%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : HEN009-3 : 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.LC1fMuEGL5 true
% Computer : n009.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 4.12s 1.22s
% Output : Refutation 4.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : HEN009-3 : TPTP v9.2.0. Released v1.0.0.
% 0.08/0.15 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.LC1fMuEGL5 true
% 0.15/0.36 % Computer : n009.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Oct 1 16:56:08 EDT 2025
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % Running portfolio for 300 s
% 0.15/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.36 % Number of cores: 8
% 0.15/0.37 % Python version: Python 3.6.8
% 0.15/0.37 % Running in FO mode
% 0.58/0.67 % Total configuration time : 435
% 0.58/0.67 % Estimated wc time : 1092
% 0.58/0.67 % Estimated cpu time (7 cpus) : 156.0
% 0.58/0.72 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.59/0.74 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.59/0.77 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.59/0.78 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.59/0.78 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.60/0.79 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.60/0.81 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 4.12/1.22 % Solved by fo/fo5.sh.
% 4.12/1.22 % done 426 iterations in 0.414s
% 4.12/1.22 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 4.12/1.22 % SZS output start Refutation
% 4.12/1.22 thf(zero_type, type, zero: $i).
% 4.12/1.22 thf(divide_type, type, divide: $i > $i > $i).
% 4.12/1.22 thf(b_type, type, b: $i).
% 4.12/1.22 thf(d_type, type, d: $i).
% 4.12/1.22 thf(less_equal_type, type, less_equal: $i > $i > $o).
% 4.12/1.22 thf(c_type, type, c: $i).
% 4.12/1.22 thf(identity_type, type, identity: $i).
% 4.12/1.22 thf(a_type, type, a: $i).
% 4.12/1.22 thf(id_divide_b_is_c, axiom, (( divide @ identity @ b ) = ( c ))).
% 4.12/1.22 thf(zip_derived_cl9, plain, (((divide @ identity @ b) = (c))),
% 4.12/1.22 inference('cnf', [status(esa)], [id_divide_b_is_c])).
% 4.12/1.22 thf(zip_derived_cl9, plain, (((divide @ identity @ b) = (c))),
% 4.12/1.22 inference('cnf', [status(esa)], [id_divide_b_is_c])).
% 4.12/1.22 thf(quotient_property, axiom,
% 4.12/1.22 (less_equal @
% 4.12/1.22 ( divide @ ( divide @ X @ Z ) @ ( divide @ Y @ Z ) ) @
% 4.12/1.22 ( divide @ ( divide @ X @ Y ) @ Z ))).
% 4.12/1.22 thf(zip_derived_cl3, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.12/1.22 (less_equal @ (divide @ (divide @ X0 @ X1) @ (divide @ X2 @ X1)) @
% 4.12/1.22 (divide @ (divide @ X0 @ X2) @ X1))),
% 4.12/1.22 inference('cnf', [status(esa)], [quotient_property])).
% 4.12/1.22 thf(less_equal_and_equal, axiom,
% 4.12/1.22 (( ~( less_equal @ X @ Y ) ) | ( ~( less_equal @ Y @ X ) ) |
% 4.12/1.22 ( ( X ) = ( Y ) ))).
% 4.12/1.22 thf(zip_derived_cl5, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i]:
% 4.12/1.22 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 4.12/1.22 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 4.12/1.22 thf(zip_derived_cl43, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.12/1.22 (((divide @ (divide @ X2 @ X0) @ (divide @ X1 @ X0))
% 4.12/1.22 = (divide @ (divide @ X2 @ X1) @ X0))
% 4.12/1.22 | ~ (less_equal @ (divide @ (divide @ X2 @ X1) @ X0) @
% 4.12/1.22 (divide @ (divide @ X2 @ X0) @ (divide @ X1 @ X0))))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl5])).
% 4.12/1.22 thf(zip_derived_cl219, plain,
% 4.12/1.22 (![X0 : $i]:
% 4.12/1.22 (~ (less_equal @ (divide @ (divide @ X0 @ identity) @ b) @
% 4.12/1.22 (divide @ (divide @ X0 @ b) @ c))
% 4.12/1.22 | ((divide @ (divide @ X0 @ b) @ (divide @ identity @ b))
% 4.12/1.22 = (divide @ (divide @ X0 @ identity) @ b)))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl43])).
