%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : HEN010-1 : TPTP v9.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ERkUZPJFm0 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 Oct 2 04:37:24 PM UTC 2025
% Result : Unsatisfiable 10.39s 7.18s
% Output : Refutation 10.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/1.23 % Problem : HEN010-1 : TPTP v9.2.0. Released v1.0.0.
% 0.09/1.34 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ERkUZPJFm0 true
% 0.11/1.70 % Computer : n025.cluster.edu
% 0.11/1.70 % Model : x86_64 x86_64
% 0.11/1.70 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/1.70 % Memory : 8042.1875MB
% 0.11/1.70 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/1.70 % CPULimit : 300
% 0.11/1.70 % WCLimit : 300
% 0.11/1.70 % DateTime : Wed Oct 1 16:54:39 EDT 2025
% 0.13/1.72 % CPUTime :
% 0.13/1.72 % Running portfolio for 300 s
% 0.13/1.72 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/1.73 % Number of cores: 8
% 0.13/1.75 % Python version: Python 3.6.8
% 0.13/1.77 % Running in FO mode
% 0.33/2.40 % Total configuration time : 435
% 0.33/2.40 % Estimated wc time : 1092
% 0.33/2.40 % Estimated cpu time (7 cpus) : 156.0
% 0.34/2.61 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.82/2.77 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.83/2.79 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.83/2.82 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.83/2.83 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.88/2.85 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.88/2.85 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 10.39/7.18 % Solved by fo/fo13.sh.
% 10.39/7.18 % done 3126 iterations in 4.146s
% 10.39/7.18 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 10.39/7.18 % SZS output start Refutation
% 10.39/7.18 thf(divide_type, type, divide: $i > $i > $i).
% 10.39/7.18 thf(idQ_idQa_type, type, idQ_idQa: $i).
% 10.39/7.18 thf(idQa_type, type, idQa: $i).
% 10.39/7.18 thf(a_type, type, a: $i).
% 10.39/7.18 thf(identity_type, type, identity: $i).
% 10.39/7.18 thf(less_equal_type, type, less_equal: $i > $i > $o).
% 10.39/7.18 thf(idQa_Q__idQ_idQa_type, type, idQa_Q__idQ_idQa: $i).
% 10.39/7.18 thf(quotient_type, type, quotient: $i > $i > $i > $o).
% 10.39/7.18 thf(zero_type, type, zero: $i).
% 10.39/7.18 thf(closure, axiom, (quotient @ X @ Y @ ( divide @ X @ Y ))).
% 10.39/7.18 thf(zip_derived_cl7, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [closure])).
% 10.39/7.18 thf(zip_derived_cl7, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [closure])).
% 10.39/7.18 thf(zip_derived_cl7, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [closure])).
% 10.39/7.18 thf(zip_derived_cl7, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [closure])).
% 10.39/7.18 thf(zip_derived_cl7, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [closure])).
% 10.39/7.18 thf(zip_derived_cl7, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [closure])).
% 10.39/7.18 thf(zip_derived_cl7, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [closure])).
% 10.39/7.18 thf(zero_is_smallest, axiom, (less_equal @ zero @ X)).
% 10.39/7.18 thf(zip_derived_cl4, plain, (![X0 : $i]: (less_equal @ zero @ X0)),
% 10.39/7.18 inference('cnf', [status(esa)], [zero_is_smallest])).
% 10.39/7.18 thf(quotient_less_equal, axiom,
% 10.39/7.18 (( ~( less_equal @ X @ Y ) ) | ( quotient @ X @ Y @ zero ))).
% 10.39/7.18 thf(zip_derived_cl0, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]:
% 10.39/7.18 (~ (less_equal @ X0 @ X1) | (quotient @ X0 @ X1 @ zero))),
% 10.39/7.18 inference('cnf', [status(esa)], [quotient_less_equal])).
% 10.39/7.18 thf(zip_derived_cl13, plain, (![X0 : $i]: (quotient @ zero @ X0 @ zero)),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 10.39/7.18 thf(zip_derived_cl7, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [closure])).
% 10.39/7.18 thf(divisor_existence, axiom,
% 10.39/7.18 (( ~( quotient @ X @ Y @ Z ) ) | ( less_equal @ Z @ X ))).
% 10.39/7.18 thf(zip_derived_cl2, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.39/7.18 (~ (quotient @ X0 @ X1 @ X2) | (less_equal @ X2 @ X0))),
% 10.39/7.18 inference('cnf', [status(esa)], [divisor_existence])).
% 10.39/7.18 thf(zip_derived_cl20, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (less_equal @ (divide @ X1 @ X0) @ X1)),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 10.39/7.18 thf(zip_derived_cl0, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]:
% 10.39/7.18 (~ (less_equal @ X0 @ X1) | (quotient @ X0 @ X1 @ zero))),
% 10.39/7.18 inference('cnf', [status(esa)], [quotient_less_equal])).
% 10.39/7.18 thf(zip_derived_cl55, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ (divide @ X0 @ X1) @ X0 @ zero)),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl0])).
% 10.39/7.18 thf(zip_derived_cl7, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [closure])).
% 10.39/7.18 thf(quotient_property, axiom,
% 10.39/7.18 (( ~( quotient @ X @ Y @ V1 ) ) | ( ~( quotient @ Y @ Z @ V2 ) ) |
% 10.39/7.18 ( ~( quotient @ X @ Z @ V3 ) ) | ( ~( quotient @ V3 @ V2 @ V4 ) ) |
% 10.39/7.18 ( ~( quotient @ V1 @ Z @ V5 ) ) | ( less_equal @ V4 @ V5 ))).
