%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP002-1 : 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.9KCsuRCeRv true
% Computer : n005.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 04:35:23 PM UTC 2025
% Result : Unsatisfiable 41.77s 6.56s
% Output : Refutation 41.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : GRP002-1 : TPTP v9.2.0. Released v1.0.0.
% 0.03/0.10 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.9KCsuRCeRv true
% 0.09/0.30 % Computer : n005.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Wed Oct 1 14:27:23 EDT 2025
% 0.09/0.30 % CPUTime :
% 0.09/0.30 % Running portfolio for 300 s
% 0.09/0.30 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.30 % Number of cores: 8
% 0.09/0.31 % Python version: Python 3.6.8
% 0.09/0.31 % Running in FO mode
% 0.15/0.55 % Total configuration time : 435
% 0.15/0.55 % Estimated wc time : 1092
% 0.15/0.55 % Estimated cpu time (7 cpus) : 156.0
% 1.06/0.65 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 1.06/0.65 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 1.06/0.66 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 1.06/0.66 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 1.06/0.66 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 1.06/0.66 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 1.06/0.66 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 41.77/6.56 % Solved by fo/fo5.sh.
% 41.77/6.56 % done 5841 iterations in 5.878s
% 41.77/6.56 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 41.77/6.56 % SZS output start Refutation
% 41.77/6.56 thf(inverse_type, type, inverse: $i > $i).
% 41.77/6.56 thf(product_type, type, product: $i > $i > $i > $o).
% 41.77/6.56 thf(k_type, type, k: $i).
% 41.77/6.56 thf(identity_type, type, identity: $i).
% 41.77/6.56 thf(j_type, type, j: $i).
% 41.77/6.56 thf(a_type, type, a: $i).
% 41.77/6.56 thf(b_type, type, b: $i).
% 41.77/6.56 thf(d_type, type, d: $i).
% 41.77/6.56 thf(c_type, type, c: $i).
% 41.77/6.56 thf(h_type, type, h: $i).
% 41.77/6.56 thf(multiply_type, type, multiply: $i > $i > $i).
% 41.77/6.56 thf(prove_k_times_inverse_b_is_e, conjecture,
% 41.77/6.56 (product @ k @ ( inverse @ b ) @ identity)).
% 41.77/6.56 thf(zf_stmt_0, negated_conjecture,
% 41.77/6.56 (~( product @ k @ ( inverse @ b ) @ identity )),
% 41.77/6.56 inference('cnf.neg', [status(esa)], [prove_k_times_inverse_b_is_e])).
% 41.77/6.56 thf(zip_derived_cl15, plain, (~ (product @ k @ (inverse @ b) @ identity)),
% 41.77/6.56 inference('cnf', [status(esa)], [zf_stmt_0])).
% 41.77/6.56 thf(a_times_b_is_c, conjecture, (~( product @ a @ b @ c ))).
% 41.77/6.56 thf(zf_stmt_1, negated_conjecture, (product @ a @ b @ c),
% 41.77/6.56 inference('cnf.neg', [status(esa)], [a_times_b_is_c])).
% 41.77/6.56 thf(zip_derived_cl10, plain, ( (product @ a @ b @ c)),
% 41.77/6.56 inference('cnf', [status(esa)], [zf_stmt_1])).
% 41.77/6.56 thf(left_identity, axiom, (product @ identity @ X @ X)).
% 41.77/6.56 thf(zip_derived_cl0, plain, (![X0 : $i]: (product @ identity @ X0 @ X0)),
% 41.77/6.56 inference('cnf', [status(esa)], [left_identity])).
% 41.77/6.56 thf(left_inverse, axiom, (product @ ( inverse @ X ) @ X @ identity)).
% 41.77/6.56 thf(zip_derived_cl2, plain,
% 41.77/6.56 (![X0 : $i]: (product @ (inverse @ X0) @ X0 @ identity)),
% 41.77/6.56 inference('cnf', [status(esa)], [left_inverse])).
% 41.77/6.56 thf(associativity1, axiom,
% 41.77/6.56 (( ~( product @ X @ Y @ U ) ) | ( ~( product @ Y @ Z @ V ) ) |
% 41.77/6.56 ( ~( product @ U @ Z @ W ) ) | ( product @ X @ V @ W ))).
% 41.77/6.56 thf(zip_derived_cl6, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 41.77/6.56 (~ (product @ X0 @ X1 @ X2)
% 41.77/6.56 | ~ (product @ X1 @ X3 @ X4)
% 41.77/6.56 | ~ (product @ X2 @ X3 @ X5)
% 41.77/6.56 | (product @ X0 @ X4 @ X5))),
% 41.77/6.56 inference('cnf', [status(esa)], [associativity1])).
% 41.77/6.56 thf(zip_derived_cl55, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 41.77/6.56 ( (product @ (inverse @ X0) @ X2 @ X1)
% 41.77/6.56 | ~ (product @ identity @ X3 @ X1)
% 41.77/6.56 | ~ (product @ X0 @ X3 @ X2))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl6])).
% 41.77/6.56 thf(zip_derived_cl302, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i]:
% 41.77/6.56 (~ (product @ X2 @ X0 @ X1) | (product @ (inverse @ X2) @ X1 @ X0))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl55])).
% 41.77/6.56 thf(zip_derived_cl503, plain, ( (product @ (inverse @ a) @ c @ b)),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl302])).
% 41.77/6.56 thf(total_function1, axiom, (product @ X @ Y @ ( multiply @ X @ Y ))).
% 41.77/6.56 thf(zip_derived_cl4, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 41.77/6.56 inference('cnf', [status(esa)], [total_function1])).