% 4.12/1.22 thf(identity_is_largest, axiom, (less_equal @ X @ identity)).
% 4.12/1.22 thf(zip_derived_cl6, plain, (![X0 : $i]: (less_equal @ X0 @ identity)),
% 4.12/1.22 inference('cnf', [status(esa)], [identity_is_largest])).
% 4.12/1.22 thf(quotient_less_equal1, axiom,
% 4.12/1.22 (( ~( less_equal @ X @ Y ) ) | ( ( divide @ X @ Y ) = ( zero ) ))).
% 4.12/1.22 thf(zip_derived_cl0, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i]:
% 4.12/1.22 (~ (less_equal @ X0 @ X1) | ((divide @ X0 @ X1) = (zero)))),
% 4.12/1.22 inference('cnf', [status(esa)], [quotient_less_equal1])).
% 4.12/1.22 thf(zip_derived_cl15, plain,
% 4.12/1.22 (![X0 : $i]: ((divide @ X0 @ identity) = (zero))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl0])).
% 4.12/1.22 thf(zero_is_smallest, axiom, (less_equal @ zero @ X)).
% 4.12/1.22 thf(zip_derived_cl4, plain, (![X0 : $i]: (less_equal @ zero @ X0)),
% 4.12/1.22 inference('cnf', [status(esa)], [zero_is_smallest])).
% 4.12/1.22 thf(zip_derived_cl0, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i]:
% 4.12/1.22 (~ (less_equal @ X0 @ X1) | ((divide @ X0 @ X1) = (zero)))),
% 4.12/1.22 inference('cnf', [status(esa)], [quotient_less_equal1])).
% 4.12/1.22 thf(zip_derived_cl17, plain, (![X0 : $i]: ((divide @ zero @ X0) = (zero))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 4.12/1.22 thf(zip_derived_cl4, plain, (![X0 : $i]: (less_equal @ zero @ X0)),
% 4.12/1.22 inference('cnf', [status(esa)], [zero_is_smallest])).
% 4.12/1.22 thf(zip_derived_cl9, plain, (((divide @ identity @ b) = (c))),
% 4.12/1.22 inference('cnf', [status(esa)], [id_divide_b_is_c])).
% 4.12/1.22 thf(zip_derived_cl15, plain,
% 4.12/1.22 (![X0 : $i]: ((divide @ X0 @ identity) = (zero))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl0])).
% 4.12/1.22 thf(zip_derived_cl17, plain, (![X0 : $i]: ((divide @ zero @ X0) = (zero))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 4.12/1.22 thf(zip_derived_cl251, plain,
% 4.12/1.22 (![X0 : $i]: ((divide @ (divide @ X0 @ b) @ c) = (zero))),
% 4.12/1.22 inference('demod', [status(thm)],
% 4.12/1.22 [zip_derived_cl219, zip_derived_cl15, zip_derived_cl17,
% 4.12/1.22 zip_derived_cl4, zip_derived_cl9, zip_derived_cl15,
% 4.12/1.22 zip_derived_cl17])).
% 4.12/1.22 thf(zip_derived_cl306, plain, (((divide @ c @ c) = (zero))),
% 4.12/1.22 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl251])).
% 4.12/1.22 thf(zip_derived_cl9, plain, (((divide @ identity @ b) = (c))),
% 4.12/1.22 inference('cnf', [status(esa)], [id_divide_b_is_c])).
% 4.12/1.22 thf(zip_derived_cl3, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.12/1.22 (less_equal @ (divide @ (divide @ X0 @ X1) @ (divide @ X2 @ X1)) @
% 4.12/1.22 (divide @ (divide @ X0 @ X2) @ X1))),
% 4.12/1.22 inference('cnf', [status(esa)], [quotient_property])).
% 4.12/1.22 thf(zip_derived_cl50, plain,
% 4.12/1.22 (![X0 : $i]:
% 4.12/1.22 (less_equal @
% 4.12/1.22 (divide @ (divide @ identity @ X0) @ (divide @ b @ X0)) @
% 4.12/1.22 (divide @ c @ X0))),
% 4.12/1.22 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl3])).
% 4.12/1.22 thf(zip_derived_cl473, plain,
% 4.12/1.22 ( (less_equal @ (divide @ (divide @ identity @ c) @ (divide @ b @ c)) @
% 4.12/1.22 zero)),
% 4.12/1.22 inference('sup+', [status(thm)], [zip_derived_cl306, zip_derived_cl50])).