% 10.39/7.18 thf(zip_derived_cl3, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 10.39/7.18 (~ (quotient @ X0 @ X1 @ X2)
% 10.39/7.18 | ~ (quotient @ X1 @ X3 @ X4)
% 10.39/7.18 | ~ (quotient @ X0 @ X3 @ X5)
% 10.39/7.18 | ~ (quotient @ X5 @ X4 @ X6)
% 10.39/7.18 | ~ (quotient @ X2 @ X3 @ X7)
% 10.39/7.18 | (less_equal @ X6 @ X7))),
% 10.39/7.18 inference('cnf', [status(esa)], [quotient_property])).
% 10.39/7.18 thf(zip_derived_cl31, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 10.39/7.18 (~ (quotient @ X0 @ X3 @ X2)
% 10.39/7.18 | ~ (quotient @ X1 @ X3 @ X4)
% 10.39/7.18 | ~ (quotient @ X4 @ X2 @ X5)
% 10.39/7.18 | ~ (quotient @ (divide @ X1 @ X0) @ X3 @ X6)
% 10.39/7.18 | (less_equal @ X5 @ X6))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl3])).
% 10.39/7.18 thf(zip_derived_cl102, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 10.39/7.18 (~ (quotient @ X1 @ X0 @ X2)
% 10.39/7.18 | ~ (quotient @ X0 @ X0 @ X3)
% 10.39/7.18 | ~ (quotient @ X3 @ X2 @ X4)
% 10.39/7.18 | (less_equal @ X4 @ zero))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl55, zip_derived_cl31])).
% 10.39/7.18 thf(zip_derived_cl167, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.39/7.18 (~ (quotient @ X0 @ X0 @ X1)
% 10.39/7.18 | ~ (quotient @ X1 @ zero @ X2)
% 10.39/7.18 | (less_equal @ X2 @ zero))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl102])).
% 10.39/7.18 thf(zip_derived_cl173, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]:
% 10.39/7.18 (~ (quotient @ X1 @ X1 @ X0)
% 10.39/7.18 | (less_equal @ (divide @ X0 @ zero) @ zero))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl167])).
% 10.39/7.18 thf(zip_derived_cl178, plain,
% 10.39/7.18 (![X0 : $i]: (less_equal @ (divide @ (divide @ X0 @ X0) @ zero) @ zero)),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl173])).
% 10.39/7.18 thf(zip_derived_cl4, plain, (![X0 : $i]: (less_equal @ zero @ X0)),
% 10.39/7.18 inference('cnf', [status(esa)], [zero_is_smallest])).
% 10.39/7.18 thf(less_equal_and_equal, axiom,
% 10.39/7.18 (( ~( less_equal @ X @ Y ) ) | ( ~( less_equal @ Y @ X ) ) |
% 10.39/7.18 ( ( X ) = ( Y ) ))).
% 10.39/7.18 thf(zip_derived_cl5, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]:
% 10.39/7.18 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 10.39/7.18 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 10.39/7.18 thf(zip_derived_cl16, plain,
% 10.39/7.18 (![X0 : $i]: (~ (less_equal @ X0 @ zero) | ((zero) = (X0)))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 10.39/7.18 thf(zip_derived_cl254, plain,
% 10.39/7.18 (![X0 : $i]: ((zero) = (divide @ (divide @ X0 @ X0) @ zero))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl178, zip_derived_cl16])).
% 10.39/7.18 thf(zip_derived_cl7, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [closure])).
% 10.39/7.18 thf(zip_derived_cl262, plain,
% 10.39/7.18 (![X0 : $i]: (quotient @ (divide @ X0 @ X0) @ zero @ zero)),
% 10.39/7.18 inference('s_sup+', [status(thm)], [zip_derived_cl254, zip_derived_cl7])).
% 10.39/7.18 thf(less_equal_quotient, axiom,
% 10.39/7.18 (( ~( quotient @ X @ Y @ zero ) ) | ( less_equal @ X @ Y ))).
% 10.39/7.18 thf(zip_derived_cl1, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]:
% 10.39/7.18 (~ (quotient @ X0 @ X1 @ zero) | (less_equal @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [less_equal_quotient])).
% 10.39/7.18 thf(zip_derived_cl284, plain,
% 10.39/7.18 (![X0 : $i]: (less_equal @ (divide @ X0 @ X0) @ zero)),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl262, zip_derived_cl1])).
% 10.39/7.18 thf(zip_derived_cl16, plain,
% 10.39/7.18 (![X0 : $i]: (~ (less_equal @ X0 @ zero) | ((zero) = (X0)))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 10.39/7.18 thf(zip_derived_cl293, plain, (![X0 : $i]: ((zero) = (divide @ X0 @ X0))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl284, zip_derived_cl16])).
% 10.39/7.18 thf(zip_derived_cl7, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [closure])).
% 10.39/7.18 thf(zip_derived_cl306, plain, (![X0 : $i]: (quotient @ X0 @ X0 @ zero)),
% 10.39/7.18 inference('s_sup+', [status(thm)], [zip_derived_cl293, zip_derived_cl7])).
% 10.39/7.18 thf(identity_divide_idQa, axiom, (quotient @ identity @ idQa @ idQ_idQa)).
% 10.39/7.18 thf(zip_derived_cl10, plain, ( (quotient @ identity @ idQa @ idQ_idQa)),
% 10.39/7.18 inference('cnf', [status(esa)], [identity_divide_idQa])).
% 10.39/7.18 thf(zip_derived_cl7, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [closure])).
% 10.39/7.18 thf(identity_divide_a, axiom, (quotient @ identity @ a @ idQa)).
% 10.39/7.18 thf(zip_derived_cl9, plain, ( (quotient @ identity @ a @ idQa)),
% 10.39/7.18 inference('cnf', [status(esa)], [identity_divide_a])).
