TSTP Solution File: HEN011-3 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : HEN011-3 : 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.1jFVEgDOx1 true
% Computer : n025.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 21.38s 3.77s
% Output : Refutation 21.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN011-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.1jFVEgDOx1 true
% 0.18/0.35 % Computer : n025.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Thu Aug 24 13:41:21 EDT 2023
% 0.18/0.35 % CPUTime :
% 0.18/0.35 % Running portfolio for 300 s
% 0.18/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.35 % Number of cores: 8
% 0.18/0.35 % Python version: Python 3.6.8
% 0.18/0.36 % 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
% 0.22/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.22/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 1.39/0.81 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 21.38/3.77 % Solved by fo/fo5.sh.
% 21.38/3.77 % done 2813 iterations in 2.912s
% 21.38/3.77 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 21.38/3.77 % SZS output start Refutation
% 21.38/3.77 thf(zero_type, type, zero: $i).
% 21.38/3.77 thf(divide_type, type, divide: $i > $i > $i).
% 21.38/3.77 thf(b_type, type, b: $i).
% 21.38/3.77 thf(e_type, type, e: $i).
% 21.38/3.77 thf(d_type, type, d: $i).
% 21.38/3.77 thf(less_equal_type, type, less_equal: $i > $i > $o).
% 21.38/3.77 thf(g_type, type, g: $i).
% 21.38/3.77 thf(c_type, type, c: $i).
% 21.38/3.77 thf(identity_type, type, identity: $i).
% 21.38/3.77 thf(a_type, type, a: $i).
% 21.38/3.77 thf(identity_is_largest, axiom, (less_equal @ X @ identity)).
% 21.38/3.77 thf(zip_derived_cl6, plain, (![X0 : $i]: (less_equal @ X0 @ identity)),
% 21.38/3.77 inference('cnf', [status(esa)], [identity_is_largest])).
% 21.38/3.77 thf(quotient_less_equal1, axiom,
% 21.38/3.77 (( ~( less_equal @ X @ Y ) ) | ( ( divide @ X @ Y ) = ( zero ) ))).
% 21.38/3.77 thf(zip_derived_cl0, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (~ (less_equal @ X0 @ X1) | ((divide @ X0 @ X1) = (zero)))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_less_equal1])).
% 21.38/3.77 thf(zip_derived_cl17, plain,
% 21.38/3.77 (![X0 : $i]: ((divide @ X0 @ identity) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl0])).
% 21.38/3.77 thf(quotient_property, axiom,
% 21.38/3.77 (less_equal @
% 21.38/3.77 ( divide @ ( divide @ X @ Z ) @ ( divide @ Y @ Z ) ) @
% 21.38/3.77 ( divide @ ( divide @ X @ Y ) @ Z ))).
% 21.38/3.77 thf(zip_derived_cl3, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.38/3.77 (less_equal @ (divide @ (divide @ X0 @ X1) @ (divide @ X2 @ X1)) @
% 21.38/3.77 (divide @ (divide @ X0 @ X2) @ X1))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_property])).
% 21.38/3.77 thf(less_equal_and_equal, axiom,
% 21.38/3.77 (( ~( less_equal @ X @ Y ) ) | ( ~( less_equal @ Y @ X ) ) |
% 21.38/3.77 ( ( X ) = ( Y ) ))).
% 21.38/3.77 thf(zip_derived_cl5, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 21.38/3.77 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 21.38/3.77 thf(zip_derived_cl47, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.38/3.77 (((divide @ (divide @ X2 @ X0) @ (divide @ X1 @ X0))
% 21.38/3.77 = (divide @ (divide @ X2 @ X1) @ X0))
% 21.38/3.77 | ~ (less_equal @ (divide @ (divide @ X2 @ X1) @ X0) @
% 21.38/3.77 (divide @ (divide @ X2 @ X0) @ (divide @ X1 @ X0))))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl5])).
% 21.38/3.77 thf(zip_derived_cl327, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (~ (less_equal @ (divide @ zero @ X0) @
% 21.38/3.77 (divide @ (divide @ X1 @ X0) @ (divide @ identity @ X0)))
% 21.38/3.77 | ((divide @ (divide @ X1 @ X0) @ (divide @ identity @ X0))
% 21.38/3.77 = (divide @ (divide @ X1 @ identity) @ X0)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl47])).
% 21.38/3.77 thf(zero_is_smallest, axiom, (less_equal @ zero @ X)).
% 21.38/3.77 thf(zip_derived_cl4, plain, (![X0 : $i]: (less_equal @ zero @ X0)),
% 21.38/3.77 inference('cnf', [status(esa)], [zero_is_smallest])).
% 21.38/3.77 thf(zip_derived_cl0, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (~ (less_equal @ X0 @ X1) | ((divide @ X0 @ X1) = (zero)))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_less_equal1])).
% 21.38/3.77 thf(zip_derived_cl19, plain, (![X0 : $i]: ((divide @ zero @ X0) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl4, plain, (![X0 : $i]: (less_equal @ zero @ X0)),
% 21.38/3.77 inference('cnf', [status(esa)], [zero_is_smallest])).
% 21.38/3.77 thf(zip_derived_cl17, plain,
% 21.38/3.77 (![X0 : $i]: ((divide @ X0 @ identity) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl19, plain, (![X0 : $i]: ((divide @ zero @ X0) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl369, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 ((divide @ (divide @ X1 @ X0) @ (divide @ identity @ X0)) = (zero))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl327, zip_derived_cl19, zip_derived_cl4,
% 21.38/3.77 zip_derived_cl17, zip_derived_cl19])).
% 21.38/3.77 thf(quotient_less_equal2, axiom,
% 21.38/3.77 (( ( divide @ X @ Y ) != ( zero ) ) | ( less_equal @ X @ Y ))).
% 21.38/3.77 thf(zip_derived_cl1, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (((divide @ X0 @ X1) != (zero)) | (less_equal @ X0 @ X1))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_less_equal2])).
% 21.38/3.77 thf(zip_derived_cl2482, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (((zero) != (zero))
% 21.38/3.77 | (less_equal @ (divide @ X1 @ X0) @ (divide @ identity @ X0)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl369, zip_derived_cl1])).
% 21.38/3.77 thf(zip_derived_cl2569, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (less_equal @ (divide @ X1 @ X0) @ (divide @ identity @ X0))),
% 21.38/3.77 inference('simplify', [status(thm)], [zip_derived_cl2482])).
% 21.38/3.77 thf(identity_divide_c, axiom, (( divide @ identity @ c ) = ( e ))).
% 21.38/3.77 thf(zip_derived_cl10, plain, (((divide @ identity @ c) = (e))),
% 21.38/3.77 inference('cnf', [status(esa)], [identity_divide_c])).
% 21.38/3.77 thf(zip_derived_cl3, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.38/3.77 (less_equal @ (divide @ (divide @ X0 @ X1) @ (divide @ X2 @ X1)) @
% 21.38/3.77 (divide @ (divide @ X0 @ X2) @ X1))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_property])).
% 21.38/3.77 thf(zip_derived_cl63, plain,
% 21.38/3.77 (![X0 : $i]:
% 21.38/3.77 (less_equal @ (divide @ (divide @ X0 @ c) @ e) @
% 21.38/3.77 (divide @ (divide @ X0 @ identity) @ c))),
% 21.38/3.77 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl3])).
% 21.38/3.77 thf(zip_derived_cl17, plain,
% 21.38/3.77 (![X0 : $i]: ((divide @ X0 @ identity) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl19, plain, (![X0 : $i]: ((divide @ zero @ X0) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl80, plain,
% 21.38/3.77 (![X0 : $i]: (less_equal @ (divide @ (divide @ X0 @ c) @ e) @ zero)),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl63, zip_derived_cl17, zip_derived_cl19])).
% 21.38/3.77 thf(zip_derived_cl4, plain, (![X0 : $i]: (less_equal @ zero @ X0)),
% 21.38/3.77 inference('cnf', [status(esa)], [zero_is_smallest])).
% 21.38/3.77 thf(zip_derived_cl5, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 21.38/3.77 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 21.38/3.77 thf(zip_derived_cl43, plain,
% 21.38/3.77 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 21.38/3.77 thf(zip_derived_cl90, plain,
% 21.38/3.77 (![X0 : $i]: ((zero) = (divide @ (divide @ X0 @ c) @ e))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl80, zip_derived_cl43])).
% 21.38/3.77 thf(zip_derived_cl47, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.38/3.77 (((divide @ (divide @ X2 @ X0) @ (divide @ X1 @ X0))
% 21.38/3.77 = (divide @ (divide @ X2 @ X1) @ X0))
% 21.38/3.77 | ~ (less_equal @ (divide @ (divide @ X2 @ X1) @ X0) @
% 21.38/3.77 (divide @ (divide @ X2 @ X0) @ (divide @ X1 @ X0))))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl5])).
