%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP184-4 : TPTP v9.2.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.3VNUJwzq5Y true
% Computer : n019.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 04:35:57 PM UTC 2025
% Result : Unsatisfiable 36.94s 5.85s
% Output : Refutation 36.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GRP184-4 : TPTP v9.2.0. Bugfixed v1.2.1.
% 0.11/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.3VNUJwzq5Y true
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 1 14:17:08 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Running portfolio for 300 s
% 0.14/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in FO mode
% 0.50/0.60 % Total configuration time : 435
% 0.50/0.60 % Estimated wc time : 1092
% 0.50/0.60 % Estimated cpu time (7 cpus) : 156.0
% 0.53/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.53/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.53/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.53/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.53/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.53/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.53/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 36.94/5.85 % Solved by fo/fo7.sh.
% 36.94/5.85 % done 2269 iterations in 5.097s
% 36.94/5.85 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 36.94/5.85 % SZS output start Refutation
% 36.94/5.85 thf(a_type, type, a: $i).
% 36.94/5.85 thf(least_upper_bound_type, type, least_upper_bound: $i > $i > $i).
% 36.94/5.85 thf(identity_type, type, identity: $i).
% 36.94/5.85 thf(multiply_type, type, multiply: $i > $i > $i).
% 36.94/5.85 thf(greatest_lower_bound_type, type, greatest_lower_bound: $i > $i > $i).
% 36.94/5.85 thf(inverse_type, type, inverse: $i > $i).
% 36.94/5.85 thf(prove_p21x, conjecture,
% 36.94/5.85 (( multiply @
% 36.94/5.85 ( least_upper_bound @ a @ identity ) @
% 36.94/5.85 ( inverse @ ( greatest_lower_bound @ a @ identity ) ) ) =
% 36.94/5.85 ( multiply @
% 36.94/5.85 ( inverse @ ( greatest_lower_bound @ a @ identity ) ) @
% 36.94/5.85 ( least_upper_bound @ a @ identity ) ))).
% 36.94/5.85 thf(zf_stmt_0, negated_conjecture,
% 36.94/5.85 (( multiply @
% 36.94/5.85 ( least_upper_bound @ a @ identity ) @
% 36.94/5.85 ( inverse @ ( greatest_lower_bound @ a @ identity ) ) ) !=
% 36.94/5.85 ( multiply @
% 36.94/5.85 ( inverse @ ( greatest_lower_bound @ a @ identity ) ) @
% 36.94/5.85 ( least_upper_bound @ a @ identity ) )),
% 36.94/5.85 inference('cnf.neg', [status(esa)], [prove_p21x])).
% 36.94/5.85 thf(zip_derived_cl20, plain,
% 36.94/5.85 (((multiply @ (least_upper_bound @ a @ identity) @
% 36.94/5.85 (inverse @ (greatest_lower_bound @ a @ identity)))
% 36.94/5.85 != (multiply @ (inverse @ (greatest_lower_bound @ a @ identity)) @
% 36.94/5.85 (least_upper_bound @ a @ identity)))),
% 36.94/5.85 inference('cnf', [status(esa)], [zf_stmt_0])).
% 36.94/5.85 thf(symmetry_of_glb, axiom,
% 36.94/5.85 (( greatest_lower_bound @ X @ Y ) = ( greatest_lower_bound @ Y @ X ))).
% 36.94/5.85 thf(zip_derived_cl3, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((greatest_lower_bound @ X1 @ X0) = (greatest_lower_bound @ X0 @ X1))),
% 36.94/5.85 inference('cnf', [status(esa)], [symmetry_of_glb])).
% 36.94/5.85 thf(zip_derived_cl3, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((greatest_lower_bound @ X1 @ X0) = (greatest_lower_bound @ X0 @ X1))),
% 36.94/5.85 inference('cnf', [status(esa)], [symmetry_of_glb])).
% 36.94/5.85 thf(zip_derived_cl30, plain,
% 36.94/5.85 (((multiply @ (least_upper_bound @ a @ identity) @
% 36.94/5.85 (inverse @ (greatest_lower_bound @ identity @ a)))
% 36.94/5.85 != (multiply @ (inverse @ (greatest_lower_bound @ identity @ a)) @
% 36.94/5.85 (least_upper_bound @ a @ identity)))),
% 36.94/5.85 inference('demod', [status(thm)],
% 36.94/5.85 [zip_derived_cl20, zip_derived_cl3, zip_derived_cl3])).
% 36.94/5.85 thf(symmetry_of_lub, axiom,
% 36.94/5.85 (( least_upper_bound @ X @ Y ) = ( least_upper_bound @ Y @ X ))).
% 36.94/5.85 thf(zip_derived_cl4, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((least_upper_bound @ X1 @ X0) = (least_upper_bound @ X0 @ X1))),
% 36.94/5.85 inference('cnf', [status(esa)], [symmetry_of_lub])).
% 36.94/5.85 thf(zip_derived_cl4, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((least_upper_bound @ X1 @ X0) = (least_upper_bound @ X0 @ X1))),
% 36.94/5.85 inference('cnf', [status(esa)], [symmetry_of_lub])).
% 36.94/5.85 thf(zip_derived_cl35, plain,
% 36.94/5.85 (((multiply @ (least_upper_bound @ identity @ a) @
% 36.94/5.85 (inverse @ (greatest_lower_bound @ identity @ a)))
% 36.94/5.85 != (multiply @ (inverse @ (greatest_lower_bound @ identity @ a)) @
% 36.94/5.85 (least_upper_bound @ identity @ a)))),
% 36.94/5.85 inference('demod', [status(thm)],
% 36.94/5.85 [zip_derived_cl30, zip_derived_cl4, zip_derived_cl4])).