% 10.39/7.18 thf(zip_derived_cl3, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 10.39/7.18 (~ (quotient @ X0 @ X1 @ X2)
% 10.39/7.18 | ~ (quotient @ X1 @ X3 @ X4)
% 10.39/7.18 | ~ (quotient @ X0 @ X3 @ X5)
% 10.39/7.18 | ~ (quotient @ X5 @ X4 @ X6)
% 10.39/7.18 | ~ (quotient @ X2 @ X3 @ X7)
% 10.39/7.18 | (less_equal @ X6 @ X7))),
% 10.39/7.18 inference('cnf', [status(esa)], [quotient_property])).
% 10.39/7.18 thf(zip_derived_cl32, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 10.39/7.18 (~ (quotient @ a @ X1 @ X0)
% 10.39/7.18 | ~ (quotient @ identity @ X1 @ X2)
% 10.39/7.18 | ~ (quotient @ X2 @ X0 @ X3)
% 10.39/7.18 | ~ (quotient @ idQa @ X1 @ X4)
% 10.39/7.18 | (less_equal @ X3 @ X4))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl3])).
% 10.39/7.18 thf(zip_derived_cl109, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 10.39/7.18 (~ (quotient @ identity @ X0 @ X1)
% 10.39/7.18 | ~ (quotient @ X1 @ (divide @ a @ X0) @ X2)
% 10.39/7.18 | ~ (quotient @ idQa @ X0 @ X3)
% 10.39/7.18 | (less_equal @ X2 @ X3))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl32])).
% 10.39/7.18 thf(zip_derived_cl438, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]:
% 10.39/7.18 (~ (quotient @ idQ_idQa @ (divide @ a @ idQa) @ X0)
% 10.39/7.18 | ~ (quotient @ idQa @ idQa @ X1)
% 10.39/7.18 | (less_equal @ X0 @ X1))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl109])).
% 10.39/7.18 thf(zip_derived_cl725, plain,
% 10.39/7.18 (![X0 : $i]:
% 10.39/7.18 (~ (quotient @ idQ_idQa @ (divide @ a @ idQa) @ X0)
% 10.39/7.18 | (less_equal @ X0 @ zero))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl306, zip_derived_cl438])).
% 10.39/7.18 thf(zip_derived_cl728, plain,
% 10.39/7.18 ( (less_equal @ (divide @ idQ_idQa @ (divide @ a @ idQa)) @ zero)),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl725])).
% 10.39/7.18 thf(zip_derived_cl16, plain,
% 10.39/7.18 (![X0 : $i]: (~ (less_equal @ X0 @ zero) | ((zero) = (X0)))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 10.39/7.18 thf(zip_derived_cl731, plain,
% 10.39/7.18 (((zero) = (divide @ idQ_idQa @ (divide @ a @ idQa)))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl728, zip_derived_cl16])).
% 10.39/7.18 thf(zip_derived_cl7, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [closure])).
% 10.39/7.18 thf(zip_derived_cl734, plain,
% 10.39/7.18 ( (quotient @ idQ_idQa @ (divide @ a @ idQa) @ zero)),
% 10.39/7.18 inference('s_sup+', [status(thm)], [zip_derived_cl731, zip_derived_cl7])).
% 10.39/7.18 thf(zip_derived_cl1, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]:
% 10.39/7.18 (~ (quotient @ X0 @ X1 @ zero) | (less_equal @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [less_equal_quotient])).
% 10.39/7.18 thf(zip_derived_cl765, plain,
% 10.39/7.18 ( (less_equal @ idQ_idQa @ (divide @ a @ idQa))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl734, zip_derived_cl1])).
% 10.39/7.18 thf(zip_derived_cl7, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [closure])).
% 10.39/7.18 thf(zip_derived_cl7, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [closure])).
% 10.39/7.18 thf(zip_derived_cl10, plain, ( (quotient @ identity @ idQa @ idQ_idQa)),
% 10.39/7.18 inference('cnf', [status(esa)], [identity_divide_idQa])).
% 10.39/7.18 thf(zip_derived_cl7, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [closure])).
% 10.39/7.18 thf(zip_derived_cl31, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 10.39/7.18 (~ (quotient @ X0 @ X3 @ X2)
% 10.39/7.18 | ~ (quotient @ X1 @ X3 @ X4)
% 10.39/7.18 | ~ (quotient @ X4 @ X2 @ X5)
% 10.39/7.18 | ~ (quotient @ (divide @ X1 @ X0) @ X3 @ X6)
% 10.39/7.18 | (less_equal @ X5 @ X6))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl3])).
% 10.39/7.18 thf(zip_derived_cl82, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 10.39/7.18 (~ (quotient @ X1 @ X0 @ X3)
% 10.39/7.18 | ~ (quotient @ X2 @ X0 @ X4)
% 10.39/7.18 | ~ (quotient @ X4 @ X3 @ X5)
% 10.39/7.18 | (less_equal @ X5 @ (divide @ (divide @ X2 @ X1) @ X0)))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl31])).
% 10.39/7.18 thf(zip_derived_cl212, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.39/7.18 (~ (quotient @ X1 @ idQa @ X0)
% 10.39/7.18 | ~ (quotient @ X0 @ idQ_idQa @ X2)
% 10.39/7.18 | (less_equal @ X2 @ (divide @ (divide @ X1 @ identity) @ idQa)))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl82])).
% 10.39/7.18 thf(identity_is_largest, axiom, (less_equal @ X @ identity)).
% 10.39/7.18 thf(zip_derived_cl6, plain, (![X0 : $i]: (less_equal @ X0 @ identity)),
% 10.39/7.18 inference('cnf', [status(esa)], [identity_is_largest])).