% 4.12/1.22 thf(id_divide_c_is_d, axiom, (( divide @ identity @ c ) = ( d ))).
% 4.12/1.22 thf(zip_derived_cl10, plain, (((divide @ identity @ c) = (d))),
% 4.12/1.22 inference('cnf', [status(esa)], [id_divide_c_is_d])).
% 4.12/1.22 thf(zip_derived_cl481, plain,
% 4.12/1.22 ( (less_equal @ (divide @ d @ (divide @ b @ c)) @ zero)),
% 4.12/1.22 inference('demod', [status(thm)], [zip_derived_cl473, zip_derived_cl10])).
% 4.12/1.22 thf(zip_derived_cl4, plain, (![X0 : $i]: (less_equal @ zero @ X0)),
% 4.12/1.22 inference('cnf', [status(esa)], [zero_is_smallest])).
% 4.12/1.22 thf(zip_derived_cl5, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i]:
% 4.12/1.22 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 4.12/1.22 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 4.12/1.22 thf(zip_derived_cl39, plain,
% 4.12/1.22 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 4.12/1.22 thf(zip_derived_cl746, plain, (((zero) = (divide @ d @ (divide @ b @ c)))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl481, zip_derived_cl39])).
% 4.12/1.22 thf(quotient_less_equal2, axiom,
% 4.12/1.22 (( ( divide @ X @ Y ) != ( zero ) ) | ( less_equal @ X @ Y ))).
% 4.12/1.22 thf(zip_derived_cl1, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i]:
% 4.12/1.22 (((divide @ X0 @ X1) != (zero)) | (less_equal @ X0 @ X1))),
% 4.12/1.22 inference('cnf', [status(esa)], [quotient_less_equal2])).
% 4.12/1.22 thf(zip_derived_cl753, plain,
% 4.12/1.22 ((((zero) != (zero)) | (less_equal @ d @ (divide @ b @ c)))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl746, zip_derived_cl1])).
% 4.12/1.22 thf(zip_derived_cl771, plain, ( (less_equal @ d @ (divide @ b @ c))),
% 4.12/1.22 inference('simplify', [status(thm)], [zip_derived_cl753])).
% 4.12/1.22 thf(zip_derived_cl10, plain, (((divide @ identity @ c) = (d))),
% 4.12/1.22 inference('cnf', [status(esa)], [id_divide_c_is_d])).
% 4.12/1.22 thf(zip_derived_cl43, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.12/1.22 (((divide @ (divide @ X2 @ X0) @ (divide @ X1 @ X0))
% 4.12/1.22 = (divide @ (divide @ X2 @ X1) @ X0))
% 4.12/1.22 | ~ (less_equal @ (divide @ (divide @ X2 @ X1) @ X0) @
% 4.12/1.22 (divide @ (divide @ X2 @ X0) @ (divide @ X1 @ X0))))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl5])).
% 4.12/1.22 thf(zip_derived_cl220, plain,
% 4.12/1.22 (![X0 : $i]:
% 4.12/1.22 (~ (less_equal @ (divide @ (divide @ X0 @ identity) @ c) @
% 4.12/1.22 (divide @ (divide @ X0 @ c) @ d))
% 4.12/1.22 | ((divide @ (divide @ X0 @ c) @ (divide @ identity @ c))
% 4.12/1.22 = (divide @ (divide @ X0 @ identity) @ c)))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl43])).
% 4.12/1.22 thf(zip_derived_cl15, plain,
% 4.12/1.22 (![X0 : $i]: ((divide @ X0 @ identity) = (zero))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl0])).
% 4.12/1.22 thf(zip_derived_cl17, plain, (![X0 : $i]: ((divide @ zero @ X0) = (zero))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 4.12/1.22 thf(zip_derived_cl4, plain, (![X0 : $i]: (less_equal @ zero @ X0)),
% 4.12/1.22 inference('cnf', [status(esa)], [zero_is_smallest])).
% 4.12/1.22 thf(zip_derived_cl10, plain, (((divide @ identity @ c) = (d))),
% 4.12/1.22 inference('cnf', [status(esa)], [id_divide_c_is_d])).
% 4.12/1.22 thf(zip_derived_cl15, plain,
% 4.12/1.22 (![X0 : $i]: ((divide @ X0 @ identity) = (zero))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl0])).
