TSTP Solution File: GRP258-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP258-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.g17JjBSCb4 true
% Computer : n017.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 01:50:56 EDT 2023
% Result : Unsatisfiable 114.17s 17.08s
% Output : Refutation 114.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GRP258-1 : TPTP v8.1.2. Released v2.5.0.
% 0.14/0.15 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.g17JjBSCb4 true
% 0.15/0.37 % Computer : n017.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon Aug 28 22:11:58 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.15/0.37 % Running portfolio for 300 s
% 0.15/0.37 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.37 % Number of cores: 8
% 0.23/0.37 % Python version: Python 3.6.8
% 0.23/0.38 % Running in FO mode
% 0.24/0.63 % Total configuration time : 435
% 0.24/0.63 % Estimated wc time : 1092
% 0.24/0.63 % Estimated cpu time (7 cpus) : 156.0
% 0.81/0.73 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 1.21/0.74 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 1.21/0.75 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 1.21/0.75 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 1.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 1.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 1.21/0.77 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 114.17/17.08 % Solved by fo/fo1_av.sh.
% 114.17/17.08 % done 10010 iterations in 16.213s
% 114.17/17.08 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 114.17/17.08 % SZS output start Refutation
% 114.17/17.08 thf(sk_c6_type, type, sk_c6: $i).
% 114.17/17.08 thf(sk_c11_type, type, sk_c11: $i).
% 114.17/17.08 thf(sk_c8_type, type, sk_c8: $i).
% 114.17/17.08 thf(sk_c10_type, type, sk_c10: $i).
% 114.17/17.08 thf(sk_c5_type, type, sk_c5: $i).
% 114.17/17.08 thf(identity_type, type, identity: $i).
% 114.17/17.08 thf(multiply_type, type, multiply: $i > $i > $i).
% 114.17/17.08 thf(sk_c12_type, type, sk_c12: $i).
% 114.17/17.08 thf(sk_c2_type, type, sk_c2: $i).
% 114.17/17.08 thf(inverse_type, type, inverse: $i > $i).
% 114.17/17.08 thf(sk_c4_type, type, sk_c4: $i).
% 114.17/17.08 thf(sk_c7_type, type, sk_c7: $i).
% 114.17/17.08 thf(sk_c9_type, type, sk_c9: $i).
% 114.17/17.08 thf(sk_c1_type, type, sk_c1: $i).
% 114.17/17.08 thf(sk_c3_type, type, sk_c3: $i).
% 114.17/17.08 thf(prove_this_41, conjecture,
% 114.17/17.08 (~( ( ( multiply @ sk_c4 @ sk_c12 ) = ( sk_c11 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c10 @ sk_c12 ) = ( sk_c11 ) ) ))).
% 114.17/17.08 thf(zf_stmt_0, negated_conjecture,
% 114.17/17.08 (( ( multiply @ sk_c4 @ sk_c12 ) = ( sk_c11 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c10 @ sk_c12 ) = ( sk_c11 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_41])).
% 114.17/17.08 thf(zip_derived_cl43, plain,
% 114.17/17.08 ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))
% 114.17/17.08 | ((multiply @ sk_c10 @ sk_c12) = (sk_c11)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_0])).
% 114.17/17.08 thf('0', plain,
% 114.17/17.08 ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) |
% 114.17/17.08 (((multiply @ sk_c10 @ sk_c12) = (sk_c11)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl43])).
% 114.17/17.08 thf(prove_this_42, conjecture,
% 114.17/17.08 (~( ( ( inverse @ sk_c4 ) = ( sk_c12 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c10 @ sk_c12 ) = ( sk_c11 ) ) ))).
% 114.17/17.08 thf(zf_stmt_1, negated_conjecture,
% 114.17/17.08 (( ( inverse @ sk_c4 ) = ( sk_c12 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c10 @ sk_c12 ) = ( sk_c11 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_42])).
% 114.17/17.08 thf(zip_derived_cl44, plain,
% 114.17/17.08 ((((inverse @ sk_c4) = (sk_c12))
% 114.17/17.08 | ((multiply @ sk_c10 @ sk_c12) = (sk_c11)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_1])).
% 114.17/17.08 thf('1', plain,
% 114.17/17.08 ((((inverse @ sk_c4) = (sk_c12))) |
% 114.17/17.08 (((multiply @ sk_c10 @ sk_c12) = (sk_c11)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl44])).
% 114.17/17.08 thf(prove_this_43, conjecture,
% 114.17/17.08 (~( ( ( multiply @ sk_c5 @ sk_c11 ) = ( sk_c10 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c10 @ sk_c12 ) = ( sk_c11 ) ) ))).
% 114.17/17.08 thf(zf_stmt_2, negated_conjecture,
% 114.17/17.08 (( ( multiply @ sk_c5 @ sk_c11 ) = ( sk_c10 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c10 @ sk_c12 ) = ( sk_c11 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_43])).
% 114.17/17.08 thf(zip_derived_cl45, plain,
% 114.17/17.08 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))
% 114.17/17.08 | ((multiply @ sk_c10 @ sk_c12) = (sk_c11)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_2])).
% 114.17/17.08 thf('2', plain,
% 114.17/17.08 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))) |
% 114.17/17.08 (((multiply @ sk_c10 @ sk_c12) = (sk_c11)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl45])).
% 114.17/17.08 thf(prove_this_44, conjecture,
% 114.17/17.08 (~( ( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c10 @ sk_c12 ) = ( sk_c11 ) ) ))).
% 114.17/17.08 thf(zf_stmt_3, negated_conjecture,
% 114.17/17.08 (( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c10 @ sk_c12 ) = ( sk_c11 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_44])).
% 114.17/17.08 thf(zip_derived_cl46, plain,
% 114.17/17.08 ((((inverse @ sk_c5) = (sk_c11))
% 114.17/17.08 | ((multiply @ sk_c10 @ sk_c12) = (sk_c11)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_3])).
% 114.17/17.08 thf('3', plain,
% 114.17/17.08 ((((inverse @ sk_c5) = (sk_c11))) |
% 114.17/17.08 (((multiply @ sk_c10 @ sk_c12) = (sk_c11)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl46])).
% 114.17/17.08 thf(prove_this_45, conjecture,
% 114.17/17.08 (~( ( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c12 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c10 @ sk_c12 ) = ( sk_c11 ) ) ))).
% 114.17/17.08 thf(zf_stmt_4, negated_conjecture,
% 114.17/17.08 (( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c12 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c10 @ sk_c12 ) = ( sk_c11 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_45])).
% 114.17/17.08 thf(zip_derived_cl47, plain,
% 114.17/17.08 ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))
% 114.17/17.08 | ((multiply @ sk_c10 @ sk_c12) = (sk_c11)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_4])).
% 114.17/17.08 thf('4', plain,
% 114.17/17.08 ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))) |
% 114.17/17.08 (((multiply @ sk_c10 @ sk_c12) = (sk_c11)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl47])).
% 114.17/17.08 thf(prove_this_61, conjecture,
% 114.17/17.08 (~( ( ( multiply @ sk_c4 @ sk_c12 ) = ( sk_c11 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c3 ) = ( sk_c10 ) ) ))).
% 114.17/17.08 thf(zf_stmt_5, negated_conjecture,
% 114.17/17.08 (( ( multiply @ sk_c4 @ sk_c12 ) = ( sk_c11 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c3 ) = ( sk_c10 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_61])).
% 114.17/17.08 thf(zip_derived_cl63, plain,
% 114.17/17.08 ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))
% 114.17/17.08 | ((inverse @ sk_c3) = (sk_c10)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_5])).
% 114.17/17.08 thf(zip_derived_cl194, plain,
% 114.17/17.08 ((((inverse @ sk_c3) = (sk_c10))) <= ((((inverse @ sk_c3) = (sk_c10))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl63])).
% 114.17/17.08 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 114.17/17.08 thf(zip_derived_cl1, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_inverse])).
% 114.17/17.08 thf(zip_derived_cl388, plain,
% 114.17/17.08 ((((multiply @ sk_c10 @ sk_c3) = (identity)))
% 114.17/17.08 <= ((((inverse @ sk_c3) = (sk_c10))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl194, zip_derived_cl1])).
% 114.17/17.08 thf(zip_derived_cl1, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_inverse])).
% 114.17/17.08 thf(associativity, axiom,
% 114.17/17.08 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 114.17/17.08 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 114.17/17.08 thf(zip_derived_cl2, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 114.17/17.08 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 114.17/17.08 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 114.17/17.08 inference('cnf', [status(esa)], [associativity])).
% 114.17/17.08 thf(zip_derived_cl261, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i]:
% 114.17/17.08 ((multiply @ identity @ X0)
% 114.17/17.08 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 114.17/17.08 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 114.17/17.08 thf(zip_derived_cl0, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_identity])).
% 114.17/17.08 thf(zip_derived_cl263, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i]:
% 114.17/17.08 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl691, plain,
% 114.17/17.08 ((((sk_c3) = (multiply @ (inverse @ sk_c10) @ identity)))
% 114.17/17.08 <= ((((inverse @ sk_c3) = (sk_c10))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl388, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl2, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 114.17/17.08 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 114.17/17.08 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 114.17/17.08 inference('cnf', [status(esa)], [associativity])).
% 114.17/17.08 thf(zip_derived_cl796, plain,
% 114.17/17.08 ((![X0 : $i]:
% 114.17/17.08 ((multiply @ sk_c3 @ X0)
% 114.17/17.08 = (multiply @ (inverse @ sk_c10) @ (multiply @ identity @ X0))))
% 114.17/17.08 <= ((((inverse @ sk_c3) = (sk_c10))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl691, zip_derived_cl2])).
% 114.17/17.08 thf(zip_derived_cl0, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_identity])).
% 114.17/17.08 thf(zip_derived_cl799, plain,
% 114.17/17.08 ((![X0 : $i]:
% 114.17/17.08 ((multiply @ sk_c3 @ X0) = (multiply @ (inverse @ sk_c10) @ X0)))
% 114.17/17.08 <= ((((inverse @ sk_c3) = (sk_c10))))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl796, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl1, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_inverse])).
% 114.17/17.08 thf(zip_derived_cl1595, plain,
% 114.17/17.08 ((((multiply @ sk_c3 @ sk_c10) = (identity)))
% 114.17/17.08 <= ((((inverse @ sk_c3) = (sk_c10))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl799, zip_derived_cl1])).
% 114.17/17.08 thf(prove_this_51, conjecture,
% 114.17/17.08 (~( ( ( multiply @ sk_c4 @ sk_c12 ) = ( sk_c11 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c12 ) ) ))).
% 114.17/17.08 thf(zf_stmt_6, negated_conjecture,
% 114.17/17.08 (( ( multiply @ sk_c4 @ sk_c12 ) = ( sk_c11 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c12 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_51])).
% 114.17/17.08 thf(zip_derived_cl53, plain,
% 114.17/17.08 ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))
% 114.17/17.08 | ((multiply @ sk_c3 @ sk_c10) = (sk_c12)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_6])).
% 114.17/17.08 thf(zip_derived_cl174, plain,
% 114.17/17.08 ((((multiply @ sk_c3 @ sk_c10) = (sk_c12)))
% 114.17/17.08 <= ((((multiply @ sk_c3 @ sk_c10) = (sk_c12))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl53])).
% 114.17/17.08 thf(zip_derived_cl1627, plain,
% 114.17/17.08 ((((identity) = (sk_c12)))
% 114.17/17.08 <= ((((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c3) = (sk_c10))))),
% 114.17/17.08 inference('s_sup+', [status(thm)],
% 114.17/17.08 [zip_derived_cl1595, zip_derived_cl174])).
% 114.17/17.08 thf(prove_this_31, conjecture,
% 114.17/17.08 (~( ( ( multiply @ sk_c4 @ sk_c12 ) = ( sk_c11 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c2 ) = ( sk_c11 ) ) ))).
% 114.17/17.08 thf(zf_stmt_7, negated_conjecture,
% 114.17/17.08 (( ( multiply @ sk_c4 @ sk_c12 ) = ( sk_c11 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c2 ) = ( sk_c11 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_31])).
% 114.17/17.08 thf(zip_derived_cl33, plain,
% 114.17/17.08 ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))
% 114.17/17.08 | ((inverse @ sk_c2) = (sk_c11)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_7])).
% 114.17/17.08 thf(zip_derived_cl134, plain,
% 114.17/17.08 ((((inverse @ sk_c2) = (sk_c11))) <= ((((inverse @ sk_c2) = (sk_c11))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl33])).
% 114.17/17.08 thf(zip_derived_cl1, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_inverse])).
% 114.17/17.08 thf(zip_derived_cl314, plain,
% 114.17/17.08 ((((multiply @ sk_c11 @ sk_c2) = (identity)))
% 114.17/17.08 <= ((((inverse @ sk_c2) = (sk_c11))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl134, zip_derived_cl1])).
% 114.17/17.08 thf(zip_derived_cl263, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i]:
% 114.17/17.08 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl687, plain,
% 114.17/17.08 ((((sk_c2) = (multiply @ (inverse @ sk_c11) @ identity)))
% 114.17/17.08 <= ((((inverse @ sk_c2) = (sk_c11))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl314, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl2, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 114.17/17.08 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 114.17/17.08 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 114.17/17.08 inference('cnf', [status(esa)], [associativity])).
% 114.17/17.08 thf(zip_derived_cl767, plain,
% 114.17/17.08 ((![X0 : $i]:
% 114.17/17.08 ((multiply @ sk_c2 @ X0)
% 114.17/17.08 = (multiply @ (inverse @ sk_c11) @ (multiply @ identity @ X0))))
% 114.17/17.08 <= ((((inverse @ sk_c2) = (sk_c11))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl687, zip_derived_cl2])).
% 114.17/17.08 thf(zip_derived_cl0, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_identity])).
% 114.17/17.08 thf(zip_derived_cl771, plain,
% 114.17/17.08 ((![X0 : $i]:
% 114.17/17.08 ((multiply @ sk_c2 @ X0) = (multiply @ (inverse @ sk_c11) @ X0)))
% 114.17/17.08 <= ((((inverse @ sk_c2) = (sk_c11))))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl767, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl1, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_inverse])).
% 114.17/17.08 thf(zip_derived_cl1442, plain,
% 114.17/17.08 ((((multiply @ sk_c2 @ sk_c11) = (identity)))
% 114.17/17.08 <= ((((inverse @ sk_c2) = (sk_c11))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl771, zip_derived_cl1])).
% 114.17/17.08 thf(zip_derived_cl134, plain,
% 114.17/17.08 ((((inverse @ sk_c2) = (sk_c11))) <= ((((inverse @ sk_c2) = (sk_c11))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl33])).
% 114.17/17.08 thf(prove_this_3, conjecture,
% 114.17/17.08 (~( ( ( multiply @ sk_c5 @ sk_c11 ) = ( sk_c10 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c1 @ sk_c12 ) = ( sk_c11 ) ) ))).
% 114.17/17.08 thf(zf_stmt_8, negated_conjecture,
% 114.17/17.08 (( ( multiply @ sk_c5 @ sk_c11 ) = ( sk_c10 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c1 @ sk_c12 ) = ( sk_c11 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_3])).
% 114.17/17.08 thf(zip_derived_cl5, plain,
% 114.17/17.08 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))
% 114.17/17.08 | ((multiply @ sk_c1 @ sk_c12) = (sk_c11)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_8])).
% 114.17/17.08 thf(zip_derived_cl78, plain,
% 114.17/17.08 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10)))
% 114.17/17.08 <= ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl5])).
