TSTP Solution File: GRP002-10 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP002-10 : TPTP v8.1.2. Released v7.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.psv9rGmO6l true
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:49:25 EDT 2023
% Result : Unsatisfiable 100.59s 14.98s
% Output : Refutation 100.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP002-10 : TPTP v8.1.2. Released v7.3.0.
% 0.12/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.psv9rGmO6l true
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 22:27:32 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.20/0.65 % Total configuration time : 435
% 0.20/0.65 % Estimated wc time : 1092
% 0.20/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.20/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.20/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.20/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.20/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.20/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.20/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 1.35/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 100.59/14.98 % Solved by fo/fo5.sh.
% 100.59/14.98 % done 5807 iterations in 14.180s
% 100.59/14.98 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 100.59/14.98 % SZS output start Refutation
% 100.59/14.98 thf(d_type, type, d: $i).
% 100.59/14.98 thf(a_type, type, a: $i).
% 100.59/14.98 thf(k_type, type, k: $i).
% 100.59/14.98 thf(j_type, type, j: $i).
% 100.59/14.98 thf(multiply_type, type, multiply: $i > $i > $i).
% 100.59/14.98 thf(identity_type, type, identity: $i).
% 100.59/14.98 thf(h_type, type, h: $i).
% 100.59/14.98 thf(product_type, type, product: $i > $i > $i > $i).
% 100.59/14.98 thf(c_type, type, c: $i).
% 100.59/14.98 thf(ifeq2_type, type, ifeq2: $i > $i > $i > $i > $i).
% 100.59/14.98 thf(true_type, type, true: $i).
% 100.59/14.98 thf(b_type, type, b: $i).
% 100.59/14.98 thf(ifeq_type, type, ifeq: $i > $i > $i > $i > $i).
% 100.59/14.98 thf(inverse_type, type, inverse: $i > $i).
% 100.59/14.98 thf(prove_k_times_inverse_b_is_e, conjecture,
% 100.59/14.98 (( product @ k @ ( inverse @ b ) @ identity ) = ( true ))).
% 100.59/14.98 thf(zf_stmt_0, negated_conjecture,
% 100.59/14.98 (( product @ k @ ( inverse @ b ) @ identity ) != ( true )),
% 100.59/14.98 inference('cnf.neg', [status(esa)], [prove_k_times_inverse_b_is_e])).
% 100.59/14.98 thf(zip_derived_cl17, plain,
% 100.59/14.98 (((product @ k @ (inverse @ b) @ identity) != (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [zf_stmt_0])).
% 100.59/14.98 thf(total_function1, axiom,
% 100.59/14.98 (( product @ X @ Y @ ( multiply @ X @ Y ) ) = ( true ))).
% 100.59/14.98 thf(zip_derived_cl6, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((product @ X0 @ X1 @ (multiply @ X0 @ X1)) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [total_function1])).
% 100.59/14.98 thf(zip_derived_cl6, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((product @ X0 @ X1 @ (multiply @ X0 @ X1)) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [total_function1])).
% 100.59/14.98 thf(zip_derived_cl6, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((product @ X0 @ X1 @ (multiply @ X0 @ X1)) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [total_function1])).
% 100.59/14.98 thf(x_cubed_is_identity_1, axiom,
% 100.59/14.98 (( ifeq @
% 100.59/14.98 ( product @ X @ X @ Y ) @ true @ ( product @ X @ Y @ identity ) @ true ) =
% 100.59/14.98 ( true ))).
% 100.59/14.98 thf(zip_derived_cl10, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((ifeq @ (product @ X0 @ X0 @ X1) @ true @
% 100.59/14.98 (product @ X0 @ X1 @ identity) @ true) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [x_cubed_is_identity_1])).
% 100.59/14.98 thf(zip_derived_cl22, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((ifeq @ true @ true @
% 100.59/14.98 (product @ X0 @ (multiply @ X0 @ X0) @ identity) @ true) = (
% 100.59/14.98 true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl10])).
% 100.59/14.98 thf(ifeq_axiom_001, axiom, (( ifeq @ A @ A @ B @ C ) = ( B ))).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl29, plain,
% 100.59/14.98 (![X0 : $i]: ((true) = (product @ X0 @ (multiply @ X0 @ X0) @ identity))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl1])).
% 100.59/14.98 thf(total_function2, axiom,
% 100.59/14.98 (( ifeq2 @
% 100.59/14.98 ( product @ X @ Y @ W ) @ true @
% 100.59/14.98 ( ifeq2 @ ( product @ X @ Y @ Z ) @ true @ Z @ W ) @ W ) =
% 100.59/14.98 ( W ))).
% 100.59/14.98 thf(zip_derived_cl7, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 100.59/14.98 ((ifeq2 @ (product @ X1 @ X2 @ X0) @ true @
% 100.59/14.98 (ifeq2 @ (product @ X1 @ X2 @ X3) @ true @ X3 @ X0) @ X0) = (
% 100.59/14.98 X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [total_function2])).
% 100.59/14.98 thf(zip_derived_cl48, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((ifeq2 @ (product @ X1 @ (multiply @ X1 @ X1) @ X0) @ true @
% 100.59/14.98 (ifeq2 @ true @ true @ identity @ X0) @ X0) = (X0))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl29, zip_derived_cl7])).
% 100.59/14.98 thf(ifeq_axiom, axiom, (( ifeq2 @ A @ A @ B @ C ) = ( B ))).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl70, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((ifeq2 @ (product @ X1 @ (multiply @ X1 @ X1) @ X0) @ true @
% 100.59/14.98 identity @ X0) = (X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl48, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl352, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((ifeq2 @ true @ true @ identity @
% 100.59/14.98 (multiply @ X0 @ (multiply @ X0 @ X0)))
% 100.59/14.98 = (multiply @ X0 @ (multiply @ X0 @ X0)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl70])).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl357, plain,
% 100.59/14.98 (![X0 : $i]: ((identity) = (multiply @ X0 @ (multiply @ X0 @ X0)))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl352, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl6, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((product @ X0 @ X1 @ (multiply @ X0 @ X1)) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [total_function1])).
% 100.59/14.98 thf(right_inverse, axiom,
% 100.59/14.98 (( product @ X @ ( inverse @ X ) @ identity ) = ( true ))).
% 100.59/14.98 thf(zip_derived_cl5, plain,
% 100.59/14.98 (![X0 : $i]: ((product @ X0 @ (inverse @ X0) @ identity) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [right_inverse])).
% 100.59/14.98 thf(zip_derived_cl6, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((product @ X0 @ X1 @ (multiply @ X0 @ X1)) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [total_function1])).
% 100.59/14.98 thf(associativity1, axiom,
% 100.59/14.98 (( ifeq @
% 100.59/14.98 ( product @ U @ Z @ W ) @ true @
% 100.59/14.98 ( ifeq @
% 100.59/14.98 ( product @ Y @ Z @ V ) @ true @
% 100.59/14.98 ( ifeq @
% 100.59/14.98 ( product @ X @ Y @ U ) @ true @ ( product @ X @ V @ W ) @ true ) @
% 100.59/14.98 true ) @
% 100.59/14.98 true ) =
% 100.59/14.98 ( true ))).
% 100.59/14.98 thf(zip_derived_cl8, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 100.59/14.98 ((ifeq @ (product @ X0 @ X1 @ X2) @ true @
% 100.59/14.98 (ifeq @ (product @ X3 @ X1 @ X4) @ true @
% 100.59/14.98 (ifeq @ (product @ X5 @ X3 @ X0) @ true @
% 100.59/14.98 (product @ X5 @ X4 @ X2) @ true) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [associativity1])).
% 100.59/14.98 thf(zip_derived_cl128, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 100.59/14.98 ((ifeq @ true @ true @
% 100.59/14.98 (ifeq @ (product @ X4 @ X0 @ X2) @ true @
% 100.59/14.98 (ifeq @ (product @ X3 @ X4 @ X1) @ true @
% 100.59/14.98 (product @ X3 @ X2 @ (multiply @ X1 @ X0)) @ true) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl8])).
% 100.59/14.98 thf(zip_derived_cl1678, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((ifeq @ true @ true @
% 100.59/14.98 (ifeq @ (product @ (inverse @ X2) @ X0 @ X1) @ true @
% 100.59/14.98 (ifeq @ true @ true @
% 100.59/14.98 (product @ X2 @ X1 @ (multiply @ identity @ X0)) @ true) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl128])).
% 100.59/14.98 thf(zip_derived_cl6, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((product @ X0 @ X1 @ (multiply @ X0 @ X1)) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [total_function1])).
% 100.59/14.98 thf(left_identity, axiom, (( product @ identity @ X @ X ) = ( true ))).
% 100.59/14.98 thf(zip_derived_cl2, plain,
% 100.59/14.98 (![X0 : $i]: ((product @ identity @ X0 @ X0) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [left_identity])).
% 100.59/14.98 thf(zip_derived_cl7, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 100.59/14.98 ((ifeq2 @ (product @ X1 @ X2 @ X0) @ true @
% 100.59/14.98 (ifeq2 @ (product @ X1 @ X2 @ X3) @ true @ X3 @ X0) @ X0) = (
% 100.59/14.98 X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [total_function2])).
% 100.59/14.98 thf(zip_derived_cl49, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((ifeq2 @ (product @ identity @ X1 @ X0) @ true @
% 100.59/14.98 (ifeq2 @ true @ true @ X1 @ X0) @ X0) = (X0))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl7])).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl71, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((ifeq2 @ (product @ identity @ X1 @ X0) @ true @ X1 @ X0) = (X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl49, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl184, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((ifeq2 @ true @ true @ X0 @ (multiply @ identity @ X0))
% 100.59/14.98 = (multiply @ identity @ X0))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl71])).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl189, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (multiply @ identity @ X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl184, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl1718, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((ifeq @ (product @ (inverse @ X2) @ X0 @ X1) @ true @
% 100.59/14.98 (product @ X2 @ X1 @ X0) @ true) = (true))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1678, zip_derived_cl189, zip_derived_cl1,
% 100.59/14.98 zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl1771, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((ifeq @ true @ true @
% 100.59/14.98 (product @ X1 @ (multiply @ (inverse @ X1) @ X0) @ X0) @ true)
% 100.59/14.98 = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1718])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl2168, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((true) = (product @ X1 @ (multiply @ (inverse @ X1) @ X0) @ X0))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl1771, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl2224, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((true)
% 100.59/14.98 = (product @ X0 @ identity @
% 100.59/14.98 (multiply @ (inverse @ X0) @ (inverse @ X0))))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl357, zip_derived_cl2168])).
% 100.59/14.98 thf(zip_derived_cl6, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((product @ X0 @ X1 @ (multiply @ X0 @ X1)) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [total_function1])).
% 100.59/14.98 thf(zip_derived_cl7, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 100.59/14.98 ((ifeq2 @ (product @ X1 @ X2 @ X0) @ true @
% 100.59/14.98 (ifeq2 @ (product @ X1 @ X2 @ X3) @ true @ X3 @ X0) @ X0) = (
% 100.59/14.98 X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [total_function2])).