% 4.12/1.22 thf(zip_derived_cl17, plain, (![X0 : $i]: ((divide @ zero @ X0) = (zero))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 4.12/1.22 thf(zip_derived_cl252, plain,
% 4.12/1.22 (![X0 : $i]: ((divide @ (divide @ X0 @ c) @ d) = (zero))),
% 4.12/1.22 inference('demod', [status(thm)],
% 4.12/1.22 [zip_derived_cl220, zip_derived_cl15, zip_derived_cl17,
% 4.12/1.22 zip_derived_cl4, zip_derived_cl10, zip_derived_cl15,
% 4.12/1.22 zip_derived_cl17])).
% 4.12/1.22 thf(zip_derived_cl1, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i]:
% 4.12/1.22 (((divide @ X0 @ X1) != (zero)) | (less_equal @ X0 @ X1))),
% 4.12/1.22 inference('cnf', [status(esa)], [quotient_less_equal2])).
% 4.12/1.22 thf(zip_derived_cl389, plain,
% 4.12/1.22 (![X0 : $i]: (((zero) != (zero)) | (less_equal @ (divide @ X0 @ c) @ d))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl252, zip_derived_cl1])).
% 4.12/1.22 thf(zip_derived_cl411, plain,
% 4.12/1.22 (![X0 : $i]: (less_equal @ (divide @ X0 @ c) @ d)),
% 4.12/1.22 inference('simplify', [status(thm)], [zip_derived_cl389])).
% 4.12/1.22 thf(zip_derived_cl5, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i]:
% 4.12/1.22 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 4.12/1.22 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 4.12/1.22 thf(zip_derived_cl464, plain,
% 4.12/1.22 (![X0 : $i]:
% 4.12/1.22 (((divide @ X0 @ c) = (d)) | ~ (less_equal @ d @ (divide @ X0 @ c)))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl411, zip_derived_cl5])).
% 4.12/1.22 thf(zip_derived_cl784, plain, (((divide @ b @ c) = (d))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl771, zip_derived_cl464])).
% 4.12/1.22 thf(quotient_smaller_than_numerator, axiom,
% 4.12/1.22 (less_equal @ ( divide @ X @ Y ) @ X)).
% 4.12/1.22 thf(zip_derived_cl2, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i]: (less_equal @ (divide @ X0 @ X1) @ X0)),
% 4.12/1.22 inference('cnf', [status(esa)], [quotient_smaller_than_numerator])).
% 4.12/1.22 thf(zip_derived_cl5, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i]:
% 4.12/1.22 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 4.12/1.22 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 4.12/1.22 thf(zip_derived_cl38, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i]:
% 4.12/1.22 (((divide @ X0 @ X1) = (X0))
% 4.12/1.22 | ~ (less_equal @ X0 @ (divide @ X0 @ X1)))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl5])).
% 4.12/1.22 thf(zip_derived_cl792, plain,
% 4.12/1.22 ((~ (less_equal @ b @ d) | ((divide @ b @ c) = (b)))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl784, zip_derived_cl38])).
% 4.12/1.22 thf(zip_derived_cl784, plain, (((divide @ b @ c) = (d))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl771, zip_derived_cl464])).
% 4.12/1.22 thf(zip_derived_cl809, plain, ((~ (less_equal @ b @ d) | ((d) = (b)))),
% 4.12/1.22 inference('demod', [status(thm)], [zip_derived_cl792, zip_derived_cl784])).
% 4.12/1.22 thf(prove_b_equals_d, conjecture, (( b ) = ( d ))).
% 4.12/1.22 thf(zf_stmt_0, negated_conjecture, (( b ) != ( d )),
% 4.12/1.22 inference('cnf.neg', [status(esa)], [prove_b_equals_d])).
% 4.12/1.22 thf(zip_derived_cl11, plain, (((b) != (d))),
% 4.12/1.22 inference('cnf', [status(esa)], [zf_stmt_0])).
% 4.12/1.22 thf(zip_derived_cl810, plain, (~ (less_equal @ b @ d)),
% 4.12/1.22 inference('simplify_reflect-', [status(thm)],
% 4.12/1.22 [zip_derived_cl809, zip_derived_cl11])).
% 4.12/1.22 thf(id_divide_a_is_b, axiom, (( divide @ identity @ a ) = ( b ))).
