TSTP Solution File: HEN011-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : HEN011-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.aSXGiQSU1V true
% Computer : n017.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 01:57:54 EDT 2023
% Result : Unsatisfiable 268.22s 39.34s
% Output : Refutation 268.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : HEN011-1 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.aSXGiQSU1V true
% 0.14/0.37 % Computer : n017.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Thu Aug 24 13:02:09 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.14/0.37 % Running portfolio for 300 s
% 0.14/0.37 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.37 % Number of cores: 8
% 0.14/0.37 % Python version: Python 3.6.8
% 0.14/0.37 % Running in FO mode
% 0.22/0.65 % Total configuration time : 435
% 0.22/0.65 % Estimated wc time : 1092
% 0.22/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.84/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.84/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.84/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.84/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.84/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.84/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.84/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 268.22/39.34 % Solved by fo/fo5.sh.
% 268.22/39.34 % done 32827 iterations in 38.547s
% 268.22/39.34 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 268.22/39.34 % SZS output start Refutation
% 268.22/39.34 thf(divide_type, type, divide: $i > $i > $i).
% 268.22/39.34 thf(b_type, type, b: $i).
% 268.22/39.34 thf(idQa_type, type, idQa: $i).
% 268.22/39.34 thf(idQa_Q__idQ_idQb_type, type, idQa_Q__idQ_idQb: $i).
% 268.22/39.34 thf(a_type, type, a: $i).
% 268.22/39.34 thf(identity_type, type, identity: $i).
% 268.22/39.34 thf(less_equal_type, type, less_equal: $i > $i > $o).
% 268.22/39.34 thf(idQ_idQa_type, type, idQ_idQa: $i).
% 268.22/39.34 thf(idQ_idQb_type, type, idQ_idQb: $i).
% 268.22/39.34 thf(idQb_Q__idQ_idQa_type, type, idQb_Q__idQ_idQa: $i).
% 268.22/39.34 thf(idQb_type, type, idQb: $i).
% 268.22/39.34 thf(quotient_type, type, quotient: $i > $i > $i > $o).
% 268.22/39.34 thf(zero_type, type, zero: $i).
% 268.22/39.34 thf(closure, axiom, (quotient @ X @ Y @ ( divide @ X @ Y ))).
% 268.22/39.34 thf(zip_derived_cl7, plain,
% 268.22/39.34 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.34 inference('cnf', [status(esa)], [closure])).
% 268.22/39.34 thf(zip_derived_cl7, plain,
% 268.22/39.34 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.34 inference('cnf', [status(esa)], [closure])).
% 268.22/39.34 thf(idQb_divide_idQ_idQa, axiom,
% 268.22/39.34 (quotient @ idQb @ idQ_idQa @ idQb_Q__idQ_idQa)).
% 268.22/39.34 thf(zip_derived_cl14, plain,
% 268.22/39.34 ( (quotient @ idQb @ idQ_idQa @ idQb_Q__idQ_idQa)),
% 268.22/39.34 inference('cnf', [status(esa)], [idQb_divide_idQ_idQa])).
% 268.22/39.34 thf(zip_derived_cl7, plain,
% 268.22/39.34 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.34 inference('cnf', [status(esa)], [closure])).
% 268.22/39.34 thf(identity_divide_idQb, axiom, (quotient @ identity @ idQb @ idQ_idQb)).
% 268.22/39.34 thf(zip_derived_cl11, plain, ( (quotient @ identity @ idQb @ idQ_idQb)),
% 268.22/39.34 inference('cnf', [status(esa)], [identity_divide_idQb])).
% 268.22/39.34 thf(quotient_property, axiom,
% 268.22/39.34 (( ~( quotient @ X @ Y @ V1 ) ) | ( ~( quotient @ Y @ Z @ V2 ) ) |
% 268.22/39.34 ( ~( quotient @ X @ Z @ V3 ) ) | ( ~( quotient @ V3 @ V2 @ V4 ) ) |
% 268.22/39.34 ( ~( quotient @ V1 @ Z @ V5 ) ) | ( less_equal @ V4 @ V5 ))).
% 268.22/39.34 thf(zip_derived_cl3, plain,
% 268.22/39.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 268.22/39.34 (~ (quotient @ X0 @ X1 @ X2)
% 268.22/39.34 | ~ (quotient @ X1 @ X3 @ X4)
% 268.22/39.34 | ~ (quotient @ X0 @ X3 @ X5)
% 268.22/39.34 | ~ (quotient @ X5 @ X4 @ X6)
% 268.22/39.34 | ~ (quotient @ X2 @ X3 @ X7)
% 268.22/39.34 | (less_equal @ X6 @ X7))),
% 268.22/39.34 inference('cnf', [status(esa)], [quotient_property])).
% 268.22/39.34 thf(zip_derived_cl52, plain,
% 268.22/39.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 268.22/39.34 ( (less_equal @ X1 @ X0)
% 268.22/39.34 | ~ (quotient @ idQ_idQb @ X2 @ X0)
% 268.22/39.34 | ~ (quotient @ X4 @ X3 @ X1)
% 268.22/39.34 | ~ (quotient @ identity @ X2 @ X4)
% 268.22/39.34 | ~ (quotient @ idQb @ X2 @ X3))),
% 268.22/39.34 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl3])).
% 268.22/39.34 thf(zip_derived_cl325, plain,
% 268.22/39.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 268.22/39.34 (~ (quotient @ idQb @ X0 @ X1)
% 268.22/39.34 | ~ (quotient @ identity @ X0 @ X2)
% 268.22/39.34 | ~ (quotient @ X2 @ X1 @ X3)
% 268.22/39.34 | (less_equal @ X3 @ (divide @ idQ_idQb @ X0)))),
% 268.22/39.34 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl52])).
% 268.22/39.34 thf(zip_derived_cl1857, plain,
% 268.22/39.34 (![X0 : $i, X1 : $i]:
% 268.22/39.34 ( (less_equal @ X0 @ (divide @ idQ_idQb @ idQ_idQa))
% 268.22/39.34 | ~ (quotient @ X1 @ idQb_Q__idQ_idQa @ X0)
% 268.22/39.34 | ~ (quotient @ identity @ idQ_idQa @ X1))),
% 268.22/39.34 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl325])).
% 268.22/39.34 thf(zip_derived_cl13882, plain,
% 268.22/39.34 (![X0 : $i]:
% 268.22/39.34 (~ (quotient @ (divide @ identity @ idQ_idQa) @ idQb_Q__idQ_idQa @ X0)
% 268.22/39.34 | (less_equal @ X0 @ (divide @ idQ_idQb @ idQ_idQa)))),
% 268.22/39.34 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl1857])).
% 268.22/39.34 thf(zip_derived_cl13884, plain,
% 268.22/39.34 ( (less_equal @
% 268.22/39.34 (divide @ (divide @ identity @ idQ_idQa) @ idQb_Q__idQ_idQa) @
% 268.22/39.34 (divide @ idQ_idQb @ idQ_idQa))),
% 268.22/39.34 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl13882])).
% 268.22/39.34 thf(quotient_less_equal, axiom,
% 268.22/39.34 (( ~( less_equal @ X @ Y ) ) | ( quotient @ X @ Y @ zero ))).
% 268.22/39.34 thf(zip_derived_cl0, plain,
% 268.22/39.34 (![X0 : $i, X1 : $i]:
% 268.22/39.34 (~ (less_equal @ X0 @ X1) | (quotient @ X0 @ X1 @ zero))),
% 268.22/39.34 inference('cnf', [status(esa)], [quotient_less_equal])).
% 268.22/39.34 thf(zip_derived_cl14084, plain,
% 268.22/39.34 ( (quotient @
% 268.22/39.34 (divide @ (divide @ identity @ idQ_idQa) @ idQb_Q__idQ_idQa) @
% 268.22/39.34 (divide @ idQ_idQb @ idQ_idQa) @ zero)),
% 268.22/39.34 inference('sup-', [status(thm)], [zip_derived_cl13884, zip_derived_cl0])).
% 268.22/39.34 thf(zip_derived_cl7, plain,
% 268.22/39.34 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.34 inference('cnf', [status(esa)], [closure])).
% 268.22/39.34 thf(well_defined, axiom,
% 268.22/39.34 (( ~( quotient @ X @ Y @ Z ) ) | ( ~( quotient @ X @ Y @ W ) ) |
% 268.22/39.34 ( ( Z ) = ( W ) ))).
% 268.22/39.34 thf(zip_derived_cl8, plain,
% 268.22/39.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 268.22/39.34 (~ (quotient @ X0 @ X1 @ X2)
% 268.22/39.34 | ~ (quotient @ X0 @ X1 @ X3)
% 268.22/39.34 | ((X2) = (X3)))),
% 268.22/39.34 inference('cnf', [status(esa)], [well_defined])).
% 268.22/39.34 thf(zip_derived_cl36, plain,
% 268.22/39.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 268.22/39.34 (((divide @ X1 @ X0) = (X2)) | ~ (quotient @ X1 @ X0 @ X2))),
% 268.22/39.34 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl8])).
% 268.22/39.34 thf(zip_derived_cl25567, plain,
% 268.22/39.34 (((divide @
% 268.22/39.34 (divide @ (divide @ identity @ idQ_idQa) @ idQb_Q__idQ_idQa) @
% 268.22/39.34 (divide @ idQ_idQb @ idQ_idQa)) = (zero))),
% 268.22/39.34 inference('sup-', [status(thm)], [zip_derived_cl14084, zip_derived_cl36])).
% 268.22/39.34 thf(zip_derived_cl7, plain,
% 268.22/39.34 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.34 inference('cnf', [status(esa)], [closure])).
% 268.22/39.34 thf(zip_derived_cl7, plain,
% 268.22/39.34 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.34 inference('cnf', [status(esa)], [closure])).
% 268.22/39.34 thf(identity_divide_a, axiom, (quotient @ identity @ a @ idQa)).
% 268.22/39.34 thf(zip_derived_cl9, plain, ( (quotient @ identity @ a @ idQa)),
% 268.22/39.34 inference('cnf', [status(esa)], [identity_divide_a])).
% 268.22/39.34 thf(zip_derived_cl7, plain,
% 268.22/39.34 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.34 inference('cnf', [status(esa)], [closure])).
% 268.22/39.34 thf(zip_derived_cl7, plain,
% 268.22/39.34 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.34 inference('cnf', [status(esa)], [closure])).
% 268.22/39.34 thf(zip_derived_cl3, plain,
% 268.22/39.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 268.22/39.34 (~ (quotient @ X0 @ X1 @ X2)
% 268.22/39.34 | ~ (quotient @ X1 @ X3 @ X4)
% 268.22/39.34 | ~ (quotient @ X0 @ X3 @ X5)
% 268.22/39.34 | ~ (quotient @ X5 @ X4 @ X6)
% 268.22/39.34 | ~ (quotient @ X2 @ X3 @ X7)
% 268.22/39.34 | (less_equal @ X6 @ X7))),
% 268.22/39.34 inference('cnf', [status(esa)], [quotient_property])).
% 268.22/39.34 thf(zip_derived_cl46, plain,
% 268.22/39.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 268.22/39.34 ( (less_equal @ X3 @ X2)
% 268.22/39.34 | ~ (quotient @ (divide @ X1 @ X0) @ X4 @ X2)
% 268.22/39.34 | ~ (quotient @ X6 @ X5 @ X3)
% 268.22/39.34 | ~ (quotient @ X1 @ X4 @ X6)
% 268.22/39.34 | ~ (quotient @ X0 @ X4 @ X5))),
% 268.22/39.34 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl3])).