% 36.94/5.85 thf(p21x_2, axiom, (( inverse @ ( inverse @ X ) ) = ( X ))).
% 36.94/5.85 thf(zip_derived_cl16, plain,
% 36.94/5.85 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 36.94/5.85 inference('cnf', [status(esa)], [p21x_2])).
% 36.94/5.85 thf(p21x_1, axiom, (( inverse @ identity ) = ( identity ))).
% 36.94/5.85 thf(zip_derived_cl15, plain, (((inverse @ identity) = (identity))),
% 36.94/5.85 inference('cnf', [status(esa)], [p21x_1])).
% 36.94/5.85 thf(p21x_4, axiom,
% 36.94/5.85 (( inverse @ ( greatest_lower_bound @ X @ Y ) ) =
% 36.94/5.85 ( least_upper_bound @ ( inverse @ X ) @ ( inverse @ Y ) ))).
% 36.94/5.85 thf(zip_derived_cl18, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((inverse @ (greatest_lower_bound @ X0 @ X1))
% 36.94/5.85 = (least_upper_bound @ (inverse @ X0) @ (inverse @ X1)))),
% 36.94/5.85 inference('cnf', [status(esa)], [p21x_4])).
% 36.94/5.85 thf(zip_derived_cl82, plain,
% 36.94/5.85 (![X0 : $i]:
% 36.94/5.85 ((inverse @ (greatest_lower_bound @ X0 @ identity))
% 36.94/5.85 = (least_upper_bound @ (inverse @ X0) @ identity))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl15, zip_derived_cl18])).
% 36.94/5.85 thf(zip_derived_cl94, plain,
% 36.94/5.85 (![X0 : $i]:
% 36.94/5.85 ((inverse @ (greatest_lower_bound @ (inverse @ X0) @ identity))
% 36.94/5.85 = (least_upper_bound @ X0 @ identity))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl16, zip_derived_cl82])).
% 36.94/5.85 thf(zip_derived_cl3, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((greatest_lower_bound @ X1 @ X0) = (greatest_lower_bound @ X0 @ X1))),
% 36.94/5.85 inference('cnf', [status(esa)], [symmetry_of_glb])).
% 36.94/5.85 thf(zip_derived_cl96, plain,
% 36.94/5.85 (![X0 : $i]:
% 36.94/5.85 ((inverse @ (greatest_lower_bound @ identity @ (inverse @ X0)))
% 36.94/5.85 = (least_upper_bound @ X0 @ identity))),
% 36.94/5.85 inference('demod', [status(thm)], [zip_derived_cl94, zip_derived_cl3])).
% 36.94/5.85 thf(zip_derived_cl4, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((least_upper_bound @ X1 @ X0) = (least_upper_bound @ X0 @ X1))),
% 36.94/5.85 inference('cnf', [status(esa)], [symmetry_of_lub])).
% 36.94/5.85 thf(zip_derived_cl97, plain,
% 36.94/5.85 (![X0 : $i]:
% 36.94/5.85 ((least_upper_bound @ identity @ X0)
% 36.94/5.85 = (inverse @ (greatest_lower_bound @ identity @ (inverse @ X0))))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl96, zip_derived_cl4])).
% 36.94/5.85 thf(zip_derived_cl97, plain,
% 36.94/5.85 (![X0 : $i]:
% 36.94/5.85 ((least_upper_bound @ identity @ X0)
% 36.94/5.85 = (inverse @ (greatest_lower_bound @ identity @ (inverse @ X0))))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl96, zip_derived_cl4])).
% 36.94/5.85 thf(zip_derived_cl105, plain,
% 36.94/5.85 (((multiply @
% 36.94/5.85 (inverse @ (greatest_lower_bound @ identity @ (inverse @ a))) @
% 36.94/5.85 (inverse @ (greatest_lower_bound @ identity @ a)))
% 36.94/5.85 != (multiply @ (inverse @ (greatest_lower_bound @ identity @ a)) @
% 36.94/5.85 (inverse @ (greatest_lower_bound @ identity @ (inverse @ a)))))),
% 36.94/5.85 inference('demod', [status(thm)],
% 36.94/5.85 [zip_derived_cl35, zip_derived_cl97, zip_derived_cl97])).
% 36.94/5.85 thf(zip_derived_cl16, plain,
% 36.94/5.85 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 36.94/5.85 inference('cnf', [status(esa)], [p21x_2])).
% 36.94/5.85 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 36.94/5.85 thf(zip_derived_cl1, plain,
% 36.94/5.85 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 36.94/5.85 inference('cnf', [status(esa)], [left_inverse])).
% 36.94/5.85 thf(zip_derived_cl25, plain,
% 36.94/5.85 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl16, zip_derived_cl1])).
% 36.94/5.85 thf(zip_derived_cl16, plain,
% 36.94/5.85 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 36.94/5.85 inference('cnf', [status(esa)], [p21x_2])).
% 36.94/5.85 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 36.94/5.85 thf(zip_derived_cl0, plain,
% 36.94/5.85 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 36.94/5.85 inference('cnf', [status(esa)], [left_identity])).