% 4.12/1.22 thf(zip_derived_cl8, plain, (((divide @ identity @ a) = (b))),
% 4.12/1.22 inference('cnf', [status(esa)], [id_divide_a_is_b])).
% 4.12/1.22 thf(zip_derived_cl8, plain, (((divide @ identity @ a) = (b))),
% 4.12/1.22 inference('cnf', [status(esa)], [id_divide_a_is_b])).
% 4.12/1.22 thf(zip_derived_cl3, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.12/1.22 (less_equal @ (divide @ (divide @ X0 @ X1) @ (divide @ X2 @ X1)) @
% 4.12/1.22 (divide @ (divide @ X0 @ X2) @ X1))),
% 4.12/1.22 inference('cnf', [status(esa)], [quotient_property])).
% 4.12/1.22 thf(zip_derived_cl56, plain,
% 4.12/1.22 (![X0 : $i]:
% 4.12/1.22 (less_equal @ (divide @ (divide @ X0 @ a) @ b) @
% 4.12/1.22 (divide @ (divide @ X0 @ identity) @ a))),
% 4.12/1.22 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl3])).
% 4.12/1.22 thf(zip_derived_cl15, plain,
% 4.12/1.22 (![X0 : $i]: ((divide @ X0 @ identity) = (zero))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl0])).
% 4.12/1.22 thf(zip_derived_cl17, plain, (![X0 : $i]: ((divide @ zero @ X0) = (zero))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 4.12/1.22 thf(zip_derived_cl71, plain,
% 4.12/1.22 (![X0 : $i]: (less_equal @ (divide @ (divide @ X0 @ a) @ b) @ zero)),
% 4.12/1.22 inference('demod', [status(thm)],
% 4.12/1.22 [zip_derived_cl56, zip_derived_cl15, zip_derived_cl17])).
% 4.12/1.22 thf(zip_derived_cl102, plain, ( (less_equal @ (divide @ b @ b) @ zero)),
% 4.12/1.22 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl71])).
% 4.12/1.22 thf(zip_derived_cl39, plain,
% 4.12/1.22 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 4.12/1.22 thf(zip_derived_cl166, plain, (((zero) = (divide @ b @ b))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl102, zip_derived_cl39])).
% 4.12/1.22 thf(zip_derived_cl8, plain, (((divide @ identity @ a) = (b))),
% 4.12/1.22 inference('cnf', [status(esa)], [id_divide_a_is_b])).
% 4.12/1.22 thf(zip_derived_cl3, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.12/1.22 (less_equal @ (divide @ (divide @ X0 @ X1) @ (divide @ X2 @ X1)) @
% 4.12/1.22 (divide @ (divide @ X0 @ X2) @ X1))),
% 4.12/1.22 inference('cnf', [status(esa)], [quotient_property])).
% 4.12/1.22 thf(zip_derived_cl49, plain,
% 4.12/1.22 (![X0 : $i]:
% 4.12/1.22 (less_equal @
% 4.12/1.22 (divide @ (divide @ identity @ X0) @ (divide @ a @ X0)) @
% 4.12/1.22 (divide @ b @ X0))),
% 4.12/1.22 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl3])).
% 4.12/1.22 thf(zip_derived_cl424, plain,
% 4.12/1.22 ( (less_equal @ (divide @ (divide @ identity @ b) @ (divide @ a @ b)) @
% 4.12/1.22 zero)),
% 4.12/1.22 inference('sup+', [status(thm)], [zip_derived_cl166, zip_derived_cl49])).
% 4.12/1.22 thf(zip_derived_cl9, plain, (((divide @ identity @ b) = (c))),
% 4.12/1.22 inference('cnf', [status(esa)], [id_divide_b_is_c])).
% 4.12/1.22 thf(zip_derived_cl431, plain,
% 4.12/1.22 ( (less_equal @ (divide @ c @ (divide @ a @ b)) @ zero)),
% 4.12/1.22 inference('demod', [status(thm)], [zip_derived_cl424, zip_derived_cl9])).
% 4.12/1.22 thf(zip_derived_cl39, plain,
% 4.12/1.22 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 4.12/1.22 thf(zip_derived_cl905, plain, (((zero) = (divide @ c @ (divide @ a @ b)))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl431, zip_derived_cl39])).