% 100.59/14.98 thf(zip_derived_cl45, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((ifeq2 @ (product @ X2 @ X1 @ X0) @ true @
% 100.59/14.98 (ifeq2 @ true @ true @ (multiply @ X2 @ X1) @ X0) @ X0) = (X0))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl7])).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl67, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((ifeq2 @ (product @ X2 @ X1 @ X0) @ true @ (multiply @ X2 @ X1) @ X0)
% 100.59/14.98 = (X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl2366, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((ifeq2 @ true @ true @ (multiply @ X0 @ identity) @
% 100.59/14.98 (multiply @ (inverse @ X0) @ (inverse @ X0)))
% 100.59/14.98 = (multiply @ (inverse @ X0) @ (inverse @ X0)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl2224, zip_derived_cl67])).
% 100.59/14.98 thf(zip_derived_cl6, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((product @ X0 @ X1 @ (multiply @ X0 @ X1)) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [total_function1])).
% 100.59/14.98 thf(right_identity, axiom, (( product @ X @ identity @ X ) = ( true ))).
% 100.59/14.98 thf(zip_derived_cl3, plain,
% 100.59/14.98 (![X0 : $i]: ((product @ X0 @ identity @ X0) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [right_identity])).
% 100.59/14.98 thf(zip_derived_cl7, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 100.59/14.98 ((ifeq2 @ (product @ X1 @ X2 @ X0) @ true @
% 100.59/14.98 (ifeq2 @ (product @ X1 @ X2 @ X3) @ true @ X3 @ X0) @ X0) = (
% 100.59/14.98 X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [total_function2])).
% 100.59/14.98 thf(zip_derived_cl46, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((ifeq2 @ (product @ X1 @ identity @ X0) @ true @
% 100.59/14.98 (ifeq2 @ true @ true @ X1 @ X0) @ X0) = (X0))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl7])).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl68, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((ifeq2 @ (product @ X1 @ identity @ X0) @ true @ X1 @ X0) = (X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl85, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((ifeq2 @ true @ true @ X0 @ (multiply @ X0 @ identity))
% 100.59/14.98 = (multiply @ X0 @ identity))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl68])).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl89, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl85, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl2424, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (multiply @ (inverse @ X0) @ (inverse @ X0)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl2366, zip_derived_cl89, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl6, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((product @ X0 @ X1 @ (multiply @ X0 @ X1)) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [total_function1])).
% 100.59/14.98 thf(zip_derived_cl2456, plain,
% 100.59/14.98 (![X0 : $i]: ((product @ (inverse @ X0) @ (inverse @ X0) @ X0) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl2424, zip_derived_cl6])).
% 100.59/14.98 thf(d_times_inverse_b_is_h, conjecture,
% 100.59/14.98 (( product @ d @ ( inverse @ b ) @ h ) != ( true ))).
% 100.59/14.98 thf(zf_stmt_1, negated_conjecture,
% 100.59/14.98 (( product @ d @ ( inverse @ b ) @ h ) = ( true )),
% 100.59/14.98 inference('cnf.neg', [status(esa)], [d_times_inverse_b_is_h])).
% 100.59/14.98 thf(zip_derived_cl14, plain, (((product @ d @ (inverse @ b) @ h) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [zf_stmt_1])).
% 100.59/14.98 thf(associativity2, axiom,
% 100.59/14.98 (( ifeq @
% 100.59/14.98 ( product @ Y @ Z @ V ) @ true @
% 100.59/14.98 ( ifeq @
% 100.59/14.98 ( product @ X @ V @ W ) @ true @
% 100.59/14.98 ( ifeq @
% 100.59/14.98 ( product @ X @ Y @ U ) @ true @ ( product @ U @ Z @ W ) @ true ) @
% 100.59/14.98 true ) @
% 100.59/14.98 true ) =
% 100.59/14.98 ( true ))).
% 100.59/14.98 thf(zip_derived_cl9, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 100.59/14.98 ((ifeq @ (product @ X0 @ X1 @ X2) @ true @
% 100.59/14.98 (ifeq @ (product @ X3 @ X2 @ X4) @ true @
% 100.59/14.98 (ifeq @ (product @ X3 @ X0 @ X5) @ true @
% 100.59/14.98 (product @ X5 @ X1 @ X4) @ true) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [associativity2])).
% 100.59/14.98 thf(zip_derived_cl225, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((ifeq @ (product @ X2 @ X0 @ (inverse @ b)) @ true @
% 100.59/14.98 (ifeq @ true @ true @
% 100.59/14.98 (ifeq @ (product @ d @ X2 @ X1) @ true @ (product @ X1 @ X0 @ h) @
% 100.59/14.98 true) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl9])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl258, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((ifeq @ (product @ X2 @ X0 @ (inverse @ b)) @ true @
% 100.59/14.98 (ifeq @ (product @ d @ X2 @ X1) @ true @ (product @ X1 @ X0 @ h) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl225, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl19663, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((ifeq @ true @ true @
% 100.59/14.98 (ifeq @ (product @ d @ (inverse @ (inverse @ b)) @ X0) @ true @
% 100.59/14.98 (product @ X0 @ (inverse @ (inverse @ b)) @ h) @ true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl2456, zip_derived_cl258])).
% 100.59/14.98 thf(zip_derived_cl5, plain,
% 100.59/14.98 (![X0 : $i]: ((product @ X0 @ (inverse @ X0) @ identity) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [right_inverse])).
% 100.59/14.98 thf(zip_derived_cl1718, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((ifeq @ (product @ (inverse @ X2) @ X0 @ X1) @ true @
% 100.59/14.98 (product @ X2 @ X1 @ X0) @ true) = (true))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1678, zip_derived_cl189, zip_derived_cl1,
% 100.59/14.98 zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl1773, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((ifeq @ true @ true @
% 100.59/14.98 (product @ X0 @ identity @ (inverse @ (inverse @ X0))) @ true)
% 100.59/14.98 = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl1718])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl1783, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((true) = (product @ X0 @ identity @ (inverse @ (inverse @ X0))))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl1773, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl67, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((ifeq2 @ (product @ X2 @ X1 @ X0) @ true @ (multiply @ X2 @ X1) @ X0)
% 100.59/14.98 = (X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl1799, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((ifeq2 @ true @ true @ (multiply @ X0 @ identity) @
% 100.59/14.98 (inverse @ (inverse @ X0))) = (inverse @ (inverse @ X0)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl1783, zip_derived_cl67])).
% 100.59/14.98 thf(zip_derived_cl89, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl85, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl1839, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1799, zip_derived_cl89, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl1839, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1799, zip_derived_cl89, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl19693, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((ifeq @ (product @ d @ b @ X0) @ true @ (product @ X0 @ b @ h) @ true)
% 100.59/14.98 = (true))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl19663, zip_derived_cl1839, zip_derived_cl1839,
% 100.59/14.98 zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl24457, plain,
% 100.59/14.98 (((ifeq @ true @ true @ (product @ (multiply @ d @ b) @ b @ h) @ true)
% 100.59/14.98 = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl19693])).
% 100.59/14.98 thf(zip_derived_cl6, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((product @ X0 @ X1 @ (multiply @ X0 @ X1)) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [total_function1])).
% 100.59/14.98 thf(zip_derived_cl6, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((product @ X0 @ X1 @ (multiply @ X0 @ X1)) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [total_function1])).
% 100.59/14.98 thf(h_times_b_is_j, conjecture, (( product @ h @ b @ j ) != ( true ))).
% 100.59/14.98 thf(zf_stmt_2, negated_conjecture, (( product @ h @ b @ j ) = ( true )),
% 100.59/14.98 inference('cnf.neg', [status(esa)], [h_times_b_is_j])).
% 100.59/14.98 thf(zip_derived_cl15, plain, (((product @ h @ b @ j) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [zf_stmt_2])).
% 100.59/14.98 thf(zip_derived_cl7, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 100.59/14.98 ((ifeq2 @ (product @ X1 @ X2 @ X0) @ true @
% 100.59/14.98 (ifeq2 @ (product @ X1 @ X2 @ X3) @ true @ X3 @ X0) @ X0) = (
% 100.59/14.98 X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [total_function2])).
% 100.59/14.98 thf(zip_derived_cl54, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((ifeq2 @ (product @ h @ b @ X0) @ true @
% 100.59/14.98 (ifeq2 @ true @ true @ j @ X0) @ X0) = (X0))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl15, zip_derived_cl7])).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl76, plain,
% 100.59/14.98 (![X0 : $i]: ((ifeq2 @ (product @ h @ b @ X0) @ true @ j @ X0) = (X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl54, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl172, plain,
% 100.59/14.98 (((ifeq2 @ true @ true @ j @ (multiply @ h @ b)) = (multiply @ h @ b))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl76])).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl174, plain, (((j) = (multiply @ h @ b))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl172, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl1839, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1799, zip_derived_cl89, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl2168, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((true) = (product @ X1 @ (multiply @ (inverse @ X1) @ X0) @ X0))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl1771, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl2227, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((true) = (product @ (inverse @ X0) @ (multiply @ X0 @ X1) @ X1))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl1839, zip_derived_cl2168])).
% 100.59/14.98 thf(zip_derived_cl3664, plain,
% 100.59/14.98 (((true) = (product @ (inverse @ h) @ j @ b))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl174, zip_derived_cl2227])).
% 100.59/14.98 thf(j_times_inverse_h_is_k, conjecture,
% 100.59/14.98 (( product @ j @ ( inverse @ h ) @ k ) != ( true ))).
% 100.59/14.98 thf(zf_stmt_3, negated_conjecture,
% 100.59/14.98 (( product @ j @ ( inverse @ h ) @ k ) = ( true )),
% 100.59/14.98 inference('cnf.neg', [status(esa)], [j_times_inverse_h_is_k])).
% 100.59/14.98 thf(zip_derived_cl16, plain, (((product @ j @ (inverse @ h) @ k) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [zf_stmt_3])).
% 100.59/14.98 thf(zip_derived_cl8, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 100.59/14.98 ((ifeq @ (product @ X0 @ X1 @ X2) @ true @
% 100.59/14.98 (ifeq @ (product @ X3 @ X1 @ X4) @ true @
% 100.59/14.98 (ifeq @ (product @ X5 @ X3 @ X0) @ true @
% 100.59/14.98 (product @ X5 @ X4 @ X2) @ true) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [associativity1])).
% 100.59/14.98 thf(zip_derived_cl116, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((ifeq @ (product @ k @ X2 @ X0) @ true @
% 100.59/14.98 (ifeq @ (product @ (inverse @ h) @ X2 @ X1) @ true @
% 100.59/14.98 (ifeq @ true @ true @ (product @ j @ X1 @ X0) @ true) @ true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl16, zip_derived_cl8])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl149, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((ifeq @ (product @ k @ X2 @ X0) @ true @
% 100.59/14.98 (ifeq @ (product @ (inverse @ h) @ X2 @ X1) @ true @
% 100.59/14.98 (product @ j @ X1 @ X0) @ true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl116, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl5906, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((ifeq @ (product @ k @ j @ X0) @ true @
% 100.59/14.98 (ifeq @ true @ true @ (product @ j @ b @ X0) @ true) @ true)
% 100.59/14.98 = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl3664, zip_derived_cl149])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl5930, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((ifeq @ (product @ k @ j @ X0) @ true @ (product @ j @ b @ X0) @ true)
% 100.59/14.98 = (true))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl5906, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl6, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((product @ X0 @ X1 @ (multiply @ X0 @ X1)) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [total_function1])).