% 36.94/5.85 thf(p21x_3, axiom,
% 36.94/5.85 (( inverse @ ( multiply @ X @ Y ) ) =
% 36.94/5.85 ( multiply @ ( inverse @ Y ) @ ( inverse @ X ) ))).
% 36.94/5.85 thf(zip_derived_cl17, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((inverse @ (multiply @ X1 @ X0))
% 36.94/5.85 = (multiply @ (inverse @ X0) @ (inverse @ X1)))),
% 36.94/5.85 inference('cnf', [status(esa)], [p21x_3])).
% 36.94/5.85 thf(zip_derived_cl59, plain,
% 36.94/5.85 (![X0 : $i]:
% 36.94/5.85 ((inverse @ X0) = (multiply @ (inverse @ X0) @ (inverse @ identity)))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl17])).
% 36.94/5.85 thf(zip_derived_cl15, plain, (((inverse @ identity) = (identity))),
% 36.94/5.85 inference('cnf', [status(esa)], [p21x_1])).
% 36.94/5.85 thf(zip_derived_cl62, plain,
% 36.94/5.85 (![X0 : $i]: ((inverse @ X0) = (multiply @ (inverse @ X0) @ identity))),
% 36.94/5.85 inference('demod', [status(thm)], [zip_derived_cl59, zip_derived_cl15])).
% 36.94/5.85 thf(zip_derived_cl68, plain,
% 36.94/5.85 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (multiply @ X0 @ identity))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl16, zip_derived_cl62])).
% 36.94/5.85 thf(zip_derived_cl16, plain,
% 36.94/5.85 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 36.94/5.85 inference('cnf', [status(esa)], [p21x_2])).
% 36.94/5.85 thf(zip_derived_cl71, plain,
% 36.94/5.85 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 36.94/5.85 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl16])).
% 36.94/5.85 thf(monotony_lub1, axiom,
% 36.94/5.85 (( multiply @ X @ ( least_upper_bound @ Y @ Z ) ) =
% 36.94/5.85 ( least_upper_bound @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ))).
% 36.94/5.85 thf(zip_derived_cl11, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 36.94/5.85 ((multiply @ X0 @ (least_upper_bound @ X1 @ X2))
% 36.94/5.85 = (least_upper_bound @ (multiply @ X0 @ X1) @ (multiply @ X0 @ X2)))),
% 36.94/5.85 inference('cnf', [status(esa)], [monotony_lub1])).
% 36.94/5.85 thf(p21x_5, axiom,
% 36.94/5.85 (( inverse @ ( least_upper_bound @ X @ Y ) ) =
% 36.94/5.85 ( greatest_lower_bound @ ( inverse @ X ) @ ( inverse @ Y ) ))).
% 36.94/5.85 thf(zip_derived_cl19, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((inverse @ (least_upper_bound @ X0 @ X1))
% 36.94/5.85 = (greatest_lower_bound @ (inverse @ X0) @ (inverse @ X1)))),
% 36.94/5.85 inference('cnf', [status(esa)], [p21x_5])).
% 36.94/5.85 thf(zip_derived_cl16, plain,
% 36.94/5.85 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 36.94/5.85 inference('cnf', [status(esa)], [p21x_2])).
% 36.94/5.85 thf(zip_derived_cl301, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((inverse @ (greatest_lower_bound @ (inverse @ X1) @ (inverse @ X0)))
% 36.94/5.85 = (least_upper_bound @ X1 @ X0))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl16])).
% 36.94/5.85 thf(zip_derived_cl2884, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 36.94/5.85 ((multiply @ X0 @
% 36.94/5.85 (inverse @ (greatest_lower_bound @ (inverse @ X1) @ (inverse @ X2))))
% 36.94/5.85 = (least_upper_bound @ (multiply @ X0 @ X1) @ (multiply @ X0 @ X2)))),
% 36.94/5.85 inference('demod', [status(thm)], [zip_derived_cl11, zip_derived_cl301])).
% 36.94/5.85 thf(zip_derived_cl2888, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((multiply @ X0 @
% 36.94/5.85 (inverse @
% 36.94/5.85 (greatest_lower_bound @ (inverse @ X1) @ (inverse @ identity))))
% 36.94/5.85 = (least_upper_bound @ (multiply @ X0 @ X1) @ X0))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl71, zip_derived_cl2884])).
% 36.94/5.85 thf(zip_derived_cl15, plain, (((inverse @ identity) = (identity))),
% 36.94/5.85 inference('cnf', [status(esa)], [p21x_1])).
% 36.94/5.85 thf(zip_derived_cl3, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((greatest_lower_bound @ X1 @ X0) = (greatest_lower_bound @ X0 @ X1))),
% 36.94/5.85 inference('cnf', [status(esa)], [symmetry_of_glb])).
% 36.94/5.85 thf(zip_derived_cl3, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((greatest_lower_bound @ X1 @ X0) = (greatest_lower_bound @ X0 @ X1))),
% 36.94/5.85 inference('cnf', [status(esa)], [symmetry_of_glb])).
% 36.94/5.85 thf(lub_absorbtion, axiom,
% 36.94/5.85 (( least_upper_bound @ X @ ( greatest_lower_bound @ X @ Y ) ) = ( X ))).
% 36.94/5.85 thf(zip_derived_cl9, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((least_upper_bound @ X0 @ (greatest_lower_bound @ X0 @ X1)) = (X0))),
% 36.94/5.85 inference('cnf', [status(esa)], [lub_absorbtion])).