% 114.17/17.08 thf(prove_this_71, conjecture,
% 114.17/17.08 (~( ( ( multiply @ X8 @ X3 ) != ( X9 ) ) |
% 114.17/17.08 ( ( inverse @ X9 ) != ( X3 ) ) | ( ( inverse @ X8 ) != ( X9 ) ) |
% 114.17/17.08 ( ( multiply @ X3 @ sk_c11 ) != ( sk_c12 ) ) |
% 114.17/17.08 ( ( inverse @ X7 ) != ( X3 ) ) |
% 114.17/17.08 ( ( multiply @ X7 @ X3 ) != ( sk_c12 ) ) |
% 114.17/17.08 ( ( inverse @ X2 ) != ( sk_c11 ) ) |
% 114.17/17.08 ( ( multiply @ X2 @ sk_c11 ) != ( sk_c10 ) ) |
% 114.17/17.08 ( ( inverse @ X1 ) != ( sk_c12 ) ) |
% 114.17/17.08 ( ( multiply @ X1 @ sk_c12 ) != ( sk_c11 ) ) |
% 114.17/17.08 ( ( inverse @ X6 ) != ( sk_c10 ) ) |
% 114.17/17.08 ( ( multiply @ X6 @ sk_c10 ) != ( sk_c12 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c10 @ sk_c12 ) != ( sk_c11 ) ) |
% 114.17/17.08 ( ( inverse @ X5 ) != ( sk_c11 ) ) |
% 114.17/17.08 ( ( multiply @ X5 @ sk_c11 ) != ( sk_c10 ) ) |
% 114.17/17.08 ( ( inverse @ X4 ) != ( sk_c12 ) ) |
% 114.17/17.08 ( ( multiply @ X4 @ sk_c12 ) != ( sk_c11 ) ) ))).
% 114.17/17.08 thf(zf_stmt_9, negated_conjecture,
% 114.17/17.08 (( ( multiply @ X8 @ X3 ) != ( X9 ) ) | ( ( inverse @ X9 ) != ( X3 ) ) |
% 114.17/17.08 ( ( inverse @ X8 ) != ( X9 ) ) |
% 114.17/17.08 ( ( multiply @ X3 @ sk_c11 ) != ( sk_c12 ) ) |
% 114.17/17.08 ( ( inverse @ X7 ) != ( X3 ) ) |
% 114.17/17.08 ( ( multiply @ X7 @ X3 ) != ( sk_c12 ) ) |
% 114.17/17.08 ( ( inverse @ X2 ) != ( sk_c11 ) ) |
% 114.17/17.08 ( ( multiply @ X2 @ sk_c11 ) != ( sk_c10 ) ) |
% 114.17/17.08 ( ( inverse @ X1 ) != ( sk_c12 ) ) |
% 114.17/17.08 ( ( multiply @ X1 @ sk_c12 ) != ( sk_c11 ) ) |
% 114.17/17.08 ( ( inverse @ X6 ) != ( sk_c10 ) ) |
% 114.17/17.08 ( ( multiply @ X6 @ sk_c10 ) != ( sk_c12 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c10 @ sk_c12 ) != ( sk_c11 ) ) |
% 114.17/17.08 ( ( inverse @ X5 ) != ( sk_c11 ) ) |
% 114.17/17.08 ( ( multiply @ X5 @ sk_c11 ) != ( sk_c10 ) ) |
% 114.17/17.08 ( ( inverse @ X4 ) != ( sk_c12 ) ) |
% 114.17/17.08 ( ( multiply @ X4 @ sk_c12 ) != ( sk_c11 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_71])).
% 114.17/17.08 thf(zip_derived_cl73, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i,
% 114.17/17.08 X7 : $i, X8 : $i]:
% 114.17/17.08 (((multiply @ X1 @ X2) != (X0))
% 114.17/17.08 | ((inverse @ X0) != (X2))
% 114.17/17.08 | ((inverse @ X1) != (X0))
% 114.17/17.08 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.17/17.08 | ((inverse @ X3) != (X2))
% 114.17/17.08 | ((multiply @ X3 @ X2) != (sk_c12))
% 114.17/17.08 | ((inverse @ X4) != (sk_c11))
% 114.17/17.08 | ((multiply @ X4 @ sk_c11) != (sk_c10))
% 114.17/17.08 | ((inverse @ X5) != (sk_c12))
% 114.17/17.08 | ((multiply @ X5 @ sk_c12) != (sk_c11))
% 114.17/17.08 | ((inverse @ X6) != (sk_c10))
% 114.17/17.08 | ((multiply @ X6 @ sk_c10) != (sk_c12))
% 114.17/17.08 | ((multiply @ sk_c10 @ sk_c12) != (sk_c11))
% 114.17/17.08 | ((inverse @ X7) != (sk_c11))
% 114.17/17.08 | ((multiply @ X7 @ sk_c11) != (sk_c10))
% 114.17/17.08 | ((inverse @ X8) != (sk_c12))
% 114.17/17.08 | ((multiply @ X8 @ sk_c12) != (sk_c11)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_9])).
% 114.17/17.08 thf(zip_derived_cl219, plain,
% 114.17/17.08 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.17/17.08 (((inverse @ X0) != (X2))
% 114.17/17.08 | ((multiply @ X1 @ X2) != (X0))
% 114.17/17.08 | ((inverse @ X1) != (X0))
% 114.17/17.08 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.17/17.08 | ((inverse @ X3) != (X2))
% 114.17/17.08 | ((multiply @ X3 @ X2) != (sk_c12))))
% 114.17/17.08 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.17/17.08 (((inverse @ X0) != (X2))
% 114.17/17.08 | ((multiply @ X1 @ X2) != (X0))
% 114.17/17.08 | ((inverse @ X1) != (X0))
% 114.17/17.08 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.17/17.08 | ((inverse @ X3) != (X2))
% 114.17/17.08 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl73])).
% 114.17/17.08 thf(zip_derived_cl310, plain,
% 114.17/17.08 ((![X0 : $i, X1 : $i]:
% 114.17/17.08 (((inverse @ X0) != (sk_c11))
% 114.17/17.08 | ((sk_c10) != (X0))
% 114.17/17.08 | ((inverse @ sk_c5) != (X0))
% 114.17/17.08 | ((multiply @ sk_c11 @ sk_c11) != (sk_c12))
% 114.17/17.08 | ((inverse @ X1) != (sk_c11))
% 114.17/17.08 | ((multiply @ X1 @ sk_c11) != (sk_c12))))
% 114.17/17.08 <= ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.17/17.08 (((inverse @ X0) != (X2))
% 114.17/17.08 | ((multiply @ X1 @ X2) != (X0))
% 114.17/17.08 | ((inverse @ X1) != (X0))
% 114.17/17.08 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.17/17.08 | ((inverse @ X3) != (X2))
% 114.17/17.08 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 114.17/17.08 inference('s_sup-', [status(thm)], [zip_derived_cl78, zip_derived_cl219])).
% 114.17/17.08 thf(zip_derived_cl373, plain,
% 114.17/17.08 ((![X1 : $i]:
% 114.17/17.08 (((inverse @ X1) != (sk_c11))
% 114.17/17.08 | ((multiply @ X1 @ sk_c11) != (sk_c12))))
% 114.17/17.08 <= ((![X1 : $i]:
% 114.17/17.08 (((inverse @ X1) != (sk_c11))
% 114.17/17.08 | ((multiply @ X1 @ sk_c11) != (sk_c12)))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl310])).
% 114.17/17.08 thf(zip_derived_cl382, plain,
% 114.17/17.08 (((((sk_c11) != (sk_c11)) | ((multiply @ sk_c2 @ sk_c11) != (sk_c12))))
% 114.17/17.08 <= ((((inverse @ sk_c2) = (sk_c11))) &
% 114.17/17.08 (![X1 : $i]:
% 114.17/17.08 (((inverse @ X1) != (sk_c11))
% 114.17/17.08 | ((multiply @ X1 @ sk_c11) != (sk_c12)))))),
% 114.17/17.08 inference('s_sup-', [status(thm)], [zip_derived_cl134, zip_derived_cl373])).
% 114.17/17.08 thf(zip_derived_cl384, plain,
% 114.17/17.08 ((((multiply @ sk_c2 @ sk_c11) != (sk_c12)))
% 114.17/17.08 <= ((((inverse @ sk_c2) = (sk_c11))) &
% 114.17/17.08 (![X1 : $i]:
% 114.17/17.08 (((inverse @ X1) != (sk_c11))
% 114.17/17.08 | ((multiply @ X1 @ sk_c11) != (sk_c12)))))),
% 114.17/17.08 inference('simplify', [status(thm)], [zip_derived_cl382])).
% 114.17/17.08 thf(zip_derived_cl1539, plain,
% 114.17/17.08 ((((identity) != (sk_c12)))
% 114.17/17.08 <= ((((inverse @ sk_c2) = (sk_c11))) &
% 114.17/17.08 (![X1 : $i]:
% 114.17/17.08 (((inverse @ X1) != (sk_c11))
% 114.17/17.08 | ((multiply @ X1 @ sk_c11) != (sk_c12)))))),
% 114.17/17.08 inference('s_sup-', [status(thm)],
% 114.17/17.08 [zip_derived_cl1442, zip_derived_cl384])).
% 114.17/17.08 thf(zip_derived_cl38335, plain,
% 114.17/17.08 ((((identity) != (identity)))
% 114.17/17.08 <= ((((inverse @ sk_c2) = (sk_c11))) &
% 114.17/17.08 (((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c3) = (sk_c10))) &
% 114.17/17.08 (![X1 : $i]:
% 114.17/17.08 (((inverse @ X1) != (sk_c11))
% 114.17/17.08 | ((multiply @ X1 @ sk_c11) != (sk_c12)))))),
% 114.17/17.08 inference('s_sup-', [status(thm)],
% 114.17/17.08 [zip_derived_cl1627, zip_derived_cl1539])).
% 114.17/17.08 thf('5', plain,
% 114.17/17.08 (~
% 114.17/17.08 (![X1 : $i]:
% 114.17/17.08 (((inverse @ X1) != (sk_c11))
% 114.17/17.08 | ((multiply @ X1 @ sk_c11) != (sk_c12)))) |
% 114.17/17.08 ~ (((inverse @ sk_c2) = (sk_c11))) |
% 114.17/17.08 ~ (((inverse @ sk_c3) = (sk_c10))) |
% 114.17/17.08 ~ (((multiply @ sk_c3 @ sk_c10) = (sk_c12)))),
% 114.17/17.08 inference('simplify', [status(thm)], [zip_derived_cl38335])).
% 114.17/17.08 thf(prove_this_34, conjecture,
% 114.17/17.08 (~( ( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c2 ) = ( sk_c11 ) ) ))).
% 114.17/17.08 thf(zf_stmt_10, negated_conjecture,
% 114.17/17.08 (( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c2 ) = ( sk_c11 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_34])).
% 114.17/17.08 thf(zip_derived_cl36, plain,
% 114.17/17.08 ((((inverse @ sk_c5) = (sk_c11)) | ((inverse @ sk_c2) = (sk_c11)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_10])).
% 114.17/17.08 thf('6', plain,
% 114.17/17.08 ((((inverse @ sk_c2) = (sk_c11))) | (((inverse @ sk_c5) = (sk_c11)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl36])).
% 114.17/17.08 thf(prove_this_54, conjecture,
% 114.17/17.08 (~( ( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c12 ) ) ))).
% 114.17/17.08 thf(zf_stmt_11, negated_conjecture,
% 114.17/17.08 (( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c12 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_54])).
% 114.17/17.08 thf(zip_derived_cl56, plain,
% 114.17/17.08 ((((inverse @ sk_c5) = (sk_c11))
% 114.17/17.08 | ((multiply @ sk_c3 @ sk_c10) = (sk_c12)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_11])).
% 114.17/17.08 thf('7', plain,
% 114.17/17.08 ((((multiply @ sk_c3 @ sk_c10) = (sk_c12))) |
% 114.17/17.08 (((inverse @ sk_c5) = (sk_c11)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl56])).
% 114.17/17.08 thf(prove_this_64, conjecture,
% 114.17/17.08 (~( ( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c3 ) = ( sk_c10 ) ) ))).
% 114.17/17.08 thf(zf_stmt_12, negated_conjecture,
% 114.17/17.08 (( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c3 ) = ( sk_c10 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_64])).
% 114.17/17.08 thf(zip_derived_cl66, plain,
% 114.17/17.08 ((((inverse @ sk_c5) = (sk_c11)) | ((inverse @ sk_c3) = (sk_c10)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_12])).
% 114.17/17.08 thf('8', plain,
% 114.17/17.08 ((((inverse @ sk_c3) = (sk_c10))) | (((inverse @ sk_c5) = (sk_c11)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl66])).
% 114.17/17.08 thf(prove_this_8, conjecture,
% 114.17/17.08 (~( ( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c1 @ sk_c12 ) = ( sk_c11 ) ) ))).
% 114.17/17.08 thf(zf_stmt_13, negated_conjecture,
% 114.17/17.08 (( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c1 @ sk_c12 ) = ( sk_c11 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_8])).
% 114.17/17.08 thf(zip_derived_cl10, plain,
% 114.17/17.08 ((((inverse @ sk_c8) = (sk_c7))
% 114.17/17.08 | ((multiply @ sk_c1 @ sk_c12) = (sk_c11)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_13])).
% 114.17/17.08 thf(zip_derived_cl88, plain,
% 114.17/17.08 ((((inverse @ sk_c8) = (sk_c7))) <= ((((inverse @ sk_c8) = (sk_c7))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl10])).
% 114.17/17.08 thf(zip_derived_cl216, plain,
% 114.17/17.08 ((![X6 : $i]:
% 114.17/17.08 (((inverse @ X6) != (sk_c10))
% 114.17/17.08 | ((multiply @ X6 @ sk_c10) != (sk_c12))))
% 114.17/17.08 <= ((![X6 : $i]:
% 114.17/17.08 (((inverse @ X6) != (sk_c10))
% 114.17/17.08 | ((multiply @ X6 @ sk_c10) != (sk_c12)))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl73])).
% 114.17/17.08 thf(zip_derived_cl234, plain,
% 114.17/17.08 (((((sk_c7) != (sk_c10)) | ((multiply @ sk_c8 @ sk_c10) != (sk_c12))))
% 114.17/17.08 <= ((((inverse @ sk_c8) = (sk_c7))) &
% 114.17/17.08 (![X6 : $i]:
% 114.17/17.08 (((inverse @ X6) != (sk_c10))
% 114.17/17.08 | ((multiply @ X6 @ sk_c10) != (sk_c12)))))),
% 114.17/17.08 inference('s_sup-', [status(thm)], [zip_derived_cl88, zip_derived_cl216])).
% 114.17/17.08 thf('9', plain,
% 114.17/17.08 (~
% 114.17/17.08 (![X6 : $i]:
% 114.17/17.08 (((inverse @ X6) != (sk_c10))
% 114.17/17.08 | ((multiply @ X6 @ sk_c10) != (sk_c12)))) |
% 114.17/17.08 ~ (((sk_c7) = (sk_c10))) |
% 114.17/17.08 ~ (((multiply @ sk_c8 @ sk_c10) = (sk_c12))) |
% 114.17/17.08 ~ (((inverse @ sk_c8) = (sk_c7)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl234])).
% 114.17/17.08 thf(prove_this_4, conjecture,
% 114.17/17.08 (~( ( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c1 @ sk_c12 ) = ( sk_c11 ) ) ))).
% 114.17/17.08 thf(zf_stmt_14, negated_conjecture,
% 114.17/17.08 (( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c1 @ sk_c12 ) = ( sk_c11 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_4])).
% 114.17/17.08 thf(zip_derived_cl6, plain,
% 114.17/17.08 ((((inverse @ sk_c5) = (sk_c11))
% 114.17/17.08 | ((multiply @ sk_c1 @ sk_c12) = (sk_c11)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_14])).
% 114.17/17.08 thf(zip_derived_cl80, plain,
% 114.17/17.08 ((((inverse @ sk_c5) = (sk_c11))) <= ((((inverse @ sk_c5) = (sk_c11))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl6])).
% 114.17/17.08 thf(zip_derived_cl1, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_inverse])).
% 114.17/17.08 thf(zip_derived_cl243, plain,
% 114.17/17.08 ((((multiply @ sk_c11 @ sk_c5) = (identity)))
% 114.17/17.08 <= ((((inverse @ sk_c5) = (sk_c11))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl80, zip_derived_cl1])).
% 114.17/17.08 thf(zip_derived_cl2, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 114.17/17.08 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 114.17/17.08 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 114.17/17.08 inference('cnf', [status(esa)], [associativity])).
