TSTP Solution File: HEN010-4 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : HEN010-4 : 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.IliPfc5RmO 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 01:57:53 EDT 2023
% Result : Unsatisfiable 1.59s 0.95s
% Output : Refutation 1.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : HEN010-4 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.IliPfc5RmO true
% 0.15/0.35 % Computer : n025.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 24 13:46:06 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % Running portfolio for 300 s
% 0.15/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.35 % Number of cores: 8
% 0.15/0.35 % Python version: Python 3.6.8
% 0.15/0.35 % Running in FO mode
% 0.21/0.65 % Total configuration time : 435
% 0.21/0.65 % Estimated wc time : 1092
% 0.21/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 1.17/0.83 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 1.59/0.95 % Solved by fo/fo6_bce.sh.
% 1.59/0.95 % BCE start: 17
% 1.59/0.95 % BCE eliminated: 0
% 1.59/0.95 % PE start: 17
% 1.59/0.95 logic: eq
% 1.59/0.95 % PE eliminated: 0
% 1.59/0.95 % done 187 iterations in 0.181s
% 1.59/0.95 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.59/0.95 % SZS output start Refutation
% 1.59/0.95 thf(zero_type, type, zero: $i).
% 1.59/0.95 thf(divide_type, type, divide: $i > $i > $i).
% 1.59/0.95 thf(a_type, type, a: $i).
% 1.59/0.95 thf(less_equal_type, type, less_equal: $i > $i > $o).
% 1.59/0.95 thf(identity_type, type, identity: $i).
% 1.59/0.95 thf(everything_divide_id_is_zero, axiom,
% 1.59/0.95 (( divide @ X @ identity ) = ( zero ))).
% 1.59/0.95 thf(zip_derived_cl7, plain,
% 1.59/0.95 (![X0 : $i]: ((divide @ X0 @ identity) = (zero))),
% 1.59/0.95 inference('cnf', [status(esa)], [everything_divide_id_is_zero])).
% 1.59/0.95 thf(one_inversion_equals_three, axiom,
% 1.59/0.95 (( divide @ identity @ ( divide @ identity @ ( divide @ identity @ X ) ) ) =
% 1.59/0.95 ( divide @ identity @ X ))).
% 1.59/0.95 thf(zip_derived_cl15, plain,
% 1.59/0.95 (![X0 : $i]:
% 1.59/0.95 ((divide @ identity @ (divide @ identity @ (divide @ identity @ X0)))
% 1.59/0.95 = (divide @ identity @ X0))),
% 1.59/0.95 inference('cnf', [status(esa)], [one_inversion_equals_three])).
% 1.59/0.95 thf(zip_derived_cl61, plain,
% 1.59/0.95 (((divide @ identity @ (divide @ identity @ zero)) = (zero))),
% 1.59/0.95 inference('s_sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl15])).
% 1.59/0.95 thf(quotient_less_equal2, axiom,
% 1.59/0.95 (( ( divide @ X @ Y ) != ( zero ) ) | ( less_equal @ X @ Y ))).
% 1.59/0.95 thf(zip_derived_cl1, plain,
% 1.59/0.95 (![X0 : $i, X1 : $i]:
% 1.59/0.95 (((divide @ X0 @ X1) != (zero)) | (less_equal @ X0 @ X1))),
% 1.59/0.95 inference('cnf', [status(esa)], [quotient_less_equal2])).
% 1.59/0.95 thf(identity_is_largest, axiom, (less_equal @ X @ identity)).
% 1.59/0.95 thf(zip_derived_cl6, plain, (![X0 : $i]: (less_equal @ X0 @ identity)),
% 1.59/0.95 inference('cnf', [status(esa)], [identity_is_largest])).
% 1.59/0.95 thf(less_equal_and_equal, axiom,
% 1.59/0.95 (( ~( less_equal @ X @ Y ) ) | ( ~( less_equal @ Y @ X ) ) |
% 1.59/0.95 ( ( X ) = ( Y ) ))).