% 36.94/5.85 thf(zip_derived_cl31, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((least_upper_bound @ X0 @ (greatest_lower_bound @ X1 @ X0)) = (X0))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl9])).
% 36.94/5.85 thf(zip_derived_cl4, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((least_upper_bound @ X1 @ X0) = (least_upper_bound @ X0 @ X1))),
% 36.94/5.85 inference('cnf', [status(esa)], [symmetry_of_lub])).
% 36.94/5.85 thf(glb_absorbtion, axiom,
% 36.94/5.85 (( greatest_lower_bound @ X @ ( least_upper_bound @ X @ Y ) ) = ( X ))).
% 36.94/5.85 thf(zip_derived_cl10, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((greatest_lower_bound @ X0 @ (least_upper_bound @ X0 @ X1)) = (X0))),
% 36.94/5.85 inference('cnf', [status(esa)], [glb_absorbtion])).
% 36.94/5.85 thf(zip_derived_cl39, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((greatest_lower_bound @ X0 @ (least_upper_bound @ X1 @ X0)) = (X0))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl10])).
% 36.94/5.85 thf(zip_derived_cl54, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((greatest_lower_bound @ (greatest_lower_bound @ X1 @ X0) @ X0)
% 36.94/5.85 = (greatest_lower_bound @ X1 @ X0))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl31, zip_derived_cl39])).
% 36.94/5.85 thf(zip_derived_cl3, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((greatest_lower_bound @ X1 @ X0) = (greatest_lower_bound @ X0 @ X1))),
% 36.94/5.85 inference('cnf', [status(esa)], [symmetry_of_glb])).
% 36.94/5.85 thf(zip_derived_cl198, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((greatest_lower_bound @ X0 @ (greatest_lower_bound @ X1 @ X0))
% 36.94/5.85 = (greatest_lower_bound @ X1 @ X0))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl54, zip_derived_cl3])).
% 36.94/5.85 thf(zip_derived_cl433, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((greatest_lower_bound @ X1 @ (greatest_lower_bound @ X1 @ X0))
% 36.94/5.85 = (greatest_lower_bound @ X0 @ X1))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl198])).
% 36.94/5.85 thf(zip_derived_cl82, plain,
% 36.94/5.85 (![X0 : $i]:
% 36.94/5.85 ((inverse @ (greatest_lower_bound @ X0 @ identity))
% 36.94/5.85 = (least_upper_bound @ (inverse @ X0) @ identity))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl15, zip_derived_cl18])).
% 36.94/5.85 thf(zip_derived_cl4, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((least_upper_bound @ X1 @ X0) = (least_upper_bound @ X0 @ X1))),
% 36.94/5.85 inference('cnf', [status(esa)], [symmetry_of_lub])).
% 36.94/5.85 thf(zip_derived_cl88, plain,
% 36.94/5.85 (![X0 : $i]:
% 36.94/5.85 ((least_upper_bound @ identity @ (inverse @ X0))
% 36.94/5.85 = (inverse @ (greatest_lower_bound @ X0 @ identity)))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl82, zip_derived_cl4])).
% 36.94/5.85 thf(zip_derived_cl19, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((inverse @ (least_upper_bound @ X0 @ X1))
% 36.94/5.85 = (greatest_lower_bound @ (inverse @ X0) @ (inverse @ X1)))),
% 36.94/5.85 inference('cnf', [status(esa)], [p21x_5])).
% 36.94/5.85 thf(zip_derived_cl317, plain,
% 36.94/5.85 (![X0 : $i]:
% 36.94/5.85 ((inverse @ (inverse @ (greatest_lower_bound @ X0 @ identity)))
% 36.94/5.85 = (greatest_lower_bound @ (inverse @ identity) @
% 36.94/5.85 (inverse @ (inverse @ X0))))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl88, zip_derived_cl19])).
% 36.94/5.85 thf(zip_derived_cl15, plain, (((inverse @ identity) = (identity))),
% 36.94/5.85 inference('cnf', [status(esa)], [p21x_1])).
% 36.94/5.85 thf(zip_derived_cl16, plain,
% 36.94/5.85 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 36.94/5.85 inference('cnf', [status(esa)], [p21x_2])).
% 36.94/5.85 thf(zip_derived_cl326, plain,
% 36.94/5.85 (![X0 : $i]:
% 36.94/5.85 ((inverse @ (inverse @ (greatest_lower_bound @ X0 @ identity)))
% 36.94/5.85 = (greatest_lower_bound @ identity @ X0))),
% 36.94/5.85 inference('demod', [status(thm)],
% 36.94/5.85 [zip_derived_cl317, zip_derived_cl15, zip_derived_cl16])).
% 36.94/5.85 thf(zip_derived_cl25, plain,
% 36.94/5.85 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl16, zip_derived_cl1])).
% 36.94/5.85 thf(zip_derived_cl469, plain,
% 36.94/5.85 (![X0 : $i]:
% 36.94/5.85 ((multiply @ (inverse @ (greatest_lower_bound @ X0 @ identity)) @
% 36.94/5.85 (greatest_lower_bound @ identity @ X0)) = (identity))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl326, zip_derived_cl25])).
% 36.94/5.85 thf(zip_derived_cl1347, plain,
% 36.94/5.85 (![X0 : $i]:
% 36.94/5.85 ((multiply @
% 36.94/5.85 (inverse @
% 36.94/5.85 (greatest_lower_bound @ (greatest_lower_bound @ identity @ X0) @
% 36.94/5.85 identity)) @
% 36.94/5.85 (greatest_lower_bound @ X0 @ identity)) = (identity))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl433, zip_derived_cl469])).