% 114.17/17.08 thf(zip_derived_cl613, plain,
% 114.17/17.08 ((![X0 : $i]:
% 114.17/17.08 ((multiply @ identity @ X0)
% 114.17/17.08 = (multiply @ sk_c11 @ (multiply @ sk_c5 @ X0))))
% 114.17/17.08 <= ((((inverse @ sk_c5) = (sk_c11))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl243, zip_derived_cl2])).
% 114.17/17.08 thf(zip_derived_cl0, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_identity])).
% 114.17/17.08 thf(zip_derived_cl614, plain,
% 114.17/17.08 ((![X0 : $i]: ((X0) = (multiply @ sk_c11 @ (multiply @ sk_c5 @ X0))))
% 114.17/17.08 <= ((((inverse @ sk_c5) = (sk_c11))))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl613, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl263, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i]:
% 114.17/17.08 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl685, plain,
% 114.17/17.08 ((![X0 : $i]:
% 114.17/17.08 ((multiply @ sk_c5 @ X0) = (multiply @ (inverse @ sk_c11) @ X0)))
% 114.17/17.08 <= ((((inverse @ sk_c5) = (sk_c11))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl614, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl1, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_inverse])).
% 114.17/17.08 thf(zip_derived_cl1171, plain,
% 114.17/17.08 ((((multiply @ sk_c5 @ sk_c11) = (identity)))
% 114.17/17.08 <= ((((inverse @ sk_c5) = (sk_c11))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl685, zip_derived_cl1])).
% 114.17/17.08 thf(zip_derived_cl78, plain,
% 114.17/17.08 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10)))
% 114.17/17.08 <= ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl5])).
% 114.17/17.08 thf(zip_derived_cl1256, plain,
% 114.17/17.08 ((((identity) = (sk_c10)))
% 114.17/17.08 <= ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.08 (((inverse @ sk_c5) = (sk_c11))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl1171, zip_derived_cl78])).
% 114.17/17.08 thf(zip_derived_cl154, plain,
% 114.17/17.08 ((((multiply @ sk_c10 @ sk_c12) = (sk_c11)))
% 114.17/17.08 <= ((((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl43])).
% 114.17/17.08 thf(zip_derived_cl1810, plain,
% 114.17/17.08 ((((multiply @ identity @ sk_c12) = (sk_c11)))
% 114.17/17.08 <= ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.08 (((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.08 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.08 inference('s_sup+', [status(thm)],
% 114.17/17.08 [zip_derived_cl1256, zip_derived_cl154])).
% 114.17/17.08 thf(zip_derived_cl0, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_identity])).
% 114.17/17.08 thf(zip_derived_cl1850, plain,
% 114.17/17.08 ((((sk_c12) = (sk_c11)))
% 114.17/17.08 <= ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.08 (((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.08 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl1810, zip_derived_cl0])).
% 114.17/17.08 thf(prove_this_2, conjecture,
% 114.17/17.08 (~( ( ( inverse @ sk_c4 ) = ( sk_c12 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c1 @ sk_c12 ) = ( sk_c11 ) ) ))).
% 114.17/17.08 thf(zf_stmt_15, negated_conjecture,
% 114.17/17.08 (( ( inverse @ sk_c4 ) = ( sk_c12 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c1 @ sk_c12 ) = ( sk_c11 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_2])).
% 114.17/17.08 thf(zip_derived_cl4, plain,
% 114.17/17.08 ((((inverse @ sk_c4) = (sk_c12))
% 114.17/17.08 | ((multiply @ sk_c1 @ sk_c12) = (sk_c11)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_15])).
% 114.17/17.08 thf(zip_derived_cl76, plain,
% 114.17/17.08 ((((inverse @ sk_c4) = (sk_c12))) <= ((((inverse @ sk_c4) = (sk_c12))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl4])).
% 114.17/17.08 thf(zip_derived_cl1, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_inverse])).
% 114.17/17.08 thf(zip_derived_cl242, plain,
% 114.17/17.08 ((((multiply @ sk_c12 @ sk_c4) = (identity)))
% 114.17/17.08 <= ((((inverse @ sk_c4) = (sk_c12))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl76, zip_derived_cl1])).
% 114.17/17.08 thf(zip_derived_cl2, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 114.17/17.08 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 114.17/17.08 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 114.17/17.08 inference('cnf', [status(esa)], [associativity])).
% 114.17/17.08 thf(zip_derived_cl607, plain,
% 114.17/17.08 ((![X0 : $i]:
% 114.17/17.08 ((multiply @ identity @ X0)
% 114.17/17.08 = (multiply @ sk_c12 @ (multiply @ sk_c4 @ X0))))
% 114.17/17.08 <= ((((inverse @ sk_c4) = (sk_c12))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl242, zip_derived_cl2])).
% 114.17/17.08 thf(zip_derived_cl0, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_identity])).
% 114.17/17.08 thf(zip_derived_cl608, plain,
% 114.17/17.08 ((![X0 : $i]: ((X0) = (multiply @ sk_c12 @ (multiply @ sk_c4 @ X0))))
% 114.17/17.08 <= ((((inverse @ sk_c4) = (sk_c12))))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl607, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl263, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i]:
% 114.17/17.08 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl682, plain,
% 114.17/17.08 ((![X0 : $i]:
% 114.17/17.08 ((multiply @ sk_c4 @ X0) = (multiply @ (inverse @ sk_c12) @ X0)))
% 114.17/17.08 <= ((((inverse @ sk_c4) = (sk_c12))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl608, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl1, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_inverse])).
% 114.17/17.08 thf(zip_derived_cl1103, plain,
% 114.17/17.08 ((((multiply @ sk_c4 @ sk_c12) = (identity)))
% 114.17/17.08 <= ((((inverse @ sk_c4) = (sk_c12))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl682, zip_derived_cl1])).
% 114.17/17.08 thf(prove_this_1, conjecture,
% 114.17/17.08 (~( ( ( multiply @ sk_c4 @ sk_c12 ) = ( sk_c11 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c1 @ sk_c12 ) = ( sk_c11 ) ) ))).
% 114.17/17.08 thf(zf_stmt_16, negated_conjecture,
% 114.17/17.08 (( ( multiply @ sk_c4 @ sk_c12 ) = ( sk_c11 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c1 @ sk_c12 ) = ( sk_c11 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_1])).
% 114.17/17.08 thf(zip_derived_cl3, plain,
% 114.17/17.08 ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))
% 114.17/17.08 | ((multiply @ sk_c1 @ sk_c12) = (sk_c11)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_16])).
% 114.17/17.08 thf(zip_derived_cl75, plain,
% 114.17/17.08 ((((multiply @ sk_c4 @ sk_c12) = (sk_c11)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl3])).
% 114.17/17.08 thf(zip_derived_cl1116, plain,
% 114.17/17.08 ((((identity) = (sk_c11)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl1103, zip_derived_cl75])).
% 114.17/17.08 thf(zip_derived_cl1959, plain,
% 114.17/17.08 ((((identity) = (sk_c12)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.08 (((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.08 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.08 inference('s_sup+', [status(thm)],
% 114.17/17.08 [zip_derived_cl1850, zip_derived_cl1116])).
% 114.17/17.08 thf(zip_derived_cl242, plain,
% 114.17/17.08 ((((multiply @ sk_c12 @ sk_c4) = (identity)))
% 114.17/17.08 <= ((((inverse @ sk_c4) = (sk_c12))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl76, zip_derived_cl1])).
% 114.17/17.08 thf(zip_derived_cl263, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i]:
% 114.17/17.08 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl684, plain,
% 114.17/17.08 ((((sk_c4) = (multiply @ (inverse @ sk_c12) @ identity)))
% 114.17/17.08 <= ((((inverse @ sk_c4) = (sk_c12))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl242, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl2166, plain,
% 114.17/17.08 ((((sk_c4) = (multiply @ (inverse @ identity) @ identity)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.08 (((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.08 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.08 inference('s_sup+', [status(thm)],
% 114.17/17.08 [zip_derived_cl1959, zip_derived_cl684])).
% 114.17/17.08 thf(zip_derived_cl1, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_inverse])).
% 114.17/17.08 thf(zip_derived_cl2231, plain,
% 114.17/17.08 ((((sk_c4) = (identity)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.08 (((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.08 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl2166, zip_derived_cl1])).
% 114.17/17.08 thf(zip_derived_cl1256, plain,
% 114.17/17.08 ((((identity) = (sk_c10)))
% 114.17/17.08 <= ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.08 (((inverse @ sk_c5) = (sk_c11))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl1171, zip_derived_cl78])).
% 114.17/17.08 thf(prove_this_6, conjecture,
% 114.17/17.08 (~( ( ( inverse @ sk_c6 ) = ( sk_c9 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c1 @ sk_c12 ) = ( sk_c11 ) ) ))).
% 114.17/17.08 thf(zf_stmt_17, negated_conjecture,
% 114.17/17.08 (( ( inverse @ sk_c6 ) = ( sk_c9 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c1 @ sk_c12 ) = ( sk_c11 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_6])).
% 114.17/17.08 thf(zip_derived_cl8, plain,
% 114.17/17.08 ((((inverse @ sk_c6) = (sk_c9))
% 114.17/17.08 | ((multiply @ sk_c1 @ sk_c12) = (sk_c11)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_17])).
% 114.17/17.08 thf(zip_derived_cl84, plain,
% 114.17/17.08 ((((inverse @ sk_c6) = (sk_c9))) <= ((((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl8])).
% 114.17/17.08 thf(zip_derived_cl1, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_inverse])).
% 114.17/17.08 thf(zip_derived_cl244, plain,
% 114.17/17.08 ((((multiply @ sk_c9 @ sk_c6) = (identity)))
% 114.17/17.08 <= ((((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl84, zip_derived_cl1])).
% 114.17/17.08 thf(zip_derived_cl263, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i]:
% 114.17/17.08 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl694, plain,
% 114.17/17.08 ((((sk_c6) = (multiply @ (inverse @ sk_c9) @ identity)))
% 114.17/17.08 <= ((((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl244, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl2, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 114.17/17.08 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 114.17/17.08 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 114.17/17.08 inference('cnf', [status(esa)], [associativity])).
% 114.17/17.08 thf(zip_derived_cl886, plain,
% 114.17/17.08 ((![X0 : $i]:
% 114.17/17.08 ((multiply @ sk_c6 @ X0)
% 114.17/17.08 = (multiply @ (inverse @ sk_c9) @ (multiply @ identity @ X0))))
% 114.17/17.08 <= ((((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl694, zip_derived_cl2])).
% 114.17/17.08 thf(zip_derived_cl0, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_identity])).
% 114.17/17.08 thf(zip_derived_cl890, plain,
% 114.17/17.08 ((![X0 : $i]:
% 114.17/17.08 ((multiply @ sk_c6 @ X0) = (multiply @ (inverse @ sk_c9) @ X0)))
% 114.17/17.08 <= ((((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl886, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl1, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_inverse])).
% 114.17/17.08 thf(zip_derived_cl1726, plain,
% 114.17/17.08 ((((multiply @ sk_c6 @ sk_c9) = (identity)))
% 114.17/17.08 <= ((((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl890, zip_derived_cl1])).
% 114.17/17.08 thf(zip_derived_cl244, plain,
% 114.17/17.08 ((((multiply @ sk_c9 @ sk_c6) = (identity)))
% 114.17/17.08 <= ((((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl84, zip_derived_cl1])).
% 114.17/17.08 thf(zip_derived_cl2, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 114.17/17.08 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 114.17/17.08 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 114.17/17.08 inference('cnf', [status(esa)], [associativity])).
% 114.17/17.08 thf(zip_derived_cl616, plain,
% 114.17/17.08 ((![X0 : $i]:
% 114.17/17.08 ((multiply @ identity @ X0)
% 114.17/17.08 = (multiply @ sk_c9 @ (multiply @ sk_c6 @ X0))))
% 114.17/17.08 <= ((((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl244, zip_derived_cl2])).
% 114.17/17.08 thf(zip_derived_cl0, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_identity])).
% 114.17/17.08 thf(zip_derived_cl617, plain,
% 114.17/17.08 ((![X0 : $i]: ((X0) = (multiply @ sk_c9 @ (multiply @ sk_c6 @ X0))))
% 114.17/17.08 <= ((((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl616, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl1759, plain,
% 114.17/17.08 ((((sk_c9) = (multiply @ sk_c9 @ identity)))
% 114.17/17.08 <= ((((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)],
% 114.17/17.08 [zip_derived_cl1726, zip_derived_cl617])).
% 114.17/17.08 thf(zip_derived_cl1116, plain,
% 114.17/17.08 ((((identity) = (sk_c11)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl1103, zip_derived_cl75])).
% 114.17/17.08 thf(prove_this_7, conjecture,
% 114.17/17.08 (~( ( ( multiply @ sk_c9 @ sk_c11 ) = ( sk_c12 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c1 @ sk_c12 ) = ( sk_c11 ) ) ))).
% 114.17/17.08 thf(zf_stmt_18, negated_conjecture,
% 114.17/17.08 (( ( multiply @ sk_c9 @ sk_c11 ) = ( sk_c12 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c1 @ sk_c12 ) = ( sk_c11 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_7])).
% 114.17/17.08 thf(zip_derived_cl9, plain,
% 114.17/17.08 ((((multiply @ sk_c9 @ sk_c11) = (sk_c12))
% 114.17/17.08 | ((multiply @ sk_c1 @ sk_c12) = (sk_c11)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_18])).
% 114.17/17.08 thf(zip_derived_cl86, plain,
% 114.17/17.08 ((((multiply @ sk_c9 @ sk_c11) = (sk_c12)))
% 114.17/17.08 <= ((((multiply @ sk_c9 @ sk_c11) = (sk_c12))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl9])).
% 114.17/17.08 thf(zip_derived_cl1179, plain,
% 114.17/17.08 ((((multiply @ sk_c9 @ identity) = (sk_c12)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c9 @ sk_c11) = (sk_c12))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl1116, zip_derived_cl86])).
% 114.17/17.08 thf(zip_derived_cl20914, plain,
% 114.17/17.08 ((((sk_c9) = (sk_c12)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c6) = (sk_c9))) &
% 114.17/17.08 (((multiply @ sk_c9 @ sk_c11) = (sk_c12))))),
% 114.17/17.08 inference('s_sup+', [status(thm)],
% 114.17/17.08 [zip_derived_cl1759, zip_derived_cl1179])).
% 114.17/17.08 thf(zip_derived_cl694, plain,
% 114.17/17.08 ((((sk_c6) = (multiply @ (inverse @ sk_c9) @ identity)))
% 114.17/17.08 <= ((((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl244, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl263, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i]:
% 114.17/17.08 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl887, plain,
% 114.17/17.08 ((((identity) = (multiply @ (inverse @ (inverse @ sk_c9)) @ sk_c6)))
% 114.17/17.08 <= ((((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl694, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl263, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i]:
% 114.17/17.08 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl4068, plain,
% 114.17/17.08 ((((sk_c6)
% 114.17/17.08 = (multiply @ (inverse @ (inverse @ (inverse @ sk_c9))) @ identity)))
% 114.17/17.08 <= ((((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl887, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl1, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_inverse])).
% 114.17/17.08 thf(zip_derived_cl263, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i]:
% 114.17/17.08 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl679, plain,
% 114.17/17.08 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl6609, plain,
% 114.17/17.08 ((((inverse @ sk_c9) = (sk_c6))) <= ((((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)],
% 114.17/17.08 [zip_derived_cl4068, zip_derived_cl679])).
% 114.17/17.08 thf(zip_derived_cl22071, plain,
% 114.17/17.08 ((((inverse @ sk_c12) = (sk_c6)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c6) = (sk_c9))) &
% 114.17/17.08 (((multiply @ sk_c9 @ sk_c11) = (sk_c12))))),
% 114.17/17.08 inference('s_sup+', [status(thm)],
% 114.17/17.08 [zip_derived_cl20914, zip_derived_cl6609])).