% 41.77/6.56 thf(x_cubed_is_identity_1, axiom,
% 41.77/6.56 (( ~( product @ X @ X @ Y ) ) | ( product @ X @ Y @ identity ))).
% 41.77/6.56 thf(zip_derived_cl8, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]:
% 41.77/6.56 (~ (product @ X0 @ X0 @ X1) | (product @ X0 @ X1 @ identity))),
% 41.77/6.56 inference('cnf', [status(esa)], [x_cubed_is_identity_1])).
% 41.77/6.56 thf(zip_derived_cl16, plain,
% 41.77/6.56 (![X0 : $i]: (product @ X0 @ (multiply @ X0 @ X0) @ identity)),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl8])).
% 41.77/6.56 thf(zip_derived_cl4, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 41.77/6.56 inference('cnf', [status(esa)], [total_function1])).
% 41.77/6.56 thf(total_function2, axiom,
% 41.77/6.56 (( ~( product @ X @ Y @ Z ) ) | ( ~( product @ X @ Y @ W ) ) |
% 41.77/6.56 ( ( Z ) = ( W ) ))).
% 41.77/6.56 thf(zip_derived_cl5, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 41.77/6.56 (~ (product @ X0 @ X1 @ X2)
% 41.77/6.56 | ~ (product @ X0 @ X1 @ X3)
% 41.77/6.56 | ((X2) = (X3)))),
% 41.77/6.56 inference('cnf', [status(esa)], [total_function2])).
% 41.77/6.56 thf(zip_derived_cl24, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i]:
% 41.77/6.56 (((multiply @ X1 @ X0) = (X2)) | ~ (product @ X1 @ X0 @ X2))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 41.77/6.56 thf(zip_derived_cl121, plain,
% 41.77/6.56 (![X0 : $i]: ((multiply @ X0 @ (multiply @ X0 @ X0)) = (identity))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl24])).
% 41.77/6.56 thf(zip_derived_cl4, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 41.77/6.56 inference('cnf', [status(esa)], [total_function1])).
% 41.77/6.56 thf(zip_derived_cl0, plain, (![X0 : $i]: (product @ identity @ X0 @ X0)),
% 41.77/6.56 inference('cnf', [status(esa)], [left_identity])).
% 41.77/6.56 thf(right_inverse, axiom, (product @ X @ ( inverse @ X ) @ identity)).
% 41.77/6.56 thf(zip_derived_cl3, plain,
% 41.77/6.56 (![X0 : $i]: (product @ X0 @ (inverse @ X0) @ identity)),
% 41.77/6.56 inference('cnf', [status(esa)], [right_inverse])).
% 41.77/6.56 thf(zip_derived_cl6, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 41.77/6.56 (~ (product @ X0 @ X1 @ X2)
% 41.77/6.56 | ~ (product @ X1 @ X3 @ X4)
% 41.77/6.56 | ~ (product @ X2 @ X3 @ X5)
% 41.77/6.56 | (product @ X0 @ X4 @ X5))),
% 41.77/6.56 inference('cnf', [status(esa)], [associativity1])).
% 41.77/6.56 thf(zip_derived_cl52, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 41.77/6.56 ( (product @ X0 @ X2 @ X1)
% 41.77/6.56 | ~ (product @ identity @ X3 @ X1)
% 41.77/6.56 | ~ (product @ (inverse @ X0) @ X3 @ X2))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 41.77/6.56 thf(zip_derived_cl237, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i]:
% 41.77/6.56 (~ (product @ (inverse @ X2) @ X0 @ X1) | (product @ X2 @ X1 @ X0))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl52])).
% 41.77/6.56 thf(zip_derived_cl355, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]:
% 41.77/6.56 (product @ X1 @ (multiply @ (inverse @ X1) @ X0) @ X0)),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl237])).
% 41.77/6.56 thf(zip_derived_cl24, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i]:
% 41.77/6.56 (((multiply @ X1 @ X0) = (X2)) | ~ (product @ X1 @ X0 @ X2))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 41.77/6.56 thf(zip_derived_cl451, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]:
% 41.77/6.56 ((multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)) = (X0))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl355, zip_derived_cl24])).
% 41.77/6.56 thf(zip_derived_cl693, plain,
% 41.77/6.56 (![X0 : $i]:
% 41.77/6.56 ((multiply @ X0 @ identity)
% 41.77/6.56 = (multiply @ (inverse @ X0) @ (inverse @ X0)))),
% 41.77/6.56 inference('sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl451])).
% 41.77/6.56 thf(zip_derived_cl4, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 41.77/6.56 inference('cnf', [status(esa)], [total_function1])).
% 41.77/6.56 thf(right_identity, axiom, (product @ X @ identity @ X)).
% 41.77/6.56 thf(zip_derived_cl1, plain, (![X0 : $i]: (product @ X0 @ identity @ X0)),
% 41.77/6.56 inference('cnf', [status(esa)], [right_identity])).
% 41.77/6.56 thf(zip_derived_cl5, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 41.77/6.56 (~ (product @ X0 @ X1 @ X2)
% 41.77/6.56 | ~ (product @ X0 @ X1 @ X3)
% 41.77/6.56 | ((X2) = (X3)))),
% 41.77/6.56 inference('cnf', [status(esa)], [total_function2])).
% 41.77/6.56 thf(zip_derived_cl25, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]: (((X0) = (X1)) | ~ (product @ X0 @ identity @ X1))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl5])).
% 41.77/6.56 thf(zip_derived_cl43, plain,
% 41.77/6.56 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl25])).
