TSTP Solution File: HEN009-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : HEN009-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.LQlO68TWXI true
% Computer : n026.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 01:57:50 EDT 2023
% Result : Unsatisfiable 11.76s 2.31s
% Output : Refutation 11.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : HEN009-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.LQlO68TWXI true
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 13:47:47 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in FO mode
% 0.22/0.68 % Total configuration time : 435
% 0.22/0.68 % Estimated wc time : 1092
% 0.22/0.68 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.70 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.74 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.74 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 11.76/2.31 % Solved by fo/fo13.sh.
% 11.76/2.31 % done 3378 iterations in 1.409s
% 11.76/2.31 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 11.76/2.31 % SZS output start Refutation
% 11.76/2.31 thf(divide_type, type, divide: $i > $i > $i).
% 11.76/2.31 thf(idQ_idQa_type, type, idQ_idQa: $i).
% 11.76/2.31 thf(idQa_type, type, idQa: $i).
% 11.76/2.31 thf(a_type, type, a: $i).
% 11.76/2.31 thf(identity_type, type, identity: $i).
% 11.76/2.31 thf(less_equal_type, type, less_equal: $i > $i > $o).
% 11.76/2.31 thf(idQ__idQ_idQa_type, type, idQ__idQ_idQa: $i).
% 11.76/2.31 thf(quotient_type, type, quotient: $i > $i > $i > $o).
% 11.76/2.31 thf(zero_type, type, zero: $i).
% 11.76/2.31 thf(closure, axiom, (quotient @ X @ Y @ ( divide @ X @ Y ))).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(identity_divide_a, axiom, (quotient @ identity @ a @ idQa)).
% 11.76/2.31 thf(zip_derived_cl9, plain, ( (quotient @ identity @ a @ idQa)),
% 11.76/2.31 inference('cnf', [status(esa)], [identity_divide_a])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(identity_divide_idQ_idQa, axiom,
% 11.76/2.31 (quotient @ identity @ idQ_idQa @ idQ__idQ_idQa)).
% 11.76/2.31 thf(zip_derived_cl11, plain,
% 11.76/2.31 ( (quotient @ identity @ idQ_idQa @ idQ__idQ_idQa)),
% 11.76/2.31 inference('cnf', [status(esa)], [identity_divide_idQ_idQa])).
% 11.76/2.31 thf(quotient_property, axiom,
% 11.76/2.31 (( ~( quotient @ X @ Y @ V1 ) ) | ( ~( quotient @ Y @ Z @ V2 ) ) |
% 11.76/2.31 ( ~( quotient @ X @ Z @ V3 ) ) | ( ~( quotient @ V3 @ V2 @ V4 ) ) |
% 11.76/2.31 ( ~( quotient @ V1 @ Z @ V5 ) ) | ( less_equal @ V4 @ V5 ))).
% 11.76/2.31 thf(zip_derived_cl3, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 11.76/2.31 (~ (quotient @ X0 @ X1 @ X2)
% 11.76/2.31 | ~ (quotient @ X1 @ X3 @ X4)
% 11.76/2.31 | ~ (quotient @ X0 @ X3 @ X5)
% 11.76/2.31 | ~ (quotient @ X5 @ X4 @ X6)
% 11.76/2.31 | ~ (quotient @ X2 @ X3 @ X7)
% 11.76/2.31 | (less_equal @ X6 @ X7))),
% 11.76/2.31 inference('cnf', [status(esa)], [quotient_property])).
% 11.76/2.31 thf(zip_derived_cl33, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 11.76/2.31 (~ (quotient @ idQ_idQa @ X1 @ X0)
% 11.76/2.31 | ~ (quotient @ identity @ X1 @ X2)
% 11.76/2.31 | ~ (quotient @ X2 @ X0 @ X3)
% 11.76/2.31 | ~ (quotient @ idQ__idQ_idQa @ X1 @ X4)
% 11.76/2.31 | (less_equal @ X3 @ X4))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl3])).
% 11.76/2.31 thf(zip_derived_cl144, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 11.76/2.31 (~ (quotient @ identity @ X0 @ X1)
% 11.76/2.31 | ~ (quotient @ X1 @ (divide @ idQ_idQa @ X0) @ X2)
% 11.76/2.31 | ~ (quotient @ idQ__idQ_idQa @ X0 @ X3)
% 11.76/2.31 | (less_equal @ X2 @ X3))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl33])).
% 11.76/2.31 thf(zip_derived_cl567, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]:
% 11.76/2.31 (~ (quotient @ idQa @ (divide @ idQ_idQa @ a) @ X0)
% 11.76/2.31 | ~ (quotient @ idQ__idQ_idQa @ a @ X1)
% 11.76/2.31 | (less_equal @ X0 @ X1))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl144])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(zero_is_smallest, axiom, (less_equal @ zero @ X)).
% 11.76/2.31 thf(zip_derived_cl4, plain, (![X0 : $i]: (less_equal @ zero @ X0)),
% 11.76/2.31 inference('cnf', [status(esa)], [zero_is_smallest])).
% 11.76/2.31 thf(quotient_less_equal, axiom,
% 11.76/2.31 (( ~( less_equal @ X @ Y ) ) | ( quotient @ X @ Y @ zero ))).
% 11.76/2.31 thf(zip_derived_cl0, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]:
% 11.76/2.31 (~ (less_equal @ X0 @ X1) | (quotient @ X0 @ X1 @ zero))),
% 11.76/2.31 inference('cnf', [status(esa)], [quotient_less_equal])).
% 11.76/2.31 thf(zip_derived_cl14, plain, (![X0 : $i]: (quotient @ zero @ X0 @ zero)),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(divisor_existence, axiom,
% 11.76/2.31 (( ~( quotient @ X @ Y @ Z ) ) | ( less_equal @ Z @ X ))).
% 11.76/2.31 thf(zip_derived_cl2, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.76/2.31 (~ (quotient @ X0 @ X1 @ X2) | (less_equal @ X2 @ X0))),
% 11.76/2.31 inference('cnf', [status(esa)], [divisor_existence])).