% 10.39/7.18 thf(zip_derived_cl0, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]:
% 10.39/7.18 (~ (less_equal @ X0 @ X1) | (quotient @ X0 @ X1 @ zero))),
% 10.39/7.18 inference('cnf', [status(esa)], [quotient_less_equal])).
% 10.39/7.18 thf(zip_derived_cl14, plain,
% 10.39/7.18 (![X0 : $i]: (quotient @ X0 @ identity @ zero)),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl0])).
% 10.39/7.18 thf(zip_derived_cl7, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [closure])).
% 10.39/7.18 thf(well_defined, axiom,
% 10.39/7.18 (( ~( quotient @ X @ Y @ Z ) ) | ( ~( quotient @ X @ Y @ W ) ) |
% 10.39/7.18 ( ( Z ) = ( W ) ))).
% 10.39/7.18 thf(zip_derived_cl8, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 10.39/7.18 (~ (quotient @ X0 @ X1 @ X2)
% 10.39/7.18 | ~ (quotient @ X0 @ X1 @ X3)
% 10.39/7.18 | ((X2) = (X3)))),
% 10.39/7.18 inference('cnf', [status(esa)], [well_defined])).
% 10.39/7.18 thf(zip_derived_cl26, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.39/7.18 (~ (quotient @ X1 @ X0 @ X2) | ((divide @ X1 @ X0) = (X2)))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl8])).
% 10.39/7.18 thf(zip_derived_cl68, plain,
% 10.39/7.18 (![X0 : $i]: ((divide @ X0 @ identity) = (zero))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl26])).
% 10.39/7.18 thf(zip_derived_cl20, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (less_equal @ (divide @ X1 @ X0) @ X1)),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 10.39/7.18 thf(zip_derived_cl16, plain,
% 10.39/7.18 (![X0 : $i]: (~ (less_equal @ X0 @ zero) | ((zero) = (X0)))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 10.39/7.18 thf(zip_derived_cl57, plain, (![X0 : $i]: ((zero) = (divide @ zero @ X0))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl16])).
% 10.39/7.18 thf(zip_derived_cl229, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.39/7.18 (~ (quotient @ X1 @ idQa @ X0)
% 10.39/7.18 | ~ (quotient @ X0 @ idQ_idQa @ X2)
% 10.39/7.18 | (less_equal @ X2 @ zero))),
% 10.39/7.18 inference('demod', [status(thm)],
% 10.39/7.18 [zip_derived_cl212, zip_derived_cl68, zip_derived_cl57])).
% 10.39/7.18 thf(zip_derived_cl359, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]:
% 10.39/7.18 (~ (quotient @ (divide @ X0 @ idQa) @ idQ_idQa @ X1)
% 10.39/7.18 | (less_equal @ X1 @ zero))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl229])).
% 10.39/7.18 thf(zip_derived_cl367, plain,
% 10.39/7.18 (![X0 : $i]:
% 10.39/7.18 (less_equal @ (divide @ (divide @ X0 @ idQa) @ idQ_idQa) @ zero)),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl359])).
% 10.39/7.18 thf(zip_derived_cl16, plain,
% 10.39/7.18 (![X0 : $i]: (~ (less_equal @ X0 @ zero) | ((zero) = (X0)))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 10.39/7.18 thf(zip_derived_cl376, plain,
% 10.39/7.18 (![X0 : $i]: ((zero) = (divide @ (divide @ X0 @ idQa) @ idQ_idQa))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl367, zip_derived_cl16])).
% 10.39/7.18 thf(zip_derived_cl7, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [closure])).
% 10.39/7.18 thf(zip_derived_cl390, plain,
% 10.39/7.18 (![X0 : $i]: (quotient @ (divide @ X0 @ idQa) @ idQ_idQa @ zero)),
% 10.39/7.18 inference('s_sup+', [status(thm)], [zip_derived_cl376, zip_derived_cl7])).
% 10.39/7.18 thf(zip_derived_cl1, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]:
% 10.39/7.18 (~ (quotient @ X0 @ X1 @ zero) | (less_equal @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [less_equal_quotient])).
% 10.39/7.18 thf(zip_derived_cl418, plain,
% 10.39/7.18 (![X0 : $i]: (less_equal @ (divide @ X0 @ idQa) @ idQ_idQa)),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl390, zip_derived_cl1])).
% 10.39/7.18 thf(zip_derived_cl5, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]:
% 10.39/7.18 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 10.39/7.18 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 10.39/7.18 thf(zip_derived_cl428, plain,
% 10.39/7.18 (![X0 : $i]:
% 10.39/7.18 (~ (less_equal @ idQ_idQa @ (divide @ X0 @ idQa))
% 10.39/7.18 | ((divide @ X0 @ idQa) = (idQ_idQa)))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl418, zip_derived_cl5])).
% 10.39/7.18 thf(zip_derived_cl773, plain, (((divide @ a @ idQa) = (idQ_idQa))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl765, zip_derived_cl428])).
% 10.39/7.18 thf(zip_derived_cl55, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ (divide @ X0 @ X1) @ X0 @ zero)),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl0])).
% 10.39/7.18 thf(zip_derived_cl782, plain, ( (quotient @ idQ_idQa @ a @ zero)),
% 10.39/7.18 inference('s_sup+', [status(thm)], [zip_derived_cl773, zip_derived_cl55])).
% 10.39/7.18 thf(zip_derived_cl9, plain, ( (quotient @ identity @ a @ idQa)),
% 10.39/7.18 inference('cnf', [status(esa)], [identity_divide_a])).
% 10.39/7.18 thf(zip_derived_cl7, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [closure])).
% 10.39/7.18 thf(zip_derived_cl10, plain, ( (quotient @ identity @ idQa @ idQ_idQa)),
% 10.39/7.18 inference('cnf', [status(esa)], [identity_divide_idQa])).