% 21.38/3.77 thf(zip_derived_cl326, plain,
% 21.38/3.77 (![X0 : $i]:
% 21.38/3.77 (~ (less_equal @ zero @
% 21.38/3.77 (divide @ (divide @ X0 @ e) @ (divide @ c @ e)))
% 21.38/3.77 | ((divide @ (divide @ X0 @ e) @ (divide @ c @ e))
% 21.38/3.77 = (divide @ (divide @ X0 @ c) @ e)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl90, zip_derived_cl47])).
% 21.38/3.77 thf(zip_derived_cl4, plain, (![X0 : $i]: (less_equal @ zero @ X0)),
% 21.38/3.77 inference('cnf', [status(esa)], [zero_is_smallest])).
% 21.38/3.77 thf(zip_derived_cl90, plain,
% 21.38/3.77 (![X0 : $i]: ((zero) = (divide @ (divide @ X0 @ c) @ e))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl80, zip_derived_cl43])).
% 21.38/3.77 thf(zip_derived_cl368, plain,
% 21.38/3.77 (![X0 : $i]: ((divide @ (divide @ X0 @ e) @ (divide @ c @ e)) = (zero))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl326, zip_derived_cl4, zip_derived_cl90])).
% 21.38/3.77 thf(zip_derived_cl1, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (((divide @ X0 @ X1) != (zero)) | (less_equal @ X0 @ X1))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_less_equal2])).
% 21.38/3.77 thf(zip_derived_cl820, plain,
% 21.38/3.77 (![X0 : $i]:
% 21.38/3.77 (((zero) != (zero))
% 21.38/3.77 | (less_equal @ (divide @ X0 @ e) @ (divide @ c @ e)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl368, zip_derived_cl1])).
% 21.38/3.77 thf(zip_derived_cl851, plain,
% 21.38/3.77 (![X0 : $i]: (less_equal @ (divide @ X0 @ e) @ (divide @ c @ e))),
% 21.38/3.77 inference('simplify', [status(thm)], [zip_derived_cl820])).
% 21.38/3.77 thf(zip_derived_cl5, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 21.38/3.77 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 21.38/3.77 thf(zip_derived_cl871, plain,
% 21.38/3.77 (![X0 : $i]:
% 21.38/3.77 (((divide @ X0 @ e) = (divide @ c @ e))
% 21.38/3.77 | ~ (less_equal @ (divide @ c @ e) @ (divide @ X0 @ e)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl851, zip_derived_cl5])).
% 21.38/3.77 thf(zip_derived_cl2943, plain,
% 21.38/3.77 (((divide @ identity @ e) = (divide @ c @ e))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl2569, zip_derived_cl871])).
% 21.38/3.77 thf(identity_divide_d, axiom, (( divide @ identity @ d ) = ( g ))).
% 21.38/3.77 thf(zip_derived_cl11, plain, (((divide @ identity @ d) = (g))),
% 21.38/3.77 inference('cnf', [status(esa)], [identity_divide_d])).
% 21.38/3.77 thf(zip_derived_cl3, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.38/3.77 (less_equal @ (divide @ (divide @ X0 @ X1) @ (divide @ X2 @ X1)) @
% 21.38/3.77 (divide @ (divide @ X0 @ X2) @ X1))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_property])).
% 21.38/3.77 thf(zip_derived_cl56, plain,
% 21.38/3.77 (![X0 : $i]:
% 21.38/3.77 (less_equal @
% 21.38/3.77 (divide @ (divide @ identity @ X0) @ (divide @ d @ X0)) @
% 21.38/3.77 (divide @ g @ X0))),
% 21.38/3.77 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl3])).
% 21.38/3.77 thf(zip_derived_cl3030, plain,
% 21.38/3.77 ( (less_equal @ (divide @ (divide @ c @ e) @ (divide @ d @ e)) @
% 21.38/3.77 (divide @ g @ e))),
% 21.38/3.77 inference('sup+', [status(thm)], [zip_derived_cl2943, zip_derived_cl56])).
% 21.38/3.77 thf(zip_derived_cl0, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (~ (less_equal @ X0 @ X1) | ((divide @ X0 @ X1) = (zero)))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_less_equal1])).
% 21.38/3.77 thf(zip_derived_cl3897, plain,
% 21.38/3.77 (((divide @ (divide @ (divide @ c @ e) @ (divide @ d @ e)) @
% 21.38/3.77 (divide @ g @ e)) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl3030, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl2943, plain,
% 21.38/3.77 (((divide @ identity @ e) = (divide @ c @ e))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl2569, zip_derived_cl871])).
% 21.38/3.77 thf(identity_divide_a, axiom, (( divide @ identity @ a ) = ( c ))).
% 21.38/3.77 thf(zip_derived_cl8, plain, (((divide @ identity @ a) = (c))),
% 21.38/3.77 inference('cnf', [status(esa)], [identity_divide_a])).
% 21.38/3.77 thf(zip_derived_cl3, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.38/3.77 (less_equal @ (divide @ (divide @ X0 @ X1) @ (divide @ X2 @ X1)) @
% 21.38/3.77 (divide @ (divide @ X0 @ X2) @ X1))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_property])).
% 21.38/3.77 thf(zip_derived_cl68, plain,
% 21.38/3.77 (![X0 : $i]:
% 21.38/3.77 (less_equal @ (divide @ c @ (divide @ X0 @ a)) @
% 21.38/3.77 (divide @ (divide @ identity @ X0) @ a))),
% 21.38/3.77 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl3])).
% 21.38/3.77 thf(zip_derived_cl3031, plain,
% 21.38/3.77 ( (less_equal @ (divide @ c @ (divide @ e @ a)) @
% 21.38/3.77 (divide @ (divide @ c @ e) @ a))),
% 21.38/3.77 inference('sup+', [status(thm)], [zip_derived_cl2943, zip_derived_cl68])).
% 21.38/3.77 thf(zip_derived_cl8, plain, (((divide @ identity @ a) = (c))),
% 21.38/3.77 inference('cnf', [status(esa)], [identity_divide_a])).
% 21.38/3.77 thf(zip_derived_cl8, plain, (((divide @ identity @ a) = (c))),
% 21.38/3.77 inference('cnf', [status(esa)], [identity_divide_a])).
% 21.38/3.77 thf(zip_derived_cl3, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.38/3.77 (less_equal @ (divide @ (divide @ X0 @ X1) @ (divide @ X2 @ X1)) @
% 21.38/3.77 (divide @ (divide @ X0 @ X2) @ X1))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_property])).
% 21.38/3.77 thf(zip_derived_cl61, plain,
% 21.38/3.77 (![X0 : $i]:
% 21.38/3.77 (less_equal @ (divide @ (divide @ X0 @ a) @ c) @
% 21.38/3.77 (divide @ (divide @ X0 @ identity) @ a))),
% 21.38/3.77 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl3])).
% 21.38/3.77 thf(zip_derived_cl17, plain,
% 21.38/3.77 (![X0 : $i]: ((divide @ X0 @ identity) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl19, plain, (![X0 : $i]: ((divide @ zero @ X0) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl78, plain,
% 21.38/3.77 (![X0 : $i]: (less_equal @ (divide @ (divide @ X0 @ a) @ c) @ zero)),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl61, zip_derived_cl17, zip_derived_cl19])).
% 21.38/3.77 thf(zip_derived_cl166, plain, ( (less_equal @ (divide @ c @ c) @ zero)),
% 21.38/3.77 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl78])).
% 21.38/3.77 thf(zip_derived_cl43, plain,
% 21.38/3.77 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 21.38/3.77 thf(zip_derived_cl173, plain, (((zero) = (divide @ c @ c))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl166, zip_derived_cl43])).
% 21.38/3.77 thf(zip_derived_cl8, plain, (((divide @ identity @ a) = (c))),
% 21.38/3.77 inference('cnf', [status(esa)], [identity_divide_a])).
% 21.38/3.77 thf(zip_derived_cl3, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.38/3.77 (less_equal @ (divide @ (divide @ X0 @ X1) @ (divide @ X2 @ X1)) @
% 21.38/3.77 (divide @ (divide @ X0 @ X2) @ X1))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_property])).
% 21.38/3.77 thf(zip_derived_cl53, plain,
% 21.38/3.77 (![X0 : $i]:
% 21.38/3.77 (less_equal @
% 21.38/3.77 (divide @ (divide @ identity @ X0) @ (divide @ a @ X0)) @
% 21.38/3.77 (divide @ c @ X0))),
% 21.38/3.77 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl3])).
% 21.38/3.77 thf(zip_derived_cl553, plain,
% 21.38/3.77 ( (less_equal @ (divide @ (divide @ identity @ c) @ (divide @ a @ c)) @
% 21.38/3.77 zero)),
% 21.38/3.77 inference('sup+', [status(thm)], [zip_derived_cl173, zip_derived_cl53])).
% 21.38/3.77 thf(zip_derived_cl10, plain, (((divide @ identity @ c) = (e))),
% 21.38/3.77 inference('cnf', [status(esa)], [identity_divide_c])).
% 21.38/3.77 thf(zip_derived_cl561, plain,
% 21.38/3.77 ( (less_equal @ (divide @ e @ (divide @ a @ c)) @ zero)),
% 21.38/3.77 inference('demod', [status(thm)], [zip_derived_cl553, zip_derived_cl10])).