% 36.94/5.85 thf(zip_derived_cl9, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((least_upper_bound @ X0 @ (greatest_lower_bound @ X0 @ X1)) = (X0))),
% 36.94/5.85 inference('cnf', [status(esa)], [lub_absorbtion])).
% 36.94/5.85 thf(zip_derived_cl39, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((greatest_lower_bound @ X0 @ (least_upper_bound @ X1 @ X0)) = (X0))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl10])).
% 36.94/5.85 thf(zip_derived_cl53, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((greatest_lower_bound @ (greatest_lower_bound @ X0 @ X1) @ X0)
% 36.94/5.85 = (greatest_lower_bound @ X0 @ X1))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl39])).
% 36.94/5.85 thf(zip_derived_cl1369, plain,
% 36.94/5.85 (![X0 : $i]:
% 36.94/5.85 ((multiply @ (inverse @ (greatest_lower_bound @ identity @ X0)) @
% 36.94/5.85 (greatest_lower_bound @ X0 @ identity)) = (identity))),
% 36.94/5.85 inference('demod', [status(thm)], [zip_derived_cl1347, zip_derived_cl53])).
% 36.94/5.85 thf(zip_derived_cl25, plain,
% 36.94/5.85 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl16, zip_derived_cl1])).
% 36.94/5.85 thf(associativity, axiom,
% 36.94/5.85 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 36.94/5.85 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 36.94/5.85 thf(zip_derived_cl2, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 36.94/5.85 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 36.94/5.85 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 36.94/5.85 inference('cnf', [status(esa)], [associativity])).
% 36.94/5.85 thf(zip_derived_cl604, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((multiply @ identity @ X0)
% 36.94/5.85 = (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl25, zip_derived_cl2])).
% 36.94/5.85 thf(zip_derived_cl0, plain,
% 36.94/5.85 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 36.94/5.85 inference('cnf', [status(esa)], [left_identity])).
% 36.94/5.85 thf(zip_derived_cl611, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((X0) = (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)))),
% 36.94/5.85 inference('demod', [status(thm)], [zip_derived_cl604, zip_derived_cl0])).
% 36.94/5.85 thf(zip_derived_cl2412, plain,
% 36.94/5.85 (![X0 : $i]:
% 36.94/5.85 ((greatest_lower_bound @ X0 @ identity)
% 36.94/5.85 = (multiply @ (greatest_lower_bound @ identity @ X0) @ identity))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl1369, zip_derived_cl611])).
% 36.94/5.85 thf(zip_derived_cl71, plain,
% 36.94/5.85 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 36.94/5.85 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl16])).
% 36.94/5.85 thf(zip_derived_cl2916, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((multiply @ X0 @
% 36.94/5.85 (inverse @ (greatest_lower_bound @ identity @ (inverse @ X1))))
% 36.94/5.85 = (least_upper_bound @ (multiply @ X0 @ X1) @ X0))),
% 36.94/5.85 inference('demod', [status(thm)],
% 36.94/5.85 [zip_derived_cl2888, zip_derived_cl15, zip_derived_cl2412,
% 36.94/5.85 zip_derived_cl71])).
% 36.94/5.85 thf(zip_derived_cl4628, plain,
% 36.94/5.85 (![X0 : $i]:
% 36.94/5.85 ((multiply @ X0 @
% 36.94/5.85 (inverse @
% 36.94/5.85 (greatest_lower_bound @ identity @ (inverse @ (inverse @ X0)))))
% 36.94/5.85 = (least_upper_bound @ identity @ X0))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl25, zip_derived_cl2916])).
% 36.94/5.85 thf(zip_derived_cl16, plain,
% 36.94/5.85 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 36.94/5.85 inference('cnf', [status(esa)], [p21x_2])).
% 36.94/5.85 thf(zip_derived_cl97, plain,
% 36.94/5.85 (![X0 : $i]:
% 36.94/5.85 ((least_upper_bound @ identity @ X0)
% 36.94/5.85 = (inverse @ (greatest_lower_bound @ identity @ (inverse @ X0))))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl96, zip_derived_cl4])).
% 36.94/5.85 thf(zip_derived_cl4644, plain,
% 36.94/5.85 (![X0 : $i]:
% 36.94/5.85 ((multiply @ X0 @ (inverse @ (greatest_lower_bound @ identity @ X0)))
% 36.94/5.85 = (inverse @ (greatest_lower_bound @ identity @ (inverse @ X0))))),
% 36.94/5.85 inference('demod', [status(thm)],
% 36.94/5.85 [zip_derived_cl4628, zip_derived_cl16, zip_derived_cl97])).
% 36.94/5.85 thf(zip_derived_cl2, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 36.94/5.85 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 36.94/5.85 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 36.94/5.85 inference('cnf', [status(esa)], [associativity])).
% 36.94/5.85 thf(zip_derived_cl4644, plain,
% 36.94/5.85 (![X0 : $i]:
% 36.94/5.85 ((multiply @ X0 @ (inverse @ (greatest_lower_bound @ identity @ X0)))
% 36.94/5.85 = (inverse @ (greatest_lower_bound @ identity @ (inverse @ X0))))),
% 36.94/5.85 inference('demod', [status(thm)],
% 36.94/5.85 [zip_derived_cl4628, zip_derived_cl16, zip_derived_cl97])).