% 1.59/0.95 thf(zip_derived_cl5, plain,
% 1.59/0.95 (![X0 : $i, X1 : $i]:
% 1.59/0.95 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 1.59/0.95 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 1.59/0.95 thf(zip_derived_cl107, plain,
% 1.59/0.95 (![X0 : $i]: (~ (less_equal @ identity @ X0) | ((X0) = (identity)))),
% 1.59/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl5])).
% 1.59/0.95 thf(zip_derived_cl113, plain,
% 1.59/0.95 (![X0 : $i]: (((divide @ identity @ X0) != (zero)) | ((X0) = (identity)))),
% 1.59/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl107])).
% 1.59/0.95 thf(zip_derived_cl118, plain,
% 1.59/0.95 ((((zero) != (zero)) | ((divide @ identity @ zero) = (identity)))),
% 1.59/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl61, zip_derived_cl113])).
% 1.59/0.95 thf(zip_derived_cl121, plain, (((divide @ identity @ zero) = (identity))),
% 1.59/0.95 inference('simplify', [status(thm)], [zip_derived_cl118])).
% 1.59/0.95 thf(x_divide_zero_is_x, axiom, (( divide @ a @ zero ) = ( a ))).
% 1.59/0.95 thf(zip_derived_cl10, plain, (((divide @ a @ zero) = (a))),
% 1.59/0.95 inference('cnf', [status(esa)], [x_divide_zero_is_x])).
% 1.59/0.95 thf(quotient_property, axiom,
% 1.59/0.95 (less_equal @
% 1.59/0.95 ( divide @ ( divide @ X @ Z ) @ ( divide @ Y @ Z ) ) @
% 1.59/0.95 ( divide @ ( divide @ X @ Y ) @ Z ))).
% 1.59/0.95 thf(zip_derived_cl3, plain,
% 1.59/0.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.59/0.95 (less_equal @ (divide @ (divide @ X0 @ X1) @ (divide @ X2 @ X1)) @
% 1.59/0.95 (divide @ (divide @ X0 @ X2) @ X1))),
% 1.59/0.95 inference('cnf', [status(esa)], [quotient_property])).
% 1.59/0.95 thf(zip_derived_cl87, plain,
% 1.59/0.95 (![X0 : $i]:
% 1.59/0.95 (less_equal @ (divide @ (divide @ X0 @ zero) @ a) @
% 1.59/0.95 (divide @ (divide @ X0 @ a) @ zero))),
% 1.59/0.95 inference('s_sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl3])).
% 1.59/0.95 thf(zip_derived_cl580, plain,
% 1.59/0.95 ( (less_equal @ (divide @ identity @ a) @
% 1.59/0.95 (divide @ (divide @ identity @ a) @ zero))),
% 1.59/0.95 inference('s_sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl87])).
% 1.59/0.95 thf(zip_derived_cl580, plain,
% 1.59/0.95 ( (less_equal @ (divide @ identity @ a) @
% 1.59/0.95 (divide @ (divide @ identity @ a) @ zero))),
% 1.59/0.95 inference('s_sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl87])).
% 1.59/0.95 thf(zip_derived_cl5, plain,
% 1.59/0.95 (![X0 : $i, X1 : $i]:
% 1.59/0.95 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 1.59/0.95 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 1.59/0.95 thf(zip_derived_cl594, plain,
% 1.59/0.95 ((~ (less_equal @ (divide @ (divide @ identity @ a) @ zero) @
% 1.59/0.95 (divide @ identity @ a))
% 1.59/0.95 | ((divide @ identity @ a) = (divide @ (divide @ identity @ a) @ zero)))),
% 1.59/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl580, zip_derived_cl5])).
% 1.59/0.95 thf(quotient_smaller_than_numerator, axiom,
% 1.59/0.95 (less_equal @ ( divide @ X @ Y ) @ X)).
% 1.59/0.95 thf(zip_derived_cl2, plain,
% 1.59/0.95 (![X0 : $i, X1 : $i]: (less_equal @ (divide @ X0 @ X1) @ X0)),
% 1.59/0.95 inference('cnf', [status(esa)], [quotient_smaller_than_numerator])).