% 100.59/14.98 thf(zip_derived_cl5, plain,
% 100.59/14.98 (![X0 : $i]: ((product @ X0 @ (inverse @ X0) @ identity) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [right_inverse])).
% 100.59/14.98 thf(zip_derived_cl14, plain, (((product @ d @ (inverse @ b) @ h) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [zf_stmt_1])).
% 100.59/14.98 thf(zip_derived_cl8, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 100.59/14.98 ((ifeq @ (product @ X0 @ X1 @ X2) @ true @
% 100.59/14.98 (ifeq @ (product @ X3 @ X1 @ X4) @ true @
% 100.59/14.98 (ifeq @ (product @ X5 @ X3 @ X0) @ true @
% 100.59/14.98 (product @ X5 @ X4 @ X2) @ true) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [associativity1])).
% 100.59/14.98 thf(zip_derived_cl114, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((ifeq @ (product @ h @ X2 @ X0) @ true @
% 100.59/14.98 (ifeq @ (product @ (inverse @ b) @ X2 @ X1) @ true @
% 100.59/14.98 (ifeq @ true @ true @ (product @ d @ X1 @ X0) @ true) @ true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl8])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl147, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((ifeq @ (product @ h @ X2 @ X0) @ true @
% 100.59/14.98 (ifeq @ (product @ (inverse @ b) @ X2 @ X1) @ true @
% 100.59/14.98 (product @ d @ X1 @ X0) @ true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl114, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl5410, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((ifeq @ (product @ h @ (inverse @ (inverse @ b)) @ X0) @ true @
% 100.59/14.98 (ifeq @ true @ true @ (product @ d @ identity @ X0) @ true) @ true)
% 100.59/14.98 = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl147])).
% 100.59/14.98 thf(zip_derived_cl1839, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1799, zip_derived_cl89, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl5436, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((ifeq @ (product @ h @ b @ X0) @ true @
% 100.59/14.98 (product @ d @ identity @ X0) @ true) = (true))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl5410, zip_derived_cl1839, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl12284, plain,
% 100.59/14.98 (((ifeq @ true @ true @ (product @ d @ identity @ (multiply @ h @ b)) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl5436])).
% 100.59/14.98 thf(zip_derived_cl174, plain, (((j) = (multiply @ h @ b))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl172, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl12287, plain, (((product @ d @ identity @ j) = (true))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl12284, zip_derived_cl174, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl67, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((ifeq2 @ (product @ X2 @ X1 @ X0) @ true @ (multiply @ X2 @ X1) @ X0)
% 100.59/14.98 = (X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl12302, plain,
% 100.59/14.98 (((ifeq2 @ true @ true @ (multiply @ d @ identity) @ j) = (j))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl12287, zip_derived_cl67])).
% 100.59/14.98 thf(zip_derived_cl89, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl85, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl12371, plain, (((d) = (j))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl12302, zip_derived_cl89, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl12371, plain, (((d) = (j))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl12302, zip_derived_cl89, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl15841, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((ifeq @ (product @ k @ d @ X0) @ true @ (product @ d @ b @ X0) @ true)
% 100.59/14.98 = (true))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl5930, zip_derived_cl12371, zip_derived_cl12371])).
% 100.59/14.98 thf(zip_derived_cl15846, plain,
% 100.59/14.98 (((ifeq @ true @ true @ (product @ d @ b @ (multiply @ k @ d)) @ true)
% 100.59/14.98 = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl15841])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl16031, plain,
% 100.59/14.98 (((true) = (product @ d @ b @ (multiply @ k @ d)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl15846, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl6, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((product @ X0 @ X1 @ (multiply @ X0 @ X1)) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [total_function1])).
% 100.59/14.98 thf(zip_derived_cl7, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 100.59/14.98 ((ifeq2 @ (product @ X1 @ X2 @ X0) @ true @
% 100.59/14.98 (ifeq2 @ (product @ X1 @ X2 @ X3) @ true @ X3 @ X0) @ X0) = (
% 100.59/14.98 X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [total_function2])).
% 100.59/14.98 thf(zip_derived_cl56, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((ifeq2 @ true @ true @
% 100.59/14.98 (ifeq2 @ (product @ X1 @ X0 @ X2) @ true @ X2 @ (multiply @ X1 @ X0)) @
% 100.59/14.98 (multiply @ X1 @ X0)) = (multiply @ X1 @ X0))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl7])).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl382, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((multiply @ X1 @ X0)
% 100.59/14.98 = (ifeq2 @ (product @ X1 @ X0 @ X2) @ true @ X2 @
% 100.59/14.98 (multiply @ X1 @ X0)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl56, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl16210, plain,
% 100.59/14.98 (((multiply @ d @ b)
% 100.59/14.98 = (ifeq2 @ true @ true @ (multiply @ k @ d) @ (multiply @ d @ b)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl16031, zip_derived_cl382])).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl16273, plain, (((multiply @ d @ b) = (multiply @ k @ d))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl16210, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl24459, plain,
% 100.59/14.98 (((product @ (multiply @ k @ d) @ b @ h) = (true))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl24457, zip_derived_cl16273, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl382, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((multiply @ X1 @ X0)
% 100.59/14.98 = (ifeq2 @ (product @ X1 @ X0 @ X2) @ true @ X2 @
% 100.59/14.98 (multiply @ X1 @ X0)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl56, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl24496, plain,
% 100.59/14.98 (((multiply @ (multiply @ k @ d) @ b)
% 100.59/14.98 = (ifeq2 @ true @ true @ h @ (multiply @ (multiply @ k @ d) @ b)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl24459, zip_derived_cl382])).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl24575, plain,
% 100.59/14.98 (((multiply @ (multiply @ k @ d) @ b) = (h))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl24496, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl1839, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1799, zip_derived_cl89, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl2168, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((true) = (product @ X1 @ (multiply @ (inverse @ X1) @ X0) @ X0))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl1771, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl382, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((multiply @ X1 @ X0)
% 100.59/14.98 = (ifeq2 @ (product @ X1 @ X0 @ X2) @ true @ X2 @
% 100.59/14.98 (multiply @ X1 @ X0)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl56, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl2196, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ X1 @ (multiply @ (inverse @ X1) @ X0))
% 100.59/14.98 = (ifeq2 @ true @ true @ X0 @
% 100.59/14.98 (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0))))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl2168, zip_derived_cl382])).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl2242, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)) = (X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl2196, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl3275, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)) = (X1))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl1839, zip_derived_cl2242])).
% 100.59/14.98 thf(zip_derived_cl24617, plain,
% 100.59/14.98 (((multiply @ (inverse @ (multiply @ k @ d)) @ h) = (b))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl24575, zip_derived_cl3275])).
% 100.59/14.98 thf(zip_derived_cl6, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((product @ X0 @ X1 @ (multiply @ X0 @ X1)) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [total_function1])).
% 100.59/14.98 thf(zip_derived_cl6, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((product @ X0 @ X1 @ (multiply @ X0 @ X1)) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [total_function1])).
% 100.59/14.98 thf(zip_derived_cl5, plain,
% 100.59/14.98 (![X0 : $i]: ((product @ X0 @ (inverse @ X0) @ identity) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [right_inverse])).
% 100.59/14.98 thf(zip_derived_cl9, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 100.59/14.98 ((ifeq @ (product @ X0 @ X1 @ X2) @ true @
% 100.59/14.98 (ifeq @ (product @ X3 @ X2 @ X4) @ true @
% 100.59/14.98 (ifeq @ (product @ X3 @ X0 @ X5) @ true @
% 100.59/14.98 (product @ X5 @ X1 @ X4) @ true) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [associativity2])).
% 100.59/14.98 thf(zip_derived_cl230, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 100.59/14.98 ((ifeq @ true @ true @
% 100.59/14.98 (ifeq @ (product @ X3 @ identity @ X0) @ true @
% 100.59/14.98 (ifeq @ (product @ X3 @ X1 @ X2) @ true @
% 100.59/14.98 (product @ X2 @ (inverse @ X1) @ X0) @ true) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl9])).
% 100.59/14.98 thf(zip_derived_cl12175, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((ifeq @ true @ true @
% 100.59/14.98 (ifeq @ true @ true @
% 100.59/14.98 (ifeq @ (product @ X0 @ X1 @ X2) @ true @
% 100.59/14.98 (product @ X2 @ (inverse @ X1) @ (multiply @ X0 @ identity)) @
% 100.59/14.98 true) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl230])).
% 100.59/14.98 thf(zip_derived_cl89, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl85, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl12266, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((ifeq @ (product @ X0 @ X1 @ X2) @ true @
% 100.59/14.98 (product @ X2 @ (inverse @ X1) @ X0) @ true) = (true))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl12175, zip_derived_cl89, zip_derived_cl1,
% 100.59/14.98 zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl25744, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((ifeq @ true @ true @
% 100.59/14.98 (product @ (multiply @ X0 @ X1) @ (inverse @ X1) @ X0) @ true)
% 100.59/14.98 = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl12266])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl26326, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((true) = (product @ (multiply @ X0 @ X1) @ (inverse @ X1) @ X0))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl25744, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl382, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((multiply @ X1 @ X0)
% 100.59/14.98 = (ifeq2 @ (product @ X1 @ X0 @ X2) @ true @ X2 @
% 100.59/14.98 (multiply @ X1 @ X0)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl56, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl26455, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0))
% 100.59/14.98 = (ifeq2 @ true @ true @ X1 @
% 100.59/14.98 (multiply @ (multiply @ X1 @ X0) @ (inverse @ X0))))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl26326, zip_derived_cl382])).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl26704, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl26455, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl29221, plain,
% 100.59/14.98 (((multiply @ b @ (inverse @ h)) = (inverse @ (multiply @ k @ d)))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl24617, zip_derived_cl26704])).
% 100.59/14.98 thf(zip_derived_cl6, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((product @ X0 @ X1 @ (multiply @ X0 @ X1)) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [total_function1])).
% 100.59/14.98 thf(zip_derived_cl6, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((product @ X0 @ X1 @ (multiply @ X0 @ X1)) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [total_function1])).
% 100.59/14.98 thf(a_times_b_is_c, conjecture, (( product @ a @ b @ c ) != ( true ))).
% 100.59/14.98 thf(zf_stmt_4, negated_conjecture, (( product @ a @ b @ c ) = ( true )),
% 100.59/14.98 inference('cnf.neg', [status(esa)], [a_times_b_is_c])).
% 100.59/14.98 thf(zip_derived_cl12, plain, (((product @ a @ b @ c) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [zf_stmt_4])).
% 100.59/14.98 thf(zip_derived_cl8, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 100.59/14.98 ((ifeq @ (product @ X0 @ X1 @ X2) @ true @
% 100.59/14.98 (ifeq @ (product @ X3 @ X1 @ X4) @ true @
% 100.59/14.98 (ifeq @ (product @ X5 @ X3 @ X0) @ true @
% 100.59/14.98 (product @ X5 @ X4 @ X2) @ true) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [associativity1])).