% 41.77/6.56 thf(zip_derived_cl706, plain,
% 41.77/6.56 (![X0 : $i]: ((X0) = (multiply @ (inverse @ X0) @ (inverse @ X0)))),
% 41.77/6.56 inference('demod', [status(thm)], [zip_derived_cl693, zip_derived_cl43])).
% 41.77/6.56 thf(zip_derived_cl451, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]:
% 41.77/6.56 ((multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)) = (X0))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl355, zip_derived_cl24])).
% 41.77/6.56 thf(zip_derived_cl765, plain,
% 41.77/6.56 (![X0 : $i]: ((multiply @ X0 @ X0) = (inverse @ X0))),
% 41.77/6.56 inference('sup+', [status(thm)], [zip_derived_cl706, zip_derived_cl451])).
% 41.77/6.56 thf(zip_derived_cl991, plain, ( (product @ (multiply @ a @ a) @ c @ b)),
% 41.77/6.56 inference('demod', [status(thm)], [zip_derived_cl503, zip_derived_cl765])).
% 41.77/6.56 thf(zip_derived_cl4, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 41.77/6.56 inference('cnf', [status(esa)], [total_function1])).
% 41.77/6.56 thf(zip_derived_cl4, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 41.77/6.56 inference('cnf', [status(esa)], [total_function1])).
% 41.77/6.56 thf(zip_derived_cl6, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 41.77/6.56 (~ (product @ X0 @ X1 @ X2)
% 41.77/6.56 | ~ (product @ X1 @ X3 @ X4)
% 41.77/6.56 | ~ (product @ X2 @ X3 @ X5)
% 41.77/6.56 | (product @ X0 @ X4 @ X5))),
% 41.77/6.56 inference('cnf', [status(esa)], [associativity1])).
% 41.77/6.56 thf(zip_derived_cl50, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 41.77/6.56 ( (product @ X1 @ X3 @ X2)
% 41.77/6.56 | ~ (product @ (multiply @ X1 @ X0) @ X4 @ X2)
% 41.77/6.56 | ~ (product @ X0 @ X4 @ X3))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl6])).
% 41.77/6.56 thf(zip_derived_cl167, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 41.77/6.56 (~ (product @ X1 @ X0 @ X3)
% 41.77/6.56 | (product @ X2 @ X3 @ (multiply @ (multiply @ X2 @ X1) @ X0)))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl50])).
% 41.77/6.56 thf(zip_derived_cl1412, plain,
% 41.77/6.56 (![X0 : $i]:
% 41.77/6.56 (product @ X0 @ b @
% 41.77/6.56 (multiply @ (multiply @ X0 @ (multiply @ a @ a)) @ c))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl991, zip_derived_cl167])).
% 41.77/6.56 thf(zip_derived_cl4, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 41.77/6.56 inference('cnf', [status(esa)], [total_function1])).
% 41.77/6.56 thf(zip_derived_cl4, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 41.77/6.56 inference('cnf', [status(esa)], [total_function1])).
% 41.77/6.56 thf(h_times_b_is_j, conjecture, (~( product @ h @ b @ j ))).
% 41.77/6.56 thf(zf_stmt_2, negated_conjecture, (product @ h @ b @ j),
% 41.77/6.56 inference('cnf.neg', [status(esa)], [h_times_b_is_j])).
% 41.77/6.56 thf(zip_derived_cl13, plain, ( (product @ h @ b @ j)),
% 41.77/6.56 inference('cnf', [status(esa)], [zf_stmt_2])).
% 41.77/6.56 thf(zip_derived_cl5, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 41.77/6.56 (~ (product @ X0 @ X1 @ X2)
% 41.77/6.56 | ~ (product @ X0 @ X1 @ X3)
% 41.77/6.56 | ((X2) = (X3)))),
% 41.77/6.56 inference('cnf', [status(esa)], [total_function2])).
% 41.77/6.56 thf(zip_derived_cl33, plain,
% 41.77/6.56 (![X0 : $i]: (((j) = (X0)) | ~ (product @ h @ b @ X0))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl5])).
% 41.77/6.56 thf(zip_derived_cl39, plain, (((j) = (multiply @ h @ b))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl33])).
% 41.77/6.56 thf(zip_derived_cl13, plain, ( (product @ h @ b @ j)),
% 41.77/6.56 inference('cnf', [status(esa)], [zf_stmt_2])).
% 41.77/6.56 thf(zip_derived_cl2, plain,
% 41.77/6.56 (![X0 : $i]: (product @ (inverse @ X0) @ X0 @ identity)),
% 41.77/6.56 inference('cnf', [status(esa)], [left_inverse])).
% 41.77/6.56 thf(d_times_inverse_b_is_h, conjecture,
% 41.77/6.56 (~( product @ d @ ( inverse @ b ) @ h ))).
% 41.77/6.56 thf(zf_stmt_3, negated_conjecture, (product @ d @ ( inverse @ b ) @ h),
% 41.77/6.56 inference('cnf.neg', [status(esa)], [d_times_inverse_b_is_h])).
% 41.77/6.56 thf(zip_derived_cl12, plain, ( (product @ d @ (inverse @ b) @ h)),
% 41.77/6.56 inference('cnf', [status(esa)], [zf_stmt_3])).
% 41.77/6.56 thf(zip_derived_cl6, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 41.77/6.56 (~ (product @ X0 @ X1 @ X2)
% 41.77/6.56 | ~ (product @ X1 @ X3 @ X4)
% 41.77/6.56 | ~ (product @ X2 @ X3 @ X5)
% 41.77/6.56 | (product @ X0 @ X4 @ X5))),
% 41.77/6.56 inference('cnf', [status(esa)], [associativity1])).