% 21.38/3.77 thf(zip_derived_cl43, plain,
% 21.38/3.77 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 21.38/3.77 thf(zip_derived_cl603, plain, (((zero) = (divide @ e @ (divide @ a @ c)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl561, zip_derived_cl43])).
% 21.38/3.77 thf(zip_derived_cl1, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (((divide @ X0 @ X1) != (zero)) | (less_equal @ X0 @ X1))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_less_equal2])).
% 21.38/3.77 thf(zip_derived_cl608, plain,
% 21.38/3.77 ((((zero) != (zero)) | (less_equal @ e @ (divide @ a @ c)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl603, zip_derived_cl1])).
% 21.38/3.77 thf(zip_derived_cl622, plain, ( (less_equal @ e @ (divide @ a @ c))),
% 21.38/3.77 inference('simplify', [status(thm)], [zip_derived_cl608])).
% 21.38/3.77 thf(zip_derived_cl90, plain,
% 21.38/3.77 (![X0 : $i]: ((zero) = (divide @ (divide @ X0 @ c) @ e))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl80, zip_derived_cl43])).
% 21.38/3.77 thf(zip_derived_cl1, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (((divide @ X0 @ X1) != (zero)) | (less_equal @ X0 @ X1))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_less_equal2])).
% 21.38/3.77 thf(zip_derived_cl116, plain,
% 21.38/3.77 (![X0 : $i]: (((zero) != (zero)) | (less_equal @ (divide @ X0 @ c) @ e))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl90, zip_derived_cl1])).
% 21.38/3.77 thf(zip_derived_cl126, plain,
% 21.38/3.77 (![X0 : $i]: (less_equal @ (divide @ X0 @ c) @ e)),
% 21.38/3.77 inference('simplify', [status(thm)], [zip_derived_cl116])).
% 21.38/3.77 thf(zip_derived_cl5, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 21.38/3.77 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 21.38/3.77 thf(zip_derived_cl130, plain,
% 21.38/3.77 (![X0 : $i]:
% 21.38/3.77 (((divide @ X0 @ c) = (e)) | ~ (less_equal @ e @ (divide @ X0 @ c)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl126, zip_derived_cl5])).
% 21.38/3.77 thf(zip_derived_cl649, plain, (((divide @ a @ c) = (e))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl622, zip_derived_cl130])).
% 21.38/3.77 thf(quotient_smaller_than_numerator, axiom,
% 21.38/3.77 (less_equal @ ( divide @ X @ Y ) @ X)).
% 21.38/3.77 thf(zip_derived_cl2, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]: (less_equal @ (divide @ X0 @ X1) @ X0)),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_smaller_than_numerator])).
% 21.38/3.77 thf(zip_derived_cl0, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (~ (less_equal @ X0 @ X1) | ((divide @ X0 @ X1) = (zero)))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_less_equal1])).
% 21.38/3.77 thf(zip_derived_cl18, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]: ((divide @ (divide @ X0 @ X1) @ X0) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl657, plain, (((divide @ e @ a) = (zero))),
% 21.38/3.77 inference('sup+', [status(thm)], [zip_derived_cl649, zip_derived_cl18])).
% 21.38/3.77 thf(zip_derived_cl3056, plain,
% 21.38/3.77 ( (less_equal @ (divide @ c @ zero) @ (divide @ (divide @ c @ e) @ a))),
% 21.38/3.77 inference('demod', [status(thm)], [zip_derived_cl3031, zip_derived_cl657])).
% 21.38/3.77 thf(zip_derived_cl18, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]: ((divide @ (divide @ X0 @ X1) @ X0) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl18, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]: ((divide @ (divide @ X0 @ X1) @ X0) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl3, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.38/3.77 (less_equal @ (divide @ (divide @ X0 @ X1) @ (divide @ X2 @ X1)) @
% 21.38/3.77 (divide @ (divide @ X0 @ X2) @ X1))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_property])).
% 21.38/3.77 thf(zip_derived_cl49, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (less_equal @ (divide @ (divide @ X0 @ X0) @ (divide @ X1 @ X0)) @
% 21.38/3.77 zero)),
% 21.38/3.77 inference('sup+', [status(thm)], [zip_derived_cl18, zip_derived_cl3])).
% 21.38/3.77 thf(zip_derived_cl449, plain,
% 21.38/3.77 (![X0 : $i]: (less_equal @ (divide @ (divide @ X0 @ X0) @ zero) @ zero)),
% 21.38/3.77 inference('sup+', [status(thm)], [zip_derived_cl18, zip_derived_cl49])).
% 21.38/3.77 thf(zip_derived_cl43, plain,
% 21.38/3.77 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 21.38/3.77 thf(zip_derived_cl737, plain,
% 21.38/3.77 (![X0 : $i]: ((zero) = (divide @ (divide @ X0 @ X0) @ zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl449, zip_derived_cl43])).
% 21.38/3.77 thf(zip_derived_cl1, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (((divide @ X0 @ X1) != (zero)) | (less_equal @ X0 @ X1))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_less_equal2])).
% 21.38/3.77 thf(zip_derived_cl877, plain,
% 21.38/3.77 (![X0 : $i]:
% 21.38/3.77 (((zero) != (zero)) | (less_equal @ (divide @ X0 @ X0) @ zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl737, zip_derived_cl1])).
% 21.38/3.77 thf(zip_derived_cl905, plain,
% 21.38/3.77 (![X0 : $i]: (less_equal @ (divide @ X0 @ X0) @ zero)),
% 21.38/3.77 inference('simplify', [status(thm)], [zip_derived_cl877])).
% 21.38/3.77 thf(zip_derived_cl43, plain,
% 21.38/3.77 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 21.38/3.77 thf(zip_derived_cl983, plain, (![X0 : $i]: ((zero) = (divide @ X0 @ X0))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl905, zip_derived_cl43])).
% 21.38/3.77 thf(zip_derived_cl19, plain, (![X0 : $i]: ((divide @ zero @ X0) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl3, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.38/3.77 (less_equal @ (divide @ (divide @ X0 @ X1) @ (divide @ X2 @ X1)) @
% 21.38/3.77 (divide @ (divide @ X0 @ X2) @ X1))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_property])).
% 21.38/3.77 thf(zip_derived_cl60, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (less_equal @ (divide @ (divide @ X1 @ X0) @ zero) @
% 21.38/3.77 (divide @ (divide @ X1 @ zero) @ X0))),
% 21.38/3.77 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl3])).
% 21.38/3.77 thf(zip_derived_cl1048, plain,
% 21.38/3.77 (![X0 : $i]:
% 21.38/3.77 (less_equal @
% 21.38/3.77 (divide @ (divide @ X0 @ (divide @ X0 @ zero)) @ zero) @ zero)),
% 21.38/3.77 inference('sup+', [status(thm)], [zip_derived_cl983, zip_derived_cl60])).
% 21.38/3.77 thf(zip_derived_cl43, plain,
% 21.38/3.77 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 21.38/3.77 thf(zip_derived_cl6470, plain,
% 21.38/3.77 (![X0 : $i]:
% 21.38/3.77 ((zero) = (divide @ (divide @ X0 @ (divide @ X0 @ zero)) @ zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl1048, zip_derived_cl43])).
% 21.38/3.77 thf(zip_derived_cl1, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (((divide @ X0 @ X1) != (zero)) | (less_equal @ X0 @ X1))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_less_equal2])).
% 21.38/3.77 thf(zip_derived_cl6939, plain,
% 21.38/3.77 (![X0 : $i]:
% 21.38/3.77 (((zero) != (zero))
% 21.38/3.77 | (less_equal @ (divide @ X0 @ (divide @ X0 @ zero)) @ zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl6470, zip_derived_cl1])).
% 21.38/3.77 thf(zip_derived_cl7012, plain,
% 21.38/3.77 (![X0 : $i]: (less_equal @ (divide @ X0 @ (divide @ X0 @ zero)) @ zero)),
% 21.38/3.77 inference('simplify', [status(thm)], [zip_derived_cl6939])).
% 21.38/3.77 thf(zip_derived_cl43, plain,
% 21.38/3.77 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 21.38/3.77 thf(zip_derived_cl7438, plain,
% 21.38/3.77 (![X0 : $i]: ((zero) = (divide @ X0 @ (divide @ X0 @ zero)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl7012, zip_derived_cl43])).
% 21.38/3.77 thf(zip_derived_cl1, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (((divide @ X0 @ X1) != (zero)) | (less_equal @ X0 @ X1))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_less_equal2])).
% 21.38/3.77 thf(zip_derived_cl7459, plain,
% 21.38/3.77 (![X0 : $i]:
% 21.38/3.77 (((zero) != (zero)) | (less_equal @ X0 @ (divide @ X0 @ zero)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl7438, zip_derived_cl1])).
% 21.38/3.77 thf(zip_derived_cl7582, plain,
% 21.38/3.77 (![X0 : $i]: (less_equal @ X0 @ (divide @ X0 @ zero))),
% 21.38/3.77 inference('simplify', [status(thm)], [zip_derived_cl7459])).