% 11.76/2.31 thf(zip_derived_cl20, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (less_equal @ (divide @ X1 @ X0) @ X1)),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 11.76/2.31 thf(zip_derived_cl0, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]:
% 11.76/2.31 (~ (less_equal @ X0 @ X1) | (quotient @ X0 @ X1 @ zero))),
% 11.76/2.31 inference('cnf', [status(esa)], [quotient_less_equal])).
% 11.76/2.31 thf(zip_derived_cl41, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ (divide @ X0 @ X1) @ X0 @ zero)),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl0])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(zip_derived_cl3, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 11.76/2.31 (~ (quotient @ X0 @ X1 @ X2)
% 11.76/2.31 | ~ (quotient @ X1 @ X3 @ X4)
% 11.76/2.31 | ~ (quotient @ X0 @ X3 @ X5)
% 11.76/2.31 | ~ (quotient @ X5 @ X4 @ X6)
% 11.76/2.31 | ~ (quotient @ X2 @ X3 @ X7)
% 11.76/2.31 | (less_equal @ X6 @ X7))),
% 11.76/2.31 inference('cnf', [status(esa)], [quotient_property])).
% 11.76/2.31 thf(zip_derived_cl29, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 11.76/2.31 (~ (quotient @ X0 @ X3 @ X2)
% 11.76/2.31 | ~ (quotient @ X1 @ X3 @ X4)
% 11.76/2.31 | ~ (quotient @ X4 @ X2 @ X5)
% 11.76/2.31 | ~ (quotient @ (divide @ X1 @ X0) @ X3 @ X6)
% 11.76/2.31 | (less_equal @ X5 @ X6))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl3])).
% 11.76/2.31 thf(zip_derived_cl88, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 11.76/2.31 (~ (quotient @ X1 @ X0 @ X2)
% 11.76/2.31 | ~ (quotient @ X0 @ X0 @ X3)
% 11.76/2.31 | ~ (quotient @ X3 @ X2 @ X4)
% 11.76/2.31 | (less_equal @ X4 @ zero))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl29])).
% 11.76/2.31 thf(zip_derived_cl268, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.76/2.31 (~ (quotient @ X0 @ X0 @ X1)
% 11.76/2.31 | ~ (quotient @ X1 @ zero @ X2)
% 11.76/2.31 | (less_equal @ X2 @ zero))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl88])).
% 11.76/2.31 thf(zip_derived_cl275, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]:
% 11.76/2.31 (~ (quotient @ X1 @ X1 @ X0)
% 11.76/2.31 | (less_equal @ (divide @ X0 @ zero) @ zero))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl268])).
% 11.76/2.31 thf(zip_derived_cl437, plain,
% 11.76/2.31 (![X0 : $i]: (less_equal @ (divide @ (divide @ X0 @ X0) @ zero) @ zero)),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl275])).
% 11.76/2.31 thf(zip_derived_cl4, plain, (![X0 : $i]: (less_equal @ zero @ X0)),
% 11.76/2.31 inference('cnf', [status(esa)], [zero_is_smallest])).
% 11.76/2.31 thf(less_equal_and_equal, axiom,
% 11.76/2.31 (( ~( less_equal @ X @ Y ) ) | ( ~( less_equal @ Y @ X ) ) |
% 11.76/2.31 ( ( X ) = ( Y ) ))).
% 11.76/2.31 thf(zip_derived_cl5, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]:
% 11.76/2.31 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 11.76/2.31 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 11.76/2.31 thf(zip_derived_cl16, plain,
% 11.76/2.31 (![X0 : $i]: (~ (less_equal @ X0 @ zero) | ((zero) = (X0)))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 11.76/2.31 thf(zip_derived_cl460, plain,
% 11.76/2.31 (![X0 : $i]: ((zero) = (divide @ (divide @ X0 @ X0) @ zero))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl437, zip_derived_cl16])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(zip_derived_cl472, plain,
% 11.76/2.31 (![X0 : $i]: (quotient @ (divide @ X0 @ X0) @ zero @ zero)),
% 11.76/2.31 inference('s_sup+', [status(thm)], [zip_derived_cl460, zip_derived_cl7])).
% 11.76/2.31 thf(less_equal_quotient, axiom,
% 11.76/2.31 (( ~( quotient @ X @ Y @ zero ) ) | ( less_equal @ X @ Y ))).
% 11.76/2.31 thf(zip_derived_cl1, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]:
% 11.76/2.31 (~ (quotient @ X0 @ X1 @ zero) | (less_equal @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [less_equal_quotient])).
% 11.76/2.31 thf(zip_derived_cl512, plain,
% 11.76/2.31 (![X0 : $i]: (less_equal @ (divide @ X0 @ X0) @ zero)),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl472, zip_derived_cl1])).
% 11.76/2.31 thf(zip_derived_cl16, plain,
% 11.76/2.31 (![X0 : $i]: (~ (less_equal @ X0 @ zero) | ((zero) = (X0)))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 11.76/2.31 thf(zip_derived_cl527, plain, (![X0 : $i]: ((zero) = (divide @ X0 @ X0))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl512, zip_derived_cl16])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(zip_derived_cl537, plain, (![X0 : $i]: (quotient @ X0 @ X0 @ zero)),
% 11.76/2.31 inference('s_sup+', [status(thm)], [zip_derived_cl527, zip_derived_cl7])).
% 11.76/2.31 thf(identity_divide_idQa, axiom, (quotient @ identity @ idQa @ idQ_idQa)).
% 11.76/2.31 thf(zip_derived_cl10, plain, ( (quotient @ identity @ idQa @ idQ_idQa)),
% 11.76/2.31 inference('cnf', [status(esa)], [identity_divide_idQa])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(zip_derived_cl9, plain, ( (quotient @ identity @ a @ idQa)),
% 11.76/2.31 inference('cnf', [status(esa)], [identity_divide_a])).
% 11.76/2.31 thf(zip_derived_cl3, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 11.76/2.31 (~ (quotient @ X0 @ X1 @ X2)
% 11.76/2.31 | ~ (quotient @ X1 @ X3 @ X4)
% 11.76/2.31 | ~ (quotient @ X0 @ X3 @ X5)
% 11.76/2.31 | ~ (quotient @ X5 @ X4 @ X6)
% 11.76/2.31 | ~ (quotient @ X2 @ X3 @ X7)
% 11.76/2.31 | (less_equal @ X6 @ X7))),
% 11.76/2.31 inference('cnf', [status(esa)], [quotient_property])).