% 4.12/1.22 thf(zip_derived_cl1, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i]:
% 4.12/1.22 (((divide @ X0 @ X1) != (zero)) | (less_equal @ X0 @ X1))),
% 4.12/1.22 inference('cnf', [status(esa)], [quotient_less_equal2])).
% 4.12/1.22 thf(zip_derived_cl912, plain,
% 4.12/1.22 ((((zero) != (zero)) | (less_equal @ c @ (divide @ a @ b)))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl905, zip_derived_cl1])).
% 4.12/1.22 thf(zip_derived_cl932, plain, ( (less_equal @ c @ (divide @ a @ b))),
% 4.12/1.22 inference('simplify', [status(thm)], [zip_derived_cl912])).
% 4.12/1.22 thf(zip_derived_cl251, plain,
% 4.12/1.22 (![X0 : $i]: ((divide @ (divide @ X0 @ b) @ c) = (zero))),
% 4.12/1.22 inference('demod', [status(thm)],
% 4.12/1.22 [zip_derived_cl219, zip_derived_cl15, zip_derived_cl17,
% 4.12/1.22 zip_derived_cl4, zip_derived_cl9, zip_derived_cl15,
% 4.12/1.22 zip_derived_cl17])).
% 4.12/1.22 thf(zip_derived_cl1, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i]:
% 4.12/1.22 (((divide @ X0 @ X1) != (zero)) | (less_equal @ X0 @ X1))),
% 4.12/1.22 inference('cnf', [status(esa)], [quotient_less_equal2])).
% 4.12/1.22 thf(zip_derived_cl287, plain,
% 4.12/1.22 (![X0 : $i]: (((zero) != (zero)) | (less_equal @ (divide @ X0 @ b) @ c))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl251, zip_derived_cl1])).
% 4.12/1.22 thf(zip_derived_cl308, plain,
% 4.12/1.22 (![X0 : $i]: (less_equal @ (divide @ X0 @ b) @ c)),
% 4.12/1.22 inference('simplify', [status(thm)], [zip_derived_cl287])).
% 4.12/1.22 thf(zip_derived_cl5, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i]:
% 4.12/1.22 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 4.12/1.22 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 4.12/1.22 thf(zip_derived_cl377, plain,
% 4.12/1.22 (![X0 : $i]:
% 4.12/1.22 (((divide @ X0 @ b) = (c)) | ~ (less_equal @ c @ (divide @ X0 @ b)))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl308, zip_derived_cl5])).
% 4.12/1.22 thf(zip_derived_cl969, plain, (((divide @ a @ b) = (c))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl932, zip_derived_cl377])).
% 4.12/1.22 thf(zip_derived_cl2, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i]: (less_equal @ (divide @ X0 @ X1) @ X0)),
% 4.12/1.22 inference('cnf', [status(esa)], [quotient_smaller_than_numerator])).
% 4.12/1.22 thf(zip_derived_cl0, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i]:
% 4.12/1.22 (~ (less_equal @ X0 @ X1) | ((divide @ X0 @ X1) = (zero)))),
% 4.12/1.22 inference('cnf', [status(esa)], [quotient_less_equal1])).
% 4.12/1.22 thf(zip_derived_cl16, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i]: ((divide @ (divide @ X0 @ X1) @ X0) = (zero))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 4.12/1.22 thf(zip_derived_cl976, plain, (((divide @ c @ a) = (zero))),
% 4.12/1.22 inference('sup+', [status(thm)], [zip_derived_cl969, zip_derived_cl16])).
% 4.12/1.22 thf(zip_derived_cl8, plain, (((divide @ identity @ a) = (b))),
% 4.12/1.22 inference('cnf', [status(esa)], [id_divide_a_is_b])).
% 4.12/1.22 thf(zip_derived_cl3, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.12/1.22 (less_equal @ (divide @ (divide @ X0 @ X1) @ (divide @ X2 @ X1)) @
% 4.12/1.22 (divide @ (divide @ X0 @ X2) @ X1))),
% 4.12/1.22 inference('cnf', [status(esa)], [quotient_property])).
% 4.12/1.22 thf(zip_derived_cl62, plain,
% 4.12/1.22 (![X0 : $i]:
% 4.12/1.22 (less_equal @ (divide @ b @ (divide @ X0 @ a)) @
% 4.12/1.22 (divide @ (divide @ identity @ X0) @ a))),
% 4.12/1.22 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl3])).