% 1.59/0.95 thf(zip_derived_cl597, plain,
% 1.59/0.95 (((divide @ identity @ a) = (divide @ (divide @ identity @ a) @ zero))),
% 1.59/0.95 inference('demod', [status(thm)], [zip_derived_cl594, zip_derived_cl2])).
% 1.59/0.95 thf(zip_derived_cl656, plain,
% 1.59/0.95 ( (less_equal @ (divide @ identity @ a) @ (divide @ identity @ a))),
% 1.59/0.95 inference('demod', [status(thm)], [zip_derived_cl580, zip_derived_cl597])).
% 1.59/0.95 thf(property_of_divide1, axiom,
% 1.59/0.95 (( ~( less_equal @ ( divide @ X @ Y ) @ Z ) ) |
% 1.59/0.95 ( less_equal @ ( divide @ X @ Z ) @ Y ))).
% 1.59/0.95 thf(zip_derived_cl12, plain,
% 1.59/0.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.59/0.95 (~ (less_equal @ (divide @ X0 @ X1) @ X2)
% 1.59/0.95 | (less_equal @ (divide @ X0 @ X2) @ X1))),
% 1.59/0.95 inference('cnf', [status(esa)], [property_of_divide1])).
% 1.59/0.95 thf(zip_derived_cl698, plain,
% 1.59/0.95 ( (less_equal @ (divide @ identity @ (divide @ identity @ a)) @ a)),
% 1.59/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl656, zip_derived_cl12])).
% 1.59/0.95 thf(quotient_less_equal1, axiom,
% 1.59/0.95 (( ~( less_equal @ X @ Y ) ) | ( ( divide @ X @ Y ) = ( zero ) ))).
% 1.59/0.95 thf(zip_derived_cl0, plain,
% 1.59/0.95 (![X0 : $i, X1 : $i]:
% 1.59/0.95 (~ (less_equal @ X0 @ X1) | ((divide @ X0 @ X1) = (zero)))),
% 1.59/0.95 inference('cnf', [status(esa)], [quotient_less_equal1])).
% 1.59/0.95 thf(zip_derived_cl763, plain,
% 1.59/0.95 (((divide @ (divide @ identity @ (divide @ identity @ a)) @ a) = (zero))),
% 1.59/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl698, zip_derived_cl0])).
% 1.59/0.95 thf(zip_derived_cl3, plain,
% 1.59/0.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.59/0.95 (less_equal @ (divide @ (divide @ X0 @ X1) @ (divide @ X2 @ X1)) @
% 1.59/0.95 (divide @ (divide @ X0 @ X2) @ X1))),
% 1.59/0.95 inference('cnf', [status(esa)], [quotient_property])).
% 1.59/0.95 thf(zip_derived_cl5, plain,
% 1.59/0.95 (![X0 : $i, X1 : $i]:
% 1.59/0.95 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 1.59/0.95 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 1.59/0.95 thf(zip_derived_cl109, plain,
% 1.59/0.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.59/0.95 (~ (less_equal @ (divide @ (divide @ X2 @ X1) @ X0) @
% 1.59/0.95 (divide @ (divide @ X2 @ X0) @ (divide @ X1 @ X0)))
% 1.59/0.95 | ((divide @ (divide @ X2 @ X0) @ (divide @ X1 @ X0))
% 1.59/0.95 = (divide @ (divide @ X2 @ X1) @ X0)))),
% 1.59/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl5])).
% 1.59/0.95 thf(zip_derived_cl943, plain,
% 1.59/0.95 ((~ (less_equal @ zero @
% 1.59/0.95 (divide @ (divide @ identity @ a) @
% 1.59/0.95 (divide @ (divide @ identity @ a) @ a)))
% 1.59/0.95 | ((divide @ (divide @ identity @ a) @
% 1.59/0.95 (divide @ (divide @ identity @ a) @ a)) = (zero)))),
% 1.59/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl763, zip_derived_cl109])).
