_596,c_54]) ).
cnf(c_94,plain,
divide(divide(A,idQa),idQ_idQa) = zero,
inference(copy,[status(thm)],[c_597]) ).
cnf(c_598,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_599,plain,
zero = divide(idQ__idQ_idQa,divide(idQa,idQ_idQa)),
inference(resolve,[status(thm)],[c_598,c_63]) ).
cnf(c_96,plain,
divide(idQ__idQ_idQa,divide(idQa,idQ_idQa)) = zero,
inference(copy,[status(thm)],[c_599]) ).
cnf(c_600,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_601,plain,
zero = divide(idQ_idQa,divide(a,idQa)),
inference(resolve,[status(thm)],[c_600,c_66]) ).
cnf(c_99,plain,
divide(idQ_idQa,divide(a,idQa)) = zero,
inference(copy,[status(thm)],[c_601]) ).
cnf(c_103,plain,
quotient(divide(A,idQ_idQa),idQ__idQ_idQa,zero),
inference(paramod,[status(thm)],[c_93,c_8]) ).
cnf(c_106,plain,
less_equal(divide(divide(A,idQ__idQ_idQa),divide(idQ_idQa,idQ__idQ_idQa)),zero),
inference(paramod,[status(thm)],[c_93,c_17]) ).
cnf(c_108,plain,
less_equal(divide(A,idQ_idQa),idQ__idQ_idQa),
inference(resolve,[status(thm)],[c_2,c_103]) ).
cnf(c_110,plain,
quotient(divide(A,idQa),idQ_idQa,zero),
inference(paramod,[status(thm)],[c_94,c_8]) ).
cnf(c_116,plain,
less_equal(divide(A,idQa),idQ_idQa),
inference(resolve,[status(thm)],[c_2,c_110]) ).
cnf(c_125,plain,
quotient(idQ__idQ_idQa,divide(idQa,idQ_idQa),zero),
inference(paramod,[status(thm)],[c_96,c_8]) ).
cnf(c_132,plain,
less_equal(idQ__idQ_idQa,divide(idQa,idQ_idQa)),
inference(resolve,[status(thm)],[c_2,c_125]) ).
cnf(c_602,plain,
( divide(A,idQ_idQa) = idQ__idQ_idQa
| ~ less_equal(idQ__idQ_idQa,divide(A,idQ_idQa)) ),
inference(resolve,[status(thm)],[c_6,c_108]) ).
cnf(c_134,plain,
divide(idQa,idQ_idQa) = idQ__idQ_idQa,
inference(resolve,[status(thm)],[c_602,c_132]) ).
cnf(c_136,plain,
less_equal(idQ__idQ_idQa,idQa),
inference(paramod,[status(thm)],[c_134,c_18]) ).
cnf(c_139,plain,
quotient(idQ__idQ_idQa,idQa,zero),
inference(paramod,[status(thm)],[c_134,c_58]) ).
cnf(c_603,plain,
( idQa = idQ__idQ_idQa
| ~ less_equal(idQa,idQ__idQ_idQa) ),
inference(resolve,[status(thm)],[c_6,c_136]) ).
cnf(c_604,plain,
idQa != idQ__idQ_idQa,
inference(copy,[status(thm)],[c_14]) ).
cnf(c_143,plain,
~ less_equal(idQa,idQ__idQ_idQa),
inference(resolve,[status(thm)],[c_603,c_604]) ).
cnf(c_150,plain,
~ quotient(idQ__idQ_idQa,A,idQa),
inference(resolve,[status(thm)],[c_3,c_143]) ).
cnf(c_605,plain,
( less_equal(F,V6)
| ~ quotient(zero,B,V6)
| ~ quotient(E,C,F)
| ~ quotient(divide(A,D),B,E)
| ~ quotient(A,B,C) ),
inference(resolve,[status(thm)],[c_4,c_58]) ).
cnf(c_606,plain,
( less_equal(C,D)
| ~ quotient(zero,idQa,D)
| ~ quotient(B,zero,C)
| ~ quotient(divide(idQ__idQ_idQa,A),idQa,B) ),
inference(resolve,[status(thm)],[c_605,c_139]) ).
cnf(c_607,plain,
( less_equal(B,C)
| ~ quotient(zero,idQa,C)
| ~ quotient(divide(divide(idQ__idQ_idQa,A),idQa),zero,B) ),
inference(resolve,[status(thm)],[c_606,c_8]) ).
cnf(c_608,plain,
( less_equal(divide(divide(divide(idQ__idQ_idQa,B),idQa),zero),A)
| ~ quotient(zero,idQa,A) ),
inference(resolve,[status(thm)],[c_607,c_8]) ).
cnf(c_153,plain,
less_equal(divide(divide(divide(idQ__idQ_idQa,A),idQa),zero),zero),
inference(resolve,[status(thm)],[c_608,c_15]) ).
cnf(c_157,plain,
quotient(idQ_idQa,divide(a,idQa),zero),
inference(paramod,[status(thm)],[c_99,c_8]) ).