% 11.76/2.31 thf(zip_derived_cl31, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 11.76/2.31 (~ (quotient @ a @ X1 @ X0)
% 11.76/2.31 | ~ (quotient @ identity @ X1 @ X2)
% 11.76/2.31 | ~ (quotient @ X2 @ X0 @ X3)
% 11.76/2.31 | ~ (quotient @ idQa @ X1 @ X4)
% 11.76/2.31 | (less_equal @ X3 @ X4))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl3])).
% 11.76/2.31 thf(zip_derived_cl120, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 11.76/2.31 (~ (quotient @ identity @ X0 @ X1)
% 11.76/2.31 | ~ (quotient @ X1 @ (divide @ a @ X0) @ X2)
% 11.76/2.31 | ~ (quotient @ idQa @ X0 @ X3)
% 11.76/2.31 | (less_equal @ X2 @ X3))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl31])).
% 11.76/2.31 thf(zip_derived_cl434, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]:
% 11.76/2.31 (~ (quotient @ idQ_idQa @ (divide @ a @ idQa) @ X0)
% 11.76/2.31 | ~ (quotient @ idQa @ idQa @ X1)
% 11.76/2.31 | (less_equal @ X0 @ X1))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl120])).
% 11.76/2.31 thf(zip_derived_cl746, plain,
% 11.76/2.31 (![X0 : $i]:
% 11.76/2.31 (~ (quotient @ idQ_idQa @ (divide @ a @ idQa) @ X0)
% 11.76/2.31 | (less_equal @ X0 @ zero))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl537, zip_derived_cl434])).
% 11.76/2.31 thf(zip_derived_cl749, plain,
% 11.76/2.31 ( (less_equal @ (divide @ idQ_idQa @ (divide @ a @ idQa)) @ zero)),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl746])).
% 11.76/2.31 thf(zip_derived_cl16, plain,
% 11.76/2.31 (![X0 : $i]: (~ (less_equal @ X0 @ zero) | ((zero) = (X0)))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 11.76/2.31 thf(zip_derived_cl803, plain,
% 11.76/2.31 (((zero) = (divide @ idQ_idQa @ (divide @ a @ idQa)))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl749, zip_derived_cl16])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(zip_derived_cl806, plain,
% 11.76/2.31 ( (quotient @ idQ_idQa @ (divide @ a @ idQa) @ zero)),
% 11.76/2.31 inference('s_sup+', [status(thm)], [zip_derived_cl803, zip_derived_cl7])).
% 11.76/2.31 thf(zip_derived_cl1, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]:
% 11.76/2.31 (~ (quotient @ X0 @ X1 @ zero) | (less_equal @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [less_equal_quotient])).
% 11.76/2.31 thf(zip_derived_cl844, plain,
% 11.76/2.31 ( (less_equal @ idQ_idQa @ (divide @ a @ idQa))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl806, zip_derived_cl1])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(zip_derived_cl14, plain, (![X0 : $i]: (quotient @ zero @ X0 @ zero)),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(zip_derived_cl10, plain, ( (quotient @ identity @ idQa @ idQ_idQa)),
% 11.76/2.31 inference('cnf', [status(esa)], [identity_divide_idQa])).
% 11.76/2.31 thf(identity_is_largest, axiom, (less_equal @ X @ identity)).
% 11.76/2.31 thf(zip_derived_cl6, plain, (![X0 : $i]: (less_equal @ X0 @ identity)),
% 11.76/2.31 inference('cnf', [status(esa)], [identity_is_largest])).
% 11.76/2.31 thf(zip_derived_cl0, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]:
% 11.76/2.31 (~ (less_equal @ X0 @ X1) | (quotient @ X0 @ X1 @ zero))),
% 11.76/2.31 inference('cnf', [status(esa)], [quotient_less_equal])).
% 11.76/2.31 thf(zip_derived_cl13, plain,
% 11.76/2.31 (![X0 : $i]: (quotient @ X0 @ identity @ zero)),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl0])).
% 11.76/2.31 thf(zip_derived_cl3, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 11.76/2.31 (~ (quotient @ X0 @ X1 @ X2)
% 11.76/2.31 | ~ (quotient @ X1 @ X3 @ X4)
% 11.76/2.31 | ~ (quotient @ X0 @ X3 @ X5)
% 11.76/2.31 | ~ (quotient @ X5 @ X4 @ X6)
% 11.76/2.31 | ~ (quotient @ X2 @ X3 @ X7)
% 11.76/2.31 | (less_equal @ X6 @ X7))),
% 11.76/2.31 inference('cnf', [status(esa)], [quotient_property])).
% 11.76/2.31 thf(zip_derived_cl30, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 11.76/2.31 (~ (quotient @ identity @ X2 @ X1)
% 11.76/2.31 | ~ (quotient @ X0 @ X2 @ X3)
% 11.76/2.31 | ~ (quotient @ X3 @ X1 @ X4)
% 11.76/2.31 | ~ (quotient @ zero @ X2 @ X5)
% 11.76/2.31 | (less_equal @ X4 @ X5))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl3])).
% 11.76/2.31 thf(zip_derived_cl109, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 11.76/2.31 (~ (quotient @ X1 @ idQa @ X0)
% 11.76/2.31 | ~ (quotient @ X0 @ idQ_idQa @ X2)
% 11.76/2.31 | ~ (quotient @ zero @ idQa @ X3)
% 11.76/2.31 | (less_equal @ X2 @ X3))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl30])).
% 11.76/2.31 thf(zip_derived_cl136, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.76/2.31 (~ (quotient @ (divide @ X0 @ idQa) @ idQ_idQa @ X1)
% 11.76/2.31 | ~ (quotient @ zero @ idQa @ X2)
% 11.76/2.31 | (less_equal @ X1 @ X2))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl109])).
% 11.76/2.31 thf(zip_derived_cl148, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]:
% 11.76/2.31 (~ (quotient @ (divide @ X1 @ idQa) @ idQ_idQa @ X0)
% 11.76/2.31 | (less_equal @ X0 @ zero))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl136])).