% 4.12/1.22 thf(zip_derived_cl1021, plain,
% 4.12/1.22 ( (less_equal @ (divide @ b @ zero) @
% 4.12/1.22 (divide @ (divide @ identity @ c) @ a))),
% 4.12/1.22 inference('sup+', [status(thm)], [zip_derived_cl976, zip_derived_cl62])).
% 4.12/1.22 thf(zip_derived_cl10, plain, (((divide @ identity @ c) = (d))),
% 4.12/1.22 inference('cnf', [status(esa)], [id_divide_c_is_d])).
% 4.12/1.22 thf(zip_derived_cl1037, plain,
% 4.12/1.22 ( (less_equal @ (divide @ b @ zero) @ (divide @ d @ a))),
% 4.12/1.22 inference('demod', [status(thm)], [zip_derived_cl1021, zip_derived_cl10])).
% 4.12/1.22 thf(zip_derived_cl0, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i]:
% 4.12/1.22 (~ (less_equal @ X0 @ X1) | ((divide @ X0 @ X1) = (zero)))),
% 4.12/1.22 inference('cnf', [status(esa)], [quotient_less_equal1])).
% 4.12/1.22 thf(zip_derived_cl1094, plain,
% 4.12/1.22 (((divide @ (divide @ b @ zero) @ (divide @ d @ a)) = (zero))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl1037, zip_derived_cl0])).
% 4.12/1.22 thf(zip_derived_cl43, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.12/1.22 (((divide @ (divide @ X2 @ X0) @ (divide @ X1 @ X0))
% 4.12/1.22 = (divide @ (divide @ X2 @ X1) @ X0))
% 4.12/1.22 | ~ (less_equal @ (divide @ (divide @ X2 @ X1) @ X0) @
% 4.12/1.22 (divide @ (divide @ X2 @ X0) @ (divide @ X1 @ X0))))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl5])).
% 4.12/1.22 thf(zip_derived_cl2628, plain,
% 4.12/1.22 ((~ (less_equal @ zero @
% 4.12/1.22 (divide @ (divide @ b @ (divide @ d @ a)) @
% 4.12/1.22 (divide @ zero @ (divide @ d @ a))))
% 4.12/1.22 | ((divide @ (divide @ b @ (divide @ d @ a)) @
% 4.12/1.22 (divide @ zero @ (divide @ d @ a)))
% 4.12/1.22 = (divide @ (divide @ b @ zero) @ (divide @ d @ a))))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl1094, zip_derived_cl43])).
% 4.12/1.22 thf(zip_derived_cl17, plain, (![X0 : $i]: ((divide @ zero @ X0) = (zero))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 4.12/1.22 thf(zip_derived_cl4, plain, (![X0 : $i]: (less_equal @ zero @ X0)),
% 4.12/1.22 inference('cnf', [status(esa)], [zero_is_smallest])).
% 4.12/1.22 thf(zip_derived_cl17, plain, (![X0 : $i]: ((divide @ zero @ X0) = (zero))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 4.12/1.22 thf(zip_derived_cl1094, plain,
% 4.12/1.22 (((divide @ (divide @ b @ zero) @ (divide @ d @ a)) = (zero))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl1037, zip_derived_cl0])).
% 4.12/1.22 thf(zip_derived_cl2669, plain,
% 4.12/1.22 (((divide @ (divide @ b @ (divide @ d @ a)) @ zero) = (zero))),
% 4.12/1.22 inference('demod', [status(thm)],
% 4.12/1.22 [zip_derived_cl2628, zip_derived_cl17, zip_derived_cl4,
% 4.12/1.22 zip_derived_cl17, zip_derived_cl1094])).
% 4.12/1.22 thf(zip_derived_cl1, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i]:
% 4.12/1.22 (((divide @ X0 @ X1) != (zero)) | (less_equal @ X0 @ X1))),
% 4.12/1.22 inference('cnf', [status(esa)], [quotient_less_equal2])).
% 4.12/1.22 thf(zip_derived_cl2931, plain,
% 4.12/1.22 ((((zero) != (zero))
% 4.12/1.22 | (less_equal @ (divide @ b @ (divide @ d @ a)) @ zero))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl2669, zip_derived_cl1])).