% 268.22/39.34 thf(zip_derived_cl125, plain,
% 268.22/39.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 268.22/39.34 (~ (quotient @ X1 @ X0 @ X3)
% 268.22/39.34 | ~ (quotient @ X2 @ X0 @ X4)
% 268.22/39.34 | ~ (quotient @ X4 @ X3 @ X5)
% 268.22/39.34 | (less_equal @ X5 @ (divide @ (divide @ X2 @ X1) @ X0)))),
% 268.22/39.34 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl46])).
% 268.22/39.34 thf(zip_derived_cl711, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i]:
% 268.22/39.35 ( (less_equal @ X1 @ (divide @ (divide @ X0 @ identity) @ a))
% 268.22/39.35 | ~ (quotient @ X2 @ idQa @ X1)
% 268.22/39.35 | ~ (quotient @ X0 @ a @ X2))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl125])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(identity_is_largest, axiom, (less_equal @ X @ identity)).
% 268.22/39.35 thf(zip_derived_cl6, plain, (![X0 : $i]: (less_equal @ X0 @ identity)),
% 268.22/39.35 inference('cnf', [status(esa)], [identity_is_largest])).
% 268.22/39.35 thf(zip_derived_cl0, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (less_equal @ X0 @ X1) | (quotient @ X0 @ X1 @ zero))),
% 268.22/39.35 inference('cnf', [status(esa)], [quotient_less_equal])).
% 268.22/39.35 thf(zip_derived_cl16, plain,
% 268.22/39.35 (![X0 : $i]: (quotient @ X0 @ identity @ zero)),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl0])).
% 268.22/39.35 thf(zip_derived_cl8, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 268.22/39.35 (~ (quotient @ X0 @ X1 @ X2)
% 268.22/39.35 | ~ (quotient @ X0 @ X1 @ X3)
% 268.22/39.35 | ((X2) = (X3)))),
% 268.22/39.35 inference('cnf', [status(esa)], [well_defined])).
% 268.22/39.35 thf(zip_derived_cl37, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (((zero) = (X1)) | ~ (quotient @ X0 @ identity @ X1))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl8])).
% 268.22/39.35 thf(zip_derived_cl68, plain,
% 268.22/39.35 (![X0 : $i]: ((zero) = (divide @ X0 @ identity))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl37])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(divisor_existence, axiom,
% 268.22/39.35 (( ~( quotient @ X @ Y @ Z ) ) | ( less_equal @ Z @ X ))).
% 268.22/39.35 thf(zip_derived_cl2, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i]:
% 268.22/39.35 (~ (quotient @ X0 @ X1 @ X2) | (less_equal @ X2 @ X0))),
% 268.22/39.35 inference('cnf', [status(esa)], [divisor_existence])).
% 268.22/39.35 thf(zip_derived_cl23, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (less_equal @ (divide @ X1 @ X0) @ X1)),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 268.22/39.35 thf(zero_is_smallest, axiom, (less_equal @ zero @ X)).
% 268.22/39.35 thf(zip_derived_cl4, plain, (![X0 : $i]: (less_equal @ zero @ X0)),
% 268.22/39.35 inference('cnf', [status(esa)], [zero_is_smallest])).
% 268.22/39.35 thf(less_equal_and_equal, axiom,
% 268.22/39.35 (( ~( less_equal @ X @ Y ) ) | ( ~( less_equal @ Y @ X ) ) |
% 268.22/39.35 ( ( X ) = ( Y ) ))).
% 268.22/39.35 thf(zip_derived_cl5, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 268.22/39.35 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 268.22/39.35 thf(zip_derived_cl19, plain,
% 268.22/39.35 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl63, plain, (![X0 : $i]: ((zero) = (divide @ zero @ X0))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl19])).
% 268.22/39.35 thf(zip_derived_cl727, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i]:
% 268.22/39.35 ( (less_equal @ X1 @ zero)
% 268.22/39.35 | ~ (quotient @ X2 @ idQa @ X1)
% 268.22/39.35 | ~ (quotient @ X0 @ a @ X2))),
% 268.22/39.35 inference('demod', [status(thm)],
% 268.22/39.35 [zip_derived_cl711, zip_derived_cl68, zip_derived_cl63])).
% 268.22/39.35 thf(zip_derived_cl2598, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (quotient @ X1 @ a @ X0)
% 268.22/39.35 | (less_equal @ (divide @ X0 @ idQa) @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl727])).
% 268.22/39.35 thf(zip_derived_cl2616, plain,
% 268.22/39.35 (![X0 : $i]: (less_equal @ (divide @ (divide @ X0 @ a) @ idQa) @ zero)),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl2598])).
% 268.22/39.35 thf(zip_derived_cl19, plain,
% 268.22/39.35 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl2638, plain,
% 268.22/39.35 (![X0 : $i]: ((zero) = (divide @ (divide @ X0 @ a) @ idQa))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl2616, zip_derived_cl19])).
% 268.22/39.35 thf(identity_divide_idQa, axiom, (quotient @ identity @ idQa @ idQ_idQa)).
% 268.22/39.35 thf(zip_derived_cl13, plain, ( (quotient @ identity @ idQa @ idQ_idQa)),
% 268.22/39.35 inference('cnf', [status(esa)], [identity_divide_idQa])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl125, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 268.22/39.35 (~ (quotient @ X1 @ X0 @ X3)
% 268.22/39.35 | ~ (quotient @ X2 @ X0 @ X4)
% 268.22/39.35 | ~ (quotient @ X4 @ X3 @ X5)
% 268.22/39.35 | (less_equal @ X5 @ (divide @ (divide @ X2 @ X1) @ X0)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl46])).
% 268.22/39.35 thf(zip_derived_cl708, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 268.22/39.35 ( (less_equal @ X3 @ (divide @ (divide @ X2 @ X1) @ X0))
% 268.22/39.35 | ~ (quotient @ X4 @ (divide @ X1 @ X0) @ X3)
% 268.22/39.35 | ~ (quotient @ X2 @ X0 @ X4))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl125])).
% 268.22/39.35 thf(zip_derived_cl4927, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 268.22/39.35 (~ (quotient @ X3 @ X0 @ X2)
% 268.22/39.35 | (less_equal @ (divide @ X2 @ (divide @ X1 @ X0)) @
% 268.22/39.35 (divide @ (divide @ X3 @ X1) @ X0)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl708])).
% 268.22/39.35 thf(zip_derived_cl27967, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 (less_equal @ (divide @ idQ_idQa @ (divide @ X0 @ idQa)) @
% 268.22/39.35 (divide @ (divide @ identity @ X0) @ idQa))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl4927])).
% 268.22/39.35 thf(zip_derived_cl47057, plain,
% 268.22/39.35 ( (less_equal @ (divide @ idQ_idQa @ (divide @ a @ idQa)) @ zero)),
% 268.22/39.35 inference('sup+', [status(thm)],
% 268.22/39.35 [zip_derived_cl2638, zip_derived_cl27967])).
% 268.22/39.35 thf(zip_derived_cl19, plain,
% 268.22/39.35 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl47163, plain,
% 268.22/39.35 (((zero) = (divide @ idQ_idQa @ (divide @ a @ idQa)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl47057, zip_derived_cl19])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl47172, plain,
% 268.22/39.35 ( (quotient @ idQ_idQa @ (divide @ a @ idQa) @ zero)),
% 268.22/39.35 inference('sup+', [status(thm)], [zip_derived_cl47163, zip_derived_cl7])).
% 268.22/39.35 thf(less_equal_quotient, axiom,
% 268.22/39.35 (( ~( quotient @ X @ Y @ zero ) ) | ( less_equal @ X @ Y ))).
% 268.22/39.35 thf(zip_derived_cl1, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (quotient @ X0 @ X1 @ zero) | (less_equal @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [less_equal_quotient])).
% 268.22/39.35 thf(zip_derived_cl47258, plain,
% 268.22/39.35 ( (less_equal @ idQ_idQa @ (divide @ a @ idQa))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl47172, zip_derived_cl1])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl13, plain, ( (quotient @ identity @ idQa @ idQ_idQa)),
% 268.22/39.35 inference('cnf', [status(esa)], [identity_divide_idQa])).
% 268.22/39.35 thf(zip_derived_cl125, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 268.22/39.35 (~ (quotient @ X1 @ X0 @ X3)
% 268.22/39.35 | ~ (quotient @ X2 @ X0 @ X4)
% 268.22/39.35 | ~ (quotient @ X4 @ X3 @ X5)
% 268.22/39.35 | (less_equal @ X5 @ (divide @ (divide @ X2 @ X1) @ X0)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl46])).
% 268.22/39.35 thf(zip_derived_cl712, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i]:
% 268.22/39.35 ( (less_equal @ X1 @ (divide @ (divide @ X0 @ identity) @ idQa))
% 268.22/39.35 | ~ (quotient @ X2 @ idQ_idQa @ X1)
% 268.22/39.35 | ~ (quotient @ X0 @ idQa @ X2))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl125])).
% 268.22/39.35 thf(zip_derived_cl68, plain,
% 268.22/39.35 (![X0 : $i]: ((zero) = (divide @ X0 @ identity))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl37])).
% 268.22/39.35 thf(zip_derived_cl63, plain, (![X0 : $i]: ((zero) = (divide @ zero @ X0))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl19])).
% 268.22/39.35 thf(zip_derived_cl728, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i]:
% 268.22/39.35 ( (less_equal @ X1 @ zero)
% 268.22/39.35 | ~ (quotient @ X2 @ idQ_idQa @ X1)
% 268.22/39.35 | ~ (quotient @ X0 @ idQa @ X2))),
% 268.22/39.35 inference('demod', [status(thm)],
% 268.22/39.35 [zip_derived_cl712, zip_derived_cl68, zip_derived_cl63])).
% 268.22/39.35 thf(zip_derived_cl3054, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (quotient @ X1 @ idQa @ X0)
% 268.22/39.35 | (less_equal @ (divide @ X0 @ idQ_idQa) @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl728])).
% 268.22/39.35 thf(zip_derived_cl3068, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 (less_equal @ (divide @ (divide @ X0 @ idQa) @ idQ_idQa) @ zero)),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl3054])).
% 268.22/39.35 thf(zip_derived_cl19, plain,
% 268.22/39.35 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl3096, plain,
% 268.22/39.35 (![X0 : $i]: ((zero) = (divide @ (divide @ X0 @ idQa) @ idQ_idQa))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl3068, zip_derived_cl19])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl3164, plain,
% 268.22/39.35 (![X0 : $i]: (quotient @ (divide @ X0 @ idQa) @ idQ_idQa @ zero)),
% 268.22/39.35 inference('sup+', [status(thm)], [zip_derived_cl3096, zip_derived_cl7])).
% 268.22/39.35 thf(zip_derived_cl1, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (quotient @ X0 @ X1 @ zero) | (less_equal @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [less_equal_quotient])).
% 268.22/39.35 thf(zip_derived_cl3231, plain,
% 268.22/39.35 (![X0 : $i]: (less_equal @ (divide @ X0 @ idQa) @ idQ_idQa)),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl3164, zip_derived_cl1])).
% 268.22/39.35 thf(zip_derived_cl5, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 268.22/39.35 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 268.22/39.35 thf(zip_derived_cl3303, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 (((divide @ X0 @ idQa) = (idQ_idQa))
% 268.22/39.35 | ~ (less_equal @ idQ_idQa @ (divide @ X0 @ idQa)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl3231, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl47280, plain, (((divide @ a @ idQa) = (idQ_idQa))),
% 268.22/39.35 inference('sup-', [status(thm)],
% 268.22/39.35 [zip_derived_cl47258, zip_derived_cl3303])).