% 1.59/0.95 thf(zero_is_smallest, axiom, (less_equal @ zero @ X)).
% 1.59/0.95 thf(zip_derived_cl4, plain, (![X0 : $i]: (less_equal @ zero @ X0)),
% 1.59/0.95 inference('cnf', [status(esa)], [zero_is_smallest])).
% 1.59/0.95 thf(zip_derived_cl979, plain,
% 1.59/0.95 (((divide @ (divide @ identity @ a) @
% 1.59/0.95 (divide @ (divide @ identity @ a) @ a)) = (zero))),
% 1.59/0.95 inference('demod', [status(thm)], [zip_derived_cl943, zip_derived_cl4])).
% 1.59/0.95 thf(zip_derived_cl109, plain,
% 1.59/0.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.59/0.95 (~ (less_equal @ (divide @ (divide @ X2 @ X1) @ X0) @
% 1.59/0.95 (divide @ (divide @ X2 @ X0) @ (divide @ X1 @ X0)))
% 1.59/0.95 | ((divide @ (divide @ X2 @ X0) @ (divide @ X1 @ X0))
% 1.59/0.95 = (divide @ (divide @ X2 @ X1) @ X0)))),
% 1.59/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl5])).
% 1.59/0.95 thf(zip_derived_cl1045, plain,
% 1.59/0.95 ((~ (less_equal @ zero @
% 1.59/0.95 (divide @
% 1.59/0.95 (divide @ identity @ (divide @ (divide @ identity @ a) @ a)) @
% 1.59/0.95 (divide @ a @ (divide @ (divide @ identity @ a) @ a))))
% 1.59/0.95 | ((divide @
% 1.59/0.95 (divide @ identity @ (divide @ (divide @ identity @ a) @ a)) @
% 1.59/0.95 (divide @ a @ (divide @ (divide @ identity @ a) @ a))) = (zero)))),
% 1.59/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl979, zip_derived_cl109])).
% 1.59/0.95 thf(zip_derived_cl4, plain, (![X0 : $i]: (less_equal @ zero @ X0)),
% 1.59/0.95 inference('cnf', [status(esa)], [zero_is_smallest])).
% 1.59/0.95 thf(zip_derived_cl1066, plain,
% 1.59/0.95 (((divide @
% 1.59/0.95 (divide @ identity @ (divide @ (divide @ identity @ a) @ a)) @
% 1.59/0.95 (divide @ a @ (divide @ (divide @ identity @ a) @ a))) = (zero))),
% 1.59/0.95 inference('demod', [status(thm)], [zip_derived_cl1045, zip_derived_cl4])).
% 1.59/0.95 thf(zip_derived_cl979, plain,
% 1.59/0.95 (((divide @ (divide @ identity @ a) @
% 1.59/0.95 (divide @ (divide @ identity @ a) @ a)) = (zero))),
% 1.59/0.95 inference('demod', [status(thm)], [zip_derived_cl943, zip_derived_cl4])).
% 1.59/0.95 thf(zip_derived_cl1, plain,
% 1.59/0.95 (![X0 : $i, X1 : $i]:
% 1.59/0.95 (((divide @ X0 @ X1) != (zero)) | (less_equal @ X0 @ X1))),
% 1.59/0.95 inference('cnf', [status(esa)], [quotient_less_equal2])).
% 1.59/0.95 thf(zip_derived_cl5, plain,
% 1.59/0.95 (![X0 : $i, X1 : $i]:
% 1.59/0.95 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 1.59/0.95 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 1.59/0.95 thf(zip_derived_cl106, plain,
% 1.59/0.95 (![X0 : $i, X1 : $i]:
% 1.59/0.95 (((divide @ X1 @ X0) != (zero))
% 1.59/0.95 | ~ (less_equal @ X0 @ X1)
% 1.59/0.95 | ((X1) = (X0)))),
% 1.59/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl5])).