% 21.38/3.77 thf(zip_derived_cl2, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]: (less_equal @ (divide @ X0 @ X1) @ X0)),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_smaller_than_numerator])).
% 21.38/3.77 thf(zip_derived_cl5, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 21.38/3.77 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 21.38/3.77 thf(zip_derived_cl42, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (((divide @ X0 @ X1) = (X0))
% 21.38/3.77 | ~ (less_equal @ X0 @ (divide @ X0 @ X1)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl5])).
% 21.38/3.77 thf(zip_derived_cl8204, plain, (![X0 : $i]: ((divide @ X0 @ zero) = (X0))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl7582, zip_derived_cl42])).
% 21.38/3.77 thf(zip_derived_cl8416, plain,
% 21.38/3.77 ( (less_equal @ c @ (divide @ (divide @ c @ e) @ a))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl3056, zip_derived_cl8204])).
% 21.38/3.77 thf(zip_derived_cl78, plain,
% 21.38/3.77 (![X0 : $i]: (less_equal @ (divide @ (divide @ X0 @ a) @ c) @ zero)),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl61, zip_derived_cl17, zip_derived_cl19])).
% 21.38/3.77 thf(zip_derived_cl43, plain,
% 21.38/3.77 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 21.38/3.77 thf(zip_derived_cl161, plain,
% 21.38/3.77 (![X0 : $i]: ((zero) = (divide @ (divide @ X0 @ a) @ c))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl78, zip_derived_cl43])).
% 21.38/3.77 thf(zip_derived_cl1, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (((divide @ X0 @ X1) != (zero)) | (less_equal @ X0 @ X1))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_less_equal2])).
% 21.38/3.77 thf(zip_derived_cl273, plain,
% 21.38/3.77 (![X0 : $i]: (((zero) != (zero)) | (less_equal @ (divide @ X0 @ a) @ c))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl161, zip_derived_cl1])).
% 21.38/3.77 thf(zip_derived_cl291, plain,
% 21.38/3.77 (![X0 : $i]: (less_equal @ (divide @ X0 @ a) @ c)),
% 21.38/3.77 inference('simplify', [status(thm)], [zip_derived_cl273])).
% 21.38/3.77 thf(zip_derived_cl5, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 21.38/3.77 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 21.38/3.77 thf(zip_derived_cl440, plain,
% 21.38/3.77 (![X0 : $i]:
% 21.38/3.77 (((divide @ X0 @ a) = (c)) | ~ (less_equal @ c @ (divide @ X0 @ a)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl291, zip_derived_cl5])).
% 21.38/3.77 thf(zip_derived_cl8749, plain, (((divide @ (divide @ c @ e) @ a) = (c))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl8416, zip_derived_cl440])).
% 21.38/3.77 thf(zip_derived_cl42, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (((divide @ X0 @ X1) = (X0))
% 21.38/3.77 | ~ (less_equal @ X0 @ (divide @ X0 @ X1)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl5])).
% 21.38/3.77 thf(zip_derived_cl8756, plain,
% 21.38/3.77 ((~ (less_equal @ (divide @ c @ e) @ c)
% 21.38/3.77 | ((divide @ (divide @ c @ e) @ a) = (divide @ c @ e)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl8749, zip_derived_cl42])).
% 21.38/3.77 thf(zip_derived_cl368, plain,
% 21.38/3.77 (![X0 : $i]: ((divide @ (divide @ X0 @ e) @ (divide @ c @ e)) = (zero))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl326, zip_derived_cl4, zip_derived_cl90])).
% 21.38/3.77 thf(zip_derived_cl18, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]: ((divide @ (divide @ X0 @ X1) @ X0) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl3, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.38/3.77 (less_equal @ (divide @ (divide @ X0 @ X1) @ (divide @ X2 @ X1)) @
% 21.38/3.77 (divide @ (divide @ X0 @ X2) @ X1))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_property])).
% 21.38/3.77 thf(zip_derived_cl59, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.38/3.77 (less_equal @ (divide @ (divide @ X2 @ X0) @ zero) @
% 21.38/3.77 (divide @ (divide @ X2 @ (divide @ X0 @ X1)) @ X0))),
% 21.38/3.77 inference('sup+', [status(thm)], [zip_derived_cl18, zip_derived_cl3])).
% 21.38/3.77 thf(zip_derived_cl838, plain,
% 21.38/3.77 (![X0 : $i]:
% 21.38/3.77 (less_equal @ (divide @ (divide @ (divide @ X0 @ e) @ c) @ zero) @
% 21.38/3.77 (divide @ zero @ c))),
% 21.38/3.77 inference('sup+', [status(thm)], [zip_derived_cl368, zip_derived_cl59])).
% 21.38/3.77 thf(zip_derived_cl19, plain, (![X0 : $i]: ((divide @ zero @ X0) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl864, plain,
% 21.38/3.77 (![X0 : $i]:
% 21.38/3.77 (less_equal @ (divide @ (divide @ (divide @ X0 @ e) @ c) @ zero) @
% 21.38/3.77 zero)),
% 21.38/3.77 inference('demod', [status(thm)], [zip_derived_cl838, zip_derived_cl19])).
% 21.38/3.77 thf(zip_derived_cl43, plain,
% 21.38/3.77 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 21.38/3.77 thf(zip_derived_cl5561, plain,
% 21.38/3.77 (![X0 : $i]:
% 21.38/3.77 ((zero) = (divide @ (divide @ (divide @ X0 @ e) @ c) @ zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl864, zip_derived_cl43])).
% 21.38/3.77 thf(zip_derived_cl1, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (((divide @ X0 @ X1) != (zero)) | (less_equal @ X0 @ X1))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_less_equal2])).
% 21.38/3.77 thf(zip_derived_cl5729, plain,
% 21.38/3.77 (![X0 : $i]:
% 21.38/3.77 (((zero) != (zero))
% 21.38/3.77 | (less_equal @ (divide @ (divide @ X0 @ e) @ c) @ zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl5561, zip_derived_cl1])).
% 21.38/3.77 thf(zip_derived_cl5795, plain,
% 21.38/3.77 (![X0 : $i]: (less_equal @ (divide @ (divide @ X0 @ e) @ c) @ zero)),
% 21.38/3.77 inference('simplify', [status(thm)], [zip_derived_cl5729])).
% 21.38/3.77 thf(zip_derived_cl43, plain,
% 21.38/3.77 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 21.38/3.77 thf(zip_derived_cl5836, plain,
% 21.38/3.77 (![X0 : $i]: ((zero) = (divide @ (divide @ X0 @ e) @ c))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl5795, zip_derived_cl43])).
% 21.38/3.77 thf(zip_derived_cl1, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (((divide @ X0 @ X1) != (zero)) | (less_equal @ X0 @ X1))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_less_equal2])).
% 21.38/3.77 thf(zip_derived_cl5855, plain,
% 21.38/3.77 (![X0 : $i]: (((zero) != (zero)) | (less_equal @ (divide @ X0 @ e) @ c))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl5836, zip_derived_cl1])).
% 21.38/3.77 thf(zip_derived_cl5918, plain,
% 21.38/3.77 (![X0 : $i]: (less_equal @ (divide @ X0 @ e) @ c)),
% 21.38/3.77 inference('simplify', [status(thm)], [zip_derived_cl5855])).
% 21.38/3.77 thf(zip_derived_cl8749, plain, (((divide @ (divide @ c @ e) @ a) = (c))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl8416, zip_derived_cl440])).
% 21.38/3.77 thf(zip_derived_cl8797, plain, (((c) = (divide @ c @ e))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl8756, zip_derived_cl5918, zip_derived_cl8749])).
% 21.38/3.77 thf(zip_derived_cl8833, plain,
% 21.38/3.77 (((divide @ (divide @ c @ (divide @ d @ e)) @ (divide @ g @ e)) = (zero))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl3897, zip_derived_cl8797])).
% 21.38/3.77 thf(zip_derived_cl18, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]: ((divide @ (divide @ X0 @ X1) @ X0) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl47, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.38/3.77 (((divide @ (divide @ X2 @ X0) @ (divide @ X1 @ X0))
% 21.38/3.77 = (divide @ (divide @ X2 @ X1) @ X0))
% 21.38/3.77 | ~ (less_equal @ (divide @ (divide @ X2 @ X1) @ X0) @
% 21.38/3.77 (divide @ (divide @ X2 @ X0) @ (divide @ X1 @ X0))))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl5])).
% 21.38/3.77 thf(zip_derived_cl299, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.38/3.77 (~ (less_equal @ (divide @ (divide @ X2 @ (divide @ X0 @ X1)) @ X0) @
% 21.38/3.77 (divide @ (divide @ X2 @ X0) @ zero))
% 21.38/3.77 | ((divide @ (divide @ X2 @ X0) @ (divide @ (divide @ X0 @ X1) @ X0))
% 21.38/3.77 = (divide @ (divide @ X2 @ (divide @ X0 @ X1)) @ X0)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl47])).