% 268.22/39.35 thf(zip_derived_cl9, plain, ( (quotient @ identity @ a @ idQa)),
% 268.22/39.35 inference('cnf', [status(esa)], [identity_divide_a])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl23, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (less_equal @ (divide @ X1 @ X0) @ X1)),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 268.22/39.35 thf(zip_derived_cl0, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (less_equal @ X0 @ X1) | (quotient @ X0 @ X1 @ zero))),
% 268.22/39.35 inference('cnf', [status(esa)], [quotient_less_equal])).
% 268.22/39.35 thf(zip_derived_cl61, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ (divide @ X0 @ X1) @ X0 @ zero)),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 268.22/39.35 thf(zip_derived_cl125, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 268.22/39.35 (~ (quotient @ X1 @ X0 @ X3)
% 268.22/39.35 | ~ (quotient @ X2 @ X0 @ X4)
% 268.22/39.35 | ~ (quotient @ X4 @ X3 @ X5)
% 268.22/39.35 | (less_equal @ X5 @ (divide @ (divide @ X2 @ X1) @ X0)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl46])).
% 268.22/39.35 thf(zip_derived_cl715, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 268.22/39.35 ( (less_equal @ X3 @
% 268.22/39.35 (divide @ (divide @ X2 @ (divide @ X0 @ X1)) @ X0))
% 268.22/39.35 | ~ (quotient @ X4 @ zero @ X3)
% 268.22/39.35 | ~ (quotient @ X2 @ X0 @ X4))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl61, zip_derived_cl125])).
% 268.22/39.35 thf(zip_derived_cl5026, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 268.22/39.35 (~ (quotient @ X2 @ X1 @ X0)
% 268.22/39.35 | (less_equal @ (divide @ X0 @ zero) @
% 268.22/39.35 (divide @ (divide @ X2 @ (divide @ X1 @ X3)) @ X1)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl715])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl4, plain, (![X0 : $i]: (less_equal @ zero @ X0)),
% 268.22/39.35 inference('cnf', [status(esa)], [zero_is_smallest])).
% 268.22/39.35 thf(zip_derived_cl0, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (less_equal @ X0 @ X1) | (quotient @ X0 @ X1 @ zero))),
% 268.22/39.35 inference('cnf', [status(esa)], [quotient_less_equal])).
% 268.22/39.35 thf(zip_derived_cl17, plain, (![X0 : $i]: (quotient @ zero @ X0 @ zero)),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl17, plain, (![X0 : $i]: (quotient @ zero @ X0 @ zero)),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 268.22/39.35 thf(zip_derived_cl61, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ (divide @ X0 @ X1) @ X0 @ zero)),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 268.22/39.35 thf(zip_derived_cl46, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 268.22/39.35 ( (less_equal @ X3 @ X2)
% 268.22/39.35 | ~ (quotient @ (divide @ X1 @ X0) @ X4 @ X2)
% 268.22/39.35 | ~ (quotient @ X6 @ X5 @ X3)
% 268.22/39.35 | ~ (quotient @ X1 @ X4 @ X6)
% 268.22/39.35 | ~ (quotient @ X0 @ X4 @ X5))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl3])).
% 268.22/39.35 thf(zip_derived_cl144, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 268.22/39.35 (~ (quotient @ X1 @ X0 @ X2)
% 268.22/39.35 | ~ (quotient @ X0 @ X0 @ X3)
% 268.22/39.35 | ~ (quotient @ X3 @ X2 @ X4)
% 268.22/39.35 | (less_equal @ X4 @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl61, zip_derived_cl46])).
% 268.22/39.35 thf(zip_derived_cl356, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i]:
% 268.22/39.35 ( (less_equal @ X1 @ zero)
% 268.22/39.35 | ~ (quotient @ X2 @ zero @ X1)
% 268.22/39.35 | ~ (quotient @ X0 @ X0 @ X2))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl144])).
% 268.22/39.35 thf(zip_derived_cl672, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (quotient @ X1 @ X1 @ X0)
% 268.22/39.35 | (less_equal @ (divide @ X0 @ zero) @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl356])).
% 268.22/39.35 thf(zip_derived_cl680, plain,
% 268.22/39.35 (![X0 : $i]: (less_equal @ (divide @ (divide @ X0 @ X0) @ zero) @ zero)),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl672])).
% 268.22/39.35 thf(zip_derived_cl19, plain,
% 268.22/39.35 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl766, plain,
% 268.22/39.35 (![X0 : $i]: ((zero) = (divide @ (divide @ X0 @ X0) @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl680, zip_derived_cl19])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl782, plain,
% 268.22/39.35 (![X0 : $i]: (quotient @ (divide @ X0 @ X0) @ zero @ zero)),
% 268.22/39.35 inference('sup+', [status(thm)], [zip_derived_cl766, zip_derived_cl7])).
% 268.22/39.35 thf(zip_derived_cl1, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (quotient @ X0 @ X1 @ zero) | (less_equal @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [less_equal_quotient])).
% 268.22/39.35 thf(zip_derived_cl806, plain,
% 268.22/39.35 (![X0 : $i]: (less_equal @ (divide @ X0 @ X0) @ zero)),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl782, zip_derived_cl1])).
% 268.22/39.35 thf(zip_derived_cl19, plain,
% 268.22/39.35 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl818, plain, (![X0 : $i]: ((zero) = (divide @ X0 @ X0))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl806, zip_derived_cl19])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl838, plain, (![X0 : $i]: (quotient @ X0 @ X0 @ zero)),
% 268.22/39.35 inference('sup+', [status(thm)], [zip_derived_cl818, zip_derived_cl7])).
% 268.22/39.35 thf(zip_derived_cl46, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 268.22/39.35 ( (less_equal @ X3 @ X2)
% 268.22/39.35 | ~ (quotient @ (divide @ X1 @ X0) @ X4 @ X2)
% 268.22/39.35 | ~ (quotient @ X6 @ X5 @ X3)
% 268.22/39.35 | ~ (quotient @ X1 @ X4 @ X6)
% 268.22/39.35 | ~ (quotient @ X0 @ X4 @ X5))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl3])).
% 268.22/39.35 thf(zip_derived_cl924, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 268.22/39.35 (~ (quotient @ X0 @ (divide @ X1 @ X0) @ X2)
% 268.22/39.35 | ~ (quotient @ X1 @ (divide @ X1 @ X0) @ X3)
% 268.22/39.35 | ~ (quotient @ X3 @ X2 @ X4)
% 268.22/39.35 | (less_equal @ X4 @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl838, zip_derived_cl46])).
% 268.22/39.35 thf(zip_derived_cl6749, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i]:
% 268.22/39.35 ( (less_equal @ X1 @ zero)
% 268.22/39.35 | ~ (quotient @ X2 @ zero @ X1)
% 268.22/39.35 | ~ (quotient @ X0 @ (divide @ X0 @ zero) @ X2))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl924])).
% 268.22/39.35 thf(zip_derived_cl19850, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (quotient @ (divide @ X0 @ (divide @ X0 @ zero)) @ zero @ X1)
% 268.22/39.35 | (less_equal @ X1 @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl6749])).
% 268.22/39.35 thf(zip_derived_cl19957, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 (less_equal @
% 268.22/39.35 (divide @ (divide @ X0 @ (divide @ X0 @ zero)) @ zero) @ zero)),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl19850])).
% 268.22/39.35 thf(zip_derived_cl19, plain,
% 268.22/39.35 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl19999, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 ((zero) = (divide @ (divide @ X0 @ (divide @ X0 @ zero)) @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl19957, zip_derived_cl19])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl20054, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 (quotient @ (divide @ X0 @ (divide @ X0 @ zero)) @ zero @ zero)),
% 268.22/39.35 inference('sup+', [status(thm)], [zip_derived_cl19999, zip_derived_cl7])).
% 268.22/39.35 thf(zip_derived_cl1, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (quotient @ X0 @ X1 @ zero) | (less_equal @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [less_equal_quotient])).
% 268.22/39.35 thf(zip_derived_cl20229, plain,
% 268.22/39.35 (![X0 : $i]: (less_equal @ (divide @ X0 @ (divide @ X0 @ zero)) @ zero)),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl20054, zip_derived_cl1])).
% 268.22/39.35 thf(zip_derived_cl19, plain,
% 268.22/39.35 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl20361, plain,
% 268.22/39.35 (![X0 : $i]: ((zero) = (divide @ X0 @ (divide @ X0 @ zero)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl20229, zip_derived_cl19])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl20411, plain,
% 268.22/39.35 (![X0 : $i]: (quotient @ X0 @ (divide @ X0 @ zero) @ zero)),
% 268.22/39.35 inference('sup+', [status(thm)], [zip_derived_cl20361, zip_derived_cl7])).
% 268.22/39.35 thf(zip_derived_cl1, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (quotient @ X0 @ X1 @ zero) | (less_equal @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [less_equal_quotient])).
% 268.22/39.35 thf(zip_derived_cl20543, plain,
% 268.22/39.35 (![X0 : $i]: (less_equal @ X0 @ (divide @ X0 @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl20411, zip_derived_cl1])).
% 268.22/39.35 thf(zip_derived_cl23, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (less_equal @ (divide @ X1 @ X0) @ X1)),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 268.22/39.35 thf(zip_derived_cl5, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 268.22/39.35 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 268.22/39.35 thf(zip_derived_cl62, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (((divide @ X0 @ X1) = (X0))
% 268.22/39.35 | ~ (less_equal @ X0 @ (divide @ X0 @ X1)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl20742, plain, (![X0 : $i]: ((divide @ X0 @ zero) = (X0))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl20543, zip_derived_cl62])).
% 268.22/39.35 thf(zip_derived_cl30079, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 268.22/39.35 (~ (quotient @ X2 @ X1 @ X0)
% 268.22/39.35 | (less_equal @ X0 @
% 268.22/39.35 (divide @ (divide @ X2 @ (divide @ X1 @ X3)) @ X1)))),
% 268.22/39.35 inference('demod', [status(thm)],
% 268.22/39.35 [zip_derived_cl5026, zip_derived_cl20742])).
% 268.22/39.35 thf(zip_derived_cl30089, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 (less_equal @ idQa @
% 268.22/39.35 (divide @ (divide @ identity @ (divide @ a @ X0)) @ a))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl30079])).
% 268.22/39.35 thf(zip_derived_cl2638, plain,
% 268.22/39.35 (![X0 : $i]: ((zero) = (divide @ (divide @ X0 @ a) @ idQa))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl2616, zip_derived_cl19])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl2677, plain,
% 268.22/39.35 (![X0 : $i]: (quotient @ (divide @ X0 @ a) @ idQa @ zero)),
% 268.22/39.35 inference('sup+', [status(thm)], [zip_derived_cl2638, zip_derived_cl7])).
% 268.22/39.35 thf(zip_derived_cl1, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (quotient @ X0 @ X1 @ zero) | (less_equal @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [less_equal_quotient])).
% 268.22/39.35 thf(zip_derived_cl2757, plain,
% 268.22/39.35 (![X0 : $i]: (less_equal @ (divide @ X0 @ a) @ idQa)),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl2677, zip_derived_cl1])).
% 268.22/39.35 thf(zip_derived_cl5, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 268.22/39.35 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 268.22/39.35 thf(zip_derived_cl2808, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 (((divide @ X0 @ a) = (idQa))
% 268.22/39.35 | ~ (less_equal @ idQa @ (divide @ X0 @ a)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl2757, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl31235, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 ((divide @ (divide @ identity @ (divide @ a @ X0)) @ a) = (idQa))),
% 268.22/39.35 inference('sup-', [status(thm)],
% 268.22/39.35 [zip_derived_cl30089, zip_derived_cl2808])).