% 11.76/2.31 thf(zip_derived_cl150, plain,
% 11.76/2.31 (![X0 : $i]:
% 11.76/2.31 (less_equal @ (divide @ (divide @ X0 @ idQa) @ idQ_idQa) @ zero)),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl148])).
% 11.76/2.31 thf(zip_derived_cl16, plain,
% 11.76/2.31 (![X0 : $i]: (~ (less_equal @ X0 @ zero) | ((zero) = (X0)))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 11.76/2.31 thf(zip_derived_cl157, plain,
% 11.76/2.31 (![X0 : $i]: ((zero) = (divide @ (divide @ X0 @ idQa) @ idQ_idQa))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl150, zip_derived_cl16])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(zip_derived_cl166, plain,
% 11.76/2.31 (![X0 : $i]: (quotient @ (divide @ X0 @ idQa) @ idQ_idQa @ zero)),
% 11.76/2.31 inference('s_sup+', [status(thm)], [zip_derived_cl157, zip_derived_cl7])).
% 11.76/2.31 thf(zip_derived_cl1, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]:
% 11.76/2.31 (~ (quotient @ X0 @ X1 @ zero) | (less_equal @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [less_equal_quotient])).
% 11.76/2.31 thf(zip_derived_cl240, plain,
% 11.76/2.31 (![X0 : $i]: (less_equal @ (divide @ X0 @ idQa) @ idQ_idQa)),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl166, zip_derived_cl1])).
% 11.76/2.31 thf(zip_derived_cl5, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]:
% 11.76/2.31 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 11.76/2.31 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 11.76/2.31 thf(zip_derived_cl248, plain,
% 11.76/2.31 (![X0 : $i]:
% 11.76/2.31 (~ (less_equal @ idQ_idQa @ (divide @ X0 @ idQa))
% 11.76/2.31 | ((divide @ X0 @ idQa) = (idQ_idQa)))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl240, zip_derived_cl5])).
% 11.76/2.31 thf(zip_derived_cl887, plain, (((divide @ a @ idQa) = (idQ_idQa))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl844, zip_derived_cl248])).
% 11.76/2.31 thf(zip_derived_cl41, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ (divide @ X0 @ X1) @ X0 @ zero)),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl0])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(well_defined, axiom,
% 11.76/2.31 (( ~( quotient @ X @ Y @ Z ) ) | ( ~( quotient @ X @ Y @ W ) ) |
% 11.76/2.31 ( ( Z ) = ( W ) ))).
% 11.76/2.31 thf(zip_derived_cl8, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 11.76/2.31 (~ (quotient @ X0 @ X1 @ X2)
% 11.76/2.31 | ~ (quotient @ X0 @ X1 @ X3)
% 11.76/2.31 | ((X2) = (X3)))),
% 11.76/2.31 inference('cnf', [status(esa)], [well_defined])).
% 11.76/2.31 thf(zip_derived_cl24, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.76/2.31 (~ (quotient @ X1 @ X0 @ X2) | ((divide @ X1 @ X0) = (X2)))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl8])).
% 11.76/2.31 thf(zip_derived_cl78, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: ((divide @ (divide @ X0 @ X1) @ X0) = (zero))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl24])).
% 11.76/2.31 thf(zip_derived_cl900, plain, (((divide @ idQ_idQa @ a) = (zero))),
% 11.76/2.31 inference('s_sup+', [status(thm)], [zip_derived_cl887, zip_derived_cl78])).
% 11.76/2.31 thf(zip_derived_cl1453, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]:
% 11.76/2.31 (~ (quotient @ idQa @ zero @ X0)
% 11.76/2.31 | ~ (quotient @ idQ__idQ_idQa @ a @ X1)
% 11.76/2.31 | (less_equal @ X0 @ X1))),
% 11.76/2.31 inference('demod', [status(thm)], [zip_derived_cl567, zip_derived_cl900])).
% 11.76/2.31 thf(zip_derived_cl1454, plain,
% 11.76/2.31 (![X0 : $i]:
% 11.76/2.31 (~ (quotient @ idQ__idQ_idQa @ a @ X0)
% 11.76/2.31 | (less_equal @ (divide @ idQa @ zero) @ X0))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl1453])).
% 11.76/2.31 thf(zip_derived_cl1455, plain,
% 11.76/2.31 ( (less_equal @ (divide @ idQa @ zero) @ (divide @ idQ__idQ_idQa @ a))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl1454])).
% 11.76/2.31 thf(zip_derived_cl5, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]:
% 11.76/2.31 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 11.76/2.31 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 11.76/2.31 thf(zip_derived_cl1457, plain,
% 11.76/2.31 ((~ (less_equal @ (divide @ idQ__idQ_idQa @ a) @ (divide @ idQa @ zero))
% 11.76/2.31 | ((divide @ idQa @ zero) = (divide @ idQ__idQ_idQa @ a)))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl1455, zip_derived_cl5])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(zip_derived_cl527, plain, (![X0 : $i]: ((zero) = (divide @ X0 @ X0))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl512, zip_derived_cl16])).
% 11.76/2.31 thf(zip_derived_cl14, plain, (![X0 : $i]: (quotient @ zero @ X0 @ zero)),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(zip_derived_cl29, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 11.76/2.31 (~ (quotient @ X0 @ X3 @ X2)
% 11.76/2.31 | ~ (quotient @ X1 @ X3 @ X4)
% 11.76/2.31 | ~ (quotient @ X4 @ X2 @ X5)
% 11.76/2.31 | ~ (quotient @ (divide @ X1 @ X0) @ X3 @ X6)
% 11.76/2.31 | (less_equal @ X5 @ X6))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl3])).
% 11.76/2.31 thf(zip_derived_cl86, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 11.76/2.31 (~ (quotient @ X1 @ X0 @ X3)
% 11.76/2.31 | ~ (quotient @ X2 @ X0 @ X4)
% 11.76/2.31 | ~ (quotient @ X4 @ X3 @ X5)
% 11.76/2.31 | (less_equal @ X5 @ (divide @ (divide @ X2 @ X1) @ X0)))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl29])).