% 100.59/14.98 thf(zip_derived_cl112, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((ifeq @ (product @ c @ X2 @ X0) @ true @
% 100.59/14.98 (ifeq @ (product @ b @ X2 @ X1) @ true @
% 100.59/14.98 (ifeq @ true @ true @ (product @ a @ X1 @ X0) @ true) @ true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl8])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl145, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((ifeq @ (product @ c @ X2 @ X0) @ true @
% 100.59/14.98 (ifeq @ (product @ b @ X2 @ X1) @ true @ (product @ a @ X1 @ X0) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl112, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl501, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((ifeq @ (product @ c @ X1 @ X0) @ true @
% 100.59/14.98 (ifeq @ true @ true @ (product @ a @ (multiply @ b @ X1) @ X0) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl145])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl510, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((ifeq @ (product @ c @ X1 @ X0) @ true @
% 100.59/14.98 (product @ a @ (multiply @ b @ X1) @ X0) @ true) = (true))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl501, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl1193, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((ifeq @ true @ true @
% 100.59/14.98 (product @ a @ (multiply @ b @ X0) @ (multiply @ c @ X0)) @ true)
% 100.59/14.98 = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl510])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl1445, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((true) = (product @ a @ (multiply @ b @ X0) @ (multiply @ c @ X0)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl1193, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl382, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((multiply @ X1 @ X0)
% 100.59/14.98 = (ifeq2 @ (product @ X1 @ X0 @ X2) @ true @ X2 @
% 100.59/14.98 (multiply @ X1 @ X0)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl56, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl1477, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((multiply @ a @ (multiply @ b @ X0))
% 100.59/14.98 = (ifeq2 @ true @ true @ (multiply @ c @ X0) @
% 100.59/14.98 (multiply @ a @ (multiply @ b @ X0))))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl1445, zip_derived_cl382])).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl1509, plain,
% 100.59/14.98 (![X0 : $i]: ((multiply @ a @ (multiply @ b @ X0)) = (multiply @ c @ X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl1477, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl31349, plain,
% 100.59/14.98 (((multiply @ a @ (inverse @ (multiply @ k @ d)))
% 100.59/14.98 = (multiply @ c @ (inverse @ h)))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl29221, zip_derived_cl1509])).
% 100.59/14.98 thf(zip_derived_cl16273, plain, (((multiply @ d @ b) = (multiply @ k @ d))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl16210, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl3275, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)) = (X1))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl1839, zip_derived_cl2242])).
% 100.59/14.98 thf(zip_derived_cl16305, plain,
% 100.59/14.98 (((multiply @ (inverse @ d) @ (multiply @ k @ d)) = (b))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl16273, zip_derived_cl3275])).
% 100.59/14.98 thf(zip_derived_cl26704, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl26455, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl29212, plain,
% 100.59/14.98 (((multiply @ b @ (inverse @ (multiply @ k @ d))) = (inverse @ d))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl16305, zip_derived_cl26704])).
% 100.59/14.98 thf(zip_derived_cl1509, plain,
% 100.59/14.98 (![X0 : $i]: ((multiply @ a @ (multiply @ b @ X0)) = (multiply @ c @ X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl1477, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl42782, plain,
% 100.59/14.98 (((multiply @ a @ (inverse @ d))
% 100.59/14.98 = (multiply @ c @ (inverse @ (multiply @ k @ d))))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl29212, zip_derived_cl1509])).
% 100.59/14.98 thf(zip_derived_cl6, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((product @ X0 @ X1 @ (multiply @ X0 @ X1)) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [total_function1])).
% 100.59/14.98 thf(zip_derived_cl2456, plain,
% 100.59/14.98 (![X0 : $i]: ((product @ (inverse @ X0) @ (inverse @ X0) @ X0) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl2424, zip_derived_cl6])).
% 100.59/14.98 thf(c_times_inverse_a_is_d, conjecture,
% 100.59/14.98 (( product @ c @ ( inverse @ a ) @ d ) != ( true ))).
% 100.59/14.98 thf(zf_stmt_5, negated_conjecture,
% 100.59/14.98 (( product @ c @ ( inverse @ a ) @ d ) = ( true )),
% 100.59/14.98 inference('cnf.neg', [status(esa)], [c_times_inverse_a_is_d])).
% 100.59/14.98 thf(zip_derived_cl13, plain, (((product @ c @ (inverse @ a) @ d) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [zf_stmt_5])).
% 100.59/14.98 thf(zip_derived_cl9, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 100.59/14.98 ((ifeq @ (product @ X0 @ X1 @ X2) @ true @
% 100.59/14.98 (ifeq @ (product @ X3 @ X2 @ X4) @ true @
% 100.59/14.98 (ifeq @ (product @ X3 @ X0 @ X5) @ true @
% 100.59/14.98 (product @ X5 @ X1 @ X4) @ true) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [associativity2])).
% 100.59/14.98 thf(zip_derived_cl224, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((ifeq @ (product @ X2 @ X0 @ (inverse @ a)) @ true @
% 100.59/14.98 (ifeq @ true @ true @
% 100.59/14.98 (ifeq @ (product @ c @ X2 @ X1) @ true @ (product @ X1 @ X0 @ d) @
% 100.59/14.98 true) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl9])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl257, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((ifeq @ (product @ X2 @ X0 @ (inverse @ a)) @ true @
% 100.59/14.98 (ifeq @ (product @ c @ X2 @ X1) @ true @ (product @ X1 @ X0 @ d) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl224, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl19515, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((ifeq @ true @ true @
% 100.59/14.98 (ifeq @ (product @ c @ (inverse @ (inverse @ a)) @ X0) @ true @
% 100.59/14.98 (product @ X0 @ (inverse @ (inverse @ a)) @ d) @ true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl2456, zip_derived_cl257])).
% 100.59/14.98 thf(zip_derived_cl1839, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1799, zip_derived_cl89, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl1839, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1799, zip_derived_cl89, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl19548, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((ifeq @ (product @ c @ a @ X0) @ true @ (product @ X0 @ a @ d) @ true)
% 100.59/14.98 = (true))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl19515, zip_derived_cl1839, zip_derived_cl1839,
% 100.59/14.98 zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl23874, plain,
% 100.59/14.98 (((ifeq @ true @ true @ (product @ (multiply @ c @ a) @ a @ d) @ true)
% 100.59/14.98 = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl19548])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl23880, plain,
% 100.59/14.98 (((true) = (product @ (multiply @ c @ a) @ a @ d))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl23874, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl382, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((multiply @ X1 @ X0)
% 100.59/14.98 = (ifeq2 @ (product @ X1 @ X0 @ X2) @ true @ X2 @
% 100.59/14.98 (multiply @ X1 @ X0)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl56, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl23913, plain,
% 100.59/14.98 (((multiply @ (multiply @ c @ a) @ a)
% 100.59/14.98 = (ifeq2 @ true @ true @ d @ (multiply @ (multiply @ c @ a) @ a)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl23880, zip_derived_cl382])).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl23993, plain,
% 100.59/14.98 (((multiply @ (multiply @ c @ a) @ a) = (d))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl23913, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl3275, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)) = (X1))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl1839, zip_derived_cl2242])).
% 100.59/14.98 thf(zip_derived_cl24037, plain,
% 100.59/14.98 (((multiply @ (inverse @ (multiply @ c @ a)) @ d) = (a))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl23993, zip_derived_cl3275])).
% 100.59/14.98 thf(zip_derived_cl26704, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl26455, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl29217, plain,
% 100.59/14.98 (((multiply @ a @ (inverse @ d)) = (inverse @ (multiply @ c @ a)))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl24037, zip_derived_cl26704])).
% 100.59/14.98 thf(zip_derived_cl1839, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1799, zip_derived_cl89, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl2424, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (multiply @ (inverse @ X0) @ (inverse @ X0)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl2366, zip_derived_cl89, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl2471, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((inverse @ X0) = (multiply @ (inverse @ (inverse @ X0)) @ X0))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl1839, zip_derived_cl2424])).
% 100.59/14.98 thf(zip_derived_cl1839, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1799, zip_derived_cl89, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl2475, plain,
% 100.59/14.98 (![X0 : $i]: ((inverse @ X0) = (multiply @ X0 @ X0))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl2471, zip_derived_cl1839])).
% 100.59/14.98 thf(zip_derived_cl1509, plain,
% 100.59/14.98 (![X0 : $i]: ((multiply @ a @ (multiply @ b @ X0)) = (multiply @ c @ X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl1477, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl2227, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((true) = (product @ (inverse @ X0) @ (multiply @ X0 @ X1) @ X1))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl1839, zip_derived_cl2168])).
% 100.59/14.98 thf(zip_derived_cl3657, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((true)
% 100.59/14.98 = (product @ (inverse @ a) @ (multiply @ c @ X0) @
% 100.59/14.98 (multiply @ b @ X0)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl1509, zip_derived_cl2227])).
% 100.59/14.98 thf(zip_derived_cl6074, plain,
% 100.59/14.98 (((true) = (product @ (inverse @ a) @ (inverse @ c) @ (multiply @ b @ c)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl2475, zip_derived_cl3657])).
% 100.59/14.98 thf(zip_derived_cl382, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((multiply @ X1 @ X0)
% 100.59/14.98 = (ifeq2 @ (product @ X1 @ X0 @ X2) @ true @ X2 @
% 100.59/14.98 (multiply @ X1 @ X0)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl56, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl6150, plain,
% 100.59/14.98 (((multiply @ (inverse @ a) @ (inverse @ c))
% 100.59/14.98 = (ifeq2 @ true @ true @ (multiply @ b @ c) @
% 100.59/14.98 (multiply @ (inverse @ a) @ (inverse @ c))))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl6074, zip_derived_cl382])).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl6186, plain,
% 100.59/14.98 (((multiply @ (inverse @ a) @ (inverse @ c)) = (multiply @ b @ c))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl6150, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl2242, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)) = (X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl2196, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl6212, plain,
% 100.59/14.98 (((multiply @ a @ (multiply @ b @ c)) = (inverse @ c))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl6186, zip_derived_cl2242])).
% 100.59/14.98 thf(zip_derived_cl26704, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl26455, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl3275, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)) = (X1))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl1839, zip_derived_cl2242])).
% 100.59/14.98 thf(zip_derived_cl29166, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ (multiply @ X0 @ X1)) @ X0) = (inverse @ X1))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl26704, zip_derived_cl3275])).
% 100.59/14.98 thf(zip_derived_cl31800, plain,
% 100.59/14.98 (((multiply @ (inverse @ (inverse @ c)) @ a)
% 100.59/14.98 = (inverse @ (multiply @ b @ c)))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl6212, zip_derived_cl29166])).
% 100.59/14.98 thf(zip_derived_cl1839, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1799, zip_derived_cl89, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl31854, plain,
% 100.59/14.98 (((multiply @ c @ a) = (inverse @ (multiply @ b @ c)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl31800, zip_derived_cl1839])).
% 100.59/14.98 thf(zip_derived_cl1839, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1799, zip_derived_cl89, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl32303, plain,
% 100.59/14.98 (((multiply @ b @ c) = (inverse @ (multiply @ c @ a)))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl31854, zip_derived_cl1839])).
% 100.59/14.98 thf(zip_derived_cl32499, plain,
% 100.59/14.98 (((multiply @ a @ (inverse @ d)) = (multiply @ b @ c))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl29217, zip_derived_cl32303])).