% 268.22/39.35 thf(zip_derived_cl23, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (less_equal @ (divide @ X1 @ X0) @ X1)),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 268.22/39.35 thf(zip_derived_cl31277, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 (less_equal @ idQa @ (divide @ identity @ (divide @ a @ X0)))),
% 268.22/39.35 inference('sup+', [status(thm)], [zip_derived_cl31235, zip_derived_cl23])).
% 268.22/39.35 thf(zip_derived_cl47351, plain,
% 268.22/39.35 ( (less_equal @ idQa @ (divide @ identity @ idQ_idQa))),
% 268.22/39.35 inference('sup+', [status(thm)],
% 268.22/39.35 [zip_derived_cl47280, zip_derived_cl31277])).
% 268.22/39.35 thf(zip_derived_cl5, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 268.22/39.35 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 268.22/39.35 thf(zip_derived_cl47697, plain,
% 268.22/39.35 ((((idQa) = (divide @ identity @ idQ_idQa))
% 268.22/39.35 | ~ (less_equal @ (divide @ identity @ idQ_idQa) @ idQa))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl47351, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl838, plain, (![X0 : $i]: (quotient @ X0 @ X0 @ zero)),
% 268.22/39.35 inference('sup+', [status(thm)], [zip_derived_cl818, zip_derived_cl7])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl3, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 268.22/39.35 (~ (quotient @ X0 @ X1 @ X2)
% 268.22/39.35 | ~ (quotient @ X1 @ X3 @ X4)
% 268.22/39.35 | ~ (quotient @ X0 @ X3 @ X5)
% 268.22/39.35 | ~ (quotient @ X5 @ X4 @ X6)
% 268.22/39.35 | ~ (quotient @ X2 @ X3 @ X7)
% 268.22/39.35 | (less_equal @ X6 @ X7))),
% 268.22/39.35 inference('cnf', [status(esa)], [quotient_property])).
% 268.22/39.35 thf(zip_derived_cl56, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 268.22/39.35 ( (less_equal @ X4 @ X3)
% 268.22/39.35 | ~ (quotient @ X0 @ X1 @ X3)
% 268.22/39.35 | ~ (quotient @ X0 @ X5 @ X4)
% 268.22/39.35 | ~ (quotient @ X2 @ X1 @ X0)
% 268.22/39.35 | ~ (quotient @ X1 @ X1 @ X5))),
% 268.22/39.35 inference('eq_fact', [status(thm)], [zip_derived_cl3])).
% 268.22/39.35 thf(zip_derived_cl488, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 268.22/39.35 (~ (quotient @ X0 @ X0 @ X2)
% 268.22/39.35 | ~ (quotient @ X3 @ X0 @ X1)
% 268.22/39.35 | ~ (quotient @ X1 @ X2 @ X4)
% 268.22/39.35 | (less_equal @ X4 @ (divide @ X1 @ X0)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl56])).
% 268.22/39.35 thf(zip_derived_cl3041, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 268.22/39.35 ( (less_equal @ X2 @ (divide @ X1 @ X0))
% 268.22/39.35 | ~ (quotient @ X1 @ zero @ X2)
% 268.22/39.35 | ~ (quotient @ X3 @ X0 @ X1))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl838, zip_derived_cl488])).
% 268.22/39.35 thf(zip_derived_cl18370, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i]:
% 268.22/39.35 (~ (quotient @ X2 @ X1 @ X0)
% 268.22/39.35 | (less_equal @ (divide @ X0 @ zero) @ (divide @ X0 @ X1)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl3041])).
% 268.22/39.35 thf(zip_derived_cl20742, plain, (![X0 : $i]: ((divide @ X0 @ zero) = (X0))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl20543, zip_derived_cl62])).
% 268.22/39.35 thf(zip_derived_cl20829, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i]:
% 268.22/39.35 (~ (quotient @ X2 @ X1 @ X0) | (less_equal @ X0 @ (divide @ X0 @ X1)))),
% 268.22/39.35 inference('demod', [status(thm)],
% 268.22/39.35 [zip_derived_cl18370, zip_derived_cl20742])).
% 268.22/39.35 thf(zip_derived_cl23730, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (less_equal @ (divide @ X1 @ X0) @ (divide @ (divide @ X1 @ X0) @ X0))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl20829])).
% 268.22/39.35 thf(zip_derived_cl62, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (((divide @ X0 @ X1) = (X0))
% 268.22/39.35 | ~ (less_equal @ X0 @ (divide @ X0 @ X1)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl23979, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 ((divide @ (divide @ X1 @ X0) @ X0) = (divide @ X1 @ X0))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl23730, zip_derived_cl62])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl24272, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (quotient @ (divide @ X1 @ X0) @ X0 @ (divide @ X1 @ X0))),
% 268.22/39.35 inference('sup+', [status(thm)], [zip_derived_cl23979, zip_derived_cl7])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl3164, plain,
% 268.22/39.35 (![X0 : $i]: (quotient @ (divide @ X0 @ idQa) @ idQ_idQa @ zero)),
% 268.22/39.35 inference('sup+', [status(thm)], [zip_derived_cl3096, zip_derived_cl7])).
% 268.22/39.35 thf(zip_derived_cl3, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 268.22/39.35 (~ (quotient @ X0 @ X1 @ X2)
% 268.22/39.35 | ~ (quotient @ X1 @ X3 @ X4)
% 268.22/39.35 | ~ (quotient @ X0 @ X3 @ X5)
% 268.22/39.35 | ~ (quotient @ X5 @ X4 @ X6)
% 268.22/39.35 | ~ (quotient @ X2 @ X3 @ X7)
% 268.22/39.35 | (less_equal @ X6 @ X7))),
% 268.22/39.35 inference('cnf', [status(esa)], [quotient_property])).
% 268.22/39.35 thf(zip_derived_cl57, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 268.22/39.35 ( (less_equal @ X0 @ X3)
% 268.22/39.35 | ~ (quotient @ X0 @ X4 @ X3)
% 268.22/39.35 | ~ (quotient @ X2 @ X1 @ X0)
% 268.22/39.35 | ~ (quotient @ X2 @ X4 @ X2)
% 268.22/39.35 | ~ (quotient @ X1 @ X4 @ X1))),
% 268.22/39.35 inference('eq_fact', [status(thm)], [zip_derived_cl3])).
% 268.22/39.35 thf(zip_derived_cl3229, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i]:
% 268.22/39.35 (~ (quotient @ X1 @ idQ_idQa @ X1)
% 268.22/39.35 | ~ (quotient @ X2 @ idQ_idQa @ X2)
% 268.22/39.35 | ~ (quotient @ X2 @ X1 @ (divide @ X0 @ idQa))
% 268.22/39.35 | (less_equal @ (divide @ X0 @ idQa) @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl3164, zip_derived_cl57])).
% 268.22/39.35 thf(zip_derived_cl18696, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 ( (less_equal @ (divide @ X0 @ idQa) @ zero)
% 268.22/39.35 | ~ (quotient @ X0 @ idQ_idQa @ X0)
% 268.22/39.35 | ~ (quotient @ idQa @ idQ_idQa @ idQa))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl3229])).
% 268.22/39.35 thf(zip_derived_cl47280, plain, (((divide @ a @ idQa) = (idQ_idQa))),
% 268.22/39.35 inference('sup-', [status(thm)],
% 268.22/39.35 [zip_derived_cl47258, zip_derived_cl3303])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl9, plain, ( (quotient @ identity @ a @ idQa)),
% 268.22/39.35 inference('cnf', [status(esa)], [identity_divide_a])).
% 268.22/39.35 thf(zip_derived_cl838, plain, (![X0 : $i]: (quotient @ X0 @ X0 @ zero)),
% 268.22/39.35 inference('sup+', [status(thm)], [zip_derived_cl818, zip_derived_cl7])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl9, plain, ( (quotient @ identity @ a @ idQa)),
% 268.22/39.35 inference('cnf', [status(esa)], [identity_divide_a])).
% 268.22/39.35 thf(zip_derived_cl3, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 268.22/39.35 (~ (quotient @ X0 @ X1 @ X2)
% 268.22/39.35 | ~ (quotient @ X1 @ X3 @ X4)
% 268.22/39.35 | ~ (quotient @ X0 @ X3 @ X5)
% 268.22/39.35 | ~ (quotient @ X5 @ X4 @ X6)
% 268.22/39.35 | ~ (quotient @ X2 @ X3 @ X7)
% 268.22/39.35 | (less_equal @ X6 @ X7))),
% 268.22/39.35 inference('cnf', [status(esa)], [quotient_property])).
% 268.22/39.35 thf(zip_derived_cl49, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 268.22/39.35 ( (less_equal @ X1 @ X0)
% 268.22/39.35 | ~ (quotient @ idQa @ X2 @ X0)
% 268.22/39.35 | ~ (quotient @ X4 @ X3 @ X1)
% 268.22/39.35 | ~ (quotient @ identity @ X2 @ X4)
% 268.22/39.35 | ~ (quotient @ a @ X2 @ X3))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl3])).
% 268.22/39.35 thf(zip_derived_cl218, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 268.22/39.35 (~ (quotient @ a @ X0 @ X1)
% 268.22/39.35 | ~ (quotient @ identity @ X0 @ X2)
% 268.22/39.35 | ~ (quotient @ X2 @ X1 @ X3)
% 268.22/39.35 | (less_equal @ X3 @ (divide @ idQa @ X0)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl49])).
% 268.22/39.35 thf(zip_derived_cl1704, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 ( (less_equal @ X0 @ (divide @ idQa @ a))
% 268.22/39.35 | ~ (quotient @ X1 @ zero @ X0)
% 268.22/39.35 | ~ (quotient @ identity @ a @ X1))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl838, zip_derived_cl218])).
% 268.22/39.35 thf(zip_derived_cl12847, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 (~ (quotient @ idQa @ zero @ X0)
% 268.22/39.35 | (less_equal @ X0 @ (divide @ idQa @ a)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl1704])).
% 268.22/39.35 thf(zip_derived_cl12852, plain,
% 268.22/39.35 ( (less_equal @ (divide @ idQa @ zero) @ (divide @ idQa @ a))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl12847])).
% 268.22/39.35 thf(zip_derived_cl20742, plain, (![X0 : $i]: ((divide @ X0 @ zero) = (X0))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl20543, zip_derived_cl62])).
% 268.22/39.35 thf(zip_derived_cl20808, plain, ( (less_equal @ idQa @ (divide @ idQa @ a))),
% 268.22/39.35 inference('demod', [status(thm)],
% 268.22/39.35 [zip_derived_cl12852, zip_derived_cl20742])).
% 268.22/39.35 thf(zip_derived_cl62, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (((divide @ X0 @ X1) = (X0))
% 268.22/39.35 | ~ (less_equal @ X0 @ (divide @ X0 @ X1)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl21554, plain, (((divide @ idQa @ a) = (idQa))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl20808, zip_derived_cl62])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl21565, plain, ( (quotient @ idQa @ a @ idQa)),
% 268.22/39.35 inference('sup+', [status(thm)], [zip_derived_cl21554, zip_derived_cl7])).
% 268.22/39.35 thf(zip_derived_cl30079, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 268.22/39.35 (~ (quotient @ X2 @ X1 @ X0)
% 268.22/39.35 | (less_equal @ X0 @
% 268.22/39.35 (divide @ (divide @ X2 @ (divide @ X1 @ X3)) @ X1)))),
% 268.22/39.35 inference('demod', [status(thm)],
% 268.22/39.35 [zip_derived_cl5026, zip_derived_cl20742])).