% 10.39/7.18 thf(zip_derived_cl3, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 10.39/7.18 (~ (quotient @ X0 @ X1 @ X2)
% 10.39/7.18 | ~ (quotient @ X1 @ X3 @ X4)
% 10.39/7.18 | ~ (quotient @ X0 @ X3 @ X5)
% 10.39/7.18 | ~ (quotient @ X5 @ X4 @ X6)
% 10.39/7.18 | ~ (quotient @ X2 @ X3 @ X7)
% 10.39/7.18 | (less_equal @ X6 @ X7))),
% 10.39/7.18 inference('cnf', [status(esa)], [quotient_property])).
% 10.39/7.18 thf(zip_derived_cl33, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 10.39/7.18 (~ (quotient @ idQa @ X1 @ X0)
% 10.39/7.18 | ~ (quotient @ identity @ X1 @ X2)
% 10.39/7.18 | ~ (quotient @ X2 @ X0 @ X3)
% 10.39/7.18 | ~ (quotient @ idQ_idQa @ X1 @ X4)
% 10.39/7.18 | (less_equal @ X3 @ X4))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl3])).
% 10.39/7.18 thf(zip_derived_cl124, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 10.39/7.18 (~ (quotient @ identity @ X0 @ X1)
% 10.39/7.18 | ~ (quotient @ X1 @ (divide @ idQa @ X0) @ X2)
% 10.39/7.18 | ~ (quotient @ idQ_idQa @ X0 @ X3)
% 10.39/7.18 | (less_equal @ X2 @ X3))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl33])).
% 10.39/7.18 thf(zip_derived_cl467, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]:
% 10.39/7.18 (~ (quotient @ idQa @ (divide @ idQa @ a) @ X0)
% 10.39/7.18 | ~ (quotient @ idQ_idQa @ a @ X1)
% 10.39/7.18 | (less_equal @ X0 @ X1))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl124])).
% 10.39/7.18 thf(zip_derived_cl1815, plain,
% 10.39/7.18 (![X0 : $i]:
% 10.39/7.18 (~ (quotient @ idQa @ (divide @ idQa @ a) @ X0)
% 10.39/7.18 | (less_equal @ X0 @ zero))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl782, zip_derived_cl467])).
% 10.39/7.18 thf(zip_derived_cl1819, plain,
% 10.39/7.18 ( (less_equal @ (divide @ idQa @ (divide @ idQa @ a)) @ zero)),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl1815])).
% 10.39/7.18 thf(zip_derived_cl16, plain,
% 10.39/7.18 (![X0 : $i]: (~ (less_equal @ X0 @ zero) | ((zero) = (X0)))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 10.39/7.18 thf(zip_derived_cl1831, plain,
% 10.39/7.18 (((zero) = (divide @ idQa @ (divide @ idQa @ a)))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl1819, zip_derived_cl16])).
% 10.39/7.18 thf(zip_derived_cl7, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [closure])).
% 10.39/7.18 thf(zip_derived_cl1834, plain,
% 10.39/7.18 ( (quotient @ idQa @ (divide @ idQa @ a) @ zero)),
% 10.39/7.18 inference('s_sup+', [status(thm)], [zip_derived_cl1831, zip_derived_cl7])).
% 10.39/7.18 thf(zip_derived_cl1, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]:
% 10.39/7.18 (~ (quotient @ X0 @ X1 @ zero) | (less_equal @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [less_equal_quotient])).
% 10.39/7.18 thf(zip_derived_cl1923, plain, ( (less_equal @ idQa @ (divide @ idQa @ a))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl1834, zip_derived_cl1])).
% 10.39/7.18 thf(zip_derived_cl20, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (less_equal @ (divide @ X1 @ X0) @ X1)),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 10.39/7.18 thf(zip_derived_cl5, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]:
% 10.39/7.18 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 10.39/7.18 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 10.39/7.18 thf(zip_derived_cl56, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]:
% 10.39/7.18 (~ (less_equal @ X0 @ (divide @ X0 @ X1))
% 10.39/7.18 | ((divide @ X0 @ X1) = (X0)))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl5])).
% 10.39/7.18 thf(zip_derived_cl1953, plain, (((divide @ idQa @ a) = (idQa))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl1923, zip_derived_cl56])).
% 10.39/7.18 thf(zip_derived_cl7, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [closure])).
% 10.39/7.18 thf(zip_derived_cl1971, plain, ( (quotient @ idQa @ a @ idQa)),
% 10.39/7.18 inference('s_sup+', [status(thm)], [zip_derived_cl1953, zip_derived_cl7])).
% 10.39/7.18 thf(zip_derived_cl7, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [closure])).
% 10.39/7.18 thf(identity_divide_idQ_idQa, axiom,
% 10.39/7.18 (quotient @ idQa @ idQ_idQa @ idQa_Q__idQ_idQa)).
% 10.39/7.18 thf(zip_derived_cl11, plain,
% 10.39/7.18 ( (quotient @ idQa @ idQ_idQa @ idQa_Q__idQ_idQa)),
% 10.39/7.18 inference('cnf', [status(esa)], [identity_divide_idQ_idQa])).
% 10.39/7.18 thf(zip_derived_cl3, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 10.39/7.18 (~ (quotient @ X0 @ X1 @ X2)
% 10.39/7.18 | ~ (quotient @ X1 @ X3 @ X4)
% 10.39/7.18 | ~ (quotient @ X0 @ X3 @ X5)
% 10.39/7.18 | ~ (quotient @ X5 @ X4 @ X6)
% 10.39/7.18 | ~ (quotient @ X2 @ X3 @ X7)
% 10.39/7.18 | (less_equal @ X6 @ X7))),
% 10.39/7.18 inference('cnf', [status(esa)], [quotient_property])).