% 1.59/0.95 thf(zip_derived_cl1039, plain,
% 1.59/0.95 ((((zero) != (zero))
% 1.59/0.95 | ~ (less_equal @ (divide @ (divide @ identity @ a) @ a) @
% 1.59/0.95 (divide @ identity @ a))
% 1.59/0.95 | ((divide @ identity @ a) = (divide @ (divide @ identity @ a) @ a)))),
% 1.59/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl979, zip_derived_cl106])).
% 1.59/0.95 thf(zip_derived_cl2, plain,
% 1.59/0.95 (![X0 : $i, X1 : $i]: (less_equal @ (divide @ X0 @ X1) @ X0)),
% 1.59/0.95 inference('cnf', [status(esa)], [quotient_smaller_than_numerator])).
% 1.59/0.95 thf(zip_derived_cl1063, plain,
% 1.59/0.95 ((((zero) != (zero))
% 1.59/0.95 | ((divide @ identity @ a) = (divide @ (divide @ identity @ a) @ a)))),
% 1.59/0.95 inference('demod', [status(thm)], [zip_derived_cl1039, zip_derived_cl2])).
% 1.59/0.95 thf(zip_derived_cl1064, plain,
% 1.59/0.95 (((divide @ identity @ a) = (divide @ (divide @ identity @ a) @ a))),
% 1.59/0.95 inference('simplify', [status(thm)], [zip_derived_cl1063])).
% 1.59/0.95 thf(zip_derived_cl1064, plain,
% 1.59/0.95 (((divide @ identity @ a) = (divide @ (divide @ identity @ a) @ a))),
% 1.59/0.95 inference('simplify', [status(thm)], [zip_derived_cl1063])).
% 1.59/0.95 thf(zip_derived_cl1143, plain,
% 1.59/0.95 (((divide @ (divide @ identity @ (divide @ identity @ a)) @
% 1.59/0.95 (divide @ a @ (divide @ identity @ a))) = (zero))),
% 1.59/0.95 inference('demod', [status(thm)],
% 1.59/0.95 [zip_derived_cl1066, zip_derived_cl1064, zip_derived_cl1064])).
% 1.59/0.95 thf(zip_derived_cl109, plain,
% 1.59/0.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.59/0.95 (~ (less_equal @ (divide @ (divide @ X2 @ X1) @ X0) @
% 1.59/0.95 (divide @ (divide @ X2 @ X0) @ (divide @ X1 @ X0)))
% 1.59/0.95 | ((divide @ (divide @ X2 @ X0) @ (divide @ X1 @ X0))
% 1.59/0.96 = (divide @ (divide @ X2 @ X1) @ X0)))),
% 1.59/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl5])).
% 1.59/0.96 thf(zip_derived_cl1171, plain,
% 1.59/0.96 ((~ (less_equal @ zero @
% 1.59/0.96 (divide @
% 1.59/0.96 (divide @ identity @ (divide @ a @ (divide @ identity @ a))) @
% 1.59/0.96 (divide @ (divide @ identity @ a) @
% 1.59/0.96 (divide @ a @ (divide @ identity @ a)))))
% 1.59/0.96 | ((divide @
% 1.59/0.96 (divide @ identity @ (divide @ a @ (divide @ identity @ a))) @
% 1.59/0.96 (divide @ (divide @ identity @ a) @
% 1.59/0.96 (divide @ a @ (divide @ identity @ a))))
% 1.59/0.96 = (zero)))),
% 1.59/0.96 inference('s_sup-', [status(thm)],
% 1.59/0.96 [zip_derived_cl1143, zip_derived_cl109])).
% 1.59/0.96 thf(zip_derived_cl4, plain, (![X0 : $i]: (less_equal @ zero @ X0)),
% 1.59/0.96 inference('cnf', [status(esa)], [zero_is_smallest])).
% 1.59/0.96 thf(zip_derived_cl1191, plain,
% 1.59/0.96 (((divide @
% 1.59/0.96 (divide @ identity @ (divide @ a @ (divide @ identity @ a))) @
% 1.59/0.96 (divide @ (divide @ identity @ a) @
% 1.59/0.96 (divide @ a @ (divide @ identity @ a))))
% 1.59/0.96 = (zero))),
% 1.59/0.96 inference('demod', [status(thm)], [zip_derived_cl1171, zip_derived_cl4])).