% 41.77/6.56 thf(zip_derived_cl59, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i]:
% 41.77/6.56 ( (product @ d @ X1 @ X0)
% 41.77/6.56 | ~ (product @ h @ X2 @ X0)
% 41.77/6.56 | ~ (product @ (inverse @ b) @ X2 @ X1))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl6])).
% 41.77/6.56 thf(zip_derived_cl487, plain,
% 41.77/6.56 (![X0 : $i]: (~ (product @ h @ b @ X0) | (product @ d @ identity @ X0))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl59])).
% 41.77/6.56 thf(zip_derived_cl793, plain, ( (product @ d @ identity @ j)),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl487])).
% 41.77/6.56 thf(zip_derived_cl25, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]: (((X0) = (X1)) | ~ (product @ X0 @ identity @ X1))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl5])).
% 41.77/6.56 thf(zip_derived_cl803, plain, (((d) = (j))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl793, zip_derived_cl25])).
% 41.77/6.56 thf(zip_derived_cl812, plain, (((d) = (multiply @ h @ b))),
% 41.77/6.56 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl803])).
% 41.77/6.56 thf(zip_derived_cl355, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]:
% 41.77/6.56 (product @ X1 @ (multiply @ (inverse @ X1) @ X0) @ X0)),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl237])).
% 41.77/6.56 thf(j_times_inverse_h_is_k, conjecture,
% 41.77/6.56 (~( product @ j @ ( inverse @ h ) @ k ))).
% 41.77/6.56 thf(zf_stmt_4, negated_conjecture, (product @ j @ ( inverse @ h ) @ k),
% 41.77/6.56 inference('cnf.neg', [status(esa)], [j_times_inverse_h_is_k])).
% 41.77/6.56 thf(zip_derived_cl14, plain, ( (product @ j @ (inverse @ h) @ k)),
% 41.77/6.56 inference('cnf', [status(esa)], [zf_stmt_4])).
% 41.77/6.56 thf(zip_derived_cl6, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 41.77/6.56 (~ (product @ X0 @ X1 @ X2)
% 41.77/6.56 | ~ (product @ X1 @ X3 @ X4)
% 41.77/6.56 | ~ (product @ X2 @ X3 @ X5)
% 41.77/6.56 | (product @ X0 @ X4 @ X5))),
% 41.77/6.56 inference('cnf', [status(esa)], [associativity1])).
% 41.77/6.56 thf(zip_derived_cl61, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i]:
% 41.77/6.56 ( (product @ j @ X1 @ X0)
% 41.77/6.56 | ~ (product @ k @ X2 @ X0)
% 41.77/6.56 | ~ (product @ (inverse @ h) @ X2 @ X1))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl6])).
% 41.77/6.56 thf(zip_derived_cl577, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]:
% 41.77/6.56 (~ (product @ k @ (multiply @ (inverse @ (inverse @ h)) @ X0) @ X1)
% 41.77/6.56 | (product @ j @ X0 @ X1))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl355, zip_derived_cl61])).
% 41.77/6.56 thf(zip_derived_cl3, plain,
% 41.77/6.56 (![X0 : $i]: (product @ X0 @ (inverse @ X0) @ identity)),
% 41.77/6.56 inference('cnf', [status(esa)], [right_inverse])).
% 41.77/6.56 thf(zip_derived_cl237, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i]:
% 41.77/6.56 (~ (product @ (inverse @ X2) @ X0 @ X1) | (product @ X2 @ X1 @ X0))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl52])).
% 41.77/6.56 thf(zip_derived_cl357, plain,
% 41.77/6.56 (![X0 : $i]: (product @ X0 @ identity @ (inverse @ (inverse @ X0)))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl237])).
% 41.77/6.56 thf(zip_derived_cl25, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]: (((X0) = (X1)) | ~ (product @ X0 @ identity @ X1))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl5])).
% 41.77/6.56 thf(zip_derived_cl368, plain,
% 41.77/6.56 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl357, zip_derived_cl25])).
% 41.77/6.56 thf(zip_derived_cl582, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]:
% 41.77/6.56 (~ (product @ k @ (multiply @ h @ X0) @ X1) | (product @ j @ X0 @ X1))),
% 41.77/6.56 inference('demod', [status(thm)], [zip_derived_cl577, zip_derived_cl368])).
% 41.77/6.56 thf(zip_derived_cl803, plain, (((d) = (j))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl793, zip_derived_cl25])).
% 41.77/6.56 thf(zip_derived_cl4238, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]:
% 41.77/6.56 (~ (product @ k @ (multiply @ h @ X0) @ X1) | (product @ d @ X0 @ X1))),
% 41.77/6.56 inference('demod', [status(thm)], [zip_derived_cl582, zip_derived_cl803])).
% 41.77/6.56 thf(zip_derived_cl4247, plain,
% 41.77/6.56 (![X0 : $i]: (~ (product @ k @ d @ X0) | (product @ d @ b @ X0))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl812, zip_derived_cl4238])).
% 41.77/6.56 thf(zip_derived_cl4249, plain, ( (product @ d @ b @ (multiply @ k @ d))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl4247])).
% 41.77/6.56 thf(zip_derived_cl5, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 41.77/6.56 (~ (product @ X0 @ X1 @ X2)
% 41.77/6.56 | ~ (product @ X0 @ X1 @ X3)
% 41.77/6.56 | ((X2) = (X3)))),
% 41.77/6.56 inference('cnf', [status(esa)], [total_function2])).
% 41.77/6.56 thf(zip_derived_cl4250, plain,
% 41.77/6.56 (![X0 : $i]: (((multiply @ k @ d) = (X0)) | ~ (product @ d @ b @ X0))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4249, zip_derived_cl5])).