% 114.17/17.08 thf(zip_derived_cl684, plain,
% 114.17/17.08 ((((sk_c4) = (multiply @ (inverse @ sk_c12) @ identity)))
% 114.17/17.08 <= ((((inverse @ sk_c4) = (sk_c12))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl242, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl263, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i]:
% 114.17/17.08 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl721, plain,
% 114.17/17.08 ((((identity) = (multiply @ (inverse @ (inverse @ sk_c12)) @ sk_c4)))
% 114.17/17.08 <= ((((inverse @ sk_c4) = (sk_c12))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl684, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl263, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i]:
% 114.17/17.08 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl3245, plain,
% 114.17/17.08 ((((sk_c4)
% 114.17/17.08 = (multiply @ (inverse @ (inverse @ (inverse @ sk_c12))) @ identity)))
% 114.17/17.08 <= ((((inverse @ sk_c4) = (sk_c12))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl721, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl679, plain,
% 114.17/17.08 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl5250, plain,
% 114.17/17.08 ((((inverse @ sk_c12) = (sk_c4))) <= ((((inverse @ sk_c4) = (sk_c12))))),
% 114.17/17.08 inference('s_sup+', [status(thm)],
% 114.17/17.08 [zip_derived_cl3245, zip_derived_cl679])).
% 114.17/17.08 thf(zip_derived_cl22234, plain,
% 114.17/17.08 ((((sk_c4) = (sk_c6)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c6) = (sk_c9))) &
% 114.17/17.08 (((multiply @ sk_c9 @ sk_c11) = (sk_c12))))),
% 114.17/17.08 inference('demod', [status(thm)],
% 114.17/17.08 [zip_derived_cl22071, zip_derived_cl5250])).
% 114.17/17.08 thf(prove_this_9, conjecture,
% 114.17/17.08 (~( ( ( inverse @ sk_c7 ) = ( sk_c9 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c1 @ sk_c12 ) = ( sk_c11 ) ) ))).
% 114.17/17.08 thf(zf_stmt_19, negated_conjecture,
% 114.17/17.08 (( ( inverse @ sk_c7 ) = ( sk_c9 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c1 @ sk_c12 ) = ( sk_c11 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_9])).
% 114.17/17.08 thf(zip_derived_cl11, plain,
% 114.17/17.08 ((((inverse @ sk_c7) = (sk_c9))
% 114.17/17.08 | ((multiply @ sk_c1 @ sk_c12) = (sk_c11)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_19])).
% 114.17/17.08 thf(zip_derived_cl90, plain,
% 114.17/17.08 ((((inverse @ sk_c7) = (sk_c9))) <= ((((inverse @ sk_c7) = (sk_c9))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl11])).
% 114.17/17.08 thf(zip_derived_cl1, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_inverse])).
% 114.17/17.08 thf(zip_derived_cl246, plain,
% 114.17/17.08 ((((multiply @ sk_c9 @ sk_c7) = (identity)))
% 114.17/17.08 <= ((((inverse @ sk_c7) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl90, zip_derived_cl1])).
% 114.17/17.08 thf(zip_derived_cl263, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i]:
% 114.17/17.08 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl695, plain,
% 114.17/17.08 ((((sk_c7) = (multiply @ (inverse @ sk_c9) @ identity)))
% 114.17/17.08 <= ((((inverse @ sk_c7) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl246, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl694, plain,
% 114.17/17.08 ((((sk_c6) = (multiply @ (inverse @ sk_c9) @ identity)))
% 114.17/17.08 <= ((((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl244, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl896, plain,
% 114.17/17.08 ((((sk_c6) = (sk_c7)))
% 114.17/17.08 <= ((((inverse @ sk_c6) = (sk_c9))) & (((inverse @ sk_c7) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl695, zip_derived_cl694])).
% 114.17/17.08 thf(zip_derived_cl277, plain,
% 114.17/17.08 ((((sk_c7) != (sk_c10))) <= (~ (((sk_c7) = (sk_c10))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl234])).
% 114.17/17.08 thf(zip_derived_cl951, plain,
% 114.17/17.08 ((((sk_c6) != (sk_c10)))
% 114.17/17.08 <= (~ (((sk_c7) = (sk_c10))) &
% 114.17/17.08 (((inverse @ sk_c6) = (sk_c9))) &
% 114.17/17.08 (((inverse @ sk_c7) = (sk_c9))))),
% 114.17/17.08 inference('s_sup-', [status(thm)], [zip_derived_cl896, zip_derived_cl277])).
% 114.17/17.08 thf(zip_derived_cl31405, plain,
% 114.17/17.08 ((((sk_c4) != (sk_c10)))
% 114.17/17.08 <= (~ (((sk_c7) = (sk_c10))) &
% 114.17/17.08 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c6) = (sk_c9))) &
% 114.17/17.08 (((multiply @ sk_c9 @ sk_c11) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c7) = (sk_c9))))),
% 114.17/17.08 inference('s_sup-', [status(thm)],
% 114.17/17.08 [zip_derived_cl22234, zip_derived_cl951])).
% 114.17/17.08 thf(zip_derived_cl55333, plain,
% 114.17/17.08 ((((sk_c4) != (identity)))
% 114.17/17.08 <= (~ (((sk_c7) = (sk_c10))) &
% 114.17/17.08 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.08 (((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c6) = (sk_c9))) &
% 114.17/17.08 (((multiply @ sk_c9 @ sk_c11) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c7) = (sk_c9))))),
% 114.17/17.08 inference('s_sup-', [status(thm)],
% 114.17/17.08 [zip_derived_cl1256, zip_derived_cl31405])).
% 114.17/17.08 thf(zip_derived_cl60219, plain,
% 114.17/17.08 ((((identity) != (identity)))
% 114.17/17.08 <= (~ (((sk_c7) = (sk_c10))) &
% 114.17/17.08 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.08 (((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c6) = (sk_c9))) &
% 114.17/17.08 (((multiply @ sk_c9 @ sk_c11) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c7) = (sk_c9))) &
% 114.17/17.08 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.08 inference('s_sup-', [status(thm)],
% 114.17/17.08 [zip_derived_cl2231, zip_derived_cl55333])).
% 114.17/17.08 thf('10', plain,
% 114.17/17.08 ((((sk_c7) = (sk_c10))) | ~ (((multiply @ sk_c9 @ sk_c11) = (sk_c12))) |
% 114.17/17.08 ~ (((multiply @ sk_c10 @ sk_c12) = (sk_c11))) |
% 114.17/17.08 ~ (((inverse @ sk_c6) = (sk_c9))) |
% 114.17/17.08 ~ (((inverse @ sk_c5) = (sk_c11))) |
% 114.17/17.08 ~ (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) |
% 114.17/17.08 ~ (((inverse @ sk_c4) = (sk_c12))) |
% 114.17/17.08 ~ (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) |
% 114.17/17.08 ~ (((inverse @ sk_c7) = (sk_c9)))),
% 114.17/17.08 inference('simplify', [status(thm)], [zip_derived_cl60219])).
% 114.17/17.08 thf(zip_derived_cl695, plain,
% 114.17/17.08 ((((sk_c7) = (multiply @ (inverse @ sk_c9) @ identity)))
% 114.17/17.08 <= ((((inverse @ sk_c7) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl246, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl2, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 114.17/17.08 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 114.17/17.08 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 114.17/17.08 inference('cnf', [status(esa)], [associativity])).
% 114.17/17.08 thf(zip_derived_cl893, plain,
% 114.17/17.08 ((![X0 : $i]:
% 114.17/17.08 ((multiply @ sk_c7 @ X0)
% 114.17/17.08 = (multiply @ (inverse @ sk_c9) @ (multiply @ identity @ X0))))
% 114.17/17.08 <= ((((inverse @ sk_c7) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl695, zip_derived_cl2])).
% 114.17/17.08 thf(zip_derived_cl0, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_identity])).
% 114.17/17.08 thf(zip_derived_cl898, plain,
% 114.17/17.08 ((![X0 : $i]:
% 114.17/17.08 ((multiply @ sk_c7 @ X0) = (multiply @ (inverse @ sk_c9) @ X0)))
% 114.17/17.08 <= ((((inverse @ sk_c7) = (sk_c9))))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl893, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl1, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_inverse])).
% 114.17/17.08 thf(zip_derived_cl1890, plain,
% 114.17/17.08 ((((multiply @ sk_c7 @ sk_c9) = (identity)))
% 114.17/17.08 <= ((((inverse @ sk_c7) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl898, zip_derived_cl1])).
% 114.17/17.08 thf(zip_derived_cl246, plain,
% 114.17/17.08 ((((multiply @ sk_c9 @ sk_c7) = (identity)))
% 114.17/17.08 <= ((((inverse @ sk_c7) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl90, zip_derived_cl1])).
% 114.17/17.08 thf(zip_derived_cl2, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 114.17/17.08 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 114.17/17.08 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 114.17/17.08 inference('cnf', [status(esa)], [associativity])).
% 114.17/17.08 thf(zip_derived_cl622, plain,
% 114.17/17.08 ((![X0 : $i]:
% 114.17/17.08 ((multiply @ identity @ X0)
% 114.17/17.08 = (multiply @ sk_c9 @ (multiply @ sk_c7 @ X0))))
% 114.17/17.08 <= ((((inverse @ sk_c7) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl246, zip_derived_cl2])).
% 114.17/17.08 thf(zip_derived_cl0, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_identity])).
% 114.17/17.08 thf(zip_derived_cl623, plain,
% 114.17/17.08 ((![X0 : $i]: ((X0) = (multiply @ sk_c9 @ (multiply @ sk_c7 @ X0))))
% 114.17/17.08 <= ((((inverse @ sk_c7) = (sk_c9))))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl622, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl1905, plain,
% 114.17/17.08 ((((sk_c9) = (multiply @ sk_c9 @ identity)))
% 114.17/17.08 <= ((((inverse @ sk_c7) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)],
% 114.17/17.08 [zip_derived_cl1890, zip_derived_cl623])).
% 114.17/17.08 thf(zip_derived_cl1179, plain,
% 114.17/17.08 ((((multiply @ sk_c9 @ identity) = (sk_c12)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c9 @ sk_c11) = (sk_c12))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl1116, zip_derived_cl86])).
% 114.17/17.08 thf(zip_derived_cl20915, plain,
% 114.17/17.08 ((((sk_c9) = (sk_c12)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c9 @ sk_c11) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c7) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)],
% 114.17/17.08 [zip_derived_cl1905, zip_derived_cl1179])).
% 114.17/17.08 thf(zip_derived_cl1959, plain,
% 114.17/17.08 ((((identity) = (sk_c12)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.08 (((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.08 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.08 inference('s_sup+', [status(thm)],
% 114.17/17.08 [zip_derived_cl1850, zip_derived_cl1116])).
% 114.17/17.08 thf(prove_this_5, conjecture,
% 114.17/17.08 (~( ( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c12 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c1 @ sk_c12 ) = ( sk_c11 ) ) ))).
% 114.17/17.08 thf(zf_stmt_20, negated_conjecture,
% 114.17/17.08 (( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c12 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c1 @ sk_c12 ) = ( sk_c11 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_5])).
% 114.17/17.08 thf(zip_derived_cl7, plain,
% 114.17/17.08 ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))
% 114.17/17.08 | ((multiply @ sk_c1 @ sk_c12) = (sk_c11)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_20])).
% 114.17/17.08 thf(zip_derived_cl82, plain,
% 114.17/17.08 ((((multiply @ sk_c6 @ sk_c9) = (sk_c12)))
% 114.17/17.08 <= ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl7])).
% 114.17/17.08 thf(zip_derived_cl263, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i]:
% 114.17/17.08 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl692, plain,
% 114.17/17.08 ((((sk_c9) = (multiply @ (inverse @ sk_c6) @ sk_c12)))
% 114.17/17.08 <= ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl82, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl2167, plain,
% 114.17/17.08 ((((sk_c9) = (multiply @ (inverse @ sk_c6) @ identity)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.08 (((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.08 (((multiply @ sk_c6 @ sk_c9) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.08 inference('s_sup+', [status(thm)],
% 114.17/17.08 [zip_derived_cl1959, zip_derived_cl692])).
% 114.17/17.08 thf(zip_derived_cl617, plain,
% 114.17/17.08 ((![X0 : $i]: ((X0) = (multiply @ sk_c9 @ (multiply @ sk_c6 @ X0))))
% 114.17/17.08 <= ((((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl616, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl2, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 114.17/17.08 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 114.17/17.08 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 114.17/17.08 inference('cnf', [status(esa)], [associativity])).
% 114.17/17.08 thf(zip_derived_cl263, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i]:
% 114.17/17.08 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl677, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 114.17/17.08 ((X0)
% 114.17/17.08 = (multiply @ (inverse @ (multiply @ X2 @ X1)) @
% 114.17/17.08 (multiply @ X2 @ (multiply @ X1 @ X0))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl2703, plain,
% 114.17/17.08 ((![X0 : $i, X1 : $i]:
% 114.17/17.08 ((multiply @ sk_c6 @ X0)
% 114.17/17.08 = (multiply @ (inverse @ (multiply @ X1 @ sk_c9)) @
% 114.17/17.08 (multiply @ X1 @ X0))))
% 114.17/17.08 <= ((((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl617, zip_derived_cl677])).
% 114.17/17.08 thf(zip_derived_cl92280, plain,
% 114.17/17.08 ((((multiply @ sk_c6 @ identity)
% 114.17/17.08 = (multiply @ (inverse @ (multiply @ (inverse @ sk_c6) @ sk_c9)) @
% 114.17/17.08 sk_c9)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.08 (((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.08 (((multiply @ sk_c6 @ sk_c9) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c6) = (sk_c9))) &
% 114.17/17.08 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.08 inference('s_sup+', [status(thm)],
% 114.17/17.08 [zip_derived_cl2167, zip_derived_cl2703])).
% 114.17/17.08 thf(zip_derived_cl890, plain,
% 114.17/17.08 ((![X0 : $i]:
% 114.17/17.08 ((multiply @ sk_c6 @ X0) = (multiply @ (inverse @ sk_c9) @ X0)))
% 114.17/17.08 <= ((((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl886, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl694, plain,
% 114.17/17.08 ((((sk_c6) = (multiply @ (inverse @ sk_c9) @ identity)))
% 114.17/17.08 <= ((((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl244, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl1728, plain,
% 114.17/17.08 ((((sk_c6) = (multiply @ sk_c6 @ identity)))
% 114.17/17.08 <= ((((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl890, zip_derived_cl694])).
% 114.17/17.08 thf(zip_derived_cl84, plain,
% 114.17/17.08 ((((inverse @ sk_c6) = (sk_c9))) <= ((((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl8])).
% 114.17/17.08 thf(zip_derived_cl92477, plain,
% 114.17/17.08 ((((sk_c6) = (multiply @ (inverse @ (multiply @ sk_c9 @ sk_c9)) @ sk_c9)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.08 (((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.08 (((multiply @ sk_c6 @ sk_c9) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c6) = (sk_c9))) &
% 114.17/17.08 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.08 inference('demod', [status(thm)],
% 114.17/17.08 [zip_derived_cl92280, zip_derived_cl1728, zip_derived_cl84])).
% 114.17/17.08 thf(prove_this_10, conjecture,
% 114.17/17.08 (~( ( ( multiply @ sk_c8 @ sk_c9 ) = ( sk_c7 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c1 @ sk_c12 ) = ( sk_c11 ) ) ))).
% 114.17/17.08 thf(zf_stmt_21, negated_conjecture,
% 114.17/17.08 (( ( multiply @ sk_c8 @ sk_c9 ) = ( sk_c7 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c1 @ sk_c12 ) = ( sk_c11 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_10])).
% 114.17/17.08 thf(zip_derived_cl12, plain,
% 114.17/17.08 ((((multiply @ sk_c8 @ sk_c9) = (sk_c7))
% 114.17/17.08 | ((multiply @ sk_c1 @ sk_c12) = (sk_c11)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_21])).
% 114.17/17.08 thf(zip_derived_cl92, plain,
% 114.17/17.08 ((((multiply @ sk_c8 @ sk_c9) = (sk_c7)))
% 114.17/17.08 <= ((((multiply @ sk_c8 @ sk_c9) = (sk_c7))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl12])).