% 10.39/7.18 thf(zip_derived_cl34, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 10.39/7.18 (~ (quotient @ idQ_idQa @ X1 @ X0)
% 10.39/7.18 | ~ (quotient @ idQa @ X1 @ X2)
% 10.39/7.18 | ~ (quotient @ X2 @ X0 @ X3)
% 10.39/7.18 | ~ (quotient @ idQa_Q__idQ_idQa @ X1 @ X4)
% 10.39/7.18 | (less_equal @ X3 @ X4))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl3])).
% 10.39/7.18 thf(zip_derived_cl137, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 10.39/7.18 (~ (quotient @ idQa @ X0 @ X1)
% 10.39/7.18 | ~ (quotient @ X1 @ (divide @ idQ_idQa @ X0) @ X2)
% 10.39/7.18 | ~ (quotient @ idQa_Q__idQ_idQa @ X0 @ X3)
% 10.39/7.18 | (less_equal @ X2 @ X3))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl34])).
% 10.39/7.18 thf(zip_derived_cl2016, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]:
% 10.39/7.18 (~ (quotient @ idQa @ (divide @ idQ_idQa @ a) @ X0)
% 10.39/7.18 | ~ (quotient @ idQa_Q__idQ_idQa @ a @ X1)
% 10.39/7.18 | (less_equal @ X0 @ X1))),
% 10.39/7.18 inference('s_sup-', [status(thm)],
% 10.39/7.18 [zip_derived_cl1971, zip_derived_cl137])).
% 10.39/7.18 thf(zip_derived_cl773, plain, (((divide @ a @ idQa) = (idQ_idQa))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl765, zip_derived_cl428])).
% 10.39/7.18 thf(zip_derived_cl55, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ (divide @ X0 @ X1) @ X0 @ zero)),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl0])).
% 10.39/7.18 thf(zip_derived_cl26, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.39/7.18 (~ (quotient @ X1 @ X0 @ X2) | ((divide @ X1 @ X0) = (X2)))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl8])).
% 10.39/7.18 thf(zip_derived_cl99, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: ((divide @ (divide @ X0 @ X1) @ X0) = (zero))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl55, zip_derived_cl26])).
% 10.39/7.18 thf(zip_derived_cl786, plain, (((divide @ idQ_idQa @ a) = (zero))),
% 10.39/7.18 inference('s_sup+', [status(thm)], [zip_derived_cl773, zip_derived_cl99])).
% 10.39/7.18 thf(zip_derived_cl2021, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]:
% 10.39/7.18 (~ (quotient @ idQa @ zero @ X0)
% 10.39/7.18 | ~ (quotient @ idQa_Q__idQ_idQa @ a @ X1)
% 10.39/7.18 | (less_equal @ X0 @ X1))),
% 10.39/7.18 inference('demod', [status(thm)], [zip_derived_cl2016, zip_derived_cl786])).
% 10.39/7.18 thf(zip_derived_cl2042, plain,
% 10.39/7.18 (![X0 : $i]:
% 10.39/7.18 (~ (quotient @ idQa_Q__idQ_idQa @ a @ X0)
% 10.39/7.18 | (less_equal @ (divide @ idQa @ zero) @ X0))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl2021])).
% 10.39/7.18 thf(zip_derived_cl2043, plain,
% 10.39/7.18 ( (less_equal @ (divide @ idQa @ zero) @ (divide @ idQa_Q__idQ_idQa @ a))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl2042])).
% 10.39/7.18 thf(zip_derived_cl0, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]:
% 10.39/7.18 (~ (less_equal @ X0 @ X1) | (quotient @ X0 @ X1 @ zero))),
% 10.39/7.18 inference('cnf', [status(esa)], [quotient_less_equal])).
% 10.39/7.18 thf(zip_derived_cl2044, plain,
% 10.39/7.18 ( (quotient @ (divide @ idQa @ zero) @ (divide @ idQa_Q__idQ_idQa @ a) @
% 10.39/7.18 zero)),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl2043, zip_derived_cl0])).
% 10.39/7.18 thf(zip_derived_cl26, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.39/7.18 (~ (quotient @ X1 @ X0 @ X2) | ((divide @ X1 @ X0) = (X2)))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl8])).
% 10.39/7.18 thf(zip_derived_cl2049, plain,
% 10.39/7.18 (((divide @ (divide @ idQa @ zero) @ (divide @ idQa_Q__idQ_idQa @ a))
% 10.39/7.18 = (zero))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl2044, zip_derived_cl26])).
% 10.39/7.18 thf(zip_derived_cl7, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [closure])).
% 10.39/7.18 thf(zip_derived_cl7, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [closure])).
% 10.39/7.18 thf(zip_derived_cl82, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 10.39/7.18 (~ (quotient @ X1 @ X0 @ X3)
% 10.39/7.18 | ~ (quotient @ X2 @ X0 @ X4)
% 10.39/7.18 | ~ (quotient @ X4 @ X3 @ X5)
% 10.39/7.18 | (less_equal @ X5 @ (divide @ (divide @ X2 @ X1) @ X0)))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl31])).
% 10.39/7.18 thf(zip_derived_cl208, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 10.39/7.18 (~ (quotient @ X3 @ X0 @ X2)
% 10.39/7.18 | ~ (quotient @ X2 @ (divide @ X1 @ X0) @ X4)
% 10.39/7.18 | (less_equal @ X4 @ (divide @ (divide @ X3 @ X1) @ X0)))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl82])).
% 10.39/7.18 thf(zip_derived_cl800, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 10.39/7.18 (~ (quotient @ X3 @ X0 @ X2)
% 10.39/7.18 | (less_equal @ (divide @ X2 @ (divide @ X1 @ X0)) @
% 10.39/7.18 (divide @ (divide @ X3 @ X1) @ X0)))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl208])).