% 100.59/14.98 thf(zip_derived_cl42798, plain,
% 100.59/14.98 (((multiply @ b @ c) = (multiply @ c @ (inverse @ (multiply @ k @ d))))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl42782, zip_derived_cl32499])).
% 100.59/14.98 thf(zip_derived_cl1839, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1799, zip_derived_cl89, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl26326, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((true) = (product @ (multiply @ X0 @ X1) @ (inverse @ X1) @ X0))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl25744, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl26596, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((true) = (product @ (multiply @ X1 @ (inverse @ X0)) @ X0 @ X1))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl1839, zip_derived_cl26326])).
% 100.59/14.98 thf(zip_derived_cl382, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((multiply @ X1 @ X0)
% 100.59/14.98 = (ifeq2 @ (product @ X1 @ X0 @ X2) @ true @ X2 @
% 100.59/14.98 (multiply @ X1 @ X0)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl56, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl27272, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (multiply @ X1 @ (inverse @ X0)) @ X0)
% 100.59/14.98 = (ifeq2 @ true @ true @ X1 @
% 100.59/14.98 (multiply @ (multiply @ X1 @ (inverse @ X0)) @ X0)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl26596, zip_derived_cl382])).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl27583, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (multiply @ X1 @ (inverse @ X0)) @ X0) = (X1))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl27272, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl58671, plain,
% 100.59/14.98 (((multiply @ (multiply @ b @ c) @ (multiply @ k @ d)) = (c))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl42798, zip_derived_cl27583])).
% 100.59/14.98 thf(zip_derived_cl3275, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)) = (X1))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl1839, zip_derived_cl2242])).
% 100.59/14.98 thf(zip_derived_cl2242, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)) = (X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl2196, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl2475, plain,
% 100.59/14.98 (![X0 : $i]: ((inverse @ X0) = (multiply @ X0 @ X0))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl2471, zip_derived_cl1839])).
% 100.59/14.98 thf(zip_derived_cl1839, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1799, zip_derived_cl89, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl2525, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (inverse @ (multiply @ X0 @ X0)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl2475, zip_derived_cl1839])).
% 100.59/14.98 thf(zip_derived_cl2168, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((true) = (product @ X1 @ (multiply @ (inverse @ X1) @ X0) @ X0))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl1771, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl2645, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((true) = (product @ (multiply @ X0 @ X0) @ (multiply @ X0 @ X1) @ X1))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl2525, zip_derived_cl2168])).
% 100.59/14.98 thf(zip_derived_cl7969, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((true)
% 100.59/14.98 = (product @ (multiply @ X1 @ X1) @ X0 @
% 100.59/14.98 (multiply @ (inverse @ X1) @ X0)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl2242, zip_derived_cl2645])).
% 100.59/14.98 thf(zip_derived_cl2168, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((true) = (product @ X1 @ (multiply @ (inverse @ X1) @ X0) @ X0))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl1771, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl128, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 100.59/14.98 ((ifeq @ true @ true @
% 100.59/14.98 (ifeq @ (product @ X4 @ X0 @ X2) @ true @
% 100.59/14.98 (ifeq @ (product @ X3 @ X4 @ X1) @ true @
% 100.59/14.98 (product @ X3 @ X2 @ (multiply @ X1 @ X0)) @ true) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl8])).
% 100.59/14.98 thf(zip_derived_cl2202, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 100.59/14.98 ((ifeq @ true @ true @
% 100.59/14.98 (ifeq @ (product @ (multiply @ (inverse @ X3) @ X1) @ X0 @ X2) @
% 100.59/14.98 true @
% 100.59/14.98 (ifeq @ true @ true @ (product @ X3 @ X2 @ (multiply @ X1 @ X0)) @
% 100.59/14.98 true) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl2168, zip_derived_cl128])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl2246, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 100.59/14.98 ((ifeq @ (product @ (multiply @ (inverse @ X3) @ X1) @ X0 @ X2) @
% 100.59/14.98 true @ (product @ X3 @ X2 @ (multiply @ X1 @ X0)) @ true) = (
% 100.59/14.98 true))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl2202, zip_derived_cl1, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl97105, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((ifeq @ true @ true @
% 100.59/14.98 (product @ X1 @ (multiply @ (inverse @ (inverse @ X1)) @ X0) @
% 100.59/14.98 (multiply @ (inverse @ X1) @ X0)) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl7969, zip_derived_cl2246])).
% 100.59/14.98 thf(zip_derived_cl1839, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1799, zip_derived_cl89, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl97347, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((product @ X1 @ (multiply @ X1 @ X0) @
% 100.59/14.98 (multiply @ (inverse @ X1) @ X0)) = (true))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl97105, zip_derived_cl1839, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl97668, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((product @ X1 @ (multiply @ X1 @ (multiply @ X1 @ X0)) @ X0) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl3275, zip_derived_cl97347])).
% 100.59/14.98 thf(zip_derived_cl382, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((multiply @ X1 @ X0)
% 100.59/14.98 = (ifeq2 @ (product @ X1 @ X0 @ X2) @ true @ X2 @
% 100.59/14.98 (multiply @ X1 @ X0)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl56, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl98360, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ X1 @ (multiply @ X1 @ (multiply @ X1 @ X0)))
% 100.59/14.98 = (ifeq2 @ true @ true @ X0 @
% 100.59/14.98 (multiply @ X1 @ (multiply @ X1 @ (multiply @ X1 @ X0)))))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl97668, zip_derived_cl382])).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl99030, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ X1 @ (multiply @ X1 @ (multiply @ X1 @ X0))) = (X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl98360, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl26704, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl26455, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl101099, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ (multiply @ X1 @ X0))))
% 100.59/14.98 = (X1))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl99030, zip_derived_cl26704])).
% 100.59/14.98 thf(zip_derived_cl119180, plain,
% 100.59/14.98 (((multiply @ (multiply @ k @ d) @
% 100.59/14.98 (inverse @ (multiply @ (multiply @ b @ c) @ c))) = (multiply @ b @ c))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl58671, zip_derived_cl101099])).
% 100.59/14.98 thf(zip_derived_cl6186, plain,
% 100.59/14.98 (((multiply @ (inverse @ a) @ (inverse @ c)) = (multiply @ b @ c))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl6150, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl26704, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl26455, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl29200, plain,
% 100.59/14.98 (((multiply @ (multiply @ b @ c) @ (inverse @ (inverse @ c)))
% 100.59/14.98 = (inverse @ a))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl6186, zip_derived_cl26704])).
% 100.59/14.98 thf(zip_derived_cl1839, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1799, zip_derived_cl89, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl29261, plain,
% 100.59/14.98 (((multiply @ (multiply @ b @ c) @ c) = (inverse @ a))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl29200, zip_derived_cl1839])).
% 100.59/14.98 thf(zip_derived_cl1839, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1799, zip_derived_cl89, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl119390, plain,
% 100.59/14.98 (((multiply @ (multiply @ k @ d) @ a) = (multiply @ b @ c))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl119180, zip_derived_cl29261, zip_derived_cl1839])).
% 100.59/14.98 thf(zip_derived_cl3275, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)) = (X1))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl1839, zip_derived_cl2242])).
% 100.59/14.98 thf(zip_derived_cl26326, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((true) = (product @ (multiply @ X0 @ X1) @ (inverse @ X1) @ X0))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl25744, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl26612, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((true)
% 100.59/14.98 = (product @ X0 @ (inverse @ (multiply @ X1 @ X0)) @ (inverse @ X1)))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl3275, zip_derived_cl26326])).
% 100.59/14.98 thf(zip_derived_cl382, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((multiply @ X1 @ X0)
% 100.59/14.98 = (ifeq2 @ (product @ X1 @ X0 @ X2) @ true @ X2 @
% 100.59/14.98 (multiply @ X1 @ X0)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl56, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl28695, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0)))
% 100.59/14.98 = (ifeq2 @ true @ true @ (inverse @ X1) @
% 100.59/14.98 (multiply @ X0 @ (inverse @ (multiply @ X1 @ X0)))))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl26612, zip_derived_cl382])).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl28996, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl28695, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl119524, plain,
% 100.59/14.98 (((multiply @ a @ (inverse @ (multiply @ b @ c)))
% 100.59/14.98 = (inverse @ (multiply @ k @ d)))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl119390, zip_derived_cl28996])).
% 100.59/14.98 thf(zip_derived_cl31854, plain,
% 100.59/14.98 (((multiply @ c @ a) = (inverse @ (multiply @ b @ c)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl31800, zip_derived_cl1839])).
% 100.59/14.98 thf(zip_derived_cl119564, plain,
% 100.59/14.98 (((multiply @ a @ (multiply @ c @ a)) = (inverse @ (multiply @ k @ d)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl119524, zip_derived_cl31854])).
% 100.59/14.98 thf(zip_derived_cl99030, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ X1 @ (multiply @ X1 @ (multiply @ X1 @ X0))) = (X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl98360, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl3275, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)) = (X1))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl1839, zip_derived_cl2242])).
% 100.59/14.98 thf(zip_derived_cl101076, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ X1) @ X0)
% 100.59/14.98 = (multiply @ X1 @ (multiply @ X1 @ X0)))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl99030, zip_derived_cl3275])).
% 100.59/14.98 thf(zip_derived_cl1509, plain,
% 100.59/14.98 (![X0 : $i]: ((multiply @ a @ (multiply @ b @ X0)) = (multiply @ c @ X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl1477, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl3275, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)) = (X1))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl1839, zip_derived_cl2242])).
% 100.59/14.98 thf(zip_derived_cl4288, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ a) @ (multiply @ c @ X0))
% 100.59/14.98 = (multiply @ b @ X0))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl1509, zip_derived_cl3275])).
% 100.59/14.98 thf(zip_derived_cl119672, plain,
% 100.59/14.98 (((multiply @ b @ a) = (multiply @ c @ (inverse @ h)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl31349, zip_derived_cl119564,
% 100.59/14.98 zip_derived_cl101076, zip_derived_cl4288])).
% 100.59/14.98 thf(zip_derived_cl101076, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ X1) @ X0)
% 100.59/14.98 = (multiply @ X1 @ (multiply @ X1 @ X0)))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl99030, zip_derived_cl3275])).
% 100.59/14.98 thf(zip_derived_cl120028, plain,
% 100.59/14.98 (((multiply @ (inverse @ c) @ (inverse @ h))
% 100.59/14.98 = (multiply @ c @ (multiply @ b @ a)))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl119672, zip_derived_cl101076])).
% 100.59/14.98 thf(zip_derived_cl28996, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl28695, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl3275, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)) = (X1))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl1839, zip_derived_cl2242])).
% 100.59/14.98 thf(zip_derived_cl31516, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ X1) @ (inverse @ X0))
% 100.59/14.98 = (inverse @ (multiply @ X0 @ X1)))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl28996, zip_derived_cl3275])).
% 100.59/14.98 thf(zip_derived_cl120104, plain,
% 100.59/14.98 (((inverse @ (multiply @ h @ c)) = (multiply @ c @ (multiply @ b @ a)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl120028, zip_derived_cl31516])).