% 11.76/2.31 thf(zip_derived_cl209, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 11.76/2.31 (~ (quotient @ X2 @ X0 @ X1)
% 11.76/2.31 | ~ (quotient @ X1 @ zero @ X3)
% 11.76/2.31 | (less_equal @ X3 @ (divide @ (divide @ X2 @ zero) @ X0)))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl86])).
% 11.76/2.31 thf(zip_derived_cl825, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.76/2.31 (~ (quotient @ X0 @ (divide @ X0 @ zero) @ X2)
% 11.76/2.31 | ~ (quotient @ X2 @ zero @ X1)
% 11.76/2.31 | (less_equal @ X1 @ zero))),
% 11.76/2.31 inference('s_sup+', [status(thm)], [zip_derived_cl527, zip_derived_cl209])).
% 11.76/2.31 thf(zip_derived_cl1512, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]:
% 11.76/2.31 (~ (quotient @ X1 @ (divide @ X1 @ zero) @ X0)
% 11.76/2.31 | (less_equal @ (divide @ X0 @ zero) @ zero))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl825])).
% 11.76/2.31 thf(zip_derived_cl7918, plain,
% 11.76/2.31 (![X0 : $i]:
% 11.76/2.31 (less_equal @
% 11.76/2.31 (divide @ (divide @ X0 @ (divide @ X0 @ zero)) @ zero) @ zero)),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl1512])).
% 11.76/2.31 thf(zip_derived_cl16, plain,
% 11.76/2.31 (![X0 : $i]: (~ (less_equal @ X0 @ zero) | ((zero) = (X0)))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 11.76/2.31 thf(zip_derived_cl8246, plain,
% 11.76/2.31 (![X0 : $i]:
% 11.76/2.31 ((zero) = (divide @ (divide @ X0 @ (divide @ X0 @ zero)) @ zero))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7918, zip_derived_cl16])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(zip_derived_cl8258, plain,
% 11.76/2.31 (![X0 : $i]:
% 11.76/2.31 (quotient @ (divide @ X0 @ (divide @ X0 @ zero)) @ zero @ zero)),
% 11.76/2.31 inference('s_sup+', [status(thm)], [zip_derived_cl8246, zip_derived_cl7])).
% 11.76/2.31 thf(zip_derived_cl1, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]:
% 11.76/2.31 (~ (quotient @ X0 @ X1 @ zero) | (less_equal @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [less_equal_quotient])).
% 11.76/2.31 thf(zip_derived_cl8378, plain,
% 11.76/2.31 (![X0 : $i]: (less_equal @ (divide @ X0 @ (divide @ X0 @ zero)) @ zero)),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl8258, zip_derived_cl1])).
% 11.76/2.31 thf(zip_derived_cl16, plain,
% 11.76/2.31 (![X0 : $i]: (~ (less_equal @ X0 @ zero) | ((zero) = (X0)))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 11.76/2.31 thf(zip_derived_cl8451, plain,
% 11.76/2.31 (![X0 : $i]: ((zero) = (divide @ X0 @ (divide @ X0 @ zero)))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl8378, zip_derived_cl16])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(zip_derived_cl8466, plain,
% 11.76/2.31 (![X0 : $i]: (quotient @ X0 @ (divide @ X0 @ zero) @ zero)),
% 11.76/2.31 inference('s_sup+', [status(thm)], [zip_derived_cl8451, zip_derived_cl7])).
% 11.76/2.31 thf(zip_derived_cl1, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]:
% 11.76/2.31 (~ (quotient @ X0 @ X1 @ zero) | (less_equal @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [less_equal_quotient])).
% 11.76/2.31 thf(zip_derived_cl9016, plain,
% 11.76/2.31 (![X0 : $i]: (less_equal @ X0 @ (divide @ X0 @ zero))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl8466, zip_derived_cl1])).
% 11.76/2.31 thf(zip_derived_cl20, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (less_equal @ (divide @ X1 @ X0) @ X1)),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 11.76/2.31 thf(zip_derived_cl5, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]:
% 11.76/2.31 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 11.76/2.31 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 11.76/2.31 thf(zip_derived_cl42, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]:
% 11.76/2.31 (~ (less_equal @ X0 @ (divide @ X0 @ X1))
% 11.76/2.31 | ((divide @ X0 @ X1) = (X0)))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl5])).
% 11.76/2.31 thf(zip_derived_cl9132, plain, (![X0 : $i]: ((divide @ X0 @ zero) = (X0))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl9016, zip_derived_cl42])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(zip_derived_cl537, plain, (![X0 : $i]: (quotient @ X0 @ X0 @ zero)),
% 11.76/2.31 inference('s_sup+', [status(thm)], [zip_derived_cl527, zip_derived_cl7])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(zip_derived_cl10, plain, ( (quotient @ identity @ idQa @ idQ_idQa)),
% 11.76/2.31 inference('cnf', [status(esa)], [identity_divide_idQa])).
% 11.76/2.31 thf(zip_derived_cl3, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 11.76/2.31 (~ (quotient @ X0 @ X1 @ X2)
% 11.76/2.31 | ~ (quotient @ X1 @ X3 @ X4)
% 11.76/2.31 | ~ (quotient @ X0 @ X3 @ X5)
% 11.76/2.31 | ~ (quotient @ X5 @ X4 @ X6)
% 11.76/2.31 | ~ (quotient @ X2 @ X3 @ X7)
% 11.76/2.31 | (less_equal @ X6 @ X7))),
% 11.76/2.31 inference('cnf', [status(esa)], [quotient_property])).
% 11.76/2.31 thf(zip_derived_cl32, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 11.76/2.31 (~ (quotient @ idQa @ X1 @ X0)
% 11.76/2.31 | ~ (quotient @ identity @ X1 @ X2)
% 11.76/2.31 | ~ (quotient @ X2 @ X0 @ X3)
% 11.76/2.31 | ~ (quotient @ idQ_idQa @ X1 @ X4)
% 11.76/2.31 | (less_equal @ X3 @ X4))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl3])).
% 11.76/2.31 thf(zip_derived_cl134, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 11.76/2.31 (~ (quotient @ identity @ X0 @ X1)
% 11.76/2.31 | ~ (quotient @ X1 @ (divide @ idQa @ X0) @ X2)
% 11.76/2.31 | ~ (quotient @ idQ_idQa @ X0 @ X3)
% 11.76/2.31 | (less_equal @ X2 @ X3))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl32])).