% 1.59/0.96 thf(zip_derived_cl1, plain,
% 1.59/0.96 (![X0 : $i, X1 : $i]:
% 1.59/0.96 (((divide @ X0 @ X1) != (zero)) | (less_equal @ X0 @ X1))),
% 1.59/0.96 inference('cnf', [status(esa)], [quotient_less_equal2])).
% 1.59/0.96 thf(zip_derived_cl1143, plain,
% 1.59/0.96 (((divide @ (divide @ identity @ (divide @ identity @ a)) @
% 1.59/0.96 (divide @ a @ (divide @ identity @ a))) = (zero))),
% 1.59/0.96 inference('demod', [status(thm)],
% 1.59/0.96 [zip_derived_cl1066, zip_derived_cl1064, zip_derived_cl1064])).
% 1.59/0.96 thf(zip_derived_cl106, plain,
% 1.59/0.96 (![X0 : $i, X1 : $i]:
% 1.59/0.96 (((divide @ X1 @ X0) != (zero))
% 1.59/0.96 | ~ (less_equal @ X0 @ X1)
% 1.59/0.96 | ((X1) = (X0)))),
% 1.59/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl5])).
% 1.59/0.96 thf(zip_derived_cl1165, plain,
% 1.59/0.96 ((((zero) != (zero))
% 1.59/0.96 | ~ (less_equal @ (divide @ a @ (divide @ identity @ a)) @
% 1.59/0.96 (divide @ identity @ (divide @ identity @ a)))
% 1.59/0.96 | ((divide @ identity @ (divide @ identity @ a))
% 1.59/0.96 = (divide @ a @ (divide @ identity @ a))))),
% 1.59/0.96 inference('s_sup-', [status(thm)],
% 1.59/0.96 [zip_derived_cl1143, zip_derived_cl106])).
% 1.59/0.96 thf(zip_derived_cl1189, plain,
% 1.59/0.96 ((((divide @ identity @ (divide @ identity @ a))
% 1.59/0.96 = (divide @ a @ (divide @ identity @ a)))
% 1.59/0.96 | ~ (less_equal @ (divide @ a @ (divide @ identity @ a)) @
% 1.59/0.96 (divide @ identity @ (divide @ identity @ a))))),
% 1.59/0.96 inference('simplify', [status(thm)], [zip_derived_cl1165])).
% 1.59/0.96 thf(zip_derived_cl1319, plain,
% 1.59/0.96 ((((divide @ (divide @ a @ (divide @ identity @ a)) @
% 1.59/0.96 (divide @ identity @ (divide @ identity @ a))) != (zero))
% 1.59/0.96 | ((divide @ identity @ (divide @ identity @ a))
% 1.59/0.96 = (divide @ a @ (divide @ identity @ a))))),
% 1.59/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl1189])).
% 1.59/0.96 thf(zip_derived_cl7, plain,
% 1.59/0.96 (![X0 : $i]: ((divide @ X0 @ identity) = (zero))),
% 1.59/0.96 inference('cnf', [status(esa)], [everything_divide_id_is_zero])).
% 1.59/0.96 thf(zip_derived_cl3, plain,
% 1.59/0.96 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.59/0.96 (less_equal @ (divide @ (divide @ X0 @ X1) @ (divide @ X2 @ X1)) @
% 1.59/0.96 (divide @ (divide @ X0 @ X2) @ X1))),
% 1.59/0.96 inference('cnf', [status(esa)], [quotient_property])).
% 1.59/0.96 thf(zip_derived_cl78, plain,
% 1.59/0.96 (![X0 : $i, X1 : $i]:
% 1.59/0.96 (less_equal @
% 1.59/0.96 (divide @ (divide @ X1 @ X0) @ (divide @ identity @ X0)) @
% 1.59/0.96 (divide @ zero @ X0))),
% 1.59/0.96 inference('s_sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl3])).