% 41.77/6.56 thf(zip_derived_cl22285, plain,
% 41.77/6.56 (((multiply @ k @ d)
% 41.77/6.56 = (multiply @ (multiply @ d @ (multiply @ a @ a)) @ c))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl1412, zip_derived_cl4250])).
% 41.77/6.56 thf(zip_derived_cl4, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 41.77/6.56 inference('cnf', [status(esa)], [total_function1])).
% 41.77/6.56 thf(c_times_inverse_a_is_d, conjecture,
% 41.77/6.56 (~( product @ c @ ( inverse @ a ) @ d ))).
% 41.77/6.56 thf(zf_stmt_5, negated_conjecture, (product @ c @ ( inverse @ a ) @ d),
% 41.77/6.56 inference('cnf.neg', [status(esa)], [c_times_inverse_a_is_d])).
% 41.77/6.56 thf(zip_derived_cl11, plain, ( (product @ c @ (inverse @ a) @ d)),
% 41.77/6.56 inference('cnf', [status(esa)], [zf_stmt_5])).
% 41.77/6.56 thf(zip_derived_cl765, plain,
% 41.77/6.56 (![X0 : $i]: ((multiply @ X0 @ X0) = (inverse @ X0))),
% 41.77/6.56 inference('sup+', [status(thm)], [zip_derived_cl706, zip_derived_cl451])).
% 41.77/6.56 thf(zip_derived_cl977, plain, ( (product @ c @ (multiply @ a @ a) @ d)),
% 41.77/6.56 inference('demod', [status(thm)], [zip_derived_cl11, zip_derived_cl765])).
% 41.77/6.56 thf(zip_derived_cl4, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 41.77/6.56 inference('cnf', [status(esa)], [total_function1])).
% 41.77/6.56 thf(associativity2, axiom,
% 41.77/6.56 (( ~( product @ X @ Y @ U ) ) | ( ~( product @ Y @ Z @ V ) ) |
% 41.77/6.56 ( ~( product @ X @ V @ W ) ) | ( product @ U @ Z @ W ))).
% 41.77/6.56 thf(zip_derived_cl7, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 41.77/6.56 (~ (product @ X0 @ X1 @ X2)
% 41.77/6.56 | ~ (product @ X1 @ X3 @ X4)
% 41.77/6.56 | ~ (product @ X0 @ X4 @ X5)
% 41.77/6.56 | (product @ X2 @ X3 @ X5))),
% 41.77/6.56 inference('cnf', [status(esa)], [associativity2])).
% 41.77/6.56 thf(zip_derived_cl85, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 41.77/6.56 ( (product @ (multiply @ X1 @ X0) @ X3 @ X2)
% 41.77/6.56 | ~ (product @ X1 @ X4 @ X2)
% 41.77/6.56 | ~ (product @ X0 @ X3 @ X4))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl7])).
% 41.77/6.56 thf(zip_derived_cl1377, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]:
% 41.77/6.56 (~ (product @ X1 @ X0 @ (multiply @ a @ a))
% 41.77/6.56 | (product @ (multiply @ c @ X1) @ X0 @ d))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl977, zip_derived_cl85])).
% 41.77/6.56 thf(zip_derived_cl16007, plain, ( (product @ (multiply @ c @ a) @ a @ d)),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl1377])).
% 41.77/6.56 thf(zip_derived_cl24, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i]:
% 41.77/6.56 (((multiply @ X1 @ X0) = (X2)) | ~ (product @ X1 @ X0 @ X2))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 41.77/6.56 thf(zip_derived_cl16032, plain,
% 41.77/6.56 (((multiply @ (multiply @ c @ a) @ a) = (d))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl16007, zip_derived_cl24])).
% 41.77/6.56 thf(zip_derived_cl3, plain,
% 41.77/6.56 (![X0 : $i]: (product @ X0 @ (inverse @ X0) @ identity)),
% 41.77/6.56 inference('cnf', [status(esa)], [right_inverse])).
% 41.77/6.56 thf(zip_derived_cl4, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 41.77/6.56 inference('cnf', [status(esa)], [total_function1])).
% 41.77/6.56 thf(zip_derived_cl85, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 41.77/6.56 ( (product @ (multiply @ X1 @ X0) @ X3 @ X2)
% 41.77/6.56 | ~ (product @ X1 @ X4 @ X2)
% 41.77/6.56 | ~ (product @ X0 @ X3 @ X4))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl7])).
% 41.77/6.56 thf(zip_derived_cl713, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 41.77/6.56 (~ (product @ X3 @ X2 @ X0)
% 41.77/6.56 | (product @ (multiply @ X1 @ X3) @ X2 @ (multiply @ X1 @ X0)))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl85])).
% 41.77/6.56 thf(zip_derived_cl4744, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]:
% 41.77/6.56 (product @ (multiply @ X1 @ X0) @ (inverse @ X0) @
% 41.77/6.56 (multiply @ X1 @ identity))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl713])).
% 41.77/6.56 thf(zip_derived_cl43, plain,
% 41.77/6.56 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl25])).
% 41.77/6.56 thf(zip_derived_cl4792, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]:
% 41.77/6.56 (product @ (multiply @ X1 @ X0) @ (inverse @ X0) @ X1)),
% 41.77/6.56 inference('demod', [status(thm)], [zip_derived_cl4744, zip_derived_cl43])).
% 41.77/6.56 thf(zip_derived_cl24, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i]:
% 41.77/6.56 (((multiply @ X1 @ X0) = (X2)) | ~ (product @ X1 @ X0 @ X2))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 41.77/6.56 thf(zip_derived_cl4988, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]:
% 41.77/6.56 ((multiply @ (multiply @ X0 @ X1) @ (inverse @ X1)) = (X0))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4792, zip_derived_cl24])).