% 11.76/2.31 thf(zip_derived_cl499, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.76/2.31 (~ (quotient @ (divide @ identity @ X0) @ (divide @ idQa @ X0) @ X1)
% 11.76/2.31 | ~ (quotient @ idQ_idQa @ X0 @ X2)
% 11.76/2.31 | (less_equal @ X1 @ X2))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl134])).
% 11.76/2.31 thf(zip_derived_cl1501, plain,
% 11.76/2.31 (![X0 : $i]:
% 11.76/2.31 (~ (quotient @ (divide @ identity @ idQ_idQa) @
% 11.76/2.31 (divide @ idQa @ idQ_idQa) @ X0)
% 11.76/2.31 | (less_equal @ X0 @ zero))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl537, zip_derived_cl499])).
% 11.76/2.31 thf(zip_derived_cl11, plain,
% 11.76/2.31 ( (quotient @ identity @ idQ_idQa @ idQ__idQ_idQa)),
% 11.76/2.31 inference('cnf', [status(esa)], [identity_divide_idQ_idQa])).
% 11.76/2.31 thf(zip_derived_cl24, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.76/2.31 (~ (quotient @ X1 @ X0 @ X2) | ((divide @ X1 @ X0) = (X2)))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl8])).
% 11.76/2.31 thf(zip_derived_cl57, plain,
% 11.76/2.31 (((divide @ identity @ idQ_idQa) = (idQ__idQ_idQa))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl24])).
% 11.76/2.31 thf(zip_derived_cl1506, plain,
% 11.76/2.31 (![X0 : $i]:
% 11.76/2.31 (~ (quotient @ idQ__idQ_idQa @ (divide @ idQa @ idQ_idQa) @ X0)
% 11.76/2.31 | (less_equal @ X0 @ zero))),
% 11.76/2.31 inference('demod', [status(thm)], [zip_derived_cl1501, zip_derived_cl57])).
% 11.76/2.31 thf(zip_derived_cl1509, plain,
% 11.76/2.31 ( (less_equal @ (divide @ idQ__idQ_idQa @ (divide @ idQa @ idQ_idQa)) @
% 11.76/2.31 zero)),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl1506])).
% 11.76/2.31 thf(zip_derived_cl16, plain,
% 11.76/2.31 (![X0 : $i]: (~ (less_equal @ X0 @ zero) | ((zero) = (X0)))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 11.76/2.31 thf(zip_derived_cl1520, plain,
% 11.76/2.31 (((zero) = (divide @ idQ__idQ_idQa @ (divide @ idQa @ idQ_idQa)))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl1509, zip_derived_cl16])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(zip_derived_cl1523, plain,
% 11.76/2.31 ( (quotient @ idQ__idQ_idQa @ (divide @ idQa @ idQ_idQa) @ zero)),
% 11.76/2.31 inference('s_sup+', [status(thm)], [zip_derived_cl1520, zip_derived_cl7])).
% 11.76/2.31 thf(zip_derived_cl1, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]:
% 11.76/2.31 (~ (quotient @ X0 @ X1 @ zero) | (less_equal @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [less_equal_quotient])).
% 11.76/2.31 thf(zip_derived_cl1555, plain,
% 11.76/2.31 ( (less_equal @ idQ__idQ_idQa @ (divide @ idQa @ idQ_idQa))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl1523, zip_derived_cl1])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(zip_derived_cl11, plain,
% 11.76/2.31 ( (quotient @ identity @ idQ_idQa @ idQ__idQ_idQa)),
% 11.76/2.31 inference('cnf', [status(esa)], [identity_divide_idQ_idQa])).
% 11.76/2.31 thf(zip_derived_cl86, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 11.76/2.31 (~ (quotient @ X1 @ X0 @ X3)
% 11.76/2.31 | ~ (quotient @ X2 @ X0 @ X4)
% 11.76/2.31 | ~ (quotient @ X4 @ X3 @ X5)
% 11.76/2.31 | (less_equal @ X5 @ (divide @ (divide @ X2 @ X1) @ X0)))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl29])).
% 11.76/2.31 thf(zip_derived_cl212, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.76/2.31 (~ (quotient @ X1 @ idQ_idQa @ X0)
% 11.76/2.31 | ~ (quotient @ X0 @ idQ__idQ_idQa @ X2)
% 11.76/2.31 | (less_equal @ X2 @ (divide @ (divide @ X1 @ identity) @ idQ_idQa)))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl86])).
% 11.76/2.31 thf(zip_derived_cl13, plain,
% 11.76/2.31 (![X0 : $i]: (quotient @ X0 @ identity @ zero)),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl0])).
% 11.76/2.31 thf(zip_derived_cl24, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.76/2.31 (~ (quotient @ X1 @ X0 @ X2) | ((divide @ X1 @ X0) = (X2)))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl8])).
% 11.76/2.31 thf(zip_derived_cl53, plain,
% 11.76/2.31 (![X0 : $i]: ((divide @ X0 @ identity) = (zero))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl24])).
% 11.76/2.31 thf(zip_derived_cl20, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (less_equal @ (divide @ X1 @ X0) @ X1)),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 11.76/2.31 thf(zip_derived_cl16, plain,
% 11.76/2.31 (![X0 : $i]: (~ (less_equal @ X0 @ zero) | ((zero) = (X0)))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 11.76/2.31 thf(zip_derived_cl43, plain, (![X0 : $i]: ((zero) = (divide @ zero @ X0))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl16])).
% 11.76/2.31 thf(zip_derived_cl229, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.76/2.31 (~ (quotient @ X1 @ idQ_idQa @ X0)
% 11.76/2.31 | ~ (quotient @ X0 @ idQ__idQ_idQa @ X2)
% 11.76/2.31 | (less_equal @ X2 @ zero))),
% 11.76/2.31 inference('demod', [status(thm)],
% 11.76/2.31 [zip_derived_cl212, zip_derived_cl53, zip_derived_cl43])).