% 21.38/3.77 thf(zip_derived_cl18, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]: ((divide @ (divide @ X0 @ X1) @ X0) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl341, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.38/3.77 (~ (less_equal @ (divide @ (divide @ X2 @ (divide @ X0 @ X1)) @ X0) @
% 21.38/3.77 (divide @ (divide @ X2 @ X0) @ zero))
% 21.38/3.77 | ((divide @ (divide @ X2 @ X0) @ zero)
% 21.38/3.77 = (divide @ (divide @ X2 @ (divide @ X0 @ X1)) @ X0)))),
% 21.38/3.77 inference('demod', [status(thm)], [zip_derived_cl299, zip_derived_cl18])).
% 21.38/3.77 thf(zip_derived_cl8204, plain, (![X0 : $i]: ((divide @ X0 @ zero) = (X0))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl7582, zip_derived_cl42])).
% 21.38/3.77 thf(zip_derived_cl8204, plain, (![X0 : $i]: ((divide @ X0 @ zero) = (X0))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl7582, zip_derived_cl42])).
% 21.38/3.77 thf(zip_derived_cl10618, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.38/3.77 (~ (less_equal @ (divide @ (divide @ X2 @ (divide @ X0 @ X1)) @ X0) @
% 21.38/3.77 (divide @ X2 @ X0))
% 21.38/3.77 | ((divide @ X2 @ X0)
% 21.38/3.77 = (divide @ (divide @ X2 @ (divide @ X0 @ X1)) @ X0)))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl341, zip_derived_cl8204, zip_derived_cl8204])).
% 21.38/3.77 thf(zip_derived_cl10688, plain,
% 21.38/3.77 ((~ (less_equal @ (divide @ zero @ g) @
% 21.38/3.77 (divide @ (divide @ c @ (divide @ d @ e)) @ g))
% 21.38/3.77 | ((divide @ (divide @ c @ (divide @ d @ e)) @ g)
% 21.38/3.77 = (divide @
% 21.38/3.77 (divide @ (divide @ c @ (divide @ d @ e)) @ (divide @ g @ e)) @
% 21.38/3.77 g)))),
% 21.38/3.77 inference('sup-', [status(thm)],
% 21.38/3.77 [zip_derived_cl8833, zip_derived_cl10618])).
% 21.38/3.77 thf(zip_derived_cl19, plain, (![X0 : $i]: ((divide @ zero @ X0) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl4, plain, (![X0 : $i]: (less_equal @ zero @ X0)),
% 21.38/3.77 inference('cnf', [status(esa)], [zero_is_smallest])).
% 21.38/3.77 thf(zip_derived_cl8833, plain,
% 21.38/3.77 (((divide @ (divide @ c @ (divide @ d @ e)) @ (divide @ g @ e)) = (zero))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl3897, zip_derived_cl8797])).
% 21.38/3.77 thf(zip_derived_cl19, plain, (![X0 : $i]: ((divide @ zero @ X0) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl10821, plain,
% 21.38/3.77 (((divide @ (divide @ c @ (divide @ d @ e)) @ g) = (zero))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl10688, zip_derived_cl19, zip_derived_cl4,
% 21.38/3.77 zip_derived_cl8833, zip_derived_cl19])).
% 21.38/3.77 thf(zip_derived_cl47, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.38/3.77 (((divide @ (divide @ X2 @ X0) @ (divide @ X1 @ X0))
% 21.38/3.77 = (divide @ (divide @ X2 @ X1) @ X0))
% 21.38/3.77 | ~ (less_equal @ (divide @ (divide @ X2 @ X1) @ X0) @
% 21.38/3.77 (divide @ (divide @ X2 @ X0) @ (divide @ X1 @ X0))))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl5])).
% 21.38/3.77 thf(zip_derived_cl13069, plain,
% 21.38/3.77 ((~ (less_equal @ zero @
% 21.38/3.77 (divide @ (divide @ c @ g) @ (divide @ (divide @ d @ e) @ g)))
% 21.38/3.77 | ((divide @ (divide @ c @ g) @ (divide @ (divide @ d @ e) @ g))
% 21.38/3.77 = (divide @ (divide @ c @ (divide @ d @ e)) @ g)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl10821, zip_derived_cl47])).
% 21.38/3.77 thf(zip_derived_cl4, plain, (![X0 : $i]: (less_equal @ zero @ X0)),
% 21.38/3.77 inference('cnf', [status(esa)], [zero_is_smallest])).
% 21.38/3.77 thf(zip_derived_cl10821, plain,
% 21.38/3.77 (((divide @ (divide @ c @ (divide @ d @ e)) @ g) = (zero))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl10688, zip_derived_cl19, zip_derived_cl4,
% 21.38/3.77 zip_derived_cl8833, zip_derived_cl19])).
% 21.38/3.77 thf(zip_derived_cl13118, plain,
% 21.38/3.77 (((divide @ (divide @ c @ g) @ (divide @ (divide @ d @ e) @ g)) = (zero))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl13069, zip_derived_cl4, zip_derived_cl10821])).
% 21.38/3.77 thf(zip_derived_cl10618, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.38/3.77 (~ (less_equal @ (divide @ (divide @ X2 @ (divide @ X0 @ X1)) @ X0) @
% 21.38/3.77 (divide @ X2 @ X0))
% 21.38/3.77 | ((divide @ X2 @ X0)
% 21.38/3.77 = (divide @ (divide @ X2 @ (divide @ X0 @ X1)) @ X0)))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl341, zip_derived_cl8204, zip_derived_cl8204])).
% 21.38/3.77 thf(zip_derived_cl21350, plain,
% 21.38/3.77 ((~ (less_equal @ (divide @ zero @ (divide @ d @ e)) @
% 21.38/3.77 (divide @ (divide @ c @ g) @ (divide @ d @ e)))
% 21.38/3.77 | ((divide @ (divide @ c @ g) @ (divide @ d @ e))
% 21.38/3.77 = (divide @
% 21.38/3.77 (divide @ (divide @ c @ g) @ (divide @ (divide @ d @ e) @ g)) @
% 21.38/3.77 (divide @ d @ e))))),
% 21.38/3.77 inference('sup-', [status(thm)],
% 21.38/3.77 [zip_derived_cl13118, zip_derived_cl10618])).
% 21.38/3.77 thf(zip_derived_cl19, plain, (![X0 : $i]: ((divide @ zero @ X0) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl4, plain, (![X0 : $i]: (less_equal @ zero @ X0)),
% 21.38/3.77 inference('cnf', [status(esa)], [zero_is_smallest])).
% 21.38/3.77 thf(zip_derived_cl13118, plain,
% 21.38/3.77 (((divide @ (divide @ c @ g) @ (divide @ (divide @ d @ e) @ g)) = (zero))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl13069, zip_derived_cl4, zip_derived_cl10821])).
% 21.38/3.77 thf(zip_derived_cl19, plain, (![X0 : $i]: ((divide @ zero @ X0) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl21397, plain,
% 21.38/3.77 (((divide @ (divide @ c @ g) @ (divide @ d @ e)) = (zero))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl21350, zip_derived_cl19, zip_derived_cl4,
% 21.38/3.77 zip_derived_cl13118, zip_derived_cl19])).
% 21.38/3.77 thf(zip_derived_cl1, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (((divide @ X0 @ X1) != (zero)) | (less_equal @ X0 @ X1))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_less_equal2])).
% 21.38/3.77 thf(zip_derived_cl21445, plain,
% 21.38/3.77 ((((zero) != (zero))
% 21.38/3.77 | (less_equal @ (divide @ c @ g) @ (divide @ d @ e)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl21397, zip_derived_cl1])).
% 21.38/3.77 thf(zip_derived_cl21490, plain,
% 21.38/3.77 ( (less_equal @ (divide @ c @ g) @ (divide @ d @ e))),
% 21.38/3.77 inference('simplify', [status(thm)], [zip_derived_cl21445])).
% 21.38/3.77 thf(zip_derived_cl5, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 21.38/3.77 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 21.38/3.77 thf(zip_derived_cl21529, plain,
% 21.38/3.77 ((((divide @ c @ g) = (divide @ d @ e))
% 21.38/3.77 | ~ (less_equal @ (divide @ d @ e) @ (divide @ c @ g)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl21490, zip_derived_cl5])).
% 21.38/3.77 thf(prove_commutativity, conjecture,
% 21.38/3.77 (( divide @ c @ g ) = ( divide @ d @ e ))).
% 21.38/3.77 thf(zf_stmt_0, negated_conjecture,
% 21.38/3.77 (( divide @ c @ g ) != ( divide @ d @ e )),
% 21.38/3.77 inference('cnf.neg', [status(esa)], [prove_commutativity])).
% 21.38/3.77 thf(zip_derived_cl12, plain, (((divide @ c @ g) != (divide @ d @ e))),
% 21.38/3.77 inference('cnf', [status(esa)], [zf_stmt_0])).
% 21.38/3.77 thf(zip_derived_cl21530, plain,
% 21.38/3.77 (~ (less_equal @ (divide @ d @ e) @ (divide @ c @ g))),
% 21.38/3.77 inference('simplify_reflect-', [status(thm)],
% 21.38/3.77 [zip_derived_cl21529, zip_derived_cl12])).