% 41.77/6.56 thf(zip_derived_cl16098, plain,
% 41.77/6.56 (((multiply @ d @ (inverse @ a)) = (multiply @ c @ a))),
% 41.77/6.56 inference('sup+', [status(thm)],
% 41.77/6.56 [zip_derived_cl16032, zip_derived_cl4988])).
% 41.77/6.56 thf(zip_derived_cl765, plain,
% 41.77/6.56 (![X0 : $i]: ((multiply @ X0 @ X0) = (inverse @ X0))),
% 41.77/6.56 inference('sup+', [status(thm)], [zip_derived_cl706, zip_derived_cl451])).
% 41.77/6.56 thf(zip_derived_cl16122, plain,
% 41.77/6.56 (((multiply @ d @ (multiply @ a @ a)) = (multiply @ c @ a))),
% 41.77/6.56 inference('demod', [status(thm)],
% 41.77/6.56 [zip_derived_cl16098, zip_derived_cl765])).
% 41.77/6.56 thf(zip_derived_cl22394, plain,
% 41.77/6.56 (((multiply @ k @ d) = (multiply @ (multiply @ c @ a) @ c))),
% 41.77/6.56 inference('demod', [status(thm)],
% 41.77/6.56 [zip_derived_cl22285, zip_derived_cl16122])).
% 41.77/6.56 thf(zip_derived_cl368, plain,
% 41.77/6.56 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl357, zip_derived_cl25])).
% 41.77/6.56 thf(zip_derived_cl451, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]:
% 41.77/6.56 ((multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)) = (X0))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl355, zip_derived_cl24])).
% 41.77/6.56 thf(zip_derived_cl704, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]:
% 41.77/6.56 ((multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)) = (X1))),
% 41.77/6.56 inference('sup+', [status(thm)], [zip_derived_cl368, zip_derived_cl451])).
% 41.77/6.56 thf(zip_derived_cl22408, plain,
% 41.77/6.56 (((multiply @ (inverse @ (multiply @ c @ a)) @ (multiply @ k @ d)) = (c))),
% 41.77/6.56 inference('sup+', [status(thm)], [zip_derived_cl22394, zip_derived_cl704])).
% 41.77/6.56 thf(zip_derived_cl4, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 41.77/6.56 inference('cnf', [status(esa)], [total_function1])).
% 41.77/6.56 thf(zip_derived_cl706, plain,
% 41.77/6.56 (![X0 : $i]: ((X0) = (multiply @ (inverse @ X0) @ (inverse @ X0)))),
% 41.77/6.56 inference('demod', [status(thm)], [zip_derived_cl693, zip_derived_cl43])).
% 41.77/6.56 thf(zip_derived_cl355, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]:
% 41.77/6.56 (product @ X1 @ (multiply @ (inverse @ X1) @ X0) @ X0)),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl237])).
% 41.77/6.56 thf(zip_derived_cl763, plain,
% 41.77/6.56 (![X0 : $i]: (product @ X0 @ X0 @ (inverse @ X0))),
% 41.77/6.56 inference('sup+', [status(thm)], [zip_derived_cl706, zip_derived_cl355])).
% 41.77/6.56 thf(zip_derived_cl10, plain, ( (product @ a @ b @ c)),
% 41.77/6.56 inference('cnf', [status(esa)], [zf_stmt_1])).
% 41.77/6.56 thf(zip_derived_cl6, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 41.77/6.56 (~ (product @ X0 @ X1 @ X2)
% 41.77/6.56 | ~ (product @ X1 @ X3 @ X4)
% 41.77/6.56 | ~ (product @ X2 @ X3 @ X5)
% 41.77/6.56 | (product @ X0 @ X4 @ X5))),
% 41.77/6.56 inference('cnf', [status(esa)], [associativity1])).
% 41.77/6.56 thf(zip_derived_cl57, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i]:
% 41.77/6.56 ( (product @ a @ X1 @ X0)
% 41.77/6.56 | ~ (product @ c @ X2 @ X0)
% 41.77/6.56 | ~ (product @ b @ X2 @ X1))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl6])).
% 41.77/6.56 thf(zip_derived_cl943, plain,
% 41.77/6.56 (![X0 : $i]:
% 41.77/6.56 (~ (product @ b @ c @ X0) | (product @ a @ X0 @ (inverse @ c)))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl763, zip_derived_cl57])).
% 41.77/6.56 thf(zip_derived_cl1818, plain,
% 41.77/6.56 ( (product @ a @ (multiply @ b @ c) @ (inverse @ c))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl943])).
% 41.77/6.56 thf(zip_derived_cl24, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i]:
% 41.77/6.56 (((multiply @ X1 @ X0) = (X2)) | ~ (product @ X1 @ X0 @ X2))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 41.77/6.56 thf(zip_derived_cl2475, plain,
% 41.77/6.56 (((multiply @ a @ (multiply @ b @ c)) = (inverse @ c))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl1818, zip_derived_cl24])).
% 41.77/6.56 thf(zip_derived_cl4988, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]:
% 41.77/6.56 ((multiply @ (multiply @ X0 @ X1) @ (inverse @ X1)) = (X0))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4792, zip_derived_cl24])).
% 41.77/6.56 thf(zip_derived_cl704, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]:
% 41.77/6.56 ((multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)) = (X1))),
% 41.77/6.56 inference('sup+', [status(thm)], [zip_derived_cl368, zip_derived_cl451])).