% 11.76/2.31 thf(zip_derived_cl1000, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]:
% 11.76/2.31 (~ (quotient @ (divide @ X0 @ idQ_idQa) @ idQ__idQ_idQa @ X1)
% 11.76/2.31 | (less_equal @ X1 @ zero))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl229])).
% 11.76/2.31 thf(zip_derived_cl1025, plain,
% 11.76/2.31 (![X0 : $i]:
% 11.76/2.31 (less_equal @ (divide @ (divide @ X0 @ idQ_idQa) @ idQ__idQ_idQa) @
% 11.76/2.31 zero)),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl1000])).
% 11.76/2.31 thf(zip_derived_cl16, plain,
% 11.76/2.31 (![X0 : $i]: (~ (less_equal @ X0 @ zero) | ((zero) = (X0)))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 11.76/2.31 thf(zip_derived_cl1045, plain,
% 11.76/2.31 (![X0 : $i]:
% 11.76/2.31 ((zero) = (divide @ (divide @ X0 @ idQ_idQa) @ idQ__idQ_idQa))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl1025, zip_derived_cl16])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(zip_derived_cl1061, plain,
% 11.76/2.31 (![X0 : $i]:
% 11.76/2.31 (quotient @ (divide @ X0 @ idQ_idQa) @ idQ__idQ_idQa @ zero)),
% 11.76/2.31 inference('s_sup+', [status(thm)], [zip_derived_cl1045, zip_derived_cl7])).
% 11.76/2.31 thf(zip_derived_cl1, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]:
% 11.76/2.31 (~ (quotient @ X0 @ X1 @ zero) | (less_equal @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [less_equal_quotient])).
% 11.76/2.31 thf(zip_derived_cl1101, plain,
% 11.76/2.31 (![X0 : $i]: (less_equal @ (divide @ X0 @ idQ_idQa) @ idQ__idQ_idQa)),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl1061, zip_derived_cl1])).
% 11.76/2.31 thf(zip_derived_cl5, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]:
% 11.76/2.31 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 11.76/2.31 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 11.76/2.31 thf(zip_derived_cl1117, plain,
% 11.76/2.31 (![X0 : $i]:
% 11.76/2.31 (~ (less_equal @ idQ__idQ_idQa @ (divide @ X0 @ idQ_idQa))
% 11.76/2.31 | ((divide @ X0 @ idQ_idQa) = (idQ__idQ_idQa)))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl1101, zip_derived_cl5])).
% 11.76/2.31 thf(zip_derived_cl1570, plain,
% 11.76/2.31 (((divide @ idQa @ idQ_idQa) = (idQ__idQ_idQa))),
% 11.76/2.31 inference('s_sup-', [status(thm)],
% 11.76/2.31 [zip_derived_cl1555, zip_derived_cl1117])).
% 11.76/2.31 thf(zip_derived_cl78, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: ((divide @ (divide @ X0 @ X1) @ X0) = (zero))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl24])).
% 11.76/2.31 thf(zip_derived_cl1588, plain, (((divide @ idQ__idQ_idQa @ idQa) = (zero))),
% 11.76/2.31 inference('s_sup+', [status(thm)], [zip_derived_cl1570, zip_derived_cl78])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(zip_derived_cl78, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: ((divide @ (divide @ X0 @ X1) @ X0) = (zero))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl24])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(zip_derived_cl86, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 11.76/2.31 (~ (quotient @ X1 @ X0 @ X3)
% 11.76/2.31 | ~ (quotient @ X2 @ X0 @ X4)
% 11.76/2.31 | ~ (quotient @ X4 @ X3 @ X5)
% 11.76/2.31 | (less_equal @ X5 @ (divide @ (divide @ X2 @ X1) @ X0)))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl29])).
% 11.76/2.31 thf(zip_derived_cl207, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 11.76/2.31 (~ (quotient @ X3 @ X0 @ X2)
% 11.76/2.31 | ~ (quotient @ X2 @ (divide @ X1 @ X0) @ X4)
% 11.76/2.31 | (less_equal @ X4 @ (divide @ (divide @ X3 @ X1) @ X0)))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl86])).
% 11.76/2.31 thf(zip_derived_cl780, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 11.76/2.31 (~ (quotient @ (divide @ X1 @ X2) @ X0 @ X4)
% 11.76/2.31 | ~ (quotient @ X4 @ (divide @ X1 @ X0) @ X3)
% 11.76/2.31 | (less_equal @ X3 @ (divide @ zero @ X0)))),
% 11.76/2.31 inference('s_sup+', [status(thm)], [zip_derived_cl78, zip_derived_cl207])).
% 11.76/2.31 thf(zip_derived_cl43, plain, (![X0 : $i]: ((zero) = (divide @ zero @ X0))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl16])).
% 11.76/2.31 thf(zip_derived_cl796, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 11.76/2.31 (~ (quotient @ (divide @ X1 @ X2) @ X0 @ X4)
% 11.76/2.31 | ~ (quotient @ X4 @ (divide @ X1 @ X0) @ X3)
% 11.76/2.31 | (less_equal @ X3 @ zero))),
% 11.76/2.31 inference('demod', [status(thm)], [zip_derived_cl780, zip_derived_cl43])).
% 11.76/2.31 thf(zip_derived_cl3222, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 11.76/2.31 (~ (quotient @ (divide @ (divide @ X2 @ X1) @ X0) @
% 11.76/2.31 (divide @ X2 @ X0) @ X3)
% 11.76/2.31 | (less_equal @ X3 @ zero))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl796])).
% 11.76/2.31 thf(zip_derived_cl3428, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]:
% 11.76/2.31 (~ (quotient @ (divide @ (divide @ idQ__idQ_idQa @ X1) @ idQa) @
% 11.76/2.31 zero @ X0)
% 11.76/2.31 | (less_equal @ X0 @ zero))),
% 11.76/2.31 inference('s_sup-', [status(thm)],
% 11.76/2.31 [zip_derived_cl1588, zip_derived_cl3222])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(zip_derived_cl3534, plain,
% 11.76/2.31 (![X0 : $i]:
% 11.76/2.31 (less_equal @
% 11.76/2.31 (divide @ (divide @ (divide @ idQ__idQ_idQa @ X0) @ idQa) @ zero) @
% 11.76/2.31 zero)),
% 11.76/2.31 inference('s_sup+', [status(thm)], [zip_derived_cl3428, zip_derived_cl7])).