% 36.94/5.85 thf(zip_derived_cl5480, plain,
% 36.94/5.85 (((multiply @ a @
% 36.94/5.85 (multiply @ (inverse @ (greatest_lower_bound @ identity @ a)) @
% 36.94/5.85 (inverse @ (greatest_lower_bound @ identity @ a))))
% 36.94/5.85 != (multiply @ (inverse @ (greatest_lower_bound @ identity @ a)) @
% 36.94/5.85 (multiply @ a @ (inverse @ (greatest_lower_bound @ identity @ a)))))),
% 36.94/5.85 inference('demod', [status(thm)],
% 36.94/5.85 [zip_derived_cl105, zip_derived_cl4644, zip_derived_cl2,
% 36.94/5.85 zip_derived_cl4644])).
% 36.94/5.85 thf(zip_derived_cl1, plain,
% 36.94/5.85 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 36.94/5.85 inference('cnf', [status(esa)], [left_inverse])).
% 36.94/5.85 thf(zip_derived_cl2, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 36.94/5.85 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 36.94/5.85 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 36.94/5.85 inference('cnf', [status(esa)], [associativity])).
% 36.94/5.85 thf(zip_derived_cl607, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((multiply @ identity @ X0)
% 36.94/5.85 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 36.94/5.85 thf(zip_derived_cl0, plain,
% 36.94/5.85 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 36.94/5.85 inference('cnf', [status(esa)], [left_identity])).
% 36.94/5.85 thf(zip_derived_cl613, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 36.94/5.85 inference('demod', [status(thm)], [zip_derived_cl607, zip_derived_cl0])).
% 36.94/5.85 thf(zip_derived_cl0, plain,
% 36.94/5.85 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 36.94/5.85 inference('cnf', [status(esa)], [left_identity])).
% 36.94/5.85 thf(monotony_lub2, axiom,
% 36.94/5.85 (( multiply @ ( least_upper_bound @ Y @ Z ) @ X ) =
% 36.94/5.85 ( least_upper_bound @ ( multiply @ Y @ X ) @ ( multiply @ Z @ X ) ))).
% 36.94/5.85 thf(zip_derived_cl13, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 36.94/5.85 ((multiply @ (least_upper_bound @ X0 @ X2) @ X1)
% 36.94/5.85 = (least_upper_bound @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 36.94/5.85 inference('cnf', [status(esa)], [monotony_lub2])).
% 36.94/5.85 thf(zip_derived_cl611, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((X0) = (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)))),
% 36.94/5.85 inference('demod', [status(thm)], [zip_derived_cl604, zip_derived_cl0])).
% 36.94/5.85 thf(zip_derived_cl2916, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((multiply @ X0 @
% 36.94/5.85 (inverse @ (greatest_lower_bound @ identity @ (inverse @ X1))))
% 36.94/5.85 = (least_upper_bound @ (multiply @ X0 @ X1) @ X0))),
% 36.94/5.85 inference('demod', [status(thm)],
% 36.94/5.85 [zip_derived_cl2888, zip_derived_cl15, zip_derived_cl2412,
% 36.94/5.85 zip_derived_cl71])).
% 36.94/5.85 thf(zip_derived_cl4626, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((multiply @ X1 @
% 36.94/5.85 (inverse @
% 36.94/5.85 (greatest_lower_bound @ identity @
% 36.94/5.85 (inverse @ (multiply @ (inverse @ X1) @ X0)))))
% 36.94/5.85 = (least_upper_bound @ X0 @ X1))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl611, zip_derived_cl2916])).
% 36.94/5.85 thf(zip_derived_cl16, plain,
% 36.94/5.85 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 36.94/5.85 inference('cnf', [status(esa)], [p21x_2])).
% 36.94/5.85 thf(zip_derived_cl17, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((inverse @ (multiply @ X1 @ X0))
% 36.94/5.85 = (multiply @ (inverse @ X0) @ (inverse @ X1)))),
% 36.94/5.85 inference('cnf', [status(esa)], [p21x_3])).
% 36.94/5.85 thf(zip_derived_cl16, plain,
% 36.94/5.85 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 36.94/5.85 inference('cnf', [status(esa)], [p21x_2])).
% 36.94/5.85 thf(zip_derived_cl56, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((inverse @ (multiply @ (inverse @ X1) @ (inverse @ X0)))
% 36.94/5.85 = (multiply @ X0 @ X1))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl17, zip_derived_cl16])).
% 36.94/5.85 thf(zip_derived_cl1405, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((inverse @ (multiply @ (inverse @ X1) @ X0))
% 36.94/5.85 = (multiply @ (inverse @ X0) @ X1))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl16, zip_derived_cl56])).
% 36.94/5.85 thf(zip_derived_cl4642, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((multiply @ X1 @
% 36.94/5.85 (inverse @
% 36.94/5.85 (greatest_lower_bound @ identity @ (multiply @ (inverse @ X0) @ X1))))
% 36.94/5.85 = (least_upper_bound @ X0 @ X1))),
% 36.94/5.85 inference('demod', [status(thm)],
% 36.94/5.85 [zip_derived_cl4626, zip_derived_cl1405])).
% 36.94/5.85 thf(zip_derived_cl2, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 36.94/5.85 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 36.94/5.85 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 36.94/5.85 inference('cnf', [status(esa)], [associativity])).