% 114.17/17.08 thf(zip_derived_cl263, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i]:
% 114.17/17.08 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl696, plain,
% 114.17/17.08 ((((sk_c9) = (multiply @ (inverse @ sk_c8) @ sk_c7)))
% 114.17/17.08 <= ((((multiply @ sk_c8 @ sk_c9) = (sk_c7))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl92, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl677, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 114.17/17.08 ((X0)
% 114.17/17.08 = (multiply @ (inverse @ (multiply @ X2 @ X1)) @
% 114.17/17.08 (multiply @ X2 @ (multiply @ X1 @ X0))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl2664, plain,
% 114.17/17.08 ((![X0 : $i]:
% 114.17/17.08 ((sk_c7)
% 114.17/17.08 = (multiply @ (inverse @ (multiply @ X0 @ (inverse @ sk_c8))) @
% 114.17/17.08 (multiply @ X0 @ sk_c9))))
% 114.17/17.08 <= ((((multiply @ sk_c8 @ sk_c9) = (sk_c7))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl696, zip_derived_cl677])).
% 114.17/17.08 thf(zip_derived_cl93431, plain,
% 114.17/17.08 ((((sk_c7)
% 114.17/17.08 = (multiply @
% 114.17/17.08 (inverse @
% 114.17/17.08 (multiply @ (inverse @ (multiply @ sk_c9 @ sk_c9)) @
% 114.17/17.08 (inverse @ sk_c8))) @
% 114.17/17.08 sk_c6)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.08 (((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.08 (((multiply @ sk_c6 @ sk_c9) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c6) = (sk_c9))) &
% 114.17/17.08 (((multiply @ sk_c8 @ sk_c9) = (sk_c7))) &
% 114.17/17.08 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.08 inference('s_sup+', [status(thm)],
% 114.17/17.08 [zip_derived_cl92477, zip_derived_cl2664])).
% 114.17/17.08 thf(zip_derived_cl95404, plain,
% 114.17/17.08 ((((sk_c7)
% 114.17/17.08 = (multiply @
% 114.17/17.08 (inverse @
% 114.17/17.08 (multiply @ (inverse @ (multiply @ sk_c12 @ sk_c12)) @
% 114.17/17.08 (inverse @ sk_c8))) @
% 114.17/17.08 sk_c6)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.08 (((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.08 (((multiply @ sk_c6 @ sk_c9) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c6) = (sk_c9))) &
% 114.17/17.08 (((multiply @ sk_c9 @ sk_c11) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c7) = (sk_c9))) &
% 114.17/17.08 (((multiply @ sk_c8 @ sk_c9) = (sk_c7))) &
% 114.17/17.08 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.08 inference('s_sup+', [status(thm)],
% 114.17/17.08 [zip_derived_cl20915, zip_derived_cl93431])).
% 114.17/17.08 thf(zip_derived_cl20915, plain,
% 114.17/17.08 ((((sk_c9) = (sk_c12)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c9 @ sk_c11) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c7) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)],
% 114.17/17.08 [zip_derived_cl1905, zip_derived_cl1179])).
% 114.17/17.08 thf(zip_derived_cl695, plain,
% 114.17/17.08 ((((sk_c7) = (multiply @ (inverse @ sk_c9) @ identity)))
% 114.17/17.08 <= ((((inverse @ sk_c7) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl246, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl263, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i]:
% 114.17/17.08 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl894, plain,
% 114.17/17.08 ((((identity) = (multiply @ (inverse @ (inverse @ sk_c9)) @ sk_c7)))
% 114.17/17.08 <= ((((inverse @ sk_c7) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl695, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl263, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i]:
% 114.17/17.08 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl4096, plain,
% 114.17/17.08 ((((sk_c7)
% 114.17/17.08 = (multiply @ (inverse @ (inverse @ (inverse @ sk_c9))) @ identity)))
% 114.17/17.08 <= ((((inverse @ sk_c7) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl894, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl679, plain,
% 114.17/17.08 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl6967, plain,
% 114.17/17.08 ((((inverse @ sk_c9) = (sk_c7))) <= ((((inverse @ sk_c7) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)],
% 114.17/17.08 [zip_derived_cl4096, zip_derived_cl679])).
% 114.17/17.08 thf(zip_derived_cl24020, plain,
% 114.17/17.08 ((((inverse @ sk_c12) = (sk_c7)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c9 @ sk_c11) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c7) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)],
% 114.17/17.08 [zip_derived_cl20915, zip_derived_cl6967])).
% 114.17/17.08 thf(zip_derived_cl5250, plain,
% 114.17/17.08 ((((inverse @ sk_c12) = (sk_c4))) <= ((((inverse @ sk_c4) = (sk_c12))))),
% 114.17/17.08 inference('s_sup+', [status(thm)],
% 114.17/17.08 [zip_derived_cl3245, zip_derived_cl679])).
% 114.17/17.08 thf(zip_derived_cl24178, plain,
% 114.17/17.08 ((((sk_c4) = (sk_c7)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c9 @ sk_c11) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c7) = (sk_c9))))),
% 114.17/17.08 inference('demod', [status(thm)],
% 114.17/17.08 [zip_derived_cl24020, zip_derived_cl5250])).
% 114.17/17.08 thf(zip_derived_cl2231, plain,
% 114.17/17.08 ((((sk_c4) = (identity)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.08 (((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.08 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl2166, zip_derived_cl1])).
% 114.17/17.08 thf(zip_derived_cl1726, plain,
% 114.17/17.08 ((((multiply @ sk_c6 @ sk_c9) = (identity)))
% 114.17/17.08 <= ((((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl890, zip_derived_cl1])).
% 114.17/17.08 thf(zip_derived_cl82, plain,
% 114.17/17.08 ((((multiply @ sk_c6 @ sk_c9) = (sk_c12)))
% 114.17/17.08 <= ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl7])).
% 114.17/17.08 thf(zip_derived_cl1760, plain,
% 114.17/17.08 ((((identity) = (sk_c12)))
% 114.17/17.08 <= ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl1726, zip_derived_cl82])).
% 114.17/17.08 thf(zip_derived_cl1760, plain,
% 114.17/17.08 ((((identity) = (sk_c12)))
% 114.17/17.08 <= ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl1726, zip_derived_cl82])).
% 114.17/17.08 thf(zip_derived_cl0, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_identity])).
% 114.17/17.08 thf(zip_derived_cl1116, plain,
% 114.17/17.08 ((((identity) = (sk_c11)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl1103, zip_derived_cl75])).
% 114.17/17.08 thf(zip_derived_cl243, plain,
% 114.17/17.08 ((((multiply @ sk_c11 @ sk_c5) = (identity)))
% 114.17/17.08 <= ((((inverse @ sk_c5) = (sk_c11))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl80, zip_derived_cl1])).
% 114.17/17.08 thf(zip_derived_cl263, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i]:
% 114.17/17.08 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl686, plain,
% 114.17/17.08 ((((sk_c5) = (multiply @ (inverse @ sk_c11) @ identity)))
% 114.17/17.08 <= ((((inverse @ sk_c5) = (sk_c11))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl243, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl1213, plain,
% 114.17/17.08 ((((sk_c5) = (multiply @ (inverse @ identity) @ identity)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c5) = (sk_c11))))),
% 114.17/17.08 inference('s_sup+', [status(thm)],
% 114.17/17.08 [zip_derived_cl1116, zip_derived_cl686])).
% 114.17/17.08 thf(zip_derived_cl1, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_inverse])).
% 114.17/17.08 thf(zip_derived_cl1229, plain,
% 114.17/17.08 ((((sk_c5) = (identity)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c5) = (sk_c11))))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl1213, zip_derived_cl1])).
% 114.17/17.08 thf(zip_derived_cl80, plain,
% 114.17/17.08 ((((inverse @ sk_c5) = (sk_c11))) <= ((((inverse @ sk_c5) = (sk_c11))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl6])).
% 114.17/17.08 thf(zip_derived_cl1453, plain,
% 114.17/17.08 ((((inverse @ identity) = (sk_c11)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c5) = (sk_c11))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl1229, zip_derived_cl80])).
% 114.17/17.08 thf(zip_derived_cl1116, plain,
% 114.17/17.08 ((((identity) = (sk_c11)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl1103, zip_derived_cl75])).
% 114.17/17.08 thf(zip_derived_cl1488, plain,
% 114.17/17.08 ((((inverse @ identity) = (identity)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c5) = (sk_c11))))),
% 114.17/17.08 inference('demod', [status(thm)],
% 114.17/17.08 [zip_derived_cl1453, zip_derived_cl1116])).
% 114.17/17.08 thf(zip_derived_cl0, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_identity])).
% 114.17/17.08 thf(zip_derived_cl22234, plain,
% 114.17/17.08 ((((sk_c4) = (sk_c6)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c6) = (sk_c9))) &
% 114.17/17.08 (((multiply @ sk_c9 @ sk_c11) = (sk_c12))))),
% 114.17/17.08 inference('demod', [status(thm)],
% 114.17/17.08 [zip_derived_cl22071, zip_derived_cl5250])).
% 114.17/17.08 thf(zip_derived_cl2231, plain,
% 114.17/17.08 ((((sk_c4) = (identity)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.08 (((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.08 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl2166, zip_derived_cl1])).
% 114.17/17.08 thf(zip_derived_cl679, plain,
% 114.17/17.08 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl95411, plain,
% 114.17/17.08 ((((identity) = (sk_c8)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.08 (((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.08 (((multiply @ sk_c6 @ sk_c9) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c6) = (sk_c9))) &
% 114.17/17.08 (((multiply @ sk_c9 @ sk_c11) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c7) = (sk_c9))) &
% 114.17/17.08 (((multiply @ sk_c8 @ sk_c9) = (sk_c7))) &
% 114.17/17.08 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.08 inference('demod', [status(thm)],
% 114.17/17.08 [zip_derived_cl95404, zip_derived_cl24178, zip_derived_cl2231,
% 114.17/17.08 zip_derived_cl1760, zip_derived_cl1760, zip_derived_cl0,
% 114.17/17.08 zip_derived_cl1488, zip_derived_cl0, zip_derived_cl22234,
% 114.17/17.08 zip_derived_cl2231, zip_derived_cl679])).
% 114.17/17.08 thf(zip_derived_cl276, plain,
% 114.17/17.08 ((((multiply @ sk_c8 @ sk_c10) != (sk_c12)))
% 114.17/17.08 <= (~ (((multiply @ sk_c8 @ sk_c10) = (sk_c12))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl234])).
% 114.17/17.08 thf(zip_derived_cl95450, plain,
% 114.17/17.08 ((((multiply @ identity @ sk_c10) != (sk_c12)))
% 114.17/17.08 <= (~ (((multiply @ sk_c8 @ sk_c10) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.08 (((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.08 (((multiply @ sk_c6 @ sk_c9) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c6) = (sk_c9))) &
% 114.17/17.08 (((multiply @ sk_c9 @ sk_c11) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c7) = (sk_c9))) &
% 114.17/17.08 (((multiply @ sk_c8 @ sk_c9) = (sk_c7))) &
% 114.17/17.08 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.08 inference('s_sup-', [status(thm)],
% 114.17/17.08 [zip_derived_cl95411, zip_derived_cl276])).
% 114.17/17.08 thf(zip_derived_cl1116, plain,
% 114.17/17.08 ((((identity) = (sk_c11)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl1103, zip_derived_cl75])).
% 114.17/17.08 thf(zip_derived_cl78, plain,
% 114.17/17.08 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10)))
% 114.17/17.08 <= ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl5])).
% 114.17/17.08 thf(zip_derived_cl263, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i]:
% 114.17/17.08 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl689, plain,
% 114.17/17.08 ((((sk_c11) = (multiply @ (inverse @ sk_c5) @ sk_c10)))
% 114.17/17.08 <= ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl78, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl263, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i]:
% 114.17/17.08 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.17/17.08 thf(zip_derived_cl780, plain,
% 114.17/17.08 ((((sk_c10) = (multiply @ (inverse @ (inverse @ sk_c5)) @ sk_c11)))
% 114.17/17.08 <= ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl689, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl3901, plain,
% 114.17/17.08 ((((sk_c10) = (multiply @ (inverse @ (inverse @ sk_c5)) @ identity)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))))),
% 114.17/17.08 inference('s_sup+', [status(thm)],
% 114.17/17.08 [zip_derived_cl1116, zip_derived_cl780])).
% 114.17/17.08 thf(zip_derived_cl679, plain,
% 114.17/17.08 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl263])).
% 114.17/17.08 thf(zip_derived_cl3906, plain,
% 114.17/17.08 ((((sk_c10) = (sk_c5)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl3901, zip_derived_cl679])).
% 114.17/17.08 thf(zip_derived_cl3906, plain,
% 114.17/17.08 ((((sk_c10) = (sk_c5)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl3901, zip_derived_cl679])).
% 114.17/17.08 thf(zip_derived_cl242, plain,
% 114.17/17.08 ((((multiply @ sk_c12 @ sk_c4) = (identity)))
% 114.17/17.08 <= ((((inverse @ sk_c4) = (sk_c12))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl76, zip_derived_cl1])).
% 114.17/17.08 thf(zip_derived_cl154, plain,
% 114.17/17.08 ((((multiply @ sk_c10 @ sk_c12) = (sk_c11)))
% 114.17/17.08 <= ((((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl43])).
% 114.17/17.08 thf(zip_derived_cl2, plain,
% 114.17/17.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 114.17/17.08 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 114.17/17.08 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 114.17/17.08 inference('cnf', [status(esa)], [associativity])).
% 114.17/17.08 thf(zip_derived_cl529, plain,
% 114.17/17.08 ((![X0 : $i]:
% 114.17/17.08 ((multiply @ sk_c11 @ X0)
% 114.17/17.08 = (multiply @ sk_c10 @ (multiply @ sk_c12 @ X0))))
% 114.17/17.08 <= ((((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl154, zip_derived_cl2])).
% 114.17/17.08 thf(zip_derived_cl1523, plain,
% 114.17/17.08 ((((multiply @ sk_c11 @ sk_c4) = (multiply @ sk_c10 @ identity)))
% 114.17/17.08 <= ((((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl242, zip_derived_cl529])).
% 114.17/17.08 thf(zip_derived_cl34015, plain,
% 114.17/17.08 ((((multiply @ sk_c11 @ sk_c4) = (multiply @ sk_c5 @ identity)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.08 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.08 inference('s_sup+', [status(thm)],
% 114.17/17.08 [zip_derived_cl3906, zip_derived_cl1523])).
% 114.17/17.08 thf(zip_derived_cl1116, plain,
% 114.17/17.08 ((((identity) = (sk_c11)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl1103, zip_derived_cl75])).
% 114.17/17.08 thf(zip_derived_cl0, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_identity])).
% 114.17/17.08 thf(zip_derived_cl1116, plain,
% 114.17/17.08 ((((identity) = (sk_c11)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl1103, zip_derived_cl75])).
% 114.17/17.08 thf(zip_derived_cl78, plain,
% 114.17/17.08 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10)))
% 114.17/17.08 <= ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl5])).
% 114.17/17.08 thf(zip_derived_cl1178, plain,
% 114.17/17.08 ((((multiply @ sk_c5 @ identity) = (sk_c10)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl1116, zip_derived_cl78])).
% 114.17/17.08 thf(zip_derived_cl3906, plain,
% 114.17/17.08 ((((sk_c10) = (sk_c5)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl3901, zip_derived_cl679])).
% 114.17/17.08 thf(zip_derived_cl20817, plain,
% 114.17/17.08 ((((multiply @ sk_c5 @ identity) = (sk_c5)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))))),
% 114.17/17.08 inference('demod', [status(thm)],
% 114.17/17.08 [zip_derived_cl1178, zip_derived_cl3906])).
% 114.17/17.08 thf(zip_derived_cl34020, plain,
% 114.17/17.08 ((((sk_c4) = (sk_c5)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.08 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.08 inference('demod', [status(thm)],
% 114.17/17.08 [zip_derived_cl34015, zip_derived_cl1116, zip_derived_cl0,
% 114.17/17.08 zip_derived_cl20817])).