% 4.12/1.22 thf(zip_derived_cl2981, plain,
% 4.12/1.22 ( (less_equal @ (divide @ b @ (divide @ d @ a)) @ zero)),
% 4.12/1.22 inference('simplify', [status(thm)], [zip_derived_cl2931])).
% 4.12/1.22 thf(zip_derived_cl39, plain,
% 4.12/1.22 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 4.12/1.22 thf(zip_derived_cl3022, plain, (((zero) = (divide @ b @ (divide @ d @ a)))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl2981, zip_derived_cl39])).
% 4.12/1.22 thf(zip_derived_cl1, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i]:
% 4.12/1.22 (((divide @ X0 @ X1) != (zero)) | (less_equal @ X0 @ X1))),
% 4.12/1.22 inference('cnf', [status(esa)], [quotient_less_equal2])).
% 4.12/1.22 thf(zip_derived_cl3030, plain,
% 4.12/1.22 ((((zero) != (zero)) | (less_equal @ b @ (divide @ d @ a)))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl3022, zip_derived_cl1])).
% 4.12/1.22 thf(zip_derived_cl3072, plain, ( (less_equal @ b @ (divide @ d @ a))),
% 4.12/1.22 inference('simplify', [status(thm)], [zip_derived_cl3030])).
% 4.12/1.22 thf(zip_derived_cl71, plain,
% 4.12/1.22 (![X0 : $i]: (less_equal @ (divide @ (divide @ X0 @ a) @ b) @ zero)),
% 4.12/1.22 inference('demod', [status(thm)],
% 4.12/1.22 [zip_derived_cl56, zip_derived_cl15, zip_derived_cl17])).
% 4.12/1.22 thf(zip_derived_cl39, plain,
% 4.12/1.22 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 4.12/1.22 thf(zip_derived_cl97, plain,
% 4.12/1.22 (![X0 : $i]: ((zero) = (divide @ (divide @ X0 @ a) @ b))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl39])).
% 4.12/1.22 thf(zip_derived_cl1, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i]:
% 4.12/1.22 (((divide @ X0 @ X1) != (zero)) | (less_equal @ X0 @ X1))),
% 4.12/1.22 inference('cnf', [status(esa)], [quotient_less_equal2])).
% 4.12/1.22 thf(zip_derived_cl191, plain,
% 4.12/1.22 (![X0 : $i]: (((zero) != (zero)) | (less_equal @ (divide @ X0 @ a) @ b))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl97, zip_derived_cl1])).
% 4.12/1.22 thf(zip_derived_cl206, plain,
% 4.12/1.22 (![X0 : $i]: (less_equal @ (divide @ X0 @ a) @ b)),
% 4.12/1.22 inference('simplify', [status(thm)], [zip_derived_cl191])).
% 4.12/1.22 thf(zip_derived_cl5, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i]:
% 4.12/1.22 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 4.12/1.22 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 4.12/1.22 thf(zip_derived_cl277, plain,
% 4.12/1.22 (![X0 : $i]:
% 4.12/1.22 (((divide @ X0 @ a) = (b)) | ~ (less_equal @ b @ (divide @ X0 @ a)))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl206, zip_derived_cl5])).
% 4.12/1.22 thf(zip_derived_cl3103, plain, (((divide @ d @ a) = (b))),
% 4.12/1.22 inference('sup-', [status(thm)], [zip_derived_cl3072, zip_derived_cl277])).
% 4.12/1.22 thf(zip_derived_cl2, plain,
% 4.12/1.22 (![X0 : $i, X1 : $i]: (less_equal @ (divide @ X0 @ X1) @ X0)),
% 4.12/1.22 inference('cnf', [status(esa)], [quotient_smaller_than_numerator])).
% 4.12/1.22 thf(zip_derived_cl3111, plain, ( (less_equal @ b @ d)),
% 4.12/1.22 inference('sup+', [status(thm)], [zip_derived_cl3103, zip_derived_cl2])).
% 4.12/1.22 thf(zip_derived_cl3287, plain, ($false),
% 4.12/1.22 inference('demod', [status(thm)], [zip_derived_cl810, zip_derived_cl3111])).
% 4.12/1.22
% 4.12/1.22 % SZS output end Refutation
% 4.12/1.22
% 4.12/1.22
% 4.12/1.22 % Terminating...
% 4.53/1.30 % Runner terminated.
% 4.53/1.32 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------