% 36.94/5.85 thf(zip_derived_cl7047, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 36.94/5.85 ((multiply @ X2 @
% 36.94/5.85 (multiply @
% 36.94/5.85 (inverse @
% 36.94/5.85 (greatest_lower_bound @ identity @
% 36.94/5.85 (multiply @ (inverse @ X0) @ X2))) @
% 36.94/5.85 X1))
% 36.94/5.85 = (least_upper_bound @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 36.94/5.85 inference('demod', [status(thm)],
% 36.94/5.85 [zip_derived_cl13, zip_derived_cl4642, zip_derived_cl2])).
% 36.94/5.85 thf(zip_derived_cl7056, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((multiply @ identity @
% 36.94/5.85 (multiply @
% 36.94/5.85 (inverse @
% 36.94/5.85 (greatest_lower_bound @ identity @
% 36.94/5.85 (multiply @ (inverse @ X1) @ identity))) @
% 36.94/5.85 X0))
% 36.94/5.85 = (least_upper_bound @ (multiply @ X1 @ X0) @ X0))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl7047])).
% 36.94/5.85 thf(zip_derived_cl71, plain,
% 36.94/5.85 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 36.94/5.85 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl16])).
% 36.94/5.85 thf(zip_derived_cl4644, plain,
% 36.94/5.85 (![X0 : $i]:
% 36.94/5.85 ((multiply @ X0 @ (inverse @ (greatest_lower_bound @ identity @ X0)))
% 36.94/5.85 = (inverse @ (greatest_lower_bound @ identity @ (inverse @ X0))))),
% 36.94/5.85 inference('demod', [status(thm)],
% 36.94/5.85 [zip_derived_cl4628, zip_derived_cl16, zip_derived_cl97])).
% 36.94/5.85 thf(zip_derived_cl16, plain,
% 36.94/5.85 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 36.94/5.85 inference('cnf', [status(esa)], [p21x_2])).
% 36.94/5.85 thf(zip_derived_cl5484, plain,
% 36.94/5.85 (![X0 : $i]:
% 36.94/5.85 ((inverse @
% 36.94/5.85 (multiply @ X0 @ (inverse @ (greatest_lower_bound @ identity @ X0))))
% 36.94/5.85 = (greatest_lower_bound @ identity @ (inverse @ X0)))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl4644, zip_derived_cl16])).
% 36.94/5.85 thf(zip_derived_cl16, plain,
% 36.94/5.85 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 36.94/5.85 inference('cnf', [status(esa)], [p21x_2])).
% 36.94/5.85 thf(zip_derived_cl56, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((inverse @ (multiply @ (inverse @ X1) @ (inverse @ X0)))
% 36.94/5.85 = (multiply @ X0 @ X1))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl17, zip_derived_cl16])).
% 36.94/5.85 thf(zip_derived_cl1411, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((inverse @ (multiply @ X0 @ (inverse @ X1)))
% 36.94/5.85 = (multiply @ X1 @ (inverse @ X0)))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl16, zip_derived_cl56])).
% 36.94/5.85 thf(zip_derived_cl5547, plain,
% 36.94/5.85 (![X0 : $i]:
% 36.94/5.85 ((multiply @ (greatest_lower_bound @ identity @ X0) @ (inverse @ X0))
% 36.94/5.85 = (greatest_lower_bound @ identity @ (inverse @ X0)))),
% 36.94/5.85 inference('demod', [status(thm)],
% 36.94/5.85 [zip_derived_cl5484, zip_derived_cl1411])).
% 36.94/5.85 thf(zip_derived_cl1411, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((inverse @ (multiply @ X0 @ (inverse @ X1)))
% 36.94/5.85 = (multiply @ X1 @ (inverse @ X0)))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl16, zip_derived_cl56])).
% 36.94/5.85 thf(zip_derived_cl2, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 36.94/5.85 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 36.94/5.85 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 36.94/5.85 inference('cnf', [status(esa)], [associativity])).
% 36.94/5.85 thf(zip_derived_cl0, plain,
% 36.94/5.85 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 36.94/5.85 inference('cnf', [status(esa)], [left_identity])).
% 36.94/5.85 thf(zip_derived_cl7086, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((multiply @ X1 @
% 36.94/5.85 (multiply @ (inverse @ (greatest_lower_bound @ identity @ X1)) @ X0))
% 36.94/5.85 = (least_upper_bound @ (multiply @ X1 @ X0) @ X0))),
% 36.94/5.85 inference('demod', [status(thm)],
% 36.94/5.85 [zip_derived_cl7056, zip_derived_cl71, zip_derived_cl5547,
% 36.94/5.85 zip_derived_cl1411, zip_derived_cl2, zip_derived_cl0])).
% 36.94/5.85 thf(zip_derived_cl13082, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((multiply @ (inverse @ X1) @
% 36.94/5.85 (multiply @
% 36.94/5.85 (inverse @ (greatest_lower_bound @ identity @ (inverse @ X1))) @
% 36.94/5.85 (multiply @ X1 @ X0)))
% 36.94/5.85 = (least_upper_bound @ X0 @ (multiply @ X1 @ X0)))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl613, zip_derived_cl7086])).
% 36.94/5.85 thf(zip_derived_cl5547, plain,
% 36.94/5.85 (![X0 : $i]:
% 36.94/5.85 ((multiply @ (greatest_lower_bound @ identity @ X0) @ (inverse @ X0))
% 36.94/5.85 = (greatest_lower_bound @ identity @ (inverse @ X0)))),
% 36.94/5.85 inference('demod', [status(thm)],
% 36.94/5.85 [zip_derived_cl5484, zip_derived_cl1411])).