% 11.76/2.31 thf(zip_derived_cl16, plain,
% 11.76/2.31 (![X0 : $i]: (~ (less_equal @ X0 @ zero) | ((zero) = (X0)))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 11.76/2.31 thf(zip_derived_cl3608, plain,
% 11.76/2.31 (![X0 : $i]:
% 11.76/2.31 ((zero)
% 11.76/2.31 = (divide @ (divide @ (divide @ idQ__idQ_idQa @ X0) @ idQa) @ zero))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl3534, zip_derived_cl16])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(zip_derived_cl3619, plain,
% 11.76/2.31 (![X0 : $i]:
% 11.76/2.31 (quotient @ (divide @ (divide @ idQ__idQ_idQa @ X0) @ idQa) @ zero @
% 11.76/2.31 zero)),
% 11.76/2.31 inference('s_sup+', [status(thm)], [zip_derived_cl3608, zip_derived_cl7])).
% 11.76/2.31 thf(zip_derived_cl1, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]:
% 11.76/2.31 (~ (quotient @ X0 @ X1 @ zero) | (less_equal @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [less_equal_quotient])).
% 11.76/2.31 thf(zip_derived_cl3693, plain,
% 11.76/2.31 (![X0 : $i]:
% 11.76/2.31 (less_equal @ (divide @ (divide @ idQ__idQ_idQa @ X0) @ idQa) @ zero)),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl3619, zip_derived_cl1])).
% 11.76/2.31 thf(zip_derived_cl16, plain,
% 11.76/2.31 (![X0 : $i]: (~ (less_equal @ X0 @ zero) | ((zero) = (X0)))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 11.76/2.31 thf(zip_derived_cl3729, plain,
% 11.76/2.31 (![X0 : $i]: ((zero) = (divide @ (divide @ idQ__idQ_idQa @ X0) @ idQa))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl3693, zip_derived_cl16])).
% 11.76/2.31 thf(zip_derived_cl7, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [closure])).
% 11.76/2.31 thf(zip_derived_cl3743, plain,
% 11.76/2.31 (![X0 : $i]: (quotient @ (divide @ idQ__idQ_idQa @ X0) @ idQa @ zero)),
% 11.76/2.31 inference('s_sup+', [status(thm)], [zip_derived_cl3729, zip_derived_cl7])).
% 11.76/2.31 thf(zip_derived_cl1, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]:
% 11.76/2.31 (~ (quotient @ X0 @ X1 @ zero) | (less_equal @ X0 @ X1))),
% 11.76/2.31 inference('cnf', [status(esa)], [less_equal_quotient])).
% 11.76/2.31 thf(zip_derived_cl3916, plain,
% 11.76/2.31 (![X0 : $i]: (less_equal @ (divide @ idQ__idQ_idQa @ X0) @ idQa)),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl3743, zip_derived_cl1])).
% 11.76/2.31 thf(zip_derived_cl9132, plain, (![X0 : $i]: ((divide @ X0 @ zero) = (X0))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl9016, zip_derived_cl42])).
% 11.76/2.31 thf(zip_derived_cl9161, plain, (((idQa) = (divide @ idQ__idQ_idQa @ a))),
% 11.76/2.31 inference('demod', [status(thm)],
% 11.76/2.31 [zip_derived_cl1457, zip_derived_cl9132, zip_derived_cl3916,
% 11.76/2.31 zip_derived_cl9132])).
% 11.76/2.31 thf(zip_derived_cl42, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]:
% 11.76/2.31 (~ (less_equal @ X0 @ (divide @ X0 @ X1))
% 11.76/2.31 | ((divide @ X0 @ X1) = (X0)))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl5])).
% 11.76/2.31 thf(zip_derived_cl9539, plain,
% 11.76/2.31 ((~ (less_equal @ idQ__idQ_idQa @ idQa) | ((idQa) = (idQ__idQ_idQa)))),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl9161, zip_derived_cl42])).
% 11.76/2.31 thf(zip_derived_cl1570, plain,
% 11.76/2.31 (((divide @ idQa @ idQ_idQa) = (idQ__idQ_idQa))),
% 11.76/2.31 inference('s_sup-', [status(thm)],
% 11.76/2.31 [zip_derived_cl1555, zip_derived_cl1117])).
% 11.76/2.31 thf(zip_derived_cl20, plain,
% 11.76/2.31 (![X0 : $i, X1 : $i]: (less_equal @ (divide @ X1 @ X0) @ X1)),
% 11.76/2.31 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 11.76/2.31 thf(zip_derived_cl1590, plain, ( (less_equal @ idQ__idQ_idQa @ idQa)),
% 11.76/2.31 inference('s_sup+', [status(thm)], [zip_derived_cl1570, zip_derived_cl20])).
% 11.76/2.31 thf(zip_derived_cl9607, plain, (((idQa) = (idQ__idQ_idQa))),
% 11.76/2.31 inference('demod', [status(thm)],
% 11.76/2.31 [zip_derived_cl9539, zip_derived_cl1590])).
% 11.76/2.31 thf(prove_one_inversion_equals_three, conjecture,
% 11.76/2.31 (( idQa ) = ( idQ__idQ_idQa ))).
% 11.76/2.31 thf(zf_stmt_0, negated_conjecture, (( idQa ) != ( idQ__idQ_idQa )),
% 11.76/2.31 inference('cnf.neg', [status(esa)], [prove_one_inversion_equals_three])).
% 11.76/2.31 thf(zip_derived_cl12, plain, (((idQa) != (idQ__idQ_idQa))),
% 11.76/2.31 inference('cnf', [status(esa)], [zf_stmt_0])).
% 11.76/2.31 thf(zip_derived_cl9608, plain, ($false),
% 11.76/2.31 inference('simplify_reflect-', [status(thm)],
% 11.76/2.31 [zip_derived_cl9607, zip_derived_cl12])).
% 11.76/2.31
% 11.76/2.31 % SZS output end Refutation
% 11.76/2.31
% 11.76/2.31
% 11.76/2.31 % Terminating...
% 12.66/2.45 % Runner terminated.
% 12.66/2.45 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------