% 114.17/17.08 thf(zip_derived_cl2231, plain,
% 114.17/17.08 ((((sk_c4) = (identity)))
% 114.17/17.08 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.08 (((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.08 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.08 inference('demod', [status(thm)], [zip_derived_cl2166, zip_derived_cl1])).
% 114.17/17.08 thf(zip_derived_cl0, plain,
% 114.17/17.08 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 114.17/17.08 inference('cnf', [status(esa)], [left_identity])).
% 114.17/17.08 thf(zip_derived_cl1760, plain,
% 114.17/17.08 ((((identity) = (sk_c12)))
% 114.17/17.08 <= ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl1726, zip_derived_cl82])).
% 114.17/17.08 thf(zip_derived_cl95604, plain,
% 114.17/17.08 ((((identity) != (identity)))
% 114.17/17.08 <= (~ (((multiply @ sk_c8 @ sk_c10) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.08 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.08 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.08 (((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.08 (((multiply @ sk_c6 @ sk_c9) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c6) = (sk_c9))) &
% 114.17/17.08 (((multiply @ sk_c9 @ sk_c11) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c7) = (sk_c9))) &
% 114.17/17.08 (((multiply @ sk_c8 @ sk_c9) = (sk_c7))) &
% 114.17/17.08 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.08 inference('demod', [status(thm)],
% 114.17/17.08 [zip_derived_cl95450, zip_derived_cl3906, zip_derived_cl34020,
% 114.17/17.08 zip_derived_cl2231, zip_derived_cl0, zip_derived_cl1760])).
% 114.17/17.08 thf('11', plain,
% 114.17/17.08 ((((multiply @ sk_c8 @ sk_c10) = (sk_c12))) |
% 114.17/17.08 ~ (((multiply @ sk_c8 @ sk_c9) = (sk_c7))) |
% 114.17/17.08 ~ (((multiply @ sk_c10 @ sk_c12) = (sk_c11))) |
% 114.17/17.08 ~ (((multiply @ sk_c9 @ sk_c11) = (sk_c12))) |
% 114.17/17.08 ~ (((inverse @ sk_c6) = (sk_c9))) |
% 114.17/17.08 ~ (((multiply @ sk_c6 @ sk_c9) = (sk_c12))) |
% 114.17/17.08 ~ (((inverse @ sk_c5) = (sk_c11))) |
% 114.17/17.08 ~ (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) |
% 114.17/17.08 ~ (((inverse @ sk_c4) = (sk_c12))) |
% 114.17/17.08 ~ (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) |
% 114.17/17.08 ~ (((inverse @ sk_c7) = (sk_c9)))),
% 114.17/17.08 inference('simplify', [status(thm)], [zip_derived_cl95604])).
% 114.17/17.08 thf('12', plain,
% 114.17/17.08 ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) |
% 114.17/17.08 (((inverse @ sk_c3) = (sk_c10)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl63])).
% 114.17/17.08 thf(prove_this_62, conjecture,
% 114.17/17.08 (~( ( ( inverse @ sk_c4 ) = ( sk_c12 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c3 ) = ( sk_c10 ) ) ))).
% 114.17/17.08 thf(zf_stmt_22, negated_conjecture,
% 114.17/17.08 (( ( inverse @ sk_c4 ) = ( sk_c12 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c3 ) = ( sk_c10 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_62])).
% 114.17/17.08 thf(zip_derived_cl64, plain,
% 114.17/17.08 ((((inverse @ sk_c4) = (sk_c12)) | ((inverse @ sk_c3) = (sk_c10)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_22])).
% 114.17/17.08 thf('13', plain,
% 114.17/17.08 ((((inverse @ sk_c4) = (sk_c12))) | (((inverse @ sk_c3) = (sk_c10)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl64])).
% 114.17/17.08 thf(prove_this_63, conjecture,
% 114.17/17.08 (~( ( ( multiply @ sk_c5 @ sk_c11 ) = ( sk_c10 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c3 ) = ( sk_c10 ) ) ))).
% 114.17/17.08 thf(zf_stmt_23, negated_conjecture,
% 114.17/17.08 (( ( multiply @ sk_c5 @ sk_c11 ) = ( sk_c10 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c3 ) = ( sk_c10 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_63])).
% 114.17/17.08 thf(zip_derived_cl65, plain,
% 114.17/17.08 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))
% 114.17/17.08 | ((inverse @ sk_c3) = (sk_c10)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_23])).
% 114.17/17.08 thf('14', plain,
% 114.17/17.08 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))) |
% 114.17/17.08 (((inverse @ sk_c3) = (sk_c10)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl65])).
% 114.17/17.08 thf(prove_this_67, conjecture,
% 114.17/17.08 (~( ( ( multiply @ sk_c9 @ sk_c11 ) = ( sk_c12 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c3 ) = ( sk_c10 ) ) ))).
% 114.17/17.08 thf(zf_stmt_24, negated_conjecture,
% 114.17/17.08 (( ( multiply @ sk_c9 @ sk_c11 ) = ( sk_c12 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c3 ) = ( sk_c10 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_67])).
% 114.17/17.08 thf(zip_derived_cl69, plain,
% 114.17/17.08 ((((multiply @ sk_c9 @ sk_c11) = (sk_c12))
% 114.17/17.08 | ((inverse @ sk_c3) = (sk_c10)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_24])).
% 114.17/17.08 thf('15', plain,
% 114.17/17.08 ((((multiply @ sk_c9 @ sk_c11) = (sk_c12))) |
% 114.17/17.08 (((inverse @ sk_c3) = (sk_c10)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl69])).
% 114.17/17.08 thf(prove_this_68, conjecture,
% 114.17/17.08 (~( ( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c3 ) = ( sk_c10 ) ) ))).
% 114.17/17.08 thf(zf_stmt_25, negated_conjecture,
% 114.17/17.08 (( ( inverse @ sk_c8 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c3 ) = ( sk_c10 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_68])).
% 114.17/17.08 thf(zip_derived_cl70, plain,
% 114.17/17.08 ((((inverse @ sk_c8) = (sk_c7)) | ((inverse @ sk_c3) = (sk_c10)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_25])).
% 114.17/17.08 thf('16', plain,
% 114.17/17.08 ((((inverse @ sk_c8) = (sk_c7))) | (((inverse @ sk_c3) = (sk_c10)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl70])).
% 114.17/17.08 thf(prove_this_69, conjecture,
% 114.17/17.08 (~( ( ( inverse @ sk_c7 ) = ( sk_c9 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c3 ) = ( sk_c10 ) ) ))).
% 114.17/17.08 thf(zf_stmt_26, negated_conjecture,
% 114.17/17.08 (( ( inverse @ sk_c7 ) = ( sk_c9 ) ) | ( ( inverse @ sk_c3 ) = ( sk_c10 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_69])).
% 114.17/17.08 thf(zip_derived_cl71, plain,
% 114.17/17.08 ((((inverse @ sk_c7) = (sk_c9)) | ((inverse @ sk_c3) = (sk_c10)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_26])).
% 114.17/17.08 thf('17', plain,
% 114.17/17.08 ((((inverse @ sk_c7) = (sk_c9))) | (((inverse @ sk_c3) = (sk_c10)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl71])).
% 114.17/17.08 thf(prove_this_70, conjecture,
% 114.17/17.08 (~( ( ( multiply @ sk_c8 @ sk_c9 ) = ( sk_c7 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c3 ) = ( sk_c10 ) ) ))).
% 114.17/17.08 thf(zf_stmt_27, negated_conjecture,
% 114.17/17.08 (( ( multiply @ sk_c8 @ sk_c9 ) = ( sk_c7 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c3 ) = ( sk_c10 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_70])).
% 114.17/17.08 thf(zip_derived_cl72, plain,
% 114.17/17.08 ((((multiply @ sk_c8 @ sk_c9) = (sk_c7)) | ((inverse @ sk_c3) = (sk_c10)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_27])).
% 114.17/17.08 thf('18', plain,
% 114.17/17.08 ((((multiply @ sk_c8 @ sk_c9) = (sk_c7))) |
% 114.17/17.08 (((inverse @ sk_c3) = (sk_c10)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl72])).
% 114.17/17.08 thf(zip_derived_cl1760, plain,
% 114.17/17.08 ((((identity) = (sk_c12)))
% 114.17/17.08 <= ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl1726, zip_derived_cl82])).
% 114.17/17.08 thf(zip_derived_cl1595, plain,
% 114.17/17.08 ((((multiply @ sk_c3 @ sk_c10) = (identity)))
% 114.17/17.08 <= ((((inverse @ sk_c3) = (sk_c10))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl799, zip_derived_cl1])).
% 114.17/17.08 thf(zip_derived_cl194, plain,
% 114.17/17.08 ((((inverse @ sk_c3) = (sk_c10))) <= ((((inverse @ sk_c3) = (sk_c10))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl63])).
% 114.17/17.08 thf(zip_derived_cl216, plain,
% 114.17/17.08 ((![X6 : $i]:
% 114.17/17.08 (((inverse @ X6) != (sk_c10))
% 114.17/17.08 | ((multiply @ X6 @ sk_c10) != (sk_c12))))
% 114.17/17.08 <= ((![X6 : $i]:
% 114.17/17.08 (((inverse @ X6) != (sk_c10))
% 114.17/17.08 | ((multiply @ X6 @ sk_c10) != (sk_c12)))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl73])).
% 114.17/17.08 thf(zip_derived_cl392, plain,
% 114.17/17.08 (((((sk_c10) != (sk_c10)) | ((multiply @ sk_c3 @ sk_c10) != (sk_c12))))
% 114.17/17.08 <= ((((inverse @ sk_c3) = (sk_c10))) &
% 114.17/17.08 (![X6 : $i]:
% 114.17/17.08 (((inverse @ X6) != (sk_c10))
% 114.17/17.08 | ((multiply @ X6 @ sk_c10) != (sk_c12)))))),
% 114.17/17.08 inference('s_sup-', [status(thm)], [zip_derived_cl194, zip_derived_cl216])).
% 114.17/17.08 thf(zip_derived_cl395, plain,
% 114.17/17.08 ((((multiply @ sk_c3 @ sk_c10) != (sk_c12)))
% 114.17/17.08 <= ((((inverse @ sk_c3) = (sk_c10))) &
% 114.17/17.08 (![X6 : $i]:
% 114.17/17.08 (((inverse @ X6) != (sk_c10))
% 114.17/17.08 | ((multiply @ X6 @ sk_c10) != (sk_c12)))))),
% 114.17/17.08 inference('simplify', [status(thm)], [zip_derived_cl392])).
% 114.17/17.08 thf(zip_derived_cl1628, plain,
% 114.17/17.08 ((((identity) != (sk_c12)))
% 114.17/17.08 <= ((((inverse @ sk_c3) = (sk_c10))) &
% 114.17/17.08 (![X6 : $i]:
% 114.17/17.08 (((inverse @ X6) != (sk_c10))
% 114.17/17.08 | ((multiply @ X6 @ sk_c10) != (sk_c12)))))),
% 114.17/17.08 inference('s_sup-', [status(thm)],
% 114.17/17.08 [zip_derived_cl1595, zip_derived_cl395])).
% 114.17/17.08 thf(zip_derived_cl42743, plain,
% 114.17/17.08 ((((identity) != (identity)))
% 114.17/17.08 <= ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c6) = (sk_c9))) &
% 114.17/17.08 (((inverse @ sk_c3) = (sk_c10))) &
% 114.17/17.08 (![X6 : $i]:
% 114.17/17.08 (((inverse @ X6) != (sk_c10))
% 114.17/17.08 | ((multiply @ X6 @ sk_c10) != (sk_c12)))))),
% 114.17/17.08 inference('s_sup-', [status(thm)],
% 114.17/17.08 [zip_derived_cl1760, zip_derived_cl1628])).
% 114.17/17.08 thf('19', plain,
% 114.17/17.08 (~
% 114.17/17.08 (![X6 : $i]:
% 114.17/17.08 (((inverse @ X6) != (sk_c10))
% 114.17/17.08 | ((multiply @ X6 @ sk_c10) != (sk_c12)))) |
% 114.17/17.08 ~ (((multiply @ sk_c6 @ sk_c9) = (sk_c12))) |
% 114.17/17.08 ~ (((inverse @ sk_c6) = (sk_c9))) | ~ (((inverse @ sk_c3) = (sk_c10)))),
% 114.17/17.08 inference('simplify', [status(thm)], [zip_derived_cl42743])).
% 114.17/17.08 thf(prove_this_53, conjecture,
% 114.17/17.08 (~( ( ( multiply @ sk_c5 @ sk_c11 ) = ( sk_c10 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c12 ) ) ))).
% 114.17/17.08 thf(zf_stmt_28, negated_conjecture,
% 114.17/17.08 (( ( multiply @ sk_c5 @ sk_c11 ) = ( sk_c10 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c12 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_53])).
% 114.17/17.08 thf(zip_derived_cl55, plain,
% 114.17/17.08 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))
% 114.17/17.08 | ((multiply @ sk_c3 @ sk_c10) = (sk_c12)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_28])).
% 114.17/17.08 thf('20', plain,
% 114.17/17.08 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))) |
% 114.17/17.08 (((multiply @ sk_c3 @ sk_c10) = (sk_c12)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl55])).
% 114.17/17.08 thf(prove_this_57, conjecture,
% 114.17/17.08 (~( ( ( multiply @ sk_c9 @ sk_c11 ) = ( sk_c12 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c12 ) ) ))).
% 114.17/17.08 thf(zf_stmt_29, negated_conjecture,
% 114.17/17.08 (( ( multiply @ sk_c9 @ sk_c11 ) = ( sk_c12 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c12 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_57])).
% 114.17/17.08 thf(zip_derived_cl59, plain,
% 114.17/17.08 ((((multiply @ sk_c9 @ sk_c11) = (sk_c12))
% 114.17/17.08 | ((multiply @ sk_c3 @ sk_c10) = (sk_c12)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_29])).
% 114.17/17.08 thf('21', plain,
% 114.17/17.08 ((((multiply @ sk_c9 @ sk_c11) = (sk_c12))) |
% 114.17/17.08 (((multiply @ sk_c3 @ sk_c10) = (sk_c12)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl59])).
% 114.17/17.08 thf(prove_this_58, conjecture,
% 114.17/17.08 (~( ( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c12 ) ) ))).
% 114.17/17.08 thf(zf_stmt_30, negated_conjecture,
% 114.17/17.08 (( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c12 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_58])).
% 114.17/17.08 thf(zip_derived_cl60, plain,
% 114.17/17.08 ((((inverse @ sk_c8) = (sk_c7))
% 114.17/17.08 | ((multiply @ sk_c3 @ sk_c10) = (sk_c12)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_30])).
% 114.17/17.08 thf('22', plain,
% 114.17/17.08 ((((inverse @ sk_c8) = (sk_c7))) |
% 114.17/17.08 (((multiply @ sk_c3 @ sk_c10) = (sk_c12)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl60])).
% 114.17/17.08 thf(prove_this_59, conjecture,
% 114.17/17.08 (~( ( ( inverse @ sk_c7 ) = ( sk_c9 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c12 ) ) ))).
% 114.17/17.08 thf(zf_stmt_31, negated_conjecture,
% 114.17/17.08 (( ( inverse @ sk_c7 ) = ( sk_c9 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c12 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_59])).
% 114.17/17.08 thf(zip_derived_cl61, plain,
% 114.17/17.08 ((((inverse @ sk_c7) = (sk_c9))
% 114.17/17.08 | ((multiply @ sk_c3 @ sk_c10) = (sk_c12)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_31])).
% 114.17/17.08 thf('23', plain,
% 114.17/17.08 ((((inverse @ sk_c7) = (sk_c9))) |
% 114.17/17.08 (((multiply @ sk_c3 @ sk_c10) = (sk_c12)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl61])).
% 114.17/17.08 thf(prove_this_60, conjecture,
% 114.17/17.08 (~( ( ( multiply @ sk_c8 @ sk_c9 ) = ( sk_c7 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c12 ) ) ))).