% 21.38/3.77 thf(zip_derived_cl2569, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (less_equal @ (divide @ X1 @ X0) @ (divide @ identity @ X0))),
% 21.38/3.77 inference('simplify', [status(thm)], [zip_derived_cl2482])).
% 21.38/3.77 thf(zip_derived_cl11, plain, (((divide @ identity @ d) = (g))),
% 21.38/3.77 inference('cnf', [status(esa)], [identity_divide_d])).
% 21.38/3.77 thf(zip_derived_cl47, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.38/3.77 (((divide @ (divide @ X2 @ X0) @ (divide @ X1 @ X0))
% 21.38/3.77 = (divide @ (divide @ X2 @ X1) @ X0))
% 21.38/3.77 | ~ (less_equal @ (divide @ (divide @ X2 @ X1) @ X0) @
% 21.38/3.77 (divide @ (divide @ X2 @ X0) @ (divide @ X1 @ X0))))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl5])).
% 21.38/3.77 thf(zip_derived_cl307, plain,
% 21.38/3.77 (![X0 : $i]:
% 21.38/3.77 (~ (less_equal @ (divide @ (divide @ X0 @ identity) @ d) @
% 21.38/3.77 (divide @ (divide @ X0 @ d) @ g))
% 21.38/3.77 | ((divide @ (divide @ X0 @ d) @ (divide @ identity @ d))
% 21.38/3.77 = (divide @ (divide @ X0 @ identity) @ d)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl47])).
% 21.38/3.77 thf(zip_derived_cl17, plain,
% 21.38/3.77 (![X0 : $i]: ((divide @ X0 @ identity) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl19, plain, (![X0 : $i]: ((divide @ zero @ X0) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl4, plain, (![X0 : $i]: (less_equal @ zero @ X0)),
% 21.38/3.77 inference('cnf', [status(esa)], [zero_is_smallest])).
% 21.38/3.77 thf(zip_derived_cl11, plain, (((divide @ identity @ d) = (g))),
% 21.38/3.77 inference('cnf', [status(esa)], [identity_divide_d])).
% 21.38/3.77 thf(zip_derived_cl17, plain,
% 21.38/3.77 (![X0 : $i]: ((divide @ X0 @ identity) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl19, plain, (![X0 : $i]: ((divide @ zero @ X0) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl349, plain,
% 21.38/3.77 (![X0 : $i]: ((divide @ (divide @ X0 @ d) @ g) = (zero))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl307, zip_derived_cl17, zip_derived_cl19,
% 21.38/3.77 zip_derived_cl4, zip_derived_cl11, zip_derived_cl17,
% 21.38/3.77 zip_derived_cl19])).
% 21.38/3.77 thf(zip_derived_cl47, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.38/3.77 (((divide @ (divide @ X2 @ X0) @ (divide @ X1 @ X0))
% 21.38/3.77 = (divide @ (divide @ X2 @ X1) @ X0))
% 21.38/3.77 | ~ (less_equal @ (divide @ (divide @ X2 @ X1) @ X0) @
% 21.38/3.77 (divide @ (divide @ X2 @ X0) @ (divide @ X1 @ X0))))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl5])).
% 21.38/3.77 thf(zip_derived_cl396, plain,
% 21.38/3.77 (![X0 : $i]:
% 21.38/3.77 (~ (less_equal @ zero @
% 21.38/3.77 (divide @ (divide @ X0 @ g) @ (divide @ d @ g)))
% 21.38/3.77 | ((divide @ (divide @ X0 @ g) @ (divide @ d @ g))
% 21.38/3.77 = (divide @ (divide @ X0 @ d) @ g)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl349, zip_derived_cl47])).
% 21.38/3.77 thf(zip_derived_cl4, plain, (![X0 : $i]: (less_equal @ zero @ X0)),
% 21.38/3.77 inference('cnf', [status(esa)], [zero_is_smallest])).
% 21.38/3.77 thf(zip_derived_cl349, plain,
% 21.38/3.77 (![X0 : $i]: ((divide @ (divide @ X0 @ d) @ g) = (zero))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl307, zip_derived_cl17, zip_derived_cl19,
% 21.38/3.77 zip_derived_cl4, zip_derived_cl11, zip_derived_cl17,
% 21.38/3.77 zip_derived_cl19])).
% 21.38/3.77 thf(zip_derived_cl409, plain,
% 21.38/3.77 (![X0 : $i]: ((divide @ (divide @ X0 @ g) @ (divide @ d @ g)) = (zero))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl396, zip_derived_cl4, zip_derived_cl349])).
% 21.38/3.77 thf(zip_derived_cl1, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (((divide @ X0 @ X1) != (zero)) | (less_equal @ X0 @ X1))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_less_equal2])).
% 21.38/3.77 thf(zip_derived_cl1748, plain,
% 21.38/3.77 (![X0 : $i]:
% 21.38/3.77 (((zero) != (zero))
% 21.38/3.77 | (less_equal @ (divide @ X0 @ g) @ (divide @ d @ g)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl409, zip_derived_cl1])).
% 21.38/3.77 thf(zip_derived_cl1781, plain,
% 21.38/3.77 (![X0 : $i]: (less_equal @ (divide @ X0 @ g) @ (divide @ d @ g))),
% 21.38/3.77 inference('simplify', [status(thm)], [zip_derived_cl1748])).
% 21.38/3.77 thf(zip_derived_cl5, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 21.38/3.77 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 21.38/3.77 thf(zip_derived_cl1802, plain,
% 21.38/3.77 (![X0 : $i]:
% 21.38/3.77 (((divide @ X0 @ g) = (divide @ d @ g))
% 21.38/3.77 | ~ (less_equal @ (divide @ d @ g) @ (divide @ X0 @ g)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl1781, zip_derived_cl5])).
% 21.38/3.77 thf(zip_derived_cl2944, plain,
% 21.38/3.77 (((divide @ identity @ g) = (divide @ d @ g))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl2569, zip_derived_cl1802])).
% 21.38/3.77 thf(zip_derived_cl10, plain, (((divide @ identity @ c) = (e))),
% 21.38/3.77 inference('cnf', [status(esa)], [identity_divide_c])).
% 21.38/3.77 thf(zip_derived_cl3, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.38/3.77 (less_equal @ (divide @ (divide @ X0 @ X1) @ (divide @ X2 @ X1)) @
% 21.38/3.77 (divide @ (divide @ X0 @ X2) @ X1))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_property])).
% 21.38/3.77 thf(zip_derived_cl55, plain,
% 21.38/3.77 (![X0 : $i]:
% 21.38/3.77 (less_equal @
% 21.38/3.77 (divide @ (divide @ identity @ X0) @ (divide @ c @ X0)) @
% 21.38/3.77 (divide @ e @ X0))),
% 21.38/3.77 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl3])).
% 21.38/3.77 thf(zip_derived_cl3091, plain,
% 21.38/3.77 ( (less_equal @ (divide @ (divide @ d @ g) @ (divide @ c @ g)) @
% 21.38/3.77 (divide @ e @ g))),
% 21.38/3.77 inference('sup+', [status(thm)], [zip_derived_cl2944, zip_derived_cl55])).
% 21.38/3.77 thf(zip_derived_cl0, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (~ (less_equal @ X0 @ X1) | ((divide @ X0 @ X1) = (zero)))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_less_equal1])).
% 21.38/3.77 thf(zip_derived_cl4037, plain,
% 21.38/3.77 (((divide @ (divide @ (divide @ d @ g) @ (divide @ c @ g)) @
% 21.38/3.77 (divide @ e @ g)) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl3091, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl2944, plain,
% 21.38/3.77 (((divide @ identity @ g) = (divide @ d @ g))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl2569, zip_derived_cl1802])).
% 21.38/3.77 thf(identity_divide_b, axiom, (( divide @ identity @ b ) = ( d ))).
% 21.38/3.77 thf(zip_derived_cl9, plain, (((divide @ identity @ b) = (d))),
% 21.38/3.77 inference('cnf', [status(esa)], [identity_divide_b])).
% 21.38/3.77 thf(zip_derived_cl3, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.38/3.77 (less_equal @ (divide @ (divide @ X0 @ X1) @ (divide @ X2 @ X1)) @
% 21.38/3.77 (divide @ (divide @ X0 @ X2) @ X1))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_property])).
% 21.38/3.77 thf(zip_derived_cl69, plain,
% 21.38/3.77 (![X0 : $i]:
% 21.38/3.77 (less_equal @ (divide @ d @ (divide @ X0 @ b)) @
% 21.38/3.77 (divide @ (divide @ identity @ X0) @ b))),
% 21.38/3.77 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl3])).
% 21.38/3.77 thf(zip_derived_cl3094, plain,
% 21.38/3.77 ( (less_equal @ (divide @ d @ (divide @ g @ b)) @
% 21.38/3.77 (divide @ (divide @ d @ g) @ b))),
% 21.38/3.77 inference('sup+', [status(thm)], [zip_derived_cl2944, zip_derived_cl69])).
% 21.38/3.77 thf(zip_derived_cl9, plain, (((divide @ identity @ b) = (d))),
% 21.38/3.77 inference('cnf', [status(esa)], [identity_divide_b])).