% 100.59/14.98 thf(zip_derived_cl1509, plain,
% 100.59/14.98 (![X0 : $i]: ((multiply @ a @ (multiply @ b @ X0)) = (multiply @ c @ X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl1477, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl29166, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ (multiply @ X0 @ X1)) @ X0) = (inverse @ X1))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl26704, zip_derived_cl3275])).
% 100.59/14.98 thf(zip_derived_cl31799, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ (multiply @ c @ X0)) @ a)
% 100.59/14.98 = (inverse @ (multiply @ b @ X0)))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl1509, zip_derived_cl29166])).
% 100.59/14.98 thf(zip_derived_cl136183, plain,
% 100.59/14.98 (((multiply @ (inverse @ (inverse @ (multiply @ h @ c))) @ a)
% 100.59/14.98 = (inverse @ (multiply @ b @ (multiply @ b @ a))))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl120104, zip_derived_cl31799])).
% 100.59/14.98 thf(zip_derived_cl1839, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1799, zip_derived_cl89, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl2475, plain,
% 100.59/14.98 (![X0 : $i]: ((inverse @ X0) = (multiply @ X0 @ X0))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl2471, zip_derived_cl1839])).
% 100.59/14.98 thf(zip_derived_cl2242, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)) = (X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl2196, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl1509, plain,
% 100.59/14.98 (![X0 : $i]: ((multiply @ a @ (multiply @ b @ X0)) = (multiply @ c @ X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl1477, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl3263, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((multiply @ a @ X0)
% 100.59/14.98 = (multiply @ c @ (multiply @ (inverse @ b) @ X0)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl2242, zip_derived_cl1509])).
% 100.59/14.98 thf(zip_derived_cl3275, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)) = (X1))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl1839, zip_derived_cl2242])).
% 100.59/14.98 thf(zip_derived_cl5244, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ c) @ (multiply @ a @ X0))
% 100.59/14.98 = (multiply @ (inverse @ b) @ X0))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl3263, zip_derived_cl3275])).
% 100.59/14.98 thf(zip_derived_cl7460, plain,
% 100.59/14.98 (((multiply @ (inverse @ c) @ (inverse @ a))
% 100.59/14.98 = (multiply @ (inverse @ b) @ a))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl2475, zip_derived_cl5244])).
% 100.59/14.98 thf(zip_derived_cl2242, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)) = (X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl2196, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl26326, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((true) = (product @ (multiply @ X0 @ X1) @ (inverse @ X1) @ X0))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl25744, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl26603, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((true)
% 100.59/14.98 = (product @ X0 @ (inverse @ (multiply @ (inverse @ X1) @ X0)) @ X1))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl2242, zip_derived_cl26326])).
% 100.59/14.98 thf(zip_derived_cl382, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((multiply @ X1 @ X0)
% 100.59/14.98 = (ifeq2 @ (product @ X1 @ X0 @ X2) @ true @ X2 @
% 100.59/14.98 (multiply @ X1 @ X0)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl56, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl27859, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ X0 @ (inverse @ (multiply @ (inverse @ X1) @ X0)))
% 100.59/14.98 = (ifeq2 @ true @ true @ X1 @
% 100.59/14.98 (multiply @ X0 @ (inverse @ (multiply @ (inverse @ X1) @ X0)))))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl26603, zip_derived_cl382])).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl28209, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ X0 @ (inverse @ (multiply @ (inverse @ X1) @ X0))) = (X1))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl27859, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl3275, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)) = (X1))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl1839, zip_derived_cl2242])).
% 100.59/14.98 thf(zip_derived_cl31393, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ X1) @ X0)
% 100.59/14.98 = (inverse @ (multiply @ (inverse @ X0) @ X1)))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl28209, zip_derived_cl3275])).
% 100.59/14.98 thf(zip_derived_cl36703, plain,
% 100.59/14.98 (((multiply @ (inverse @ (inverse @ a)) @ c)
% 100.59/14.98 = (inverse @ (multiply @ (inverse @ b) @ a)))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl7460, zip_derived_cl31393])).
% 100.59/14.98 thf(zip_derived_cl1839, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1799, zip_derived_cl89, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl31393, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ X1) @ X0)
% 100.59/14.98 = (inverse @ (multiply @ (inverse @ X0) @ X1)))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl28209, zip_derived_cl3275])).
% 100.59/14.98 thf(zip_derived_cl36748, plain,
% 100.59/14.98 (((multiply @ a @ c) = (multiply @ (inverse @ a) @ b))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl36703, zip_derived_cl1839, zip_derived_cl31393])).
% 100.59/14.98 thf(zip_derived_cl28996, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl28695, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl37042, plain,
% 100.59/14.98 (((multiply @ b @ (inverse @ (multiply @ a @ c)))
% 100.59/14.98 = (inverse @ (inverse @ a)))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl36748, zip_derived_cl28996])).
% 100.59/14.98 thf(zip_derived_cl1839, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1799, zip_derived_cl89, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl37066, plain,
% 100.59/14.98 (((multiply @ b @ (inverse @ (multiply @ a @ c))) = (a))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl37042, zip_derived_cl1839])).
% 100.59/14.98 thf(zip_derived_cl2424, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (multiply @ (inverse @ X0) @ (inverse @ X0)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl2366, zip_derived_cl89, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl2168, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((true) = (product @ X1 @ (multiply @ (inverse @ X1) @ X0) @ X0))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl1771, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl2469, plain,
% 100.59/14.98 (![X0 : $i]: ((true) = (product @ X0 @ X0 @ (inverse @ X0)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl2424, zip_derived_cl2168])).
% 100.59/14.98 thf(zip_derived_cl13, plain, (((product @ c @ (inverse @ a) @ d) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [zf_stmt_5])).
% 100.59/14.98 thf(zip_derived_cl128, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 100.59/14.98 ((ifeq @ true @ true @
% 100.59/14.98 (ifeq @ (product @ X4 @ X0 @ X2) @ true @
% 100.59/14.98 (ifeq @ (product @ X3 @ X4 @ X1) @ true @
% 100.59/14.98 (product @ X3 @ X2 @ (multiply @ X1 @ X0)) @ true) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl8])).
% 100.59/14.98 thf(zip_derived_cl1707, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((ifeq @ true @ true @
% 100.59/14.98 (ifeq @ true @ true @
% 100.59/14.98 (ifeq @ (product @ X1 @ c @ X0) @ true @
% 100.59/14.98 (product @ X1 @ d @ (multiply @ X0 @ (inverse @ a))) @ true) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl128])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl1747, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((ifeq @ (product @ X1 @ c @ X0) @ true @
% 100.59/14.98 (product @ X1 @ d @ (multiply @ X0 @ (inverse @ a))) @ true)
% 100.59/14.98 = (true))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1707, zip_derived_cl1, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl69988, plain,
% 100.59/14.98 (((ifeq @ true @ true @
% 100.59/14.98 (product @ c @ d @ (multiply @ (inverse @ c) @ (inverse @ a))) @ true)
% 100.59/14.98 = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl2469, zip_derived_cl1747])).
% 100.59/14.98 thf(zip_derived_cl31516, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ X1) @ (inverse @ X0))
% 100.59/14.98 = (inverse @ (multiply @ X0 @ X1)))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl28996, zip_derived_cl3275])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl70013, plain,
% 100.59/14.98 (((product @ c @ d @ (inverse @ (multiply @ a @ c))) = (true))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl69988, zip_derived_cl31516, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl67, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((ifeq2 @ (product @ X2 @ X1 @ X0) @ true @ (multiply @ X2 @ X1) @ X0)
% 100.59/14.98 = (X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl70046, plain,
% 100.59/14.98 (((ifeq2 @ true @ true @ (multiply @ c @ d) @
% 100.59/14.98 (inverse @ (multiply @ a @ c))) = (inverse @ (multiply @ a @ c)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl70013, zip_derived_cl67])).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl70143, plain,
% 100.59/14.98 (((multiply @ c @ d) = (inverse @ (multiply @ a @ c)))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl70046, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl70403, plain,
% 100.59/14.98 (((multiply @ b @ (multiply @ c @ d)) = (a))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl37066, zip_derived_cl70143])).
% 100.59/14.98 thf(zip_derived_cl99030, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ X1 @ (multiply @ X1 @ (multiply @ X1 @ X0))) = (X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl98360, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl101383, plain,
% 100.59/14.98 (((multiply @ b @ (multiply @ b @ a)) = (multiply @ c @ d))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl70403, zip_derived_cl99030])).
% 100.59/14.98 thf(zip_derived_cl70143, plain,
% 100.59/14.98 (((multiply @ c @ d) = (inverse @ (multiply @ a @ c)))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl70046, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl1839, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1799, zip_derived_cl89, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl70413, plain,
% 100.59/14.98 (((multiply @ a @ c) = (inverse @ (multiply @ c @ d)))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl70143, zip_derived_cl1839])).
% 100.59/14.98 thf(zip_derived_cl136245, plain,
% 100.59/14.98 (((multiply @ (multiply @ h @ c) @ a) = (multiply @ a @ c))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl136183, zip_derived_cl1839,
% 100.59/14.98 zip_derived_cl101383, zip_derived_cl70413])).
% 100.59/14.98 thf(zip_derived_cl2242, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)) = (X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl2196, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl97347, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((product @ X1 @ (multiply @ X1 @ X0) @
% 100.59/14.98 (multiply @ (inverse @ X1) @ X0)) = (true))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl97105, zip_derived_cl1839, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl97740, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((product @ X1 @ X0 @
% 100.59/14.98 (multiply @ (inverse @ X1) @ (multiply @ (inverse @ X1) @ X0)))
% 100.59/14.98 = (true))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl2242, zip_derived_cl97347])).
% 100.59/14.98 thf(zip_derived_cl6, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((product @ X0 @ X1 @ (multiply @ X0 @ X1)) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [total_function1])).
% 100.59/14.98 thf(left_inverse, axiom,
% 100.59/14.98 (( product @ ( inverse @ X ) @ X @ identity ) = ( true ))).
% 100.59/14.98 thf(zip_derived_cl4, plain,
% 100.59/14.98 (![X0 : $i]: ((product @ (inverse @ X0) @ X0 @ identity) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [left_inverse])).
% 100.59/14.98 thf(zip_derived_cl9, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 100.59/14.98 ((ifeq @ (product @ X0 @ X1 @ X2) @ true @
% 100.59/14.98 (ifeq @ (product @ X3 @ X2 @ X4) @ true @
% 100.59/14.98 (ifeq @ (product @ X3 @ X0 @ X5) @ true @
% 100.59/14.98 (product @ X5 @ X1 @ X4) @ true) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [associativity2])).
% 100.59/14.98 thf(zip_derived_cl233, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 100.59/14.98 ((ifeq @ true @ true @
% 100.59/14.98 (ifeq @ (product @ X3 @ identity @ X0) @ true @
% 100.59/14.98 (ifeq @ (product @ X3 @ (inverse @ X1) @ X2) @ true @
% 100.59/14.98 (product @ X2 @ X1 @ X0) @ true) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl9])).
% 100.59/14.98 thf(zip_derived_cl13408, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((ifeq @ true @ true @
% 100.59/14.98 (ifeq @ true @ true @
% 100.59/14.98 (ifeq @ (product @ X0 @ (inverse @ X1) @ X2) @ true @
% 100.59/14.98 (product @ X2 @ X1 @ (multiply @ X0 @ identity)) @ true) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl233])).