% 10.39/7.18 thf(zip_derived_cl2805, plain,
% 10.39/7.18 (![X0 : $i]:
% 10.39/7.18 (~ (quotient @ idQa @ (divide @ idQa_Q__idQ_idQa @ a) @ X0)
% 10.39/7.18 | (less_equal @
% 10.39/7.18 (divide @ X0 @ (divide @ zero @ (divide @ idQa_Q__idQ_idQa @ a))) @
% 10.39/7.18 zero))),
% 10.39/7.18 inference('s_sup+', [status(thm)],
% 10.39/7.18 [zip_derived_cl2049, zip_derived_cl800])).
% 10.39/7.18 thf(zip_derived_cl57, plain, (![X0 : $i]: ((zero) = (divide @ zero @ X0))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl16])).
% 10.39/7.18 thf(zip_derived_cl2887, plain,
% 10.39/7.18 (![X0 : $i]:
% 10.39/7.18 (~ (quotient @ idQa @ (divide @ idQa_Q__idQ_idQa @ a) @ X0)
% 10.39/7.18 | (less_equal @ (divide @ X0 @ zero) @ zero))),
% 10.39/7.18 inference('demod', [status(thm)], [zip_derived_cl2805, zip_derived_cl57])).
% 10.39/7.18 thf(zip_derived_cl7702, plain,
% 10.39/7.18 ( (less_equal @
% 10.39/7.18 (divide @ (divide @ idQa @ (divide @ idQa_Q__idQ_idQa @ a)) @ zero) @
% 10.39/7.18 zero)),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl2887])).
% 10.39/7.18 thf(zip_derived_cl16, plain,
% 10.39/7.18 (![X0 : $i]: (~ (less_equal @ X0 @ zero) | ((zero) = (X0)))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 10.39/7.18 thf(zip_derived_cl7711, plain,
% 10.39/7.18 (((zero)
% 10.39/7.18 = (divide @ (divide @ idQa @ (divide @ idQa_Q__idQ_idQa @ a)) @ zero))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7702, zip_derived_cl16])).
% 10.39/7.18 thf(zip_derived_cl7, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [closure])).
% 10.39/7.18 thf(zip_derived_cl7720, plain,
% 10.39/7.18 ( (quotient @ (divide @ idQa @ (divide @ idQa_Q__idQ_idQa @ a)) @ zero @
% 10.39/7.18 zero)),
% 10.39/7.18 inference('s_sup+', [status(thm)], [zip_derived_cl7711, zip_derived_cl7])).
% 10.39/7.18 thf(zip_derived_cl1, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]:
% 10.39/7.18 (~ (quotient @ X0 @ X1 @ zero) | (less_equal @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [less_equal_quotient])).
% 10.39/7.18 thf(zip_derived_cl7806, plain,
% 10.39/7.18 ( (less_equal @ (divide @ idQa @ (divide @ idQa_Q__idQ_idQa @ a)) @ zero)),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7720, zip_derived_cl1])).
% 10.39/7.18 thf(zip_derived_cl16, plain,
% 10.39/7.18 (![X0 : $i]: (~ (less_equal @ X0 @ zero) | ((zero) = (X0)))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 10.39/7.18 thf(zip_derived_cl7846, plain,
% 10.39/7.18 (((zero) = (divide @ idQa @ (divide @ idQa_Q__idQ_idQa @ a)))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7806, zip_derived_cl16])).
% 10.39/7.18 thf(zip_derived_cl7, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [closure])).
% 10.39/7.18 thf(zip_derived_cl7861, plain,
% 10.39/7.18 ( (quotient @ idQa @ (divide @ idQa_Q__idQ_idQa @ a) @ zero)),
% 10.39/7.18 inference('s_sup+', [status(thm)], [zip_derived_cl7846, zip_derived_cl7])).
% 10.39/7.18 thf(zip_derived_cl1, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]:
% 10.39/7.18 (~ (quotient @ X0 @ X1 @ zero) | (less_equal @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [less_equal_quotient])).
% 10.39/7.18 thf(zip_derived_cl8091, plain,
% 10.39/7.18 ( (less_equal @ idQa @ (divide @ idQa_Q__idQ_idQa @ a))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7861, zip_derived_cl1])).
% 10.39/7.18 thf(zip_derived_cl7, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [closure])).
% 10.39/7.18 thf(zip_derived_cl7, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [closure])).
% 10.39/7.18 thf(zip_derived_cl9, plain, ( (quotient @ identity @ a @ idQa)),
% 10.39/7.18 inference('cnf', [status(esa)], [identity_divide_a])).
% 10.39/7.18 thf(zip_derived_cl82, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 10.39/7.18 (~ (quotient @ X1 @ X0 @ X3)
% 10.39/7.18 | ~ (quotient @ X2 @ X0 @ X4)
% 10.39/7.18 | ~ (quotient @ X4 @ X3 @ X5)
% 10.39/7.18 | (less_equal @ X5 @ (divide @ (divide @ X2 @ X1) @ X0)))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl31])).
% 10.39/7.18 thf(zip_derived_cl211, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.39/7.18 (~ (quotient @ X1 @ a @ X0)
% 10.39/7.18 | ~ (quotient @ X0 @ idQa @ X2)
% 10.39/7.18 | (less_equal @ X2 @ (divide @ (divide @ X1 @ identity) @ a)))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl82])).
% 10.39/7.18 thf(zip_derived_cl68, plain,
% 10.39/7.18 (![X0 : $i]: ((divide @ X0 @ identity) = (zero))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl26])).
% 10.39/7.18 thf(zip_derived_cl57, plain, (![X0 : $i]: ((zero) = (divide @ zero @ X0))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl16])).