% 1.59/0.96 thf(zero_divide_anything_is_zero, axiom, (( divide @ zero @ X ) = ( zero ))).
% 1.59/0.96 thf(zip_derived_cl8, plain, (![X0 : $i]: ((divide @ zero @ X0) = (zero))),
% 1.59/0.96 inference('cnf', [status(esa)], [zero_divide_anything_is_zero])).
% 1.59/0.96 thf(zip_derived_cl376, plain,
% 1.59/0.96 (![X0 : $i, X1 : $i]:
% 1.59/0.96 (less_equal @
% 1.59/0.96 (divide @ (divide @ X1 @ X0) @ (divide @ identity @ X0)) @ zero)),
% 1.59/0.96 inference('demod', [status(thm)], [zip_derived_cl78, zip_derived_cl8])).
% 1.59/0.96 thf(zip_derived_cl5, plain,
% 1.59/0.96 (![X0 : $i, X1 : $i]:
% 1.59/0.96 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 1.59/0.96 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 1.59/0.96 thf(zip_derived_cl378, plain,
% 1.59/0.96 (![X0 : $i, X1 : $i]:
% 1.59/0.96 (~ (less_equal @ zero @
% 1.59/0.96 (divide @ (divide @ X1 @ X0) @ (divide @ identity @ X0)))
% 1.59/0.96 | ((divide @ (divide @ X1 @ X0) @ (divide @ identity @ X0)) = (zero)))),
% 1.59/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl376, zip_derived_cl5])).
% 1.59/0.96 thf(zip_derived_cl4, plain, (![X0 : $i]: (less_equal @ zero @ X0)),
% 1.59/0.96 inference('cnf', [status(esa)], [zero_is_smallest])).
% 1.59/0.96 thf(zip_derived_cl410, plain,
% 1.59/0.96 (![X0 : $i, X1 : $i]:
% 1.59/0.96 ((divide @ (divide @ X1 @ X0) @ (divide @ identity @ X0)) = (zero))),
% 1.59/0.96 inference('demod', [status(thm)], [zip_derived_cl378, zip_derived_cl4])).
% 1.59/0.96 thf(zip_derived_cl1323, plain,
% 1.59/0.96 ((((zero) != (zero))
% 1.59/0.96 | ((divide @ identity @ (divide @ identity @ a))
% 1.59/0.96 = (divide @ a @ (divide @ identity @ a))))),
% 1.59/0.96 inference('demod', [status(thm)], [zip_derived_cl1319, zip_derived_cl410])).
% 1.59/0.96 thf(zip_derived_cl1324, plain,
% 1.59/0.96 (((divide @ identity @ (divide @ identity @ a))
% 1.59/0.96 = (divide @ a @ (divide @ identity @ a)))),
% 1.59/0.96 inference('simplify', [status(thm)], [zip_derived_cl1323])).
% 1.59/0.96 thf(zip_derived_cl15, plain,
% 1.59/0.96 (![X0 : $i]:
% 1.59/0.96 ((divide @ identity @ (divide @ identity @ (divide @ identity @ X0)))
% 1.59/0.96 = (divide @ identity @ X0))),
% 1.59/0.96 inference('cnf', [status(esa)], [one_inversion_equals_three])).
% 1.59/0.96 thf(zip_derived_cl1324, plain,
% 1.59/0.96 (((divide @ identity @ (divide @ identity @ a))
% 1.59/0.96 = (divide @ a @ (divide @ identity @ a)))),
% 1.59/0.96 inference('simplify', [status(thm)], [zip_derived_cl1323])).
% 1.59/0.96 thf(zip_derived_cl1576, plain,
% 1.59/0.96 (((divide @ (divide @ identity @ a) @
% 1.59/0.96 (divide @ (divide @ identity @ a) @
% 1.59/0.96 (divide @ identity @ (divide @ identity @ a))))
% 1.59/0.96 = (zero))),
% 1.59/0.96 inference('demod', [status(thm)],
% 1.59/0.96 [zip_derived_cl1191, zip_derived_cl1324, zip_derived_cl15,
% 1.59/0.96 zip_derived_cl1324])).