% 114.17/17.08 thf(zf_stmt_32, negated_conjecture,
% 114.17/17.08 (( ( multiply @ sk_c8 @ sk_c9 ) = ( sk_c7 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c12 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_60])).
% 114.17/17.08 thf(zip_derived_cl62, plain,
% 114.17/17.08 ((((multiply @ sk_c8 @ sk_c9) = (sk_c7))
% 114.17/17.08 | ((multiply @ sk_c3 @ sk_c10) = (sk_c12)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_32])).
% 114.17/17.08 thf('24', plain,
% 114.17/17.08 ((((multiply @ sk_c8 @ sk_c9) = (sk_c7))) |
% 114.17/17.08 (((multiply @ sk_c3 @ sk_c10) = (sk_c12)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl62])).
% 114.17/17.08 thf(zip_derived_cl78, plain,
% 114.17/17.08 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10)))
% 114.17/17.08 <= ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl5])).
% 114.17/17.08 thf(zip_derived_cl80, plain,
% 114.17/17.08 ((((inverse @ sk_c5) = (sk_c11))) <= ((((inverse @ sk_c5) = (sk_c11))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl6])).
% 114.17/17.08 thf(zip_derived_cl215, plain,
% 114.17/17.08 ((![X7 : $i]:
% 114.17/17.08 (((inverse @ X7) != (sk_c11))
% 114.17/17.08 | ((multiply @ X7 @ sk_c11) != (sk_c10))))
% 114.17/17.08 <= ((![X7 : $i]:
% 114.17/17.08 (((inverse @ X7) != (sk_c11))
% 114.17/17.08 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl73])).
% 114.17/17.08 thf(zip_derived_cl227, plain,
% 114.17/17.08 (((((sk_c11) != (sk_c11)) | ((multiply @ sk_c5 @ sk_c11) != (sk_c10))))
% 114.17/17.08 <= ((((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.08 (![X7 : $i]:
% 114.17/17.08 (((inverse @ X7) != (sk_c11))
% 114.17/17.08 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 114.17/17.08 inference('s_sup-', [status(thm)], [zip_derived_cl80, zip_derived_cl215])).
% 114.17/17.08 thf(zip_derived_cl230, plain,
% 114.17/17.08 ((((multiply @ sk_c5 @ sk_c11) != (sk_c10)))
% 114.17/17.08 <= ((((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.08 (![X7 : $i]:
% 114.17/17.08 (((inverse @ X7) != (sk_c11))
% 114.17/17.08 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 114.17/17.08 inference('simplify', [status(thm)], [zip_derived_cl227])).
% 114.17/17.08 thf(zip_derived_cl312, plain,
% 114.17/17.08 ((((sk_c10) != (sk_c10)))
% 114.17/17.08 <= ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.08 (((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.08 (![X7 : $i]:
% 114.17/17.08 (((inverse @ X7) != (sk_c11))
% 114.17/17.08 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 114.17/17.08 inference('s_sup-', [status(thm)], [zip_derived_cl78, zip_derived_cl230])).
% 114.17/17.08 thf('25', plain,
% 114.17/17.08 (~
% 114.17/17.08 (![X7 : $i]:
% 114.17/17.08 (((inverse @ X7) != (sk_c11))
% 114.17/17.08 | ((multiply @ X7 @ sk_c11) != (sk_c10)))) |
% 114.17/17.08 ~ (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) |
% 114.17/17.08 ~ (((inverse @ sk_c5) = (sk_c11)))),
% 114.17/17.08 inference('simplify', [status(thm)], [zip_derived_cl312])).
% 114.17/17.08 thf(zip_derived_cl92, plain,
% 114.17/17.08 ((((multiply @ sk_c8 @ sk_c9) = (sk_c7)))
% 114.17/17.08 <= ((((multiply @ sk_c8 @ sk_c9) = (sk_c7))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl12])).
% 114.17/17.08 thf(zip_derived_cl219, plain,
% 114.17/17.08 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.17/17.08 (((inverse @ X0) != (X2))
% 114.17/17.08 | ((multiply @ X1 @ X2) != (X0))
% 114.17/17.08 | ((inverse @ X1) != (X0))
% 114.17/17.08 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.17/17.08 | ((inverse @ X3) != (X2))
% 114.17/17.08 | ((multiply @ X3 @ X2) != (sk_c12))))
% 114.17/17.08 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.17/17.08 (((inverse @ X0) != (X2))
% 114.17/17.08 | ((multiply @ X1 @ X2) != (X0))
% 114.17/17.08 | ((inverse @ X1) != (X0))
% 114.17/17.08 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.17/17.08 | ((inverse @ X3) != (X2))
% 114.17/17.08 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl73])).
% 114.17/17.08 thf(zip_derived_cl296, plain,
% 114.17/17.08 ((![X0 : $i, X1 : $i, X2 : $i]:
% 114.17/17.08 (((multiply @ X1 @ X0) != (sk_c12))
% 114.17/17.08 | ((inverse @ X1) != (X0))
% 114.17/17.08 | ((multiply @ X0 @ sk_c11) != (sk_c12))
% 114.17/17.08 | ((inverse @ X2) != (multiply @ X2 @ X0))
% 114.17/17.08 | ((inverse @ (multiply @ X2 @ X0)) != (X0))))
% 114.17/17.08 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.17/17.08 (((inverse @ X0) != (X2))
% 114.17/17.08 | ((multiply @ X1 @ X2) != (X0))
% 114.17/17.08 | ((inverse @ X1) != (X0))
% 114.17/17.08 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.17/17.08 | ((inverse @ X3) != (X2))
% 114.17/17.08 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 114.17/17.08 inference('eq_res', [status(thm)], [zip_derived_cl219])).
% 114.17/17.08 thf(zip_derived_cl1073, plain,
% 114.17/17.08 ((![X0 : $i]:
% 114.17/17.08 (((multiply @ X0 @ sk_c9) != (sk_c12))
% 114.17/17.08 | ((inverse @ X0) != (sk_c9))
% 114.17/17.08 | ((multiply @ sk_c9 @ sk_c11) != (sk_c12))
% 114.17/17.08 | ((inverse @ sk_c8) != (sk_c7))
% 114.17/17.08 | ((inverse @ sk_c7) != (sk_c9))))
% 114.17/17.08 <= ((((multiply @ sk_c8 @ sk_c9) = (sk_c7))) &
% 114.17/17.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.17/17.08 (((inverse @ X0) != (X2))
% 114.17/17.08 | ((multiply @ X1 @ X2) != (X0))
% 114.17/17.08 | ((inverse @ X1) != (X0))
% 114.17/17.08 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.17/17.08 | ((inverse @ X3) != (X2))
% 114.17/17.08 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 114.17/17.08 inference('s_sup-', [status(thm)], [zip_derived_cl92, zip_derived_cl296])).
% 114.17/17.08 thf('26', plain,
% 114.17/17.08 (~
% 114.17/17.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.17/17.08 (((inverse @ X0) != (X2))
% 114.17/17.08 | ((multiply @ X1 @ X2) != (X0))
% 114.17/17.08 | ((inverse @ X1) != (X0))
% 114.17/17.08 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.17/17.08 | ((inverse @ X3) != (X2))
% 114.17/17.08 | ((multiply @ X3 @ X2) != (sk_c12)))) |
% 114.17/17.08 ~ (((inverse @ sk_c8) = (sk_c7))) | ~ (((inverse @ sk_c7) = (sk_c9))) |
% 114.17/17.08 ~ (((multiply @ sk_c8 @ sk_c9) = (sk_c7))) |
% 114.17/17.08 ~ (((multiply @ sk_c9 @ sk_c11) = (sk_c12))) |
% 114.17/17.08 (![X1 : $i]:
% 114.17/17.08 (((inverse @ X1) != (sk_c9)) | ((multiply @ X1 @ sk_c9) != (sk_c12))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl1073])).
% 114.17/17.08 thf('27', plain,
% 114.17/17.08 ((((multiply @ sk_c1 @ sk_c12) = (sk_c11))) |
% 114.17/17.08 (((inverse @ sk_c6) = (sk_c9)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl8])).
% 114.17/17.08 thf(prove_this_26, conjecture,
% 114.17/17.08 (~( ( ( inverse @ sk_c6 ) = ( sk_c9 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c2 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 114.17/17.08 thf(zf_stmt_33, negated_conjecture,
% 114.17/17.08 (( ( inverse @ sk_c6 ) = ( sk_c9 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c2 @ sk_c11 ) = ( sk_c10 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_26])).
% 114.17/17.08 thf(zip_derived_cl28, plain,
% 114.17/17.08 ((((inverse @ sk_c6) = (sk_c9))
% 114.17/17.08 | ((multiply @ sk_c2 @ sk_c11) = (sk_c10)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_33])).
% 114.17/17.08 thf('28', plain,
% 114.17/17.08 ((((multiply @ sk_c2 @ sk_c11) = (sk_c10))) |
% 114.17/17.08 (((inverse @ sk_c6) = (sk_c9)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl28])).
% 114.17/17.08 thf(prove_this_46, conjecture,
% 114.17/17.08 (~( ( ( inverse @ sk_c6 ) = ( sk_c9 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c10 @ sk_c12 ) = ( sk_c11 ) ) ))).
% 114.17/17.08 thf(zf_stmt_34, negated_conjecture,
% 114.17/17.08 (( ( inverse @ sk_c6 ) = ( sk_c9 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c10 @ sk_c12 ) = ( sk_c11 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_46])).
% 114.17/17.08 thf(zip_derived_cl48, plain,
% 114.17/17.08 ((((inverse @ sk_c6) = (sk_c9))
% 114.17/17.08 | ((multiply @ sk_c10 @ sk_c12) = (sk_c11)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_34])).
% 114.17/17.08 thf('29', plain,
% 114.17/17.08 ((((multiply @ sk_c10 @ sk_c12) = (sk_c11))) |
% 114.17/17.08 (((inverse @ sk_c6) = (sk_c9)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl48])).
% 114.17/17.08 thf(prove_this_56, conjecture,
% 114.17/17.08 (~( ( ( inverse @ sk_c6 ) = ( sk_c9 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c12 ) ) ))).
% 114.17/17.08 thf(zf_stmt_35, negated_conjecture,
% 114.17/17.08 (( ( inverse @ sk_c6 ) = ( sk_c9 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c12 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_56])).
% 114.17/17.08 thf(zip_derived_cl58, plain,
% 114.17/17.08 ((((inverse @ sk_c6) = (sk_c9))
% 114.17/17.08 | ((multiply @ sk_c3 @ sk_c10) = (sk_c12)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_35])).
% 114.17/17.08 thf('30', plain,
% 114.17/17.08 ((((multiply @ sk_c3 @ sk_c10) = (sk_c12))) |
% 114.17/17.08 (((inverse @ sk_c6) = (sk_c9)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl58])).
% 114.17/17.08 thf(prove_this_66, conjecture,
% 114.17/17.08 (~( ( ( inverse @ sk_c6 ) = ( sk_c9 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c3 ) = ( sk_c10 ) ) ))).
% 114.17/17.08 thf(zf_stmt_36, negated_conjecture,
% 114.17/17.08 (( ( inverse @ sk_c6 ) = ( sk_c9 ) ) | ( ( inverse @ sk_c3 ) = ( sk_c10 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_66])).
% 114.17/17.08 thf(zip_derived_cl68, plain,
% 114.17/17.08 ((((inverse @ sk_c6) = (sk_c9)) | ((inverse @ sk_c3) = (sk_c10)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_36])).
% 114.17/17.08 thf('31', plain,
% 114.17/17.08 ((((inverse @ sk_c3) = (sk_c10))) | (((inverse @ sk_c6) = (sk_c9)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl68])).
% 114.17/17.08 thf(prove_this_55, conjecture,
% 114.17/17.08 (~( ( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c12 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c12 ) ) ))).
% 114.17/17.08 thf(zf_stmt_37, negated_conjecture,
% 114.17/17.08 (( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c12 ) ) |
% 114.17/17.08 ( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c12 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_55])).
% 114.17/17.08 thf(zip_derived_cl57, plain,
% 114.17/17.08 ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))
% 114.17/17.08 | ((multiply @ sk_c3 @ sk_c10) = (sk_c12)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_37])).
% 114.17/17.08 thf('32', plain,
% 114.17/17.08 ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))) |
% 114.17/17.08 (((multiply @ sk_c3 @ sk_c10) = (sk_c12)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl57])).
% 114.17/17.08 thf(prove_this_65, conjecture,
% 114.17/17.08 (~( ( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c12 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c3 ) = ( sk_c10 ) ) ))).
% 114.17/17.08 thf(zf_stmt_38, negated_conjecture,
% 114.17/17.08 (( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c12 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c3 ) = ( sk_c10 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_65])).
% 114.17/17.08 thf(zip_derived_cl67, plain,
% 114.17/17.08 ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))
% 114.17/17.08 | ((inverse @ sk_c3) = (sk_c10)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_38])).
% 114.17/17.08 thf('33', plain,
% 114.17/17.08 ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))) |
% 114.17/17.08 (((inverse @ sk_c3) = (sk_c10)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl67])).
% 114.17/17.08 thf(zip_derived_cl1627, plain,
% 114.17/17.08 ((((identity) = (sk_c12)))
% 114.17/17.08 <= ((((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c3) = (sk_c10))))),
% 114.17/17.08 inference('s_sup+', [status(thm)],
% 114.17/17.08 [zip_derived_cl1595, zip_derived_cl174])).
% 114.17/17.08 thf(zip_derived_cl1726, plain,
% 114.17/17.08 ((((multiply @ sk_c6 @ sk_c9) = (identity)))
% 114.17/17.08 <= ((((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl890, zip_derived_cl1])).
% 114.17/17.08 thf(zip_derived_cl84, plain,
% 114.17/17.08 ((((inverse @ sk_c6) = (sk_c9))) <= ((((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl8])).
% 114.17/17.08 thf(zip_derived_cl82, plain,
% 114.17/17.08 ((((multiply @ sk_c6 @ sk_c9) = (sk_c12)))
% 114.17/17.08 <= ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl7])).
% 114.17/17.08 thf(zip_derived_cl219, plain,
% 114.17/17.08 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.17/17.08 (((inverse @ X0) != (X2))
% 114.17/17.08 | ((multiply @ X1 @ X2) != (X0))
% 114.17/17.08 | ((inverse @ X1) != (X0))
% 114.17/17.08 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.17/17.08 | ((inverse @ X3) != (X2))
% 114.17/17.08 | ((multiply @ X3 @ X2) != (sk_c12))))
% 114.17/17.08 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.17/17.08 (((inverse @ X0) != (X2))
% 114.17/17.08 | ((multiply @ X1 @ X2) != (X0))
% 114.17/17.08 | ((inverse @ X1) != (X0))
% 114.17/17.08 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.17/17.08 | ((inverse @ X3) != (X2))
% 114.17/17.08 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl73])).
% 114.17/17.08 thf(zip_derived_cl355, plain,
% 114.17/17.08 ((![X0 : $i, X1 : $i]:
% 114.17/17.08 (((inverse @ X0) != (sk_c9))
% 114.17/17.08 | ((sk_c12) != (X0))
% 114.17/17.08 | ((inverse @ sk_c6) != (X0))
% 114.17/17.08 | ((multiply @ sk_c9 @ sk_c11) != (sk_c12))
% 114.17/17.08 | ((inverse @ X1) != (sk_c9))
% 114.17/17.08 | ((multiply @ X1 @ sk_c9) != (sk_c12))))
% 114.17/17.08 <= ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))) &
% 114.17/17.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.17/17.08 (((inverse @ X0) != (X2))
% 114.17/17.08 | ((multiply @ X1 @ X2) != (X0))
% 114.17/17.08 | ((inverse @ X1) != (X0))
% 114.17/17.08 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.17/17.08 | ((inverse @ X3) != (X2))
% 114.17/17.08 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 114.17/17.08 inference('s_sup-', [status(thm)], [zip_derived_cl82, zip_derived_cl219])).