cnf(c_166,plain,
less_equal(idQ_idQa,divide(a,idQa)),
inference(resolve,[status(thm)],[c_2,c_157]) ).
cnf(c_609,plain,
( divide(A,idQa) = idQ_idQa
| ~ less_equal(idQ_idQa,divide(A,idQa)) ),
inference(resolve,[status(thm)],[c_6,c_116]) ).
cnf(c_168,plain,
divide(a,idQa) = idQ_idQa,
inference(resolve,[status(thm)],[c_609,c_166]) ).
cnf(c_173,plain,
quotient(idQ_idQa,a,zero),
inference(paramod,[status(thm)],[c_168,c_58]) ).
cnf(c_610,plain,
( less_equal(F,V6)
| ~ quotient(zero,B,V6)
| ~ quotient(E,C,F)
| ~ quotient(divide(A,D),B,E)
| ~ quotient(A,B,C) ),
inference(resolve,[status(thm)],[c_4,c_58]) ).
cnf(c_611,plain,
( less_equal(C,D)
| ~ quotient(zero,a,D)
| ~ quotient(B,zero,C)
| ~ quotient(divide(idQ_idQa,A),a,B) ),
inference(resolve,[status(thm)],[c_610,c_173]) ).
cnf(c_612,plain,
( less_equal(B,C)
| ~ quotient(zero,a,C)
| ~ quotient(divide(divide(idQ_idQa,A),a),zero,B) ),
inference(resolve,[status(thm)],[c_611,c_8]) ).
cnf(c_613,plain,
( less_equal(divide(divide(divide(idQ_idQa,B),a),zero),A)
| ~ quotient(zero,a,A) ),
inference(resolve,[status(thm)],[c_612,c_8]) ).
cnf(c_186,plain,
less_equal(divide(divide(divide(idQ_idQa,A),a),zero),zero),
inference(resolve,[status(thm)],[c_613,c_15]) ).
cnf(c_614,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_615,plain,
zero = divide(divide(A,B),divide(identity,B)),
inference(resolve,[status(thm)],[c_614,c_57]) ).
cnf(c_222,plain,
divide(divide(A,B),divide(identity,B)) = zero,
inference(copy,[status(thm)],[c_615]) ).
cnf(c_616,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_617,plain,
zero = divide(divide(A,idQ__idQ_idQa),divide(idQ_idQa,idQ__idQ_idQa)),
inference(resolve,[status(thm)],[c_616,c_106]) ).
cnf(c_293,plain,
divide(divide(A,idQ__idQ_idQa),divide(idQ_idQa,idQ__idQ_idQa)) = zero,
inference(copy,[status(thm)],[c_617]) ).
cnf(c_618,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_619,plain,
zero = divide(divide(divide(idQ__idQ_idQa,A),idQa),zero),
inference(resolve,[status(thm)],[c_618,c_153]) ).
cnf(c_296,plain,
divide(divide(divide(idQ__idQ_idQa,A),idQa),zero) = zero,
inference(copy,[status(thm)],[c_619]) ).
cnf(c_620,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_621,plain,
zero = divide(divide(divide(idQ_idQa,A),a),zero),
inference(resolve,[status(thm)],[c_620,c_186]) ).
cnf(c_312,plain,
divide(divide(divide(idQ_idQa,A),a),zero) = zero,
inference(copy,[status(thm)],[c_621]) ).
cnf(c_317,plain,
quotient(divide(A,B),divide(identity,B),zero),
inference(paramod,[status(thm)],[c_222,c_8]) ).
cnf(c_327,plain,
less_equal(divide(A,B),divide(identity,B)),
inference(resolve,[status(thm)],[c_2,c_317]) ).
cnf(c_340,plain,
quotient(divide(A,idQ__idQ_idQa),divide(idQ_idQa,idQ__idQ_idQa),zero),
inference(paramod,[status(thm)],[c_293,c_8]) ).
cnf(c_351,plain,
less_equal(divide(A,idQ__idQ_idQa),divide(idQ_idQa,idQ__idQ_idQa)),
inference(resolve,[status(thm)],[c_2,c_340]) ).
cnf(c_622,plain,
( divide(B,A) = divide(identity,A)
| ~ less_equal(divide(identity,A),divide(B,A)) ),
inference(resolve,[status(thm)],[c_6,c_327]) ).
cnf(c_352,plain,
divide(idQ_idQa,idQ__idQ_idQa) = divide(identity,idQ__idQ_idQa),
inference(resolve,[status(thm)],[c_622,c_351]) ).
cnf(c_435,plain,
quotient(divide(divide(idQ__idQ_idQa,A),idQa),zero,zero),
inference(paramod,[status(thm)],[c_296,c_8]) ).
cnf(c_444,plain,
less_equal(divide(divide(idQ__idQ_idQa,A),idQa),zero),
inference(resolve,[status(thm)],[c_2,c_435]) ).