% 268.22/39.35 thf(zip_derived_cl30125, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 (less_equal @ idQa @
% 268.22/39.35 (divide @ (divide @ idQa @ (divide @ a @ X0)) @ a))),
% 268.22/39.35 inference('sup-', [status(thm)],
% 268.22/39.35 [zip_derived_cl21565, zip_derived_cl30079])).
% 268.22/39.35 thf(zip_derived_cl2808, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 (((divide @ X0 @ a) = (idQa))
% 268.22/39.35 | ~ (less_equal @ idQa @ (divide @ X0 @ a)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl2757, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl33627, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 ((divide @ (divide @ idQa @ (divide @ a @ X0)) @ a) = (idQa))),
% 268.22/39.35 inference('sup-', [status(thm)],
% 268.22/39.35 [zip_derived_cl30125, zip_derived_cl2808])).
% 268.22/39.35 thf(zip_derived_cl62, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (((divide @ X0 @ X1) = (X0))
% 268.22/39.35 | ~ (less_equal @ X0 @ (divide @ X0 @ X1)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl33658, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 (~ (less_equal @ (divide @ idQa @ (divide @ a @ X0)) @ idQa)
% 268.22/39.35 | ((divide @ (divide @ idQa @ (divide @ a @ X0)) @ a)
% 268.22/39.35 = (divide @ idQa @ (divide @ a @ X0))))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl33627, zip_derived_cl62])).
% 268.22/39.35 thf(zip_derived_cl23, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (less_equal @ (divide @ X1 @ X0) @ X1)),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 268.22/39.35 thf(zip_derived_cl33627, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 ((divide @ (divide @ idQa @ (divide @ a @ X0)) @ a) = (idQa))),
% 268.22/39.35 inference('sup-', [status(thm)],
% 268.22/39.35 [zip_derived_cl30125, zip_derived_cl2808])).
% 268.22/39.35 thf(zip_derived_cl33727, plain,
% 268.22/39.35 (![X0 : $i]: ((idQa) = (divide @ idQa @ (divide @ a @ X0)))),
% 268.22/39.35 inference('demod', [status(thm)],
% 268.22/39.35 [zip_derived_cl33658, zip_derived_cl23, zip_derived_cl33627])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl33750, plain,
% 268.22/39.35 (![X0 : $i]: (quotient @ idQa @ (divide @ a @ X0) @ idQa)),
% 268.22/39.35 inference('sup+', [status(thm)], [zip_derived_cl33727, zip_derived_cl7])).
% 268.22/39.35 thf(zip_derived_cl47354, plain, ( (quotient @ idQa @ idQ_idQa @ idQa)),
% 268.22/39.35 inference('sup+', [status(thm)],
% 268.22/39.35 [zip_derived_cl47280, zip_derived_cl33750])).
% 268.22/39.35 thf(zip_derived_cl47651, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 ( (less_equal @ (divide @ X0 @ idQa) @ zero)
% 268.22/39.35 | ~ (quotient @ X0 @ idQ_idQa @ X0))),
% 268.22/39.35 inference('demod', [status(thm)],
% 268.22/39.35 [zip_derived_cl18696, zip_derived_cl47354])).
% 268.22/39.35 thf(zip_derived_cl49543, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 (less_equal @ (divide @ (divide @ X0 @ idQ_idQa) @ idQa) @ zero)),
% 268.22/39.35 inference('sup-', [status(thm)],
% 268.22/39.35 [zip_derived_cl24272, zip_derived_cl47651])).
% 268.22/39.35 thf(zip_derived_cl19, plain,
% 268.22/39.35 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl51578, plain,
% 268.22/39.35 (![X0 : $i]: ((zero) = (divide @ (divide @ X0 @ idQ_idQa) @ idQa))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl49543, zip_derived_cl19])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl51640, plain,
% 268.22/39.35 (![X0 : $i]: (quotient @ (divide @ X0 @ idQ_idQa) @ idQa @ zero)),
% 268.22/39.35 inference('sup+', [status(thm)], [zip_derived_cl51578, zip_derived_cl7])).
% 268.22/39.35 thf(zip_derived_cl1, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (quotient @ X0 @ X1 @ zero) | (less_equal @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [less_equal_quotient])).
% 268.22/39.35 thf(zip_derived_cl51885, plain,
% 268.22/39.35 (![X0 : $i]: (less_equal @ (divide @ X0 @ idQ_idQa) @ idQa)),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl51640, zip_derived_cl1])).
% 268.22/39.35 thf(zip_derived_cl51965, plain, (((idQa) = (divide @ identity @ idQ_idQa))),
% 268.22/39.35 inference('demod', [status(thm)],
% 268.22/39.35 [zip_derived_cl47697, zip_derived_cl51885])).
% 268.22/39.35 thf(zip_derived_cl52082, plain,
% 268.22/39.35 (((divide @ (divide @ idQa @ idQb_Q__idQ_idQa) @
% 268.22/39.35 (divide @ idQ_idQb @ idQ_idQa)) = (zero))),
% 268.22/39.35 inference('demod', [status(thm)],
% 268.22/39.35 [zip_derived_cl25567, zip_derived_cl51965])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl30079, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 268.22/39.35 (~ (quotient @ X2 @ X1 @ X0)
% 268.22/39.35 | (less_equal @ X0 @
% 268.22/39.35 (divide @ (divide @ X2 @ (divide @ X1 @ X3)) @ X1)))),
% 268.22/39.35 inference('demod', [status(thm)],
% 268.22/39.35 [zip_derived_cl5026, zip_derived_cl20742])).
% 268.22/39.35 thf(zip_derived_cl30081, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i]:
% 268.22/39.35 (less_equal @ (divide @ X1 @ X0) @
% 268.22/39.35 (divide @ (divide @ X1 @ (divide @ X0 @ X2)) @ X0))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl30079])).
% 268.22/39.35 thf(zip_derived_cl123762, plain,
% 268.22/39.35 ( (less_equal @
% 268.22/39.35 (divide @ (divide @ idQa @ idQb_Q__idQ_idQa) @ idQ_idQb) @
% 268.22/39.35 (divide @ zero @ idQ_idQb))),
% 268.22/39.35 inference('sup+', [status(thm)],
% 268.22/39.35 [zip_derived_cl52082, zip_derived_cl30081])).
% 268.22/39.35 thf(zip_derived_cl63, plain, (![X0 : $i]: ((zero) = (divide @ zero @ X0))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl19])).
% 268.22/39.35 thf(zip_derived_cl124504, plain,
% 268.22/39.35 ( (less_equal @
% 268.22/39.35 (divide @ (divide @ idQa @ idQb_Q__idQ_idQa) @ idQ_idQb) @ zero)),
% 268.22/39.35 inference('demod', [status(thm)],
% 268.22/39.35 [zip_derived_cl123762, zip_derived_cl63])).
% 268.22/39.35 thf(zip_derived_cl19, plain,
% 268.22/39.35 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl124939, plain,
% 268.22/39.35 (((zero) = (divide @ (divide @ idQa @ idQb_Q__idQ_idQa) @ idQ_idQb))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl124504, zip_derived_cl19])).
% 268.22/39.35 thf(idQa_divide_idQ_idQb, axiom,
% 268.22/39.35 (quotient @ idQa @ idQ_idQb @ idQa_Q__idQ_idQb)).
% 268.22/39.35 thf(zip_derived_cl12, plain,
% 268.22/39.35 ( (quotient @ idQa @ idQ_idQb @ idQa_Q__idQ_idQb)),
% 268.22/39.35 inference('cnf', [status(esa)], [idQa_divide_idQ_idQb])).
% 268.22/39.35 thf(zip_derived_cl4927, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 268.22/39.35 (~ (quotient @ X3 @ X0 @ X2)
% 268.22/39.35 | (less_equal @ (divide @ X2 @ (divide @ X1 @ X0)) @
% 268.22/39.35 (divide @ (divide @ X3 @ X1) @ X0)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl708])).
% 268.22/39.35 thf(zip_derived_cl28002, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 (less_equal @
% 268.22/39.35 (divide @ idQa_Q__idQ_idQb @ (divide @ X0 @ idQ_idQb)) @
% 268.22/39.35 (divide @ (divide @ idQa @ X0) @ idQ_idQb))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl4927])).
% 268.22/39.35 thf(zip_derived_cl125028, plain,
% 268.22/39.35 ( (less_equal @
% 268.22/39.35 (divide @ idQa_Q__idQ_idQb @ (divide @ idQb_Q__idQ_idQa @ idQ_idQb)) @
% 268.22/39.35 zero)),
% 268.22/39.35 inference('sup+', [status(thm)],
% 268.22/39.35 [zip_derived_cl124939, zip_derived_cl28002])).
% 268.22/39.35 thf(zip_derived_cl19, plain,
% 268.22/39.35 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl125124, plain,
% 268.22/39.35 (((zero)
% 268.22/39.35 = (divide @ idQa_Q__idQ_idQb @ (divide @ idQb_Q__idQ_idQa @ idQ_idQb)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl125028, zip_derived_cl19])).
% 268.22/39.35 thf(zip_derived_cl30081, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i]:
% 268.22/39.35 (less_equal @ (divide @ X1 @ X0) @
% 268.22/39.35 (divide @ (divide @ X1 @ (divide @ X0 @ X2)) @ X0))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl30079])).
% 268.22/39.35 thf(zip_derived_cl125181, plain,
% 268.22/39.35 ( (less_equal @ (divide @ idQa_Q__idQ_idQb @ idQb_Q__idQ_idQa) @
% 268.22/39.35 (divide @ zero @ idQb_Q__idQ_idQa))),
% 268.22/39.35 inference('sup+', [status(thm)],
% 268.22/39.35 [zip_derived_cl125124, zip_derived_cl30081])).
% 268.22/39.35 thf(zip_derived_cl63, plain, (![X0 : $i]: ((zero) = (divide @ zero @ X0))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl19])).
% 268.22/39.35 thf(zip_derived_cl125247, plain,
% 268.22/39.35 ( (less_equal @ (divide @ idQa_Q__idQ_idQb @ idQb_Q__idQ_idQa) @ zero)),
% 268.22/39.35 inference('demod', [status(thm)],
% 268.22/39.35 [zip_derived_cl125181, zip_derived_cl63])).
% 268.22/39.35 thf(zip_derived_cl19, plain,
% 268.22/39.35 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl125270, plain,
% 268.22/39.35 (((zero) = (divide @ idQa_Q__idQ_idQb @ idQb_Q__idQ_idQa))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl125247, zip_derived_cl19])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl125282, plain,
% 268.22/39.35 ( (quotient @ idQa_Q__idQ_idQb @ idQb_Q__idQ_idQa @ zero)),
% 268.22/39.35 inference('sup+', [status(thm)], [zip_derived_cl125270, zip_derived_cl7])).
% 268.22/39.35 thf(zip_derived_cl1, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (quotient @ X0 @ X1 @ zero) | (less_equal @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [less_equal_quotient])).
% 268.22/39.35 thf(zip_derived_cl125445, plain,
% 268.22/39.35 ( (less_equal @ idQa_Q__idQ_idQb @ idQb_Q__idQ_idQa)),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl125282, zip_derived_cl1])).
% 268.22/39.35 thf(zip_derived_cl5, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 268.22/39.35 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 268.22/39.35 thf(zip_derived_cl125462, plain,
% 268.22/39.35 ((((idQa_Q__idQ_idQb) = (idQb_Q__idQ_idQa))
% 268.22/39.35 | ~ (less_equal @ idQb_Q__idQ_idQa @ idQa_Q__idQ_idQb))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl125445, zip_derived_cl5])).