% 21.38/3.77 thf(zip_derived_cl9, plain, (((divide @ identity @ b) = (d))),
% 21.38/3.77 inference('cnf', [status(esa)], [identity_divide_b])).
% 21.38/3.77 thf(zip_derived_cl47, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.38/3.77 (((divide @ (divide @ X2 @ X0) @ (divide @ X1 @ X0))
% 21.38/3.77 = (divide @ (divide @ X2 @ X1) @ X0))
% 21.38/3.77 | ~ (less_equal @ (divide @ (divide @ X2 @ X1) @ X0) @
% 21.38/3.77 (divide @ (divide @ X2 @ X0) @ (divide @ X1 @ X0))))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl5])).
% 21.38/3.77 thf(zip_derived_cl305, plain,
% 21.38/3.77 (![X0 : $i]:
% 21.38/3.77 (~ (less_equal @ (divide @ (divide @ X0 @ identity) @ b) @
% 21.38/3.77 (divide @ (divide @ X0 @ b) @ d))
% 21.38/3.77 | ((divide @ (divide @ X0 @ b) @ (divide @ identity @ b))
% 21.38/3.77 = (divide @ (divide @ X0 @ identity) @ b)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl47])).
% 21.38/3.77 thf(zip_derived_cl17, plain,
% 21.38/3.77 (![X0 : $i]: ((divide @ X0 @ identity) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl19, plain, (![X0 : $i]: ((divide @ zero @ X0) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl4, plain, (![X0 : $i]: (less_equal @ zero @ X0)),
% 21.38/3.77 inference('cnf', [status(esa)], [zero_is_smallest])).
% 21.38/3.77 thf(zip_derived_cl9, plain, (((divide @ identity @ b) = (d))),
% 21.38/3.77 inference('cnf', [status(esa)], [identity_divide_b])).
% 21.38/3.77 thf(zip_derived_cl17, plain,
% 21.38/3.77 (![X0 : $i]: ((divide @ X0 @ identity) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl19, plain, (![X0 : $i]: ((divide @ zero @ X0) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl347, plain,
% 21.38/3.77 (![X0 : $i]: ((divide @ (divide @ X0 @ b) @ d) = (zero))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl305, zip_derived_cl17, zip_derived_cl19,
% 21.38/3.77 zip_derived_cl4, zip_derived_cl9, zip_derived_cl17,
% 21.38/3.77 zip_derived_cl19])).
% 21.38/3.77 thf(zip_derived_cl510, plain, (((divide @ d @ d) = (zero))),
% 21.38/3.77 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl347])).
% 21.38/3.77 thf(zip_derived_cl9, plain, (((divide @ identity @ b) = (d))),
% 21.38/3.77 inference('cnf', [status(esa)], [identity_divide_b])).
% 21.38/3.77 thf(zip_derived_cl3, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.38/3.77 (less_equal @ (divide @ (divide @ X0 @ X1) @ (divide @ X2 @ X1)) @
% 21.38/3.77 (divide @ (divide @ X0 @ X2) @ X1))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_property])).
% 21.38/3.77 thf(zip_derived_cl54, plain,
% 21.38/3.77 (![X0 : $i]:
% 21.38/3.77 (less_equal @
% 21.38/3.77 (divide @ (divide @ identity @ X0) @ (divide @ b @ X0)) @
% 21.38/3.77 (divide @ d @ X0))),
% 21.38/3.77 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl3])).
% 21.38/3.77 thf(zip_derived_cl576, plain,
% 21.38/3.77 ( (less_equal @ (divide @ (divide @ identity @ d) @ (divide @ b @ d)) @
% 21.38/3.77 zero)),
% 21.38/3.77 inference('sup+', [status(thm)], [zip_derived_cl510, zip_derived_cl54])).
% 21.38/3.77 thf(zip_derived_cl11, plain, (((divide @ identity @ d) = (g))),
% 21.38/3.77 inference('cnf', [status(esa)], [identity_divide_d])).
% 21.38/3.77 thf(zip_derived_cl584, plain,
% 21.38/3.77 ( (less_equal @ (divide @ g @ (divide @ b @ d)) @ zero)),
% 21.38/3.77 inference('demod', [status(thm)], [zip_derived_cl576, zip_derived_cl11])).
% 21.38/3.77 thf(zip_derived_cl43, plain,
% 21.38/3.77 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 21.38/3.77 thf(zip_derived_cl1130, plain, (((zero) = (divide @ g @ (divide @ b @ d)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl584, zip_derived_cl43])).
% 21.38/3.77 thf(zip_derived_cl1, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (((divide @ X0 @ X1) != (zero)) | (less_equal @ X0 @ X1))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_less_equal2])).
% 21.38/3.77 thf(zip_derived_cl1160, plain,
% 21.38/3.77 ((((zero) != (zero)) | (less_equal @ g @ (divide @ b @ d)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl1130, zip_derived_cl1])).
% 21.38/3.77 thf(zip_derived_cl1178, plain, ( (less_equal @ g @ (divide @ b @ d))),
% 21.38/3.77 inference('simplify', [status(thm)], [zip_derived_cl1160])).
% 21.38/3.77 thf(zip_derived_cl349, plain,
% 21.38/3.77 (![X0 : $i]: ((divide @ (divide @ X0 @ d) @ g) = (zero))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl307, zip_derived_cl17, zip_derived_cl19,
% 21.38/3.77 zip_derived_cl4, zip_derived_cl11, zip_derived_cl17,
% 21.38/3.77 zip_derived_cl19])).
% 21.38/3.77 thf(zip_derived_cl1, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (((divide @ X0 @ X1) != (zero)) | (less_equal @ X0 @ X1))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_less_equal2])).
% 21.38/3.77 thf(zip_derived_cl381, plain,
% 21.38/3.77 (![X0 : $i]: (((zero) != (zero)) | (less_equal @ (divide @ X0 @ d) @ g))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl349, zip_derived_cl1])).
% 21.38/3.77 thf(zip_derived_cl400, plain,
% 21.38/3.77 (![X0 : $i]: (less_equal @ (divide @ X0 @ d) @ g)),
% 21.38/3.77 inference('simplify', [status(thm)], [zip_derived_cl381])).
% 21.38/3.77 thf(zip_derived_cl5, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 21.38/3.77 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 21.38/3.77 thf(zip_derived_cl435, plain,
% 21.38/3.77 (![X0 : $i]:
% 21.38/3.77 (((divide @ X0 @ d) = (g)) | ~ (less_equal @ g @ (divide @ X0 @ d)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl400, zip_derived_cl5])).
% 21.38/3.77 thf(zip_derived_cl1191, plain, (((divide @ b @ d) = (g))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl1178, zip_derived_cl435])).
% 21.38/3.77 thf(zip_derived_cl18, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]: ((divide @ (divide @ X0 @ X1) @ X0) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl1199, plain, (((divide @ g @ b) = (zero))),
% 21.38/3.77 inference('sup+', [status(thm)], [zip_derived_cl1191, zip_derived_cl18])).
% 21.38/3.77 thf(zip_derived_cl3118, plain,
% 21.38/3.77 ( (less_equal @ (divide @ d @ zero) @ (divide @ (divide @ d @ g) @ b))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl3094, zip_derived_cl1199])).
% 21.38/3.77 thf(zip_derived_cl8204, plain, (![X0 : $i]: ((divide @ X0 @ zero) = (X0))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl7582, zip_derived_cl42])).
% 21.38/3.77 thf(zip_derived_cl8417, plain,
% 21.38/3.77 ( (less_equal @ d @ (divide @ (divide @ d @ g) @ b))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl3118, zip_derived_cl8204])).
% 21.38/3.77 thf(zip_derived_cl347, plain,
% 21.38/3.77 (![X0 : $i]: ((divide @ (divide @ X0 @ b) @ d) = (zero))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl305, zip_derived_cl17, zip_derived_cl19,
% 21.38/3.77 zip_derived_cl4, zip_derived_cl9, zip_derived_cl17,
% 21.38/3.77 zip_derived_cl19])).
% 21.38/3.77 thf(zip_derived_cl1, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (((divide @ X0 @ X1) != (zero)) | (less_equal @ X0 @ X1))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_less_equal2])).
% 21.38/3.77 thf(zip_derived_cl488, plain,
% 21.38/3.77 (![X0 : $i]: (((zero) != (zero)) | (less_equal @ (divide @ X0 @ b) @ d))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl347, zip_derived_cl1])).
% 21.38/3.77 thf(zip_derived_cl511, plain,
% 21.38/3.77 (![X0 : $i]: (less_equal @ (divide @ X0 @ b) @ d)),
% 21.38/3.77 inference('simplify', [status(thm)], [zip_derived_cl488])).
% 21.38/3.77 thf(zip_derived_cl5, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 21.38/3.77 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 21.38/3.77 thf(zip_derived_cl569, plain,
% 21.38/3.77 (![X0 : $i]:
% 21.38/3.77 (((divide @ X0 @ b) = (d)) | ~ (less_equal @ d @ (divide @ X0 @ b)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl511, zip_derived_cl5])).