cnf(c_623,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_624,plain,
zero = divide(divide(idQ__idQ_idQa,A),idQa),
inference(resolve,[status(thm)],[c_623,c_444]) ).
cnf(c_445,plain,
divide(divide(idQ__idQ_idQa,A),idQa) = zero,
inference(copy,[status(thm)],[c_624]) ).
cnf(c_446,plain,
quotient(divide(idQ__idQ_idQa,A),idQa,zero),
inference(paramod,[status(thm)],[c_445,c_8]) ).
cnf(c_456,plain,
less_equal(divide(idQ__idQ_idQa,A),idQa),
inference(resolve,[status(thm)],[c_2,c_446]) ).
cnf(c_492,plain,
quotient(divide(divide(idQ_idQa,A),a),zero,zero),
inference(paramod,[status(thm)],[c_312,c_8]) ).
cnf(c_501,plain,
less_equal(divide(divide(idQ_idQa,A),a),zero),
inference(resolve,[status(thm)],[c_2,c_492]) ).
cnf(c_625,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_626,plain,
zero = divide(divide(idQ_idQa,A),a),
inference(resolve,[status(thm)],[c_625,c_501]) ).
cnf(c_504,plain,
divide(divide(idQ_idQa,A),a) = zero,
inference(copy,[status(thm)],[c_626]) ).
cnf(c_506,plain,
quotient(divide(idQ_idQa,A),a,zero),
inference(paramod,[status(thm)],[c_504,c_8]) ).
cnf(c_518,plain,
quotient(divide(identity,idQ__idQ_idQa),a,zero),
inference(paramod,[status(thm)],[c_352,c_506]) ).
cnf(c_627,plain,
( less_equal(F,V6)
| ~ quotient(divide(D,A),B,V6)
| ~ quotient(E,C,F)
| ~ quotient(D,B,E)
| ~ quotient(A,B,C) ),
inference(resolve,[status(thm)],[c_4,c_8]) ).
cnf(c_628,plain,
( less_equal(E,F)
| ~ quotient(divide(A,D),B,F)
| ~ quotient(C,divide(D,B),E)
| ~ quotient(A,B,C) ),
inference(resolve,[status(thm)],[c_627,c_8]) ).
cnf(c_629,plain,
( less_equal(B,C)
| ~ quotient(divide(identity,A),a,C)
| ~ quotient(idQa,divide(A,a),B) ),
inference(resolve,[status(thm)],[c_628,c_10]) ).
cnf(c_630,plain,
( less_equal(divide(idQa,divide(A,a)),B)
| ~ quotient(divide(identity,A),a,B) ),
inference(resolve,[status(thm)],[c_629,c_8]) ).
cnf(c_521,plain,
less_equal(divide(idQa,divide(idQ__idQ_idQa,a)),zero),
inference(resolve,[status(thm)],[c_630,c_518]) ).
cnf(c_631,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_632,plain,
zero = divide(idQa,divide(idQ__idQ_idQa,a)),
inference(resolve,[status(thm)],[c_631,c_521]) ).
cnf(c_533,plain,
divide(idQa,divide(idQ__idQ_idQa,a)) = zero,
inference(copy,[status(thm)],[c_632]) ).
cnf(c_534,plain,
quotient(idQa,divide(idQ__idQ_idQa,a),zero),
inference(paramod,[status(thm)],[c_533,c_8]) ).
cnf(c_554,plain,
less_equal(idQa,divide(idQ__idQ_idQa,a)),
inference(resolve,[status(thm)],[c_2,c_534]) ).
cnf(c_633,plain,
( divide(idQ__idQ_idQa,A) = idQa
| ~ less_equal(idQa,divide(idQ__idQ_idQa,A)) ),
inference(resolve,[status(thm)],[c_6,c_456]) ).
cnf(c_555,plain,
divide(idQ__idQ_idQa,a) = idQa,
inference(resolve,[status(thm)],[c_633,c_554]) ).
cnf(c_556,plain,
quotient(idQ__idQ_idQa,a,idQa),
inference(paramod,[status(thm)],[c_555,c_8]) ).
cnf(c_557,plain,
$false,
inference(resolve,[status(thm)],[c_556,c_150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : HEN009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.40 % Computer : n011.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Fri Sep 25 15:57:28 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.18/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.40 % Process 2422211 was started by sandbox2 on n011,
% 0.18/0.40 % Fri Sep 25 15:57:28 2026
% 0.18/0.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.41
% 0.18/0.41 % From the command line: assign(max_seconds, 300).
% 3.43/0.91
% 3.43/0.91 % SZS status Unsatisfiable for theBenchmark
% 3.43/0.91
% 3.43/0.91 % Proof 1 at 0.35 (+ 0.13) seconds.
% 3.43/0.91 % Length of proof is 77.
% 3.43/0.91 % Level of proof is 23.
% 3.43/0.91 % Maximum clause weight is 23.000.
% 3.43/0.91 % Given clauses 205.
% 3.43/0.91
% 3.43/0.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------