% 268.22/39.35 thf(prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa, conjecture,
% 268.22/39.35 (( idQa_Q__idQ_idQb ) = ( idQb_Q__idQ_idQa ))).
% 268.22/39.35 thf(zf_stmt_0, negated_conjecture,
% 268.22/39.35 (( idQa_Q__idQ_idQb ) != ( idQb_Q__idQ_idQa )),
% 268.22/39.35 inference('cnf.neg', [status(esa)],
% 268.22/39.35 [prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa])).
% 268.22/39.35 thf(zip_derived_cl15, plain, (((idQa_Q__idQ_idQb) != (idQb_Q__idQ_idQa))),
% 268.22/39.35 inference('cnf', [status(esa)], [zf_stmt_0])).
% 268.22/39.35 thf(zip_derived_cl125463, plain,
% 268.22/39.35 (~ (less_equal @ idQb_Q__idQ_idQa @ idQa_Q__idQ_idQb)),
% 268.22/39.35 inference('simplify_reflect-', [status(thm)],
% 268.22/39.35 [zip_derived_cl125462, zip_derived_cl15])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl12, plain,
% 268.22/39.35 ( (quotient @ idQa @ idQ_idQb @ idQa_Q__idQ_idQb)),
% 268.22/39.35 inference('cnf', [status(esa)], [idQa_divide_idQ_idQb])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl13, plain, ( (quotient @ identity @ idQa @ idQ_idQa)),
% 268.22/39.35 inference('cnf', [status(esa)], [identity_divide_idQa])).
% 268.22/39.35 thf(zip_derived_cl3, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 268.22/39.35 (~ (quotient @ X0 @ X1 @ X2)
% 268.22/39.35 | ~ (quotient @ X1 @ X3 @ X4)
% 268.22/39.35 | ~ (quotient @ X0 @ X3 @ X5)
% 268.22/39.35 | ~ (quotient @ X5 @ X4 @ X6)
% 268.22/39.35 | ~ (quotient @ X2 @ X3 @ X7)
% 268.22/39.35 | (less_equal @ X6 @ X7))),
% 268.22/39.35 inference('cnf', [status(esa)], [quotient_property])).
% 268.22/39.35 thf(zip_derived_cl50, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 268.22/39.35 ( (less_equal @ X1 @ X0)
% 268.22/39.35 | ~ (quotient @ idQ_idQa @ X2 @ X0)
% 268.22/39.35 | ~ (quotient @ X4 @ X3 @ X1)
% 268.22/39.35 | ~ (quotient @ identity @ X2 @ X4)
% 268.22/39.35 | ~ (quotient @ idQa @ X2 @ X3))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl3])).
% 268.22/39.35 thf(zip_derived_cl249, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 268.22/39.35 (~ (quotient @ idQa @ X0 @ X1)
% 268.22/39.35 | ~ (quotient @ identity @ X0 @ X2)
% 268.22/39.35 | ~ (quotient @ X2 @ X1 @ X3)
% 268.22/39.35 | (less_equal @ X3 @ (divide @ idQ_idQa @ X0)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl50])).
% 268.22/39.35 thf(zip_derived_cl1716, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 ( (less_equal @ X0 @ (divide @ idQ_idQa @ idQ_idQb))
% 268.22/39.35 | ~ (quotient @ X1 @ idQa_Q__idQ_idQb @ X0)
% 268.22/39.35 | ~ (quotient @ identity @ idQ_idQb @ X1))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl249])).
% 268.22/39.35 thf(zip_derived_cl13092, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 (~ (quotient @ (divide @ identity @ idQ_idQb) @ idQa_Q__idQ_idQb @ X0)
% 268.22/39.35 | (less_equal @ X0 @ (divide @ idQ_idQa @ idQ_idQb)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl1716])).
% 268.22/39.35 thf(zip_derived_cl13302, plain,
% 268.22/39.35 ( (less_equal @
% 268.22/39.35 (divide @ (divide @ identity @ idQ_idQb) @ idQa_Q__idQ_idQb) @
% 268.22/39.35 (divide @ idQ_idQa @ idQ_idQb))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl13092])).
% 268.22/39.35 thf(zip_derived_cl0, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (less_equal @ X0 @ X1) | (quotient @ X0 @ X1 @ zero))),
% 268.22/39.35 inference('cnf', [status(esa)], [quotient_less_equal])).
% 268.22/39.35 thf(zip_derived_cl13357, plain,
% 268.22/39.35 ( (quotient @
% 268.22/39.35 (divide @ (divide @ identity @ idQ_idQb) @ idQa_Q__idQ_idQb) @
% 268.22/39.35 (divide @ idQ_idQa @ idQ_idQb) @ zero)),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl13302, zip_derived_cl0])).
% 268.22/39.35 thf(zip_derived_cl36, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i]:
% 268.22/39.35 (((divide @ X1 @ X0) = (X2)) | ~ (quotient @ X1 @ X0 @ X2))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl8])).
% 268.22/39.35 thf(zip_derived_cl25360, plain,
% 268.22/39.35 (((divide @
% 268.22/39.35 (divide @ (divide @ identity @ idQ_idQb) @ idQa_Q__idQ_idQb) @
% 268.22/39.35 (divide @ idQ_idQa @ idQ_idQb)) = (zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl13357, zip_derived_cl36])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(identity_divide_b, axiom, (quotient @ identity @ b @ idQb)).
% 268.22/39.35 thf(zip_derived_cl10, plain, ( (quotient @ identity @ b @ idQb)),
% 268.22/39.35 inference('cnf', [status(esa)], [identity_divide_b])).
% 268.22/39.35 thf(zip_derived_cl125, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 268.22/39.35 (~ (quotient @ X1 @ X0 @ X3)
% 268.22/39.35 | ~ (quotient @ X2 @ X0 @ X4)
% 268.22/39.35 | ~ (quotient @ X4 @ X3 @ X5)
% 268.22/39.35 | (less_equal @ X5 @ (divide @ (divide @ X2 @ X1) @ X0)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl46])).
% 268.22/39.35 thf(zip_derived_cl713, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i]:
% 268.22/39.35 ( (less_equal @ X1 @ (divide @ (divide @ X0 @ identity) @ b))
% 268.22/39.35 | ~ (quotient @ X2 @ idQb @ X1)
% 268.22/39.35 | ~ (quotient @ X0 @ b @ X2))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl125])).
% 268.22/39.35 thf(zip_derived_cl68, plain,
% 268.22/39.35 (![X0 : $i]: ((zero) = (divide @ X0 @ identity))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl37])).
% 268.22/39.35 thf(zip_derived_cl63, plain, (![X0 : $i]: ((zero) = (divide @ zero @ X0))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl19])).
% 268.22/39.35 thf(zip_derived_cl729, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i]:
% 268.22/39.35 ( (less_equal @ X1 @ zero)
% 268.22/39.35 | ~ (quotient @ X2 @ idQb @ X1)
% 268.22/39.35 | ~ (quotient @ X0 @ b @ X2))),
% 268.22/39.35 inference('demod', [status(thm)],
% 268.22/39.35 [zip_derived_cl713, zip_derived_cl68, zip_derived_cl63])).
% 268.22/39.35 thf(zip_derived_cl3147, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (quotient @ X1 @ b @ X0)
% 268.22/39.35 | (less_equal @ (divide @ X0 @ idQb) @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl729])).
% 268.22/39.35 thf(zip_derived_cl3345, plain,
% 268.22/39.35 (![X0 : $i]: (less_equal @ (divide @ (divide @ X0 @ b) @ idQb) @ zero)),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl3147])).
% 268.22/39.35 thf(zip_derived_cl19, plain,
% 268.22/39.35 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl3488, plain,
% 268.22/39.35 (![X0 : $i]: ((zero) = (divide @ (divide @ X0 @ b) @ idQb))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl3345, zip_derived_cl19])).
% 268.22/39.35 thf(zip_derived_cl11, plain, ( (quotient @ identity @ idQb @ idQ_idQb)),
% 268.22/39.35 inference('cnf', [status(esa)], [identity_divide_idQb])).
% 268.22/39.35 thf(zip_derived_cl4927, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 268.22/39.35 (~ (quotient @ X3 @ X0 @ X2)
% 268.22/39.35 | (less_equal @ (divide @ X2 @ (divide @ X1 @ X0)) @
% 268.22/39.35 (divide @ (divide @ X3 @ X1) @ X0)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl708])).
% 268.22/39.35 thf(zip_derived_cl27969, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 (less_equal @ (divide @ idQ_idQb @ (divide @ X0 @ idQb)) @
% 268.22/39.35 (divide @ (divide @ identity @ X0) @ idQb))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl4927])).
% 268.22/39.35 thf(zip_derived_cl73303, plain,
% 268.22/39.35 ( (less_equal @ (divide @ idQ_idQb @ (divide @ b @ idQb)) @ zero)),
% 268.22/39.35 inference('sup+', [status(thm)],
% 268.22/39.35 [zip_derived_cl3488, zip_derived_cl27969])).
% 268.22/39.35 thf(zip_derived_cl19, plain,
% 268.22/39.35 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl73422, plain,
% 268.22/39.35 (((zero) = (divide @ idQ_idQb @ (divide @ b @ idQb)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl73303, zip_derived_cl19])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl73431, plain,
% 268.22/39.35 ( (quotient @ idQ_idQb @ (divide @ b @ idQb) @ zero)),
% 268.22/39.35 inference('sup+', [status(thm)], [zip_derived_cl73422, zip_derived_cl7])).
% 268.22/39.35 thf(zip_derived_cl1, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (quotient @ X0 @ X1 @ zero) | (less_equal @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [less_equal_quotient])).
% 268.22/39.35 thf(zip_derived_cl73521, plain,
% 268.22/39.35 ( (less_equal @ idQ_idQb @ (divide @ b @ idQb))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl73431, zip_derived_cl1])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl11, plain, ( (quotient @ identity @ idQb @ idQ_idQb)),
% 268.22/39.35 inference('cnf', [status(esa)], [identity_divide_idQb])).
% 268.22/39.35 thf(zip_derived_cl125, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 268.22/39.35 (~ (quotient @ X1 @ X0 @ X3)
% 268.22/39.35 | ~ (quotient @ X2 @ X0 @ X4)
% 268.22/39.35 | ~ (quotient @ X4 @ X3 @ X5)
% 268.22/39.35 | (less_equal @ X5 @ (divide @ (divide @ X2 @ X1) @ X0)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl46])).
% 268.22/39.35 thf(zip_derived_cl714, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i]:
% 268.22/39.35 ( (less_equal @ X1 @ (divide @ (divide @ X0 @ identity) @ idQb))
% 268.22/39.35 | ~ (quotient @ X2 @ idQ_idQb @ X1)
% 268.22/39.35 | ~ (quotient @ X0 @ idQb @ X2))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl125])).
% 268.22/39.35 thf(zip_derived_cl68, plain,
% 268.22/39.35 (![X0 : $i]: ((zero) = (divide @ X0 @ identity))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl37])).
% 268.22/39.35 thf(zip_derived_cl63, plain, (![X0 : $i]: ((zero) = (divide @ zero @ X0))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl19])).
% 268.22/39.35 thf(zip_derived_cl730, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i]:
% 268.22/39.35 ( (less_equal @ X1 @ zero)
% 268.22/39.35 | ~ (quotient @ X2 @ idQ_idQb @ X1)
% 268.22/39.35 | ~ (quotient @ X0 @ idQb @ X2))),
% 268.22/39.35 inference('demod', [status(thm)],
% 268.22/39.35 [zip_derived_cl714, zip_derived_cl68, zip_derived_cl63])).