% 41.77/6.56 thf(zip_derived_cl5612, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]:
% 41.77/6.56 ((multiply @ (inverse @ (multiply @ X0 @ X1)) @ X0) = (inverse @ X1))),
% 41.77/6.56 inference('sup+', [status(thm)], [zip_derived_cl4988, zip_derived_cl704])).
% 41.77/6.56 thf(zip_derived_cl8797, plain,
% 41.77/6.56 (((multiply @ (inverse @ (inverse @ c)) @ a)
% 41.77/6.56 = (inverse @ (multiply @ b @ c)))),
% 41.77/6.56 inference('sup+', [status(thm)], [zip_derived_cl2475, zip_derived_cl5612])).
% 41.77/6.56 thf(zip_derived_cl368, plain,
% 41.77/6.56 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl357, zip_derived_cl25])).
% 41.77/6.56 thf(zip_derived_cl8865, plain,
% 41.77/6.56 (((multiply @ c @ a) = (inverse @ (multiply @ b @ c)))),
% 41.77/6.56 inference('demod', [status(thm)], [zip_derived_cl8797, zip_derived_cl368])).
% 41.77/6.56 thf(zip_derived_cl368, plain,
% 41.77/6.56 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl357, zip_derived_cl25])).
% 41.77/6.56 thf(zip_derived_cl8982, plain,
% 41.77/6.56 (((multiply @ b @ c) = (inverse @ (multiply @ c @ a)))),
% 41.77/6.56 inference('sup+', [status(thm)], [zip_derived_cl8865, zip_derived_cl368])).
% 41.77/6.56 thf(zip_derived_cl22440, plain,
% 41.77/6.56 (((multiply @ (multiply @ b @ c) @ (multiply @ k @ d)) = (c))),
% 41.77/6.56 inference('demod', [status(thm)],
% 41.77/6.56 [zip_derived_cl22408, zip_derived_cl8982])).
% 41.77/6.56 thf(zip_derived_cl765, plain,
% 41.77/6.56 (![X0 : $i]: ((multiply @ X0 @ X0) = (inverse @ X0))),
% 41.77/6.56 inference('sup+', [status(thm)], [zip_derived_cl706, zip_derived_cl451])).
% 41.77/6.56 thf(zip_derived_cl368, plain,
% 41.77/6.56 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl357, zip_derived_cl25])).
% 41.77/6.56 thf(zip_derived_cl1006, plain,
% 41.77/6.56 (![X0 : $i]: ((X0) = (inverse @ (multiply @ X0 @ X0)))),
% 41.77/6.56 inference('sup+', [status(thm)], [zip_derived_cl765, zip_derived_cl368])).
% 41.77/6.56 thf(zip_derived_cl451, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]:
% 41.77/6.56 ((multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)) = (X0))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl355, zip_derived_cl24])).
% 41.77/6.56 thf(zip_derived_cl1089, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]:
% 41.77/6.56 ((multiply @ (multiply @ X0 @ X0) @ (multiply @ X0 @ X1)) = (X1))),
% 41.77/6.56 inference('sup+', [status(thm)], [zip_derived_cl1006, zip_derived_cl451])).
% 41.77/6.56 thf(zip_derived_cl46431, plain,
% 41.77/6.56 (((multiply @ (multiply @ (multiply @ b @ c) @ (multiply @ b @ c)) @ c)
% 41.77/6.56 = (multiply @ k @ d))),
% 41.77/6.56 inference('sup+', [status(thm)],
% 41.77/6.56 [zip_derived_cl22440, zip_derived_cl1089])).
% 41.77/6.56 thf(zip_derived_cl4, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 41.77/6.56 inference('cnf', [status(esa)], [total_function1])).
% 41.77/6.56 thf(zip_derived_cl167, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 41.77/6.56 (~ (product @ X1 @ X0 @ X3)
% 41.77/6.56 | (product @ X2 @ X3 @ (multiply @ (multiply @ X2 @ X1) @ X0)))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl50])).
% 41.77/6.56 thf(zip_derived_cl1398, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i]:
% 41.77/6.56 (product @ X2 @ (multiply @ X1 @ X0) @
% 41.77/6.56 (multiply @ (multiply @ X2 @ X1) @ X0))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl167])).
% 41.77/6.56 thf(zip_derived_cl24, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i]:
% 41.77/6.56 (((multiply @ X1 @ X0) = (X2)) | ~ (product @ X1 @ X0 @ X2))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 41.77/6.56 thf(zip_derived_cl17303, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i]:
% 41.77/6.56 ((multiply @ X2 @ (multiply @ X1 @ X0))
% 41.77/6.56 = (multiply @ (multiply @ X2 @ X1) @ X0))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl1398, zip_derived_cl24])).
% 41.77/6.56 thf(zip_derived_cl2475, plain,
% 41.77/6.56 (((multiply @ a @ (multiply @ b @ c)) = (inverse @ c))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl1818, zip_derived_cl24])).
% 41.77/6.56 thf(zip_derived_cl4, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 41.77/6.56 inference('cnf', [status(esa)], [total_function1])).
% 41.77/6.56 thf(zip_derived_cl2, plain,
% 41.77/6.56 (![X0 : $i]: (product @ (inverse @ X0) @ X0 @ identity)),
% 41.77/6.56 inference('cnf', [status(esa)], [left_inverse])).
% 41.77/6.56 thf(zip_derived_cl11, plain, ( (product @ c @ (inverse @ a) @ d)),
% 41.77/6.56 inference('cnf', [status(esa)], [zf_stmt_5])).