% 36.94/5.85 thf(zip_derived_cl1411, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((inverse @ (multiply @ X0 @ (inverse @ X1)))
% 36.94/5.85 = (multiply @ X1 @ (inverse @ X0)))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl16, zip_derived_cl56])).
% 36.94/5.85 thf(zip_derived_cl2, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 36.94/5.85 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 36.94/5.85 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 36.94/5.85 inference('cnf', [status(esa)], [associativity])).
% 36.94/5.85 thf(zip_derived_cl613, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 36.94/5.85 inference('demod', [status(thm)], [zip_derived_cl607, zip_derived_cl0])).
% 36.94/5.85 thf(zip_derived_cl13101, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((multiply @ (inverse @ (greatest_lower_bound @ identity @ X1)) @
% 36.94/5.85 (multiply @ X1 @ X0))
% 36.94/5.85 = (least_upper_bound @ X0 @ (multiply @ X1 @ X0)))),
% 36.94/5.85 inference('demod', [status(thm)],
% 36.94/5.85 [zip_derived_cl13082, zip_derived_cl5547, zip_derived_cl1411,
% 36.94/5.85 zip_derived_cl2, zip_derived_cl613])).
% 36.94/5.85 thf(zip_derived_cl0, plain,
% 36.94/5.85 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 36.94/5.85 inference('cnf', [status(esa)], [left_identity])).
% 36.94/5.85 thf(zip_derived_cl7047, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 36.94/5.85 ((multiply @ X2 @
% 36.94/5.85 (multiply @
% 36.94/5.85 (inverse @
% 36.94/5.85 (greatest_lower_bound @ identity @
% 36.94/5.85 (multiply @ (inverse @ X0) @ X2))) @
% 36.94/5.85 X1))
% 36.94/5.85 = (least_upper_bound @ (multiply @ X0 @ X1) @ (multiply @ X2 @ X1)))),
% 36.94/5.85 inference('demod', [status(thm)],
% 36.94/5.85 [zip_derived_cl13, zip_derived_cl4642, zip_derived_cl2])).
% 36.94/5.85 thf(zip_derived_cl7072, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((multiply @ X1 @
% 36.94/5.85 (multiply @
% 36.94/5.85 (inverse @
% 36.94/5.85 (greatest_lower_bound @ identity @
% 36.94/5.85 (multiply @ (inverse @ identity) @ X1))) @
% 36.94/5.85 X0))
% 36.94/5.85 = (least_upper_bound @ X0 @ (multiply @ X1 @ X0)))),
% 36.94/5.85 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl7047])).
% 36.94/5.85 thf(zip_derived_cl15, plain, (((inverse @ identity) = (identity))),
% 36.94/5.85 inference('cnf', [status(esa)], [p21x_1])).
% 36.94/5.85 thf(zip_derived_cl0, plain,
% 36.94/5.85 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 36.94/5.85 inference('cnf', [status(esa)], [left_identity])).
% 36.94/5.85 thf(zip_derived_cl7095, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((multiply @ X1 @
% 36.94/5.85 (multiply @ (inverse @ (greatest_lower_bound @ identity @ X1)) @ X0))
% 36.94/5.85 = (least_upper_bound @ X0 @ (multiply @ X1 @ X0)))),
% 36.94/5.85 inference('demod', [status(thm)],
% 36.94/5.85 [zip_derived_cl7072, zip_derived_cl15, zip_derived_cl0])).
% 36.94/5.85 thf(zip_derived_cl26324, plain,
% 36.94/5.85 (![X0 : $i, X1 : $i]:
% 36.94/5.85 ((multiply @ (inverse @ (greatest_lower_bound @ identity @ X1)) @
% 36.94/5.85 (multiply @ X1 @ X0))
% 36.94/5.85 = (multiply @ X1 @
% 36.94/5.85 (multiply @ (inverse @ (greatest_lower_bound @ identity @ X1)) @
% 36.94/5.85 X0)))),
% 36.94/5.85 inference('demod', [status(thm)],
% 36.94/5.85 [zip_derived_cl13101, zip_derived_cl7095])).
% 36.94/5.85 thf(zip_derived_cl26325, plain,
% 36.94/5.85 (((multiply @ a @
% 36.94/5.85 (multiply @ (inverse @ (greatest_lower_bound @ identity @ a)) @
% 36.94/5.85 (inverse @ (greatest_lower_bound @ identity @ a))))
% 36.94/5.85 != (multiply @ a @
% 36.94/5.85 (multiply @ (inverse @ (greatest_lower_bound @ identity @ a)) @
% 36.94/5.85 (inverse @ (greatest_lower_bound @ identity @ a)))))),
% 36.94/5.85 inference('demod', [status(thm)],
% 36.94/5.85 [zip_derived_cl5480, zip_derived_cl26324])).
% 36.94/5.85 thf(zip_derived_cl26326, plain, ($false),
% 36.94/5.85 inference('simplify', [status(thm)], [zip_derived_cl26325])).
% 36.94/5.85
% 36.94/5.85 % SZS output end Refutation
% 36.94/5.85
% 36.94/5.85
% 36.94/5.85 % Terminating...
% 36.94/5.92 % Runner terminated.
% 36.94/5.93 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------