% 268.22/39.35 thf(zip_derived_cl3209, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (quotient @ X1 @ idQb @ X0)
% 268.22/39.35 | (less_equal @ (divide @ X0 @ idQ_idQb) @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl730])).
% 268.22/39.35 thf(zip_derived_cl3738, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 (less_equal @ (divide @ (divide @ X0 @ idQb) @ idQ_idQb) @ zero)),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl3209])).
% 268.22/39.35 thf(zip_derived_cl19, plain,
% 268.22/39.35 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl3766, plain,
% 268.22/39.35 (![X0 : $i]: ((zero) = (divide @ (divide @ X0 @ idQb) @ idQ_idQb))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl3738, zip_derived_cl19])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl3862, plain,
% 268.22/39.35 (![X0 : $i]: (quotient @ (divide @ X0 @ idQb) @ idQ_idQb @ zero)),
% 268.22/39.35 inference('sup+', [status(thm)], [zip_derived_cl3766, zip_derived_cl7])).
% 268.22/39.35 thf(zip_derived_cl1, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (quotient @ X0 @ X1 @ zero) | (less_equal @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [less_equal_quotient])).
% 268.22/39.35 thf(zip_derived_cl3925, plain,
% 268.22/39.35 (![X0 : $i]: (less_equal @ (divide @ X0 @ idQb) @ idQ_idQb)),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl3862, zip_derived_cl1])).
% 268.22/39.35 thf(zip_derived_cl5, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 268.22/39.35 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 268.22/39.35 thf(zip_derived_cl3992, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 (((divide @ X0 @ idQb) = (idQ_idQb))
% 268.22/39.35 | ~ (less_equal @ idQ_idQb @ (divide @ X0 @ idQb)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl3925, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl73543, plain, (((divide @ b @ idQb) = (idQ_idQb))),
% 268.22/39.35 inference('sup-', [status(thm)],
% 268.22/39.35 [zip_derived_cl73521, zip_derived_cl3992])).
% 268.22/39.35 thf(zip_derived_cl10, plain, ( (quotient @ identity @ b @ idQb)),
% 268.22/39.35 inference('cnf', [status(esa)], [identity_divide_b])).
% 268.22/39.35 thf(zip_derived_cl30079, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 268.22/39.35 (~ (quotient @ X2 @ X1 @ X0)
% 268.22/39.35 | (less_equal @ X0 @
% 268.22/39.35 (divide @ (divide @ X2 @ (divide @ X1 @ X3)) @ X1)))),
% 268.22/39.35 inference('demod', [status(thm)],
% 268.22/39.35 [zip_derived_cl5026, zip_derived_cl20742])).
% 268.22/39.35 thf(zip_derived_cl30091, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 (less_equal @ idQb @
% 268.22/39.35 (divide @ (divide @ identity @ (divide @ b @ X0)) @ b))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl30079])).
% 268.22/39.35 thf(zip_derived_cl3488, plain,
% 268.22/39.35 (![X0 : $i]: ((zero) = (divide @ (divide @ X0 @ b) @ idQb))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl3345, zip_derived_cl19])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl3536, plain,
% 268.22/39.35 (![X0 : $i]: (quotient @ (divide @ X0 @ b) @ idQb @ zero)),
% 268.22/39.35 inference('sup+', [status(thm)], [zip_derived_cl3488, zip_derived_cl7])).
% 268.22/39.35 thf(zip_derived_cl1, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (quotient @ X0 @ X1 @ zero) | (less_equal @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [less_equal_quotient])).
% 268.22/39.35 thf(zip_derived_cl3595, plain,
% 268.22/39.35 (![X0 : $i]: (less_equal @ (divide @ X0 @ b) @ idQb)),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl3536, zip_derived_cl1])).
% 268.22/39.35 thf(zip_derived_cl5, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 268.22/39.35 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 268.22/39.35 thf(zip_derived_cl3661, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 (((divide @ X0 @ b) = (idQb))
% 268.22/39.35 | ~ (less_equal @ idQb @ (divide @ X0 @ b)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl3595, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl32471, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 ((divide @ (divide @ identity @ (divide @ b @ X0)) @ b) = (idQb))),
% 268.22/39.35 inference('sup-', [status(thm)],
% 268.22/39.35 [zip_derived_cl30091, zip_derived_cl3661])).
% 268.22/39.35 thf(zip_derived_cl23, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (less_equal @ (divide @ X1 @ X0) @ X1)),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 268.22/39.35 thf(zip_derived_cl32566, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 (less_equal @ idQb @ (divide @ identity @ (divide @ b @ X0)))),
% 268.22/39.35 inference('sup+', [status(thm)], [zip_derived_cl32471, zip_derived_cl23])).
% 268.22/39.35 thf(zip_derived_cl73619, plain,
% 268.22/39.35 ( (less_equal @ idQb @ (divide @ identity @ idQ_idQb))),
% 268.22/39.35 inference('sup+', [status(thm)],
% 268.22/39.35 [zip_derived_cl73543, zip_derived_cl32566])).
% 268.22/39.35 thf(zip_derived_cl5, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 268.22/39.35 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 268.22/39.35 thf(zip_derived_cl73991, plain,
% 268.22/39.35 ((((idQb) = (divide @ identity @ idQ_idQb))
% 268.22/39.35 | ~ (less_equal @ (divide @ identity @ idQ_idQb) @ idQb))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl73619, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl24272, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (quotient @ (divide @ X1 @ X0) @ X0 @ (divide @ X1 @ X0))),
% 268.22/39.35 inference('sup+', [status(thm)], [zip_derived_cl23979, zip_derived_cl7])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl3862, plain,
% 268.22/39.35 (![X0 : $i]: (quotient @ (divide @ X0 @ idQb) @ idQ_idQb @ zero)),
% 268.22/39.35 inference('sup+', [status(thm)], [zip_derived_cl3766, zip_derived_cl7])).
% 268.22/39.35 thf(zip_derived_cl57, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 268.22/39.35 ( (less_equal @ X0 @ X3)
% 268.22/39.35 | ~ (quotient @ X0 @ X4 @ X3)
% 268.22/39.35 | ~ (quotient @ X2 @ X1 @ X0)
% 268.22/39.35 | ~ (quotient @ X2 @ X4 @ X2)
% 268.22/39.35 | ~ (quotient @ X1 @ X4 @ X1))),
% 268.22/39.35 inference('eq_fact', [status(thm)], [zip_derived_cl3])).
% 268.22/39.35 thf(zip_derived_cl3923, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i]:
% 268.22/39.35 (~ (quotient @ X1 @ idQ_idQb @ X1)
% 268.22/39.35 | ~ (quotient @ X2 @ idQ_idQb @ X2)
% 268.22/39.35 | ~ (quotient @ X2 @ X1 @ (divide @ X0 @ idQb))
% 268.22/39.35 | (less_equal @ (divide @ X0 @ idQb) @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl3862, zip_derived_cl57])).
% 268.22/39.35 thf(zip_derived_cl23064, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 ( (less_equal @ (divide @ X0 @ idQb) @ zero)
% 268.22/39.35 | ~ (quotient @ X0 @ idQ_idQb @ X0)
% 268.22/39.35 | ~ (quotient @ idQb @ idQ_idQb @ idQb))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl3923])).
% 268.22/39.35 thf(zip_derived_cl73543, plain, (((divide @ b @ idQb) = (idQ_idQb))),
% 268.22/39.35 inference('sup-', [status(thm)],
% 268.22/39.35 [zip_derived_cl73521, zip_derived_cl3992])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl10, plain, ( (quotient @ identity @ b @ idQb)),
% 268.22/39.35 inference('cnf', [status(esa)], [identity_divide_b])).
% 268.22/39.35 thf(zip_derived_cl838, plain, (![X0 : $i]: (quotient @ X0 @ X0 @ zero)),
% 268.22/39.35 inference('sup+', [status(thm)], [zip_derived_cl818, zip_derived_cl7])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl10, plain, ( (quotient @ identity @ b @ idQb)),
% 268.22/39.35 inference('cnf', [status(esa)], [identity_divide_b])).
% 268.22/39.35 thf(zip_derived_cl3, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 268.22/39.35 (~ (quotient @ X0 @ X1 @ X2)
% 268.22/39.35 | ~ (quotient @ X1 @ X3 @ X4)
% 268.22/39.35 | ~ (quotient @ X0 @ X3 @ X5)
% 268.22/39.35 | ~ (quotient @ X5 @ X4 @ X6)
% 268.22/39.35 | ~ (quotient @ X2 @ X3 @ X7)
% 268.22/39.35 | (less_equal @ X6 @ X7))),
% 268.22/39.35 inference('cnf', [status(esa)], [quotient_property])).
% 268.22/39.35 thf(zip_derived_cl51, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 268.22/39.35 ( (less_equal @ X1 @ X0)
% 268.22/39.35 | ~ (quotient @ idQb @ X2 @ X0)
% 268.22/39.35 | ~ (quotient @ X4 @ X3 @ X1)
% 268.22/39.35 | ~ (quotient @ identity @ X2 @ X4)
% 268.22/39.35 | ~ (quotient @ b @ X2 @ X3))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl3])).
% 268.22/39.35 thf(zip_derived_cl286, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 268.22/39.35 (~ (quotient @ b @ X0 @ X1)
% 268.22/39.35 | ~ (quotient @ identity @ X0 @ X2)
% 268.22/39.35 | ~ (quotient @ X2 @ X1 @ X3)
% 268.22/39.35 | (less_equal @ X3 @ (divide @ idQb @ X0)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl51])).
% 268.22/39.35 thf(zip_derived_cl1843, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 ( (less_equal @ X0 @ (divide @ idQb @ b))
% 268.22/39.35 | ~ (quotient @ X1 @ zero @ X0)
% 268.22/39.35 | ~ (quotient @ identity @ b @ X1))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl838, zip_derived_cl286])).
% 268.22/39.35 thf(zip_derived_cl13575, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 (~ (quotient @ idQb @ zero @ X0)
% 268.22/39.35 | (less_equal @ X0 @ (divide @ idQb @ b)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl1843])).
% 268.22/39.35 thf(zip_derived_cl13577, plain,
% 268.22/39.35 ( (less_equal @ (divide @ idQb @ zero) @ (divide @ idQb @ b))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl13575])).
% 268.22/39.35 thf(zip_derived_cl20742, plain, (![X0 : $i]: ((divide @ X0 @ zero) = (X0))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl20543, zip_derived_cl62])).
% 268.22/39.35 thf(zip_derived_cl20819, plain, ( (less_equal @ idQb @ (divide @ idQb @ b))),
% 268.22/39.35 inference('demod', [status(thm)],
% 268.22/39.35 [zip_derived_cl13577, zip_derived_cl20742])).
% 268.22/39.35 thf(zip_derived_cl62, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (((divide @ X0 @ X1) = (X0))
% 268.22/39.35 | ~ (less_equal @ X0 @ (divide @ X0 @ X1)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl21777, plain, (((divide @ idQb @ b) = (idQb))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl20819, zip_derived_cl62])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl21787, plain, ( (quotient @ idQb @ b @ idQb)),
% 268.22/39.35 inference('sup+', [status(thm)], [zip_derived_cl21777, zip_derived_cl7])).
% 268.22/39.35 thf(zip_derived_cl30079, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 268.22/39.35 (~ (quotient @ X2 @ X1 @ X0)
% 268.22/39.35 | (less_equal @ X0 @
% 268.22/39.35 (divide @ (divide @ X2 @ (divide @ X1 @ X3)) @ X1)))),
% 268.22/39.35 inference('demod', [status(thm)],
% 268.22/39.35 [zip_derived_cl5026, zip_derived_cl20742])).