% 100.59/14.98 thf(zip_derived_cl89, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl85, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl13500, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((ifeq @ (product @ X0 @ (inverse @ X1) @ X2) @ true @
% 100.59/14.98 (product @ X2 @ X1 @ X0) @ true) = (true))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl13408, zip_derived_cl89, zip_derived_cl1,
% 100.59/14.98 zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl106614, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((ifeq @ true @ true @
% 100.59/14.98 (product @
% 100.59/14.98 (multiply @ (inverse @ X0) @
% 100.59/14.98 (multiply @ (inverse @ X0) @ (inverse @ X1))) @
% 100.59/14.98 X1 @ X0) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl97740, zip_derived_cl13500])).
% 100.59/14.98 thf(zip_derived_cl31516, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ X1) @ (inverse @ X0))
% 100.59/14.98 = (inverse @ (multiply @ X0 @ X1)))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl28996, zip_derived_cl3275])).
% 100.59/14.98 thf(zip_derived_cl31516, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ X1) @ (inverse @ X0))
% 100.59/14.98 = (inverse @ (multiply @ X0 @ X1)))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl28996, zip_derived_cl3275])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl107317, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((product @ (inverse @ (multiply @ (multiply @ X1 @ X0) @ X0)) @ X1 @
% 100.59/14.98 X0) = (true))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl106614, zip_derived_cl31516,
% 100.59/14.98 zip_derived_cl31516, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl4, plain,
% 100.59/14.98 (![X0 : $i]: ((product @ (inverse @ X0) @ X0 @ identity) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [left_inverse])).
% 100.59/14.98 thf(zip_derived_cl128, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 100.59/14.98 ((ifeq @ true @ true @
% 100.59/14.98 (ifeq @ (product @ X4 @ X0 @ X2) @ true @
% 100.59/14.98 (ifeq @ (product @ X3 @ X4 @ X1) @ true @
% 100.59/14.98 (product @ X3 @ X2 @ (multiply @ X1 @ X0)) @ true) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl8])).
% 100.59/14.98 thf(zip_derived_cl1681, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((ifeq @ true @ true @
% 100.59/14.98 (ifeq @ (product @ X2 @ X0 @ X1) @ true @
% 100.59/14.98 (ifeq @ true @ true @
% 100.59/14.98 (product @ (inverse @ X2) @ X1 @ (multiply @ identity @ X0)) @
% 100.59/14.98 true) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl128])).
% 100.59/14.98 thf(zip_derived_cl189, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (multiply @ identity @ X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl184, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl1721, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((ifeq @ (product @ X2 @ X0 @ X1) @ true @
% 100.59/14.98 (product @ (inverse @ X2) @ X1 @ X0) @ true) = (true))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1681, zip_derived_cl189, zip_derived_cl1,
% 100.59/14.98 zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl107717, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((ifeq @ true @ true @
% 100.59/14.98 (product @
% 100.59/14.98 (inverse @ (inverse @ (multiply @ (multiply @ X0 @ X1) @ X1))) @
% 100.59/14.98 X1 @ X0) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl107317, zip_derived_cl1721])).
% 100.59/14.98 thf(zip_derived_cl1839, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1799, zip_derived_cl89, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl108431, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((product @ (multiply @ (multiply @ X0 @ X1) @ X1) @ X1 @ X0) = (true))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl107717, zip_derived_cl1839, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl382, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((multiply @ X1 @ X0)
% 100.59/14.98 = (ifeq2 @ (product @ X1 @ X0 @ X2) @ true @ X2 @
% 100.59/14.98 (multiply @ X1 @ X0)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl56, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl108688, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (multiply @ (multiply @ X1 @ X0) @ X0) @ X0)
% 100.59/14.98 = (ifeq2 @ true @ true @ X1 @
% 100.59/14.98 (multiply @ (multiply @ (multiply @ X1 @ X0) @ X0) @ X0)))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl108431, zip_derived_cl382])).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl109335, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (multiply @ (multiply @ X1 @ X0) @ X0) @ X0) = (X1))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl108688, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl136310, plain,
% 100.59/14.98 (((multiply @ (multiply @ (multiply @ a @ c) @ a) @ a)
% 100.59/14.98 = (multiply @ h @ c))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl136245, zip_derived_cl109335])).
% 100.59/14.98 thf(zip_derived_cl70413, plain,
% 100.59/14.98 (((multiply @ a @ c) = (inverse @ (multiply @ c @ d)))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl70143, zip_derived_cl1839])).
% 100.59/14.98 thf(zip_derived_cl31799, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ (multiply @ c @ X0)) @ a)
% 100.59/14.98 = (inverse @ (multiply @ b @ X0)))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl1509, zip_derived_cl29166])).
% 100.59/14.98 thf(zip_derived_cl71349, plain,
% 100.59/14.98 (((multiply @ (multiply @ a @ c) @ a) = (inverse @ (multiply @ b @ d)))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl70413, zip_derived_cl31799])).
% 100.59/14.98 thf(zip_derived_cl2469, plain,
% 100.59/14.98 (![X0 : $i]: ((true) = (product @ X0 @ X0 @ (inverse @ X0)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl2424, zip_derived_cl2168])).
% 100.59/14.98 thf(zip_derived_cl14, plain, (((product @ d @ (inverse @ b) @ h) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [zf_stmt_1])).
% 100.59/14.98 thf(zip_derived_cl128, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 100.59/14.98 ((ifeq @ true @ true @
% 100.59/14.98 (ifeq @ (product @ X4 @ X0 @ X2) @ true @
% 100.59/14.98 (ifeq @ (product @ X3 @ X4 @ X1) @ true @
% 100.59/14.98 (product @ X3 @ X2 @ (multiply @ X1 @ X0)) @ true) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl8])).
% 100.59/14.98 thf(zip_derived_cl1709, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((ifeq @ true @ true @
% 100.59/14.98 (ifeq @ true @ true @
% 100.59/14.98 (ifeq @ (product @ X1 @ d @ X0) @ true @
% 100.59/14.98 (product @ X1 @ h @ (multiply @ X0 @ (inverse @ b))) @ true) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl128])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl1749, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((ifeq @ (product @ X1 @ d @ X0) @ true @
% 100.59/14.98 (product @ X1 @ h @ (multiply @ X0 @ (inverse @ b))) @ true)
% 100.59/14.98 = (true))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1709, zip_derived_cl1, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl71460, plain,
% 100.59/14.98 (((ifeq @ true @ true @
% 100.59/14.98 (product @ d @ h @ (multiply @ (inverse @ d) @ (inverse @ b))) @ true)
% 100.59/14.98 = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl2469, zip_derived_cl1749])).
% 100.59/14.98 thf(zip_derived_cl31516, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ X1) @ (inverse @ X0))
% 100.59/14.98 = (inverse @ (multiply @ X0 @ X1)))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl28996, zip_derived_cl3275])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl71489, plain,
% 100.59/14.98 (((product @ d @ h @ (inverse @ (multiply @ b @ d))) = (true))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl71460, zip_derived_cl31516, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl67, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((ifeq2 @ (product @ X2 @ X1 @ X0) @ true @ (multiply @ X2 @ X1) @ X0)
% 100.59/14.98 = (X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl72884, plain,
% 100.59/14.98 (((ifeq2 @ true @ true @ (multiply @ d @ h) @
% 100.59/14.98 (inverse @ (multiply @ b @ d))) = (inverse @ (multiply @ b @ d)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl71489, zip_derived_cl67])).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl72981, plain,
% 100.59/14.98 (((multiply @ d @ h) = (inverse @ (multiply @ b @ d)))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl72884, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl78924, plain,
% 100.59/14.98 (((multiply @ (multiply @ a @ c) @ a) = (multiply @ d @ h))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl71349, zip_derived_cl72981])).
% 100.59/14.98 thf(zip_derived_cl136350, plain,
% 100.59/14.98 (((multiply @ (multiply @ d @ h) @ a) = (multiply @ h @ c))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl136310, zip_derived_cl78924])).
% 100.59/14.98 thf(zip_derived_cl26704, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl26455, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl28996, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl28695, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl1509, plain,
% 100.59/14.98 (![X0 : $i]: ((multiply @ a @ (multiply @ b @ X0)) = (multiply @ c @ X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl1477, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl31562, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((multiply @ a @ (inverse @ X0))
% 100.59/14.98 = (multiply @ c @ (inverse @ (multiply @ X0 @ b))))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl28996, zip_derived_cl1509])).
% 100.59/14.98 thf(zip_derived_cl29166, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ (multiply @ X0 @ X1)) @ X0) = (inverse @ X1))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl26704, zip_derived_cl3275])).
% 100.59/14.98 thf(zip_derived_cl67413, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ (multiply @ a @ (inverse @ X0))) @ c)
% 100.59/14.98 = (inverse @ (inverse @ (multiply @ X0 @ b))))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl31562, zip_derived_cl29166])).
% 100.59/14.98 thf(zip_derived_cl28996, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl28695, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl2242, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)) = (X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl2196, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl31539, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ X1 @ (inverse @ X0))
% 100.59/14.98 = (inverse @ (multiply @ X0 @ (inverse @ X1))))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl28996, zip_derived_cl2242])).
% 100.59/14.98 thf(zip_derived_cl1839, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1799, zip_derived_cl89, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl67507, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((multiply @ (multiply @ X0 @ (inverse @ a)) @ c)
% 100.59/14.98 = (multiply @ X0 @ b))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl67413, zip_derived_cl31539, zip_derived_cl1839])).
% 100.59/14.98 thf(zip_derived_cl67598, plain,
% 100.59/14.98 (![X0 : $i]: ((multiply @ X0 @ c) = (multiply @ (multiply @ X0 @ a) @ b))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl26704, zip_derived_cl67507])).
% 100.59/14.98 thf(zip_derived_cl137516, plain,
% 100.59/14.98 (((multiply @ (multiply @ d @ h) @ c)
% 100.59/14.98 = (multiply @ (multiply @ h @ c) @ b))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl136350, zip_derived_cl67598])).
% 100.59/14.98 thf(zip_derived_cl78924, plain,
% 100.59/14.98 (((multiply @ (multiply @ a @ c) @ a) = (multiply @ d @ h))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl71349, zip_derived_cl72981])).
% 100.59/14.98 thf(zip_derived_cl3275, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)) = (X1))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl1839, zip_derived_cl2242])).
% 100.59/14.98 thf(zip_derived_cl78928, plain,
% 100.59/14.98 (((multiply @ (inverse @ (multiply @ a @ c)) @ (multiply @ d @ h)) = (a))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl78924, zip_derived_cl3275])).
% 100.59/14.98 thf(zip_derived_cl70143, plain,
% 100.59/14.98 (((multiply @ c @ d) = (inverse @ (multiply @ a @ c)))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl70046, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl78968, plain,
% 100.59/14.98 (((multiply @ (multiply @ c @ d) @ (multiply @ d @ h)) = (a))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl78928, zip_derived_cl70143])).
% 100.59/14.98 thf(zip_derived_cl101099, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ (multiply @ X1 @ X0))))
% 100.59/14.98 = (X1))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl99030, zip_derived_cl26704])).