% 1.59/0.96 thf(zip_derived_cl106, plain,
% 1.59/0.96 (![X0 : $i, X1 : $i]:
% 1.59/0.96 (((divide @ X1 @ X0) != (zero))
% 1.59/0.96 | ~ (less_equal @ X0 @ X1)
% 1.59/0.96 | ((X1) = (X0)))),
% 1.59/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl5])).
% 1.59/0.96 thf(zip_derived_cl1603, plain,
% 1.59/0.96 ((((zero) != (zero))
% 1.59/0.96 | ~ (less_equal @
% 1.59/0.96 (divide @ (divide @ identity @ a) @
% 1.59/0.96 (divide @ identity @ (divide @ identity @ a))) @
% 1.59/0.96 (divide @ identity @ a))
% 1.59/0.96 | ((divide @ identity @ a)
% 1.59/0.96 = (divide @ (divide @ identity @ a) @
% 1.59/0.96 (divide @ identity @ (divide @ identity @ a)))))),
% 1.59/0.96 inference('s_sup-', [status(thm)],
% 1.59/0.96 [zip_derived_cl1576, zip_derived_cl106])).
% 1.59/0.96 thf(zip_derived_cl2, plain,
% 1.59/0.96 (![X0 : $i, X1 : $i]: (less_equal @ (divide @ X0 @ X1) @ X0)),
% 1.59/0.96 inference('cnf', [status(esa)], [quotient_smaller_than_numerator])).
% 1.59/0.96 thf(zip_derived_cl1639, plain,
% 1.59/0.96 ((((zero) != (zero))
% 1.59/0.96 | ((divide @ identity @ a)
% 1.59/0.96 = (divide @ (divide @ identity @ a) @
% 1.59/0.96 (divide @ identity @ (divide @ identity @ a)))))),
% 1.59/0.96 inference('demod', [status(thm)], [zip_derived_cl1603, zip_derived_cl2])).
% 1.59/0.96 thf(zip_derived_cl1640, plain,
% 1.59/0.96 (((divide @ identity @ a)
% 1.59/0.96 = (divide @ (divide @ identity @ a) @
% 1.59/0.96 (divide @ identity @ (divide @ identity @ a))))),
% 1.59/0.96 inference('simplify', [status(thm)], [zip_derived_cl1639])).
% 1.59/0.96 thf(prove_property_of_inversion, conjecture,
% 1.59/0.96 (( divide @ identity @ a ) =
% 1.59/0.96 ( divide @
% 1.59/0.96 ( divide @ identity @ a ) @
% 1.59/0.96 ( divide @ identity @ ( divide @ identity @ a ) ) ))).
% 1.59/0.96 thf(zf_stmt_0, negated_conjecture,
% 1.59/0.96 (( divide @ identity @ a ) !=
% 1.59/0.96 ( divide @
% 1.59/0.96 ( divide @ identity @ a ) @
% 1.59/0.96 ( divide @ identity @ ( divide @ identity @ a ) ) )),
% 1.59/0.96 inference('cnf.neg', [status(esa)], [prove_property_of_inversion])).
% 1.59/0.96 thf(zip_derived_cl16, plain,
% 1.59/0.96 (((divide @ identity @ a)
% 1.59/0.96 != (divide @ (divide @ identity @ a) @
% 1.59/0.96 (divide @ identity @ (divide @ identity @ a))))),
% 1.59/0.96 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.59/0.96 thf(zip_derived_cl1641, plain, ($false),
% 1.59/0.96 inference('simplify_reflect-', [status(thm)],
% 1.59/0.96 [zip_derived_cl1640, zip_derived_cl16])).
% 1.59/0.96
% 1.59/0.96 % SZS output end Refutation
% 1.59/0.96
% 1.59/0.96
% 1.59/0.96 % Terminating...
% 1.77/1.10 % Runner terminated.
% 1.77/1.11 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------