% 10.39/7.18 thf(zip_derived_cl228, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.39/7.18 (~ (quotient @ X1 @ a @ X0)
% 10.39/7.18 | ~ (quotient @ X0 @ idQa @ X2)
% 10.39/7.18 | (less_equal @ X2 @ zero))),
% 10.39/7.18 inference('demod', [status(thm)],
% 10.39/7.18 [zip_derived_cl211, zip_derived_cl68, zip_derived_cl57])).
% 10.39/7.18 thf(zip_derived_cl554, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]:
% 10.39/7.18 (~ (quotient @ (divide @ X0 @ a) @ idQa @ X1)
% 10.39/7.18 | (less_equal @ X1 @ zero))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl228])).
% 10.39/7.18 thf(zip_derived_cl570, plain,
% 10.39/7.18 (![X0 : $i]: (less_equal @ (divide @ (divide @ X0 @ a) @ idQa) @ zero)),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl554])).
% 10.39/7.18 thf(zip_derived_cl16, plain,
% 10.39/7.18 (![X0 : $i]: (~ (less_equal @ X0 @ zero) | ((zero) = (X0)))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 10.39/7.18 thf(zip_derived_cl578, plain,
% 10.39/7.18 (![X0 : $i]: ((zero) = (divide @ (divide @ X0 @ a) @ idQa))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl570, zip_derived_cl16])).
% 10.39/7.18 thf(zip_derived_cl7, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [closure])).
% 10.39/7.18 thf(zip_derived_cl590, plain,
% 10.39/7.18 (![X0 : $i]: (quotient @ (divide @ X0 @ a) @ idQa @ zero)),
% 10.39/7.18 inference('s_sup+', [status(thm)], [zip_derived_cl578, zip_derived_cl7])).
% 10.39/7.18 thf(zip_derived_cl1, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]:
% 10.39/7.18 (~ (quotient @ X0 @ X1 @ zero) | (less_equal @ X0 @ X1))),
% 10.39/7.18 inference('cnf', [status(esa)], [less_equal_quotient])).
% 10.39/7.18 thf(zip_derived_cl623, plain,
% 10.39/7.18 (![X0 : $i]: (less_equal @ (divide @ X0 @ a) @ idQa)),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl590, zip_derived_cl1])).
% 10.39/7.18 thf(zip_derived_cl5, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]:
% 10.39/7.18 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 10.39/7.18 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 10.39/7.18 thf(zip_derived_cl633, plain,
% 10.39/7.18 (![X0 : $i]:
% 10.39/7.18 (~ (less_equal @ idQa @ (divide @ X0 @ a))
% 10.39/7.18 | ((divide @ X0 @ a) = (idQa)))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl623, zip_derived_cl5])).
% 10.39/7.18 thf(zip_derived_cl8124, plain, (((divide @ idQa_Q__idQ_idQa @ a) = (idQa))),
% 10.39/7.18 inference('s_sup-', [status(thm)],
% 10.39/7.18 [zip_derived_cl8091, zip_derived_cl633])).
% 10.39/7.18 thf(zip_derived_cl56, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i]:
% 10.39/7.18 (~ (less_equal @ X0 @ (divide @ X0 @ X1))
% 10.39/7.18 | ((divide @ X0 @ X1) = (X0)))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl5])).
% 10.39/7.18 thf(zip_derived_cl8142, plain,
% 10.39/7.18 ((~ (less_equal @ idQa_Q__idQ_idQa @ idQa)
% 10.39/7.18 | ((idQa) = (idQa_Q__idQ_idQa)))),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl8124, zip_derived_cl56])).
% 10.39/7.18 thf(zip_derived_cl11, plain,
% 10.39/7.18 ( (quotient @ idQa @ idQ_idQa @ idQa_Q__idQ_idQa)),
% 10.39/7.18 inference('cnf', [status(esa)], [identity_divide_idQ_idQa])).
% 10.39/7.18 thf(zip_derived_cl2, plain,
% 10.39/7.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.39/7.18 (~ (quotient @ X0 @ X1 @ X2) | (less_equal @ X2 @ X0))),
% 10.39/7.18 inference('cnf', [status(esa)], [divisor_existence])).
% 10.39/7.18 thf(zip_derived_cl17, plain, ( (less_equal @ idQa_Q__idQ_idQa @ idQa)),
% 10.39/7.18 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl2])).
% 10.39/7.18 thf(zip_derived_cl8207, plain, (((idQa) = (idQa_Q__idQ_idQa))),
% 10.39/7.18 inference('demod', [status(thm)], [zip_derived_cl8142, zip_derived_cl17])).
% 10.39/7.18 thf(prove_idQa_equals_idQa_Q__idQ_idQa, conjecture,
% 10.39/7.18 (( idQa ) = ( idQa_Q__idQ_idQa ))).
% 10.39/7.18 thf(zf_stmt_0, negated_conjecture, (( idQa ) != ( idQa_Q__idQ_idQa )),
% 10.39/7.18 inference('cnf.neg', [status(esa)], [prove_idQa_equals_idQa_Q__idQ_idQa])).
% 10.39/7.18 thf(zip_derived_cl12, plain, (((idQa) != (idQa_Q__idQ_idQa))),
% 10.39/7.18 inference('cnf', [status(esa)], [zf_stmt_0])).
% 10.39/7.18 thf(zip_derived_cl8208, plain, ($false),
% 10.39/7.18 inference('simplify_reflect-', [status(thm)],
% 10.39/7.18 [zip_derived_cl8207, zip_derived_cl12])).
% 10.39/7.18
% 10.39/7.18 % SZS output end Refutation
% 10.39/7.18
% 10.39/7.18
% 10.39/7.18 % Terminating...
% 10.62/7.35 % Runner terminated.
% 10.62/7.37 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------