% 41.77/6.56 thf(zip_derived_cl6, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 41.77/6.56 (~ (product @ X0 @ X1 @ X2)
% 41.77/6.56 | ~ (product @ X1 @ X3 @ X4)
% 41.77/6.56 | ~ (product @ X2 @ X3 @ X5)
% 41.77/6.56 | (product @ X0 @ X4 @ X5))),
% 41.77/6.56 inference('cnf', [status(esa)], [associativity1])).
% 41.77/6.56 thf(zip_derived_cl58, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i]:
% 41.77/6.56 ( (product @ c @ X1 @ X0)
% 41.77/6.56 | ~ (product @ d @ X2 @ X0)
% 41.77/6.56 | ~ (product @ (inverse @ a) @ X2 @ X1))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl6])).
% 41.77/6.56 thf(zip_derived_cl426, plain,
% 41.77/6.56 (![X0 : $i]: (~ (product @ d @ a @ X0) | (product @ c @ identity @ X0))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl58])).
% 41.77/6.56 thf(zip_derived_cl428, plain,
% 41.77/6.56 ( (product @ c @ identity @ (multiply @ d @ a))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl426])).
% 41.77/6.56 thf(zip_derived_cl25, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]: (((X0) = (X1)) | ~ (product @ X0 @ identity @ X1))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl5])).
% 41.77/6.56 thf(zip_derived_cl434, plain, (((c) = (multiply @ d @ a))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl428, zip_derived_cl25])).
% 41.77/6.56 thf(zip_derived_cl17303, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i]:
% 41.77/6.56 ((multiply @ X2 @ (multiply @ X1 @ X0))
% 41.77/6.56 = (multiply @ (multiply @ X2 @ X1) @ X0))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl1398, zip_derived_cl24])).
% 41.77/6.56 thf(zip_derived_cl41318, plain,
% 41.77/6.56 (![X0 : $i]: ((multiply @ d @ (multiply @ a @ X0)) = (multiply @ c @ X0))),
% 41.77/6.56 inference('sup+', [status(thm)], [zip_derived_cl434, zip_derived_cl17303])).
% 41.77/6.56 thf(zip_derived_cl42509, plain,
% 41.77/6.56 (((multiply @ d @ (inverse @ c)) = (multiply @ c @ (multiply @ b @ c)))),
% 41.77/6.56 inference('sup+', [status(thm)],
% 41.77/6.56 [zip_derived_cl2475, zip_derived_cl41318])).
% 41.77/6.56 thf(zip_derived_cl17303, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i, X2 : $i]:
% 41.77/6.56 ((multiply @ X2 @ (multiply @ X1 @ X0))
% 41.77/6.56 = (multiply @ (multiply @ X2 @ X1) @ X0))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl1398, zip_derived_cl24])).
% 41.77/6.56 thf(zip_derived_cl368, plain,
% 41.77/6.56 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl357, zip_derived_cl25])).
% 41.77/6.56 thf(zip_derived_cl4988, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]:
% 41.77/6.56 ((multiply @ (multiply @ X0 @ X1) @ (inverse @ X1)) = (X0))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4792, zip_derived_cl24])).
% 41.77/6.56 thf(zip_derived_cl5623, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]:
% 41.77/6.56 ((multiply @ (multiply @ X1 @ (inverse @ X0)) @ X0) = (X1))),
% 41.77/6.56 inference('sup+', [status(thm)], [zip_derived_cl368, zip_derived_cl4988])).
% 41.77/6.56 thf(zip_derived_cl46482, plain, (((multiply @ b @ d) = (multiply @ k @ d))),
% 41.77/6.56 inference('demod', [status(thm)],
% 41.77/6.56 [zip_derived_cl46431, zip_derived_cl17303,
% 41.77/6.56 zip_derived_cl42509, zip_derived_cl17303, zip_derived_cl5623])).
% 41.77/6.56 thf(zip_derived_cl4988, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]:
% 41.77/6.56 ((multiply @ (multiply @ X0 @ X1) @ (inverse @ X1)) = (X0))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4792, zip_derived_cl24])).
% 41.77/6.56 thf(zip_derived_cl46539, plain,
% 41.77/6.56 (((multiply @ (multiply @ k @ d) @ (inverse @ d)) = (b))),
% 41.77/6.56 inference('sup+', [status(thm)],
% 41.77/6.56 [zip_derived_cl46482, zip_derived_cl4988])).
% 41.77/6.56 thf(zip_derived_cl4988, plain,
% 41.77/6.56 (![X0 : $i, X1 : $i]:
% 41.77/6.56 ((multiply @ (multiply @ X0 @ X1) @ (inverse @ X1)) = (X0))),
% 41.77/6.56 inference('sup-', [status(thm)], [zip_derived_cl4792, zip_derived_cl24])).
% 41.77/6.56 thf(zip_derived_cl46602, plain, (((k) = (b))),
% 41.77/6.56 inference('demod', [status(thm)],
% 41.77/6.56 [zip_derived_cl46539, zip_derived_cl4988])).
% 41.77/6.56 thf(zip_derived_cl3, plain,
% 41.77/6.56 (![X0 : $i]: (product @ X0 @ (inverse @ X0) @ identity)),
% 41.77/6.56 inference('cnf', [status(esa)], [right_inverse])).
% 41.77/6.56 thf(zip_derived_cl46622, plain, ($false),
% 41.77/6.56 inference('demod', [status(thm)],
% 41.77/6.56 [zip_derived_cl15, zip_derived_cl46602, zip_derived_cl3])).
% 41.77/6.56
% 41.77/6.56 % SZS output end Refutation
% 41.77/6.56
% 41.77/6.56
% 41.77/6.56 % Terminating...
% 41.77/6.59 % Runner terminated.
% 41.80/6.61 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------