% 21.38/3.77 thf(zip_derived_cl9111, plain, (((divide @ (divide @ d @ g) @ b) = (d))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl8417, zip_derived_cl569])).
% 21.38/3.77 thf(zip_derived_cl42, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (((divide @ X0 @ X1) = (X0))
% 21.38/3.77 | ~ (less_equal @ X0 @ (divide @ X0 @ X1)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl5])).
% 21.38/3.77 thf(zip_derived_cl9118, plain,
% 21.38/3.77 ((~ (less_equal @ (divide @ d @ g) @ d)
% 21.38/3.77 | ((divide @ (divide @ d @ g) @ b) = (divide @ d @ g)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl9111, zip_derived_cl42])).
% 21.38/3.77 thf(zip_derived_cl2, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]: (less_equal @ (divide @ X0 @ X1) @ X0)),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_smaller_than_numerator])).
% 21.38/3.77 thf(zip_derived_cl9111, plain, (((divide @ (divide @ d @ g) @ b) = (d))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl8417, zip_derived_cl569])).
% 21.38/3.77 thf(zip_derived_cl9159, plain, (((d) = (divide @ d @ g))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl9118, zip_derived_cl2, zip_derived_cl9111])).
% 21.38/3.77 thf(zip_derived_cl9629, plain,
% 21.38/3.77 (((divide @ (divide @ d @ (divide @ c @ g)) @ (divide @ e @ g)) = (zero))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl4037, zip_derived_cl9159])).
% 21.38/3.77 thf(zip_derived_cl10618, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.38/3.77 (~ (less_equal @ (divide @ (divide @ X2 @ (divide @ X0 @ X1)) @ X0) @
% 21.38/3.77 (divide @ X2 @ X0))
% 21.38/3.77 | ((divide @ X2 @ X0)
% 21.38/3.77 = (divide @ (divide @ X2 @ (divide @ X0 @ X1)) @ X0)))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl341, zip_derived_cl8204, zip_derived_cl8204])).
% 21.38/3.77 thf(zip_derived_cl20282, plain,
% 21.38/3.77 ((~ (less_equal @ (divide @ zero @ e) @
% 21.38/3.77 (divide @ (divide @ d @ (divide @ c @ g)) @ e))
% 21.38/3.77 | ((divide @ (divide @ d @ (divide @ c @ g)) @ e)
% 21.38/3.77 = (divide @
% 21.38/3.77 (divide @ (divide @ d @ (divide @ c @ g)) @ (divide @ e @ g)) @
% 21.38/3.77 e)))),
% 21.38/3.77 inference('sup-', [status(thm)],
% 21.38/3.77 [zip_derived_cl9629, zip_derived_cl10618])).
% 21.38/3.77 thf(zip_derived_cl19, plain, (![X0 : $i]: ((divide @ zero @ X0) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl4, plain, (![X0 : $i]: (less_equal @ zero @ X0)),
% 21.38/3.77 inference('cnf', [status(esa)], [zero_is_smallest])).
% 21.38/3.77 thf(zip_derived_cl9629, plain,
% 21.38/3.77 (((divide @ (divide @ d @ (divide @ c @ g)) @ (divide @ e @ g)) = (zero))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl4037, zip_derived_cl9159])).
% 21.38/3.77 thf(zip_derived_cl19, plain, (![X0 : $i]: ((divide @ zero @ X0) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl20320, plain,
% 21.38/3.77 (((divide @ (divide @ d @ (divide @ c @ g)) @ e) = (zero))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl20282, zip_derived_cl19, zip_derived_cl4,
% 21.38/3.77 zip_derived_cl9629, zip_derived_cl19])).
% 21.38/3.77 thf(zip_derived_cl47, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.38/3.77 (((divide @ (divide @ X2 @ X0) @ (divide @ X1 @ X0))
% 21.38/3.77 = (divide @ (divide @ X2 @ X1) @ X0))
% 21.38/3.77 | ~ (less_equal @ (divide @ (divide @ X2 @ X1) @ X0) @
% 21.38/3.77 (divide @ (divide @ X2 @ X0) @ (divide @ X1 @ X0))))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl5])).
% 21.38/3.77 thf(zip_derived_cl20367, plain,
% 21.38/3.77 ((~ (less_equal @ zero @
% 21.38/3.77 (divide @ (divide @ d @ e) @ (divide @ (divide @ c @ g) @ e)))
% 21.38/3.77 | ((divide @ (divide @ d @ e) @ (divide @ (divide @ c @ g) @ e))
% 21.38/3.77 = (divide @ (divide @ d @ (divide @ c @ g)) @ e)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl20320, zip_derived_cl47])).
% 21.38/3.77 thf(zip_derived_cl4, plain, (![X0 : $i]: (less_equal @ zero @ X0)),
% 21.38/3.77 inference('cnf', [status(esa)], [zero_is_smallest])).
% 21.38/3.77 thf(zip_derived_cl20320, plain,
% 21.38/3.77 (((divide @ (divide @ d @ (divide @ c @ g)) @ e) = (zero))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl20282, zip_derived_cl19, zip_derived_cl4,
% 21.38/3.77 zip_derived_cl9629, zip_derived_cl19])).
% 21.38/3.77 thf(zip_derived_cl20408, plain,
% 21.38/3.77 (((divide @ (divide @ d @ e) @ (divide @ (divide @ c @ g) @ e)) = (zero))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl20367, zip_derived_cl4, zip_derived_cl20320])).
% 21.38/3.77 thf(zip_derived_cl10618, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.38/3.77 (~ (less_equal @ (divide @ (divide @ X2 @ (divide @ X0 @ X1)) @ X0) @
% 21.38/3.77 (divide @ X2 @ X0))
% 21.38/3.77 | ((divide @ X2 @ X0)
% 21.38/3.77 = (divide @ (divide @ X2 @ (divide @ X0 @ X1)) @ X0)))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl341, zip_derived_cl8204, zip_derived_cl8204])).
% 21.38/3.77 thf(zip_derived_cl28312, plain,
% 21.38/3.77 ((~ (less_equal @ (divide @ zero @ (divide @ c @ g)) @
% 21.38/3.77 (divide @ (divide @ d @ e) @ (divide @ c @ g)))
% 21.38/3.77 | ((divide @ (divide @ d @ e) @ (divide @ c @ g))
% 21.38/3.77 = (divide @
% 21.38/3.77 (divide @ (divide @ d @ e) @ (divide @ (divide @ c @ g) @ e)) @
% 21.38/3.77 (divide @ c @ g))))),
% 21.38/3.77 inference('sup-', [status(thm)],
% 21.38/3.77 [zip_derived_cl20408, zip_derived_cl10618])).
% 21.38/3.77 thf(zip_derived_cl19, plain, (![X0 : $i]: ((divide @ zero @ X0) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl4, plain, (![X0 : $i]: (less_equal @ zero @ X0)),
% 21.38/3.77 inference('cnf', [status(esa)], [zero_is_smallest])).
% 21.38/3.77 thf(zip_derived_cl20408, plain,
% 21.38/3.77 (((divide @ (divide @ d @ e) @ (divide @ (divide @ c @ g) @ e)) = (zero))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl20367, zip_derived_cl4, zip_derived_cl20320])).
% 21.38/3.77 thf(zip_derived_cl19, plain, (![X0 : $i]: ((divide @ zero @ X0) = (zero))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 21.38/3.77 thf(zip_derived_cl28368, plain,
% 21.38/3.77 (((divide @ (divide @ d @ e) @ (divide @ c @ g)) = (zero))),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl28312, zip_derived_cl19, zip_derived_cl4,
% 21.38/3.77 zip_derived_cl20408, zip_derived_cl19])).
% 21.38/3.77 thf(zip_derived_cl1, plain,
% 21.38/3.77 (![X0 : $i, X1 : $i]:
% 21.38/3.77 (((divide @ X0 @ X1) != (zero)) | (less_equal @ X0 @ X1))),
% 21.38/3.77 inference('cnf', [status(esa)], [quotient_less_equal2])).
% 21.38/3.77 thf(zip_derived_cl28385, plain,
% 21.38/3.77 ((((zero) != (zero))
% 21.38/3.77 | (less_equal @ (divide @ d @ e) @ (divide @ c @ g)))),
% 21.38/3.77 inference('sup-', [status(thm)], [zip_derived_cl28368, zip_derived_cl1])).
% 21.38/3.77 thf(zip_derived_cl28437, plain,
% 21.38/3.77 ( (less_equal @ (divide @ d @ e) @ (divide @ c @ g))),
% 21.38/3.77 inference('simplify', [status(thm)], [zip_derived_cl28385])).
% 21.38/3.77 thf(zip_derived_cl28481, plain, ($false),
% 21.38/3.77 inference('demod', [status(thm)],
% 21.38/3.77 [zip_derived_cl21530, zip_derived_cl28437])).
% 21.38/3.77
% 21.38/3.77 % SZS output end Refutation
% 21.38/3.77
% 21.38/3.77
% 21.38/3.77 % Terminating...
% 22.12/3.88 % Runner terminated.
% 22.12/3.90 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------