% 268.22/39.35 thf(zip_derived_cl30127, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 (less_equal @ idQb @
% 268.22/39.35 (divide @ (divide @ idQb @ (divide @ b @ X0)) @ b))),
% 268.22/39.35 inference('sup-', [status(thm)],
% 268.22/39.35 [zip_derived_cl21787, zip_derived_cl30079])).
% 268.22/39.35 thf(zip_derived_cl3661, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 (((divide @ X0 @ b) = (idQb))
% 268.22/39.35 | ~ (less_equal @ idQb @ (divide @ X0 @ b)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl3595, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl34045, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 ((divide @ (divide @ idQb @ (divide @ b @ X0)) @ b) = (idQb))),
% 268.22/39.35 inference('sup-', [status(thm)],
% 268.22/39.35 [zip_derived_cl30127, zip_derived_cl3661])).
% 268.22/39.35 thf(zip_derived_cl62, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (((divide @ X0 @ X1) = (X0))
% 268.22/39.35 | ~ (less_equal @ X0 @ (divide @ X0 @ X1)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl34078, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 (~ (less_equal @ (divide @ idQb @ (divide @ b @ X0)) @ idQb)
% 268.22/39.35 | ((divide @ (divide @ idQb @ (divide @ b @ X0)) @ b)
% 268.22/39.35 = (divide @ idQb @ (divide @ b @ X0))))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl34045, zip_derived_cl62])).
% 268.22/39.35 thf(zip_derived_cl23, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (less_equal @ (divide @ X1 @ X0) @ X1)),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 268.22/39.35 thf(zip_derived_cl34045, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 ((divide @ (divide @ idQb @ (divide @ b @ X0)) @ b) = (idQb))),
% 268.22/39.35 inference('sup-', [status(thm)],
% 268.22/39.35 [zip_derived_cl30127, zip_derived_cl3661])).
% 268.22/39.35 thf(zip_derived_cl34149, plain,
% 268.22/39.35 (![X0 : $i]: ((idQb) = (divide @ idQb @ (divide @ b @ X0)))),
% 268.22/39.35 inference('demod', [status(thm)],
% 268.22/39.35 [zip_derived_cl34078, zip_derived_cl23, zip_derived_cl34045])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl34172, plain,
% 268.22/39.35 (![X0 : $i]: (quotient @ idQb @ (divide @ b @ X0) @ idQb)),
% 268.22/39.35 inference('sup+', [status(thm)], [zip_derived_cl34149, zip_derived_cl7])).
% 268.22/39.35 thf(zip_derived_cl73622, plain, ( (quotient @ idQb @ idQ_idQb @ idQb)),
% 268.22/39.35 inference('sup+', [status(thm)],
% 268.22/39.35 [zip_derived_cl73543, zip_derived_cl34172])).
% 268.22/39.35 thf(zip_derived_cl73938, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 ( (less_equal @ (divide @ X0 @ idQb) @ zero)
% 268.22/39.35 | ~ (quotient @ X0 @ idQ_idQb @ X0))),
% 268.22/39.35 inference('demod', [status(thm)],
% 268.22/39.35 [zip_derived_cl23064, zip_derived_cl73622])).
% 268.22/39.35 thf(zip_derived_cl76712, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 (less_equal @ (divide @ (divide @ X0 @ idQ_idQb) @ idQb) @ zero)),
% 268.22/39.35 inference('sup-', [status(thm)],
% 268.22/39.35 [zip_derived_cl24272, zip_derived_cl73938])).
% 268.22/39.35 thf(zip_derived_cl19, plain,
% 268.22/39.35 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl79315, plain,
% 268.22/39.35 (![X0 : $i]: ((zero) = (divide @ (divide @ X0 @ idQ_idQb) @ idQb))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl76712, zip_derived_cl19])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl79381, plain,
% 268.22/39.35 (![X0 : $i]: (quotient @ (divide @ X0 @ idQ_idQb) @ idQb @ zero)),
% 268.22/39.35 inference('sup+', [status(thm)], [zip_derived_cl79315, zip_derived_cl7])).
% 268.22/39.35 thf(zip_derived_cl1, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (quotient @ X0 @ X1 @ zero) | (less_equal @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [less_equal_quotient])).
% 268.22/39.35 thf(zip_derived_cl79646, plain,
% 268.22/39.35 (![X0 : $i]: (less_equal @ (divide @ X0 @ idQ_idQb) @ idQb)),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl79381, zip_derived_cl1])).
% 268.22/39.35 thf(zip_derived_cl79730, plain, (((idQb) = (divide @ identity @ idQ_idQb))),
% 268.22/39.35 inference('demod', [status(thm)],
% 268.22/39.35 [zip_derived_cl73991, zip_derived_cl79646])).
% 268.22/39.35 thf(zip_derived_cl79814, plain,
% 268.22/39.35 (((divide @ (divide @ idQb @ idQa_Q__idQ_idQb) @
% 268.22/39.35 (divide @ idQ_idQa @ idQ_idQb)) = (zero))),
% 268.22/39.35 inference('demod', [status(thm)],
% 268.22/39.35 [zip_derived_cl25360, zip_derived_cl79730])).
% 268.22/39.35 thf(zip_derived_cl30081, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i]:
% 268.22/39.35 (less_equal @ (divide @ X1 @ X0) @
% 268.22/39.35 (divide @ (divide @ X1 @ (divide @ X0 @ X2)) @ X0))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl30079])).
% 268.22/39.35 thf(zip_derived_cl123769, plain,
% 268.22/39.35 ( (less_equal @
% 268.22/39.35 (divide @ (divide @ idQb @ idQa_Q__idQ_idQb) @ idQ_idQa) @
% 268.22/39.35 (divide @ zero @ idQ_idQa))),
% 268.22/39.35 inference('sup+', [status(thm)],
% 268.22/39.35 [zip_derived_cl79814, zip_derived_cl30081])).
% 268.22/39.35 thf(zip_derived_cl63, plain, (![X0 : $i]: ((zero) = (divide @ zero @ X0))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl19])).
% 268.22/39.35 thf(zip_derived_cl124511, plain,
% 268.22/39.35 ( (less_equal @
% 268.22/39.35 (divide @ (divide @ idQb @ idQa_Q__idQ_idQb) @ idQ_idQa) @ zero)),
% 268.22/39.35 inference('demod', [status(thm)],
% 268.22/39.35 [zip_derived_cl123769, zip_derived_cl63])).
% 268.22/39.35 thf(zip_derived_cl19, plain,
% 268.22/39.35 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl127701, plain,
% 268.22/39.35 (((zero) = (divide @ (divide @ idQb @ idQa_Q__idQ_idQb) @ idQ_idQa))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl124511, zip_derived_cl19])).
% 268.22/39.35 thf(zip_derived_cl14, plain,
% 268.22/39.35 ( (quotient @ idQb @ idQ_idQa @ idQb_Q__idQ_idQa)),
% 268.22/39.35 inference('cnf', [status(esa)], [idQb_divide_idQ_idQa])).
% 268.22/39.35 thf(zip_derived_cl4927, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 268.22/39.35 (~ (quotient @ X3 @ X0 @ X2)
% 268.22/39.35 | (less_equal @ (divide @ X2 @ (divide @ X1 @ X0)) @
% 268.22/39.35 (divide @ (divide @ X3 @ X1) @ X0)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl708])).
% 268.22/39.35 thf(zip_derived_cl28004, plain,
% 268.22/39.35 (![X0 : $i]:
% 268.22/39.35 (less_equal @
% 268.22/39.35 (divide @ idQb_Q__idQ_idQa @ (divide @ X0 @ idQ_idQa)) @
% 268.22/39.35 (divide @ (divide @ idQb @ X0) @ idQ_idQa))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl4927])).
% 268.22/39.35 thf(zip_derived_cl127792, plain,
% 268.22/39.35 ( (less_equal @
% 268.22/39.35 (divide @ idQb_Q__idQ_idQa @ (divide @ idQa_Q__idQ_idQb @ idQ_idQa)) @
% 268.22/39.35 zero)),
% 268.22/39.35 inference('sup+', [status(thm)],
% 268.22/39.35 [zip_derived_cl127701, zip_derived_cl28004])).
% 268.22/39.35 thf(zip_derived_cl19, plain,
% 268.22/39.35 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl127894, plain,
% 268.22/39.35 (((zero)
% 268.22/39.35 = (divide @ idQb_Q__idQ_idQa @ (divide @ idQa_Q__idQ_idQb @ idQ_idQa)))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl127792, zip_derived_cl19])).
% 268.22/39.35 thf(zip_derived_cl30081, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i, X2 : $i]:
% 268.22/39.35 (less_equal @ (divide @ X1 @ X0) @
% 268.22/39.35 (divide @ (divide @ X1 @ (divide @ X0 @ X2)) @ X0))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl30079])).
% 268.22/39.35 thf(zip_derived_cl127951, plain,
% 268.22/39.35 ( (less_equal @ (divide @ idQb_Q__idQ_idQa @ idQa_Q__idQ_idQb) @
% 268.22/39.35 (divide @ zero @ idQa_Q__idQ_idQb))),
% 268.22/39.35 inference('sup+', [status(thm)],
% 268.22/39.35 [zip_derived_cl127894, zip_derived_cl30081])).
% 268.22/39.35 thf(zip_derived_cl63, plain, (![X0 : $i]: ((zero) = (divide @ zero @ X0))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl19])).
% 268.22/39.35 thf(zip_derived_cl128014, plain,
% 268.22/39.35 ( (less_equal @ (divide @ idQb_Q__idQ_idQa @ idQa_Q__idQ_idQb) @ zero)),
% 268.22/39.35 inference('demod', [status(thm)],
% 268.22/39.35 [zip_derived_cl127951, zip_derived_cl63])).
% 268.22/39.35 thf(zip_derived_cl19, plain,
% 268.22/39.35 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 268.22/39.35 thf(zip_derived_cl128034, plain,
% 268.22/39.35 (((zero) = (divide @ idQb_Q__idQ_idQa @ idQa_Q__idQ_idQb))),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl128014, zip_derived_cl19])).
% 268.22/39.35 thf(zip_derived_cl7, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [closure])).
% 268.22/39.35 thf(zip_derived_cl128046, plain,
% 268.22/39.35 ( (quotient @ idQb_Q__idQ_idQa @ idQa_Q__idQ_idQb @ zero)),
% 268.22/39.35 inference('sup+', [status(thm)], [zip_derived_cl128034, zip_derived_cl7])).
% 268.22/39.35 thf(zip_derived_cl1, plain,
% 268.22/39.35 (![X0 : $i, X1 : $i]:
% 268.22/39.35 (~ (quotient @ X0 @ X1 @ zero) | (less_equal @ X0 @ X1))),
% 268.22/39.35 inference('cnf', [status(esa)], [less_equal_quotient])).
% 268.22/39.35 thf(zip_derived_cl128201, plain,
% 268.22/39.35 ( (less_equal @ idQb_Q__idQ_idQa @ idQa_Q__idQ_idQb)),
% 268.22/39.35 inference('sup-', [status(thm)], [zip_derived_cl128046, zip_derived_cl1])).
% 268.22/39.35 thf(zip_derived_cl128217, plain, ($false),
% 268.22/39.35 inference('demod', [status(thm)],
% 268.22/39.35 [zip_derived_cl125463, zip_derived_cl128201])).
% 268.22/39.35
% 268.22/39.35 % SZS output end Refutation
% 268.22/39.35
% 268.22/39.35
% 268.22/39.35 % Terminating...
% 268.48/39.44 % Runner terminated.
% 268.48/39.45 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------