% 100.59/14.98 thf(zip_derived_cl119184, plain,
% 100.59/14.98 (((multiply @ (multiply @ d @ h) @
% 100.59/14.98 (inverse @ (multiply @ (multiply @ c @ d) @ a))) = (multiply @ c @ d))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl78968, zip_derived_cl101099])).
% 100.59/14.98 thf(zip_derived_cl70143, plain,
% 100.59/14.98 (((multiply @ c @ d) = (inverse @ (multiply @ a @ c)))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl70046, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl29166, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ (multiply @ X0 @ X1)) @ X0) = (inverse @ X1))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl26704, zip_derived_cl3275])).
% 100.59/14.98 thf(zip_derived_cl70580, plain,
% 100.59/14.98 (((multiply @ (multiply @ c @ d) @ a) = (inverse @ c))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl70143, zip_derived_cl29166])).
% 100.59/14.98 thf(zip_derived_cl1839, plain,
% 100.59/14.98 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1799, zip_derived_cl89, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl119394, plain,
% 100.59/14.98 (((multiply @ (multiply @ d @ h) @ c) = (multiply @ c @ d))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl119184, zip_derived_cl70580, zip_derived_cl1839])).
% 100.59/14.98 thf(zip_derived_cl137561, plain,
% 100.59/14.98 (((multiply @ c @ d) = (multiply @ (multiply @ h @ c) @ b))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl137516, zip_derived_cl119394])).
% 100.59/14.98 thf(zip_derived_cl109335, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (multiply @ (multiply @ X1 @ X0) @ X0) @ X0) = (X1))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl108688, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl26704, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl26455, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl110800, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ X0 @ (inverse @ X1))
% 100.59/14.98 = (multiply @ (multiply @ X0 @ X1) @ X1))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl109335, zip_derived_cl26704])).
% 100.59/14.98 thf(zip_derived_cl137583, plain,
% 100.59/14.98 (((multiply @ (multiply @ h @ c) @ (inverse @ b))
% 100.59/14.98 = (multiply @ (multiply @ c @ d) @ b))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl137561, zip_derived_cl110800])).
% 100.59/14.98 thf(zip_derived_cl67598, plain,
% 100.59/14.98 (![X0 : $i]: ((multiply @ X0 @ c) = (multiply @ (multiply @ X0 @ a) @ b))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl26704, zip_derived_cl67507])).
% 100.59/14.98 thf(zip_derived_cl26704, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl26455, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl68066, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((multiply @ (multiply @ X0 @ c) @ (inverse @ b))
% 100.59/14.98 = (multiply @ X0 @ a))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl67598, zip_derived_cl26704])).
% 100.59/14.98 thf(zip_derived_cl137650, plain,
% 100.59/14.98 (((multiply @ h @ a) = (multiply @ (multiply @ c @ d) @ b))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl137583, zip_derived_cl68066])).
% 100.59/14.98 thf(zip_derived_cl31562, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((multiply @ a @ (inverse @ X0))
% 100.59/14.98 = (multiply @ c @ (inverse @ (multiply @ X0 @ b))))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl28996, zip_derived_cl1509])).
% 100.59/14.98 thf(zip_derived_cl137742, plain,
% 100.59/14.98 (((multiply @ a @ (inverse @ (multiply @ c @ d)))
% 100.59/14.98 = (multiply @ c @ (inverse @ (multiply @ h @ a))))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl137650, zip_derived_cl31562])).
% 100.59/14.98 thf(zip_derived_cl70413, plain,
% 100.59/14.98 (((multiply @ a @ c) = (inverse @ (multiply @ c @ d)))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl70143, zip_derived_cl1839])).
% 100.59/14.98 thf(zip_derived_cl36748, plain,
% 100.59/14.98 (((multiply @ a @ c) = (multiply @ (inverse @ a) @ b))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl36703, zip_derived_cl1839, zip_derived_cl31393])).
% 100.59/14.98 thf(zip_derived_cl2242, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)) = (X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl2196, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl37051, plain,
% 100.59/14.98 (((multiply @ a @ (multiply @ a @ c)) = (b))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl36748, zip_derived_cl2242])).
% 100.59/14.98 thf(zip_derived_cl6, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((product @ X0 @ X1 @ (multiply @ X0 @ X1)) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [total_function1])).
% 100.59/14.98 thf(zip_derived_cl13, plain, (((product @ c @ (inverse @ a) @ d) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [zf_stmt_5])).
% 100.59/14.98 thf(zip_derived_cl7, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 100.59/14.98 ((ifeq2 @ (product @ X1 @ X2 @ X0) @ true @
% 100.59/14.98 (ifeq2 @ (product @ X1 @ X2 @ X3) @ true @ X3 @ X0) @ X0) = (
% 100.59/14.98 X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [total_function2])).
% 100.59/14.98 thf(zip_derived_cl52, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((ifeq2 @ (product @ c @ (inverse @ a) @ X0) @ true @
% 100.59/14.98 (ifeq2 @ true @ true @ d @ X0) @ X0) = (X0))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl7])).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl74, plain,
% 100.59/14.98 (![X0 : $i]:
% 100.59/14.98 ((ifeq2 @ (product @ c @ (inverse @ a) @ X0) @ true @ d @ X0) = (X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl178, plain,
% 100.59/14.98 (((ifeq2 @ true @ true @ d @ (multiply @ c @ (inverse @ a)))
% 100.59/14.98 = (multiply @ c @ (inverse @ a)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl74])).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl180, plain, (((d) = (multiply @ c @ (inverse @ a)))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl178, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl2227, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((true) = (product @ (inverse @ X0) @ (multiply @ X0 @ X1) @ X1))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl1839, zip_derived_cl2168])).
% 100.59/14.98 thf(zip_derived_cl3661, plain,
% 100.59/14.98 (((true) = (product @ (inverse @ c) @ d @ (inverse @ a)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl180, zip_derived_cl2227])).
% 100.59/14.98 thf(zip_derived_cl16, plain, (((product @ j @ (inverse @ h) @ k) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [zf_stmt_3])).
% 100.59/14.98 thf(zip_derived_cl128, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 100.59/14.98 ((ifeq @ true @ true @
% 100.59/14.98 (ifeq @ (product @ X4 @ X0 @ X2) @ true @
% 100.59/14.98 (ifeq @ (product @ X3 @ X4 @ X1) @ true @
% 100.59/14.98 (product @ X3 @ X2 @ (multiply @ X1 @ X0)) @ true) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl8])).
% 100.59/14.98 thf(zip_derived_cl1711, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((ifeq @ true @ true @
% 100.59/14.98 (ifeq @ true @ true @
% 100.59/14.98 (ifeq @ (product @ X1 @ j @ X0) @ true @
% 100.59/14.98 (product @ X1 @ k @ (multiply @ X0 @ (inverse @ h))) @ true) @
% 100.59/14.98 true) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl16, zip_derived_cl128])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl1751, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((ifeq @ (product @ X1 @ j @ X0) @ true @
% 100.59/14.98 (product @ X1 @ k @ (multiply @ X0 @ (inverse @ h))) @ true)
% 100.59/14.98 = (true))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1711, zip_derived_cl1, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl12371, plain, (((d) = (j))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl12302, zip_derived_cl89, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl72153, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((ifeq @ (product @ X1 @ d @ X0) @ true @
% 100.59/14.98 (product @ X1 @ k @ (multiply @ X0 @ (inverse @ h))) @ true)
% 100.59/14.98 = (true))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl1751, zip_derived_cl12371])).
% 100.59/14.98 thf(zip_derived_cl72198, plain,
% 100.59/14.98 (((ifeq @ true @ true @
% 100.59/14.98 (product @ (inverse @ c) @ k @
% 100.59/14.98 (multiply @ (inverse @ a) @ (inverse @ h))) @
% 100.59/14.98 true) = (true))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl3661, zip_derived_cl72153])).
% 100.59/14.98 thf(zip_derived_cl31516, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ (inverse @ X1) @ (inverse @ X0))
% 100.59/14.98 = (inverse @ (multiply @ X0 @ X1)))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl28996, zip_derived_cl3275])).
% 100.59/14.98 thf(zip_derived_cl1, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 100.59/14.98 thf(zip_derived_cl72225, plain,
% 100.59/14.98 (((product @ (inverse @ c) @ k @ (inverse @ (multiply @ h @ a))) = (true))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl72198, zip_derived_cl31516, zip_derived_cl1])).
% 100.59/14.98 thf(zip_derived_cl382, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.59/14.98 ((multiply @ X1 @ X0)
% 100.59/14.98 = (ifeq2 @ (product @ X1 @ X0 @ X2) @ true @ X2 @
% 100.59/14.98 (multiply @ X1 @ X0)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl56, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl84343, plain,
% 100.59/14.98 (((multiply @ (inverse @ c) @ k)
% 100.59/14.98 = (ifeq2 @ true @ true @ (inverse @ (multiply @ h @ a)) @
% 100.59/14.98 (multiply @ (inverse @ c) @ k)))),
% 100.59/14.98 inference('sup+', [status(thm)], [zip_derived_cl72225, zip_derived_cl382])).
% 100.59/14.98 thf(zip_derived_cl0, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 100.59/14.98 inference('cnf', [status(esa)], [ifeq_axiom])).
% 100.59/14.98 thf(zip_derived_cl84432, plain,
% 100.59/14.98 (((multiply @ (inverse @ c) @ k) = (inverse @ (multiply @ h @ a)))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl84343, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl2242, plain,
% 100.59/14.98 (![X0 : $i, X1 : $i]:
% 100.59/14.98 ((multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)) = (X0))),
% 100.59/14.98 inference('demod', [status(thm)], [zip_derived_cl2196, zip_derived_cl0])).
% 100.59/14.98 thf(zip_derived_cl84519, plain,
% 100.59/14.98 (((multiply @ c @ (inverse @ (multiply @ h @ a))) = (k))),
% 100.59/14.98 inference('sup+', [status(thm)],
% 100.59/14.98 [zip_derived_cl84432, zip_derived_cl2242])).
% 100.59/14.98 thf(zip_derived_cl137782, plain, (((b) = (k))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl137742, zip_derived_cl70413,
% 100.59/14.98 zip_derived_cl37051, zip_derived_cl84519])).
% 100.59/14.98 thf(zip_derived_cl5, plain,
% 100.59/14.98 (![X0 : $i]: ((product @ X0 @ (inverse @ X0) @ identity) = (true))),
% 100.59/14.98 inference('cnf', [status(esa)], [right_inverse])).
% 100.59/14.98 thf(zip_derived_cl138048, plain, (((true) != (true))),
% 100.59/14.98 inference('demod', [status(thm)],
% 100.59/14.98 [zip_derived_cl17, zip_derived_cl137782, zip_derived_cl5])).
% 100.59/14.98 thf(zip_derived_cl138049, plain, ($false),
% 100.59/14.98 inference('simplify', [status(thm)], [zip_derived_cl138048])).
% 100.59/14.98
% 100.59/14.98 % SZS output end Refutation
% 100.59/14.98
% 100.59/14.98
% 100.59/14.98 % Terminating...
% 101.23/15.09 % Runner terminated.
% 101.23/15.10 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------