% 114.17/17.08 thf(zip_derived_cl418, plain,
% 114.17/17.08 ((![X1 : $i]:
% 114.17/17.08 (((inverse @ X1) != (sk_c9)) | ((multiply @ X1 @ sk_c9) != (sk_c12))))
% 114.17/17.08 <= ((![X1 : $i]:
% 114.17/17.08 (((inverse @ X1) != (sk_c9))
% 114.17/17.08 | ((multiply @ X1 @ sk_c9) != (sk_c12)))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl355])).
% 114.17/17.08 thf(zip_derived_cl424, plain,
% 114.17/17.08 (((((sk_c9) != (sk_c9)) | ((multiply @ sk_c6 @ sk_c9) != (sk_c12))))
% 114.17/17.08 <= ((((inverse @ sk_c6) = (sk_c9))) &
% 114.17/17.08 (![X1 : $i]:
% 114.17/17.08 (((inverse @ X1) != (sk_c9))
% 114.17/17.08 | ((multiply @ X1 @ sk_c9) != (sk_c12)))))),
% 114.17/17.08 inference('s_sup-', [status(thm)], [zip_derived_cl84, zip_derived_cl418])).
% 114.17/17.08 thf(zip_derived_cl429, plain,
% 114.17/17.08 ((((multiply @ sk_c6 @ sk_c9) != (sk_c12)))
% 114.17/17.08 <= ((((inverse @ sk_c6) = (sk_c9))) &
% 114.17/17.08 (![X1 : $i]:
% 114.17/17.08 (((inverse @ X1) != (sk_c9))
% 114.17/17.08 | ((multiply @ X1 @ sk_c9) != (sk_c12)))))),
% 114.17/17.08 inference('simplify', [status(thm)], [zip_derived_cl424])).
% 114.17/17.08 thf(zip_derived_cl1761, plain,
% 114.17/17.08 ((((identity) != (sk_c12)))
% 114.17/17.08 <= ((((inverse @ sk_c6) = (sk_c9))) &
% 114.17/17.08 (![X1 : $i]:
% 114.17/17.08 (((inverse @ X1) != (sk_c9))
% 114.17/17.08 | ((multiply @ X1 @ sk_c9) != (sk_c12)))))),
% 114.17/17.08 inference('s_sup-', [status(thm)],
% 114.17/17.08 [zip_derived_cl1726, zip_derived_cl429])).
% 114.17/17.08 thf(zip_derived_cl43072, plain,
% 114.17/17.08 ((((identity) != (identity)))
% 114.17/17.08 <= ((((inverse @ sk_c6) = (sk_c9))) &
% 114.17/17.08 (((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c3) = (sk_c10))) &
% 114.17/17.08 (![X1 : $i]:
% 114.17/17.08 (((inverse @ X1) != (sk_c9))
% 114.17/17.08 | ((multiply @ X1 @ sk_c9) != (sk_c12)))))),
% 114.17/17.08 inference('s_sup-', [status(thm)],
% 114.17/17.08 [zip_derived_cl1627, zip_derived_cl1761])).
% 114.17/17.08 thf('34', plain,
% 114.17/17.08 (~
% 114.17/17.08 (![X1 : $i]:
% 114.17/17.08 (((inverse @ X1) != (sk_c9)) | ((multiply @ X1 @ sk_c9) != (sk_c12)))) |
% 114.17/17.08 ~ (((multiply @ sk_c3 @ sk_c10) = (sk_c12))) |
% 114.17/17.08 ~ (((inverse @ sk_c6) = (sk_c9))) | ~ (((inverse @ sk_c3) = (sk_c10)))),
% 114.17/17.08 inference('simplify', [status(thm)], [zip_derived_cl43072])).
% 114.17/17.08 thf(prove_this_35, conjecture,
% 114.17/17.08 (~( ( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c12 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c2 ) = ( sk_c11 ) ) ))).
% 114.17/17.08 thf(zf_stmt_39, negated_conjecture,
% 114.17/17.08 (( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c12 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c2 ) = ( sk_c11 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_35])).
% 114.17/17.08 thf(zip_derived_cl37, plain,
% 114.17/17.08 ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))
% 114.17/17.08 | ((inverse @ sk_c2) = (sk_c11)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_39])).
% 114.17/17.08 thf('35', plain,
% 114.17/17.08 ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))) |
% 114.17/17.08 (((inverse @ sk_c2) = (sk_c11)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl37])).
% 114.17/17.08 thf(prove_this_36, conjecture,
% 114.17/17.08 (~( ( ( inverse @ sk_c6 ) = ( sk_c9 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c2 ) = ( sk_c11 ) ) ))).
% 114.17/17.08 thf(zf_stmt_40, negated_conjecture,
% 114.17/17.08 (( ( inverse @ sk_c6 ) = ( sk_c9 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c11 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_36])).
% 114.17/17.08 thf(zip_derived_cl38, plain,
% 114.17/17.08 ((((inverse @ sk_c6) = (sk_c9)) | ((inverse @ sk_c2) = (sk_c11)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_40])).
% 114.17/17.08 thf('36', plain,
% 114.17/17.08 ((((inverse @ sk_c2) = (sk_c11))) | (((inverse @ sk_c6) = (sk_c9)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl38])).
% 114.17/17.08 thf(zip_derived_cl82, plain,
% 114.17/17.08 ((((multiply @ sk_c6 @ sk_c9) = (sk_c12)))
% 114.17/17.08 <= ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl7])).
% 114.17/17.08 thf(zip_derived_cl429, plain,
% 114.17/17.08 ((((multiply @ sk_c6 @ sk_c9) != (sk_c12)))
% 114.17/17.08 <= ((((inverse @ sk_c6) = (sk_c9))) &
% 114.17/17.08 (![X1 : $i]:
% 114.17/17.08 (((inverse @ X1) != (sk_c9))
% 114.17/17.08 | ((multiply @ X1 @ sk_c9) != (sk_c12)))))),
% 114.17/17.08 inference('simplify', [status(thm)], [zip_derived_cl424])).
% 114.17/17.08 thf(zip_derived_cl431, plain,
% 114.17/17.08 ((((sk_c12) != (sk_c12)))
% 114.17/17.08 <= ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c6) = (sk_c9))) &
% 114.17/17.08 (![X1 : $i]:
% 114.17/17.08 (((inverse @ X1) != (sk_c9))
% 114.17/17.08 | ((multiply @ X1 @ sk_c9) != (sk_c12)))))),
% 114.17/17.08 inference('s_sup-', [status(thm)], [zip_derived_cl82, zip_derived_cl429])).
% 114.17/17.08 thf('37', plain,
% 114.17/17.08 (~
% 114.17/17.08 (![X1 : $i]:
% 114.17/17.08 (((inverse @ X1) != (sk_c9)) | ((multiply @ X1 @ sk_c9) != (sk_c12)))) |
% 114.17/17.08 ~ (((multiply @ sk_c6 @ sk_c9) = (sk_c12))) |
% 114.17/17.08 ~ (((inverse @ sk_c6) = (sk_c9)))),
% 114.17/17.08 inference('simplify', [status(thm)], [zip_derived_cl431])).
% 114.17/17.08 thf(prove_this_33, conjecture,
% 114.17/17.08 (~( ( ( multiply @ sk_c5 @ sk_c11 ) = ( sk_c10 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c2 ) = ( sk_c11 ) ) ))).
% 114.17/17.08 thf(zf_stmt_41, negated_conjecture,
% 114.17/17.08 (( ( multiply @ sk_c5 @ sk_c11 ) = ( sk_c10 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c2 ) = ( sk_c11 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_33])).
% 114.17/17.08 thf(zip_derived_cl35, plain,
% 114.17/17.08 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))
% 114.17/17.08 | ((inverse @ sk_c2) = (sk_c11)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_41])).
% 114.17/17.08 thf('38', plain,
% 114.17/17.08 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))) |
% 114.17/17.08 (((inverse @ sk_c2) = (sk_c11)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl35])).
% 114.17/17.08 thf(prove_this_37, conjecture,
% 114.17/17.08 (~( ( ( multiply @ sk_c9 @ sk_c11 ) = ( sk_c12 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c2 ) = ( sk_c11 ) ) ))).
% 114.17/17.08 thf(zf_stmt_42, negated_conjecture,
% 114.17/17.08 (( ( multiply @ sk_c9 @ sk_c11 ) = ( sk_c12 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c2 ) = ( sk_c11 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_37])).
% 114.17/17.08 thf(zip_derived_cl39, plain,
% 114.17/17.08 ((((multiply @ sk_c9 @ sk_c11) = (sk_c12))
% 114.17/17.08 | ((inverse @ sk_c2) = (sk_c11)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_42])).
% 114.17/17.08 thf('39', plain,
% 114.17/17.08 ((((multiply @ sk_c9 @ sk_c11) = (sk_c12))) |
% 114.17/17.08 (((inverse @ sk_c2) = (sk_c11)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl39])).
% 114.17/17.08 thf(prove_this_38, conjecture,
% 114.17/17.08 (~( ( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c2 ) = ( sk_c11 ) ) ))).
% 114.17/17.08 thf(zf_stmt_43, negated_conjecture,
% 114.17/17.08 (( ( inverse @ sk_c8 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c11 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_38])).
% 114.17/17.08 thf(zip_derived_cl40, plain,
% 114.17/17.08 ((((inverse @ sk_c8) = (sk_c7)) | ((inverse @ sk_c2) = (sk_c11)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_43])).
% 114.17/17.08 thf('40', plain,
% 114.17/17.08 ((((inverse @ sk_c8) = (sk_c7))) | (((inverse @ sk_c2) = (sk_c11)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl40])).
% 114.17/17.08 thf(prove_this_39, conjecture,
% 114.17/17.08 (~( ( ( inverse @ sk_c7 ) = ( sk_c9 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c2 ) = ( sk_c11 ) ) ))).
% 114.17/17.08 thf(zf_stmt_44, negated_conjecture,
% 114.17/17.08 (( ( inverse @ sk_c7 ) = ( sk_c9 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c11 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_39])).
% 114.17/17.08 thf(zip_derived_cl41, plain,
% 114.17/17.08 ((((inverse @ sk_c7) = (sk_c9)) | ((inverse @ sk_c2) = (sk_c11)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_44])).
% 114.17/17.08 thf('41', plain,
% 114.17/17.08 ((((inverse @ sk_c7) = (sk_c9))) | (((inverse @ sk_c2) = (sk_c11)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl41])).
% 114.17/17.08 thf(prove_this_40, conjecture,
% 114.17/17.08 (~( ( ( multiply @ sk_c8 @ sk_c9 ) = ( sk_c7 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c2 ) = ( sk_c11 ) ) ))).
% 114.17/17.08 thf(zf_stmt_45, negated_conjecture,
% 114.17/17.08 (( ( multiply @ sk_c8 @ sk_c9 ) = ( sk_c7 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c2 ) = ( sk_c11 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_40])).
% 114.17/17.08 thf(zip_derived_cl42, plain,
% 114.17/17.08 ((((multiply @ sk_c8 @ sk_c9) = (sk_c7)) | ((inverse @ sk_c2) = (sk_c11)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_45])).
% 114.17/17.08 thf('42', plain,
% 114.17/17.08 ((((multiply @ sk_c8 @ sk_c9) = (sk_c7))) |
% 114.17/17.08 (((inverse @ sk_c2) = (sk_c11)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl42])).
% 114.17/17.08 thf(zip_derived_cl1627, plain,
% 114.17/17.08 ((((identity) = (sk_c12)))
% 114.17/17.08 <= ((((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c3) = (sk_c10))))),
% 114.17/17.08 inference('s_sup+', [status(thm)],
% 114.17/17.08 [zip_derived_cl1595, zip_derived_cl174])).
% 114.17/17.08 thf(zip_derived_cl1171, plain,
% 114.17/17.08 ((((multiply @ sk_c5 @ sk_c11) = (identity)))
% 114.17/17.08 <= ((((inverse @ sk_c5) = (sk_c11))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl685, zip_derived_cl1])).
% 114.17/17.08 thf(zip_derived_cl80, plain,
% 114.17/17.08 ((((inverse @ sk_c5) = (sk_c11))) <= ((((inverse @ sk_c5) = (sk_c11))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl6])).
% 114.17/17.08 thf(zip_derived_cl373, plain,
% 114.17/17.08 ((![X1 : $i]:
% 114.17/17.08 (((inverse @ X1) != (sk_c11))
% 114.17/17.08 | ((multiply @ X1 @ sk_c11) != (sk_c12))))
% 114.17/17.08 <= ((![X1 : $i]:
% 114.17/17.08 (((inverse @ X1) != (sk_c11))
% 114.17/17.08 | ((multiply @ X1 @ sk_c11) != (sk_c12)))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl310])).
% 114.17/17.08 thf(zip_derived_cl378, plain,
% 114.17/17.08 (((((sk_c11) != (sk_c11)) | ((multiply @ sk_c5 @ sk_c11) != (sk_c12))))
% 114.17/17.08 <= ((((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.08 (![X1 : $i]:
% 114.17/17.08 (((inverse @ X1) != (sk_c11))
% 114.17/17.08 | ((multiply @ X1 @ sk_c11) != (sk_c12)))))),
% 114.17/17.08 inference('s_sup-', [status(thm)], [zip_derived_cl80, zip_derived_cl373])).
% 114.17/17.08 thf(zip_derived_cl383, plain,
% 114.17/17.08 ((((multiply @ sk_c5 @ sk_c11) != (sk_c12)))
% 114.17/17.08 <= ((((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.08 (![X1 : $i]:
% 114.17/17.08 (((inverse @ X1) != (sk_c11))
% 114.17/17.08 | ((multiply @ X1 @ sk_c11) != (sk_c12)))))),
% 114.17/17.08 inference('simplify', [status(thm)], [zip_derived_cl378])).
% 114.17/17.08 thf(zip_derived_cl1258, plain,
% 114.17/17.08 ((((identity) != (sk_c12)))
% 114.17/17.08 <= ((((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.08 (![X1 : $i]:
% 114.17/17.08 (((inverse @ X1) != (sk_c11))
% 114.17/17.08 | ((multiply @ X1 @ sk_c11) != (sk_c12)))))),
% 114.17/17.08 inference('s_sup-', [status(thm)],
% 114.17/17.08 [zip_derived_cl1171, zip_derived_cl383])).
% 114.17/17.08 thf(zip_derived_cl38315, plain,
% 114.17/17.08 ((((identity) != (identity)))
% 114.17/17.08 <= ((((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.08 (((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c3) = (sk_c10))) &
% 114.17/17.08 (![X1 : $i]:
% 114.17/17.08 (((inverse @ X1) != (sk_c11))
% 114.17/17.08 | ((multiply @ X1 @ sk_c11) != (sk_c12)))))),
% 114.17/17.08 inference('s_sup-', [status(thm)],
% 114.17/17.08 [zip_derived_cl1627, zip_derived_cl1258])).
% 114.17/17.08 thf('43', plain,
% 114.17/17.08 (~
% 114.17/17.08 (![X1 : $i]:
% 114.17/17.08 (((inverse @ X1) != (sk_c11))
% 114.17/17.08 | ((multiply @ X1 @ sk_c11) != (sk_c12)))) |
% 114.17/17.08 ~ (((inverse @ sk_c5) = (sk_c11))) |
% 114.17/17.08 ~ (((multiply @ sk_c3 @ sk_c10) = (sk_c12))) |
% 114.17/17.08 ~ (((inverse @ sk_c3) = (sk_c10)))),
% 114.17/17.08 inference('simplify', [status(thm)], [zip_derived_cl38315])).
% 114.17/17.08 thf(zip_derived_cl174, plain,
% 114.17/17.08 ((((multiply @ sk_c3 @ sk_c10) = (sk_c12)))
% 114.17/17.08 <= ((((multiply @ sk_c3 @ sk_c10) = (sk_c12))))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl53])).
% 114.17/17.08 thf(zip_derived_cl395, plain,
% 114.17/17.08 ((((multiply @ sk_c3 @ sk_c10) != (sk_c12)))
% 114.17/17.08 <= ((((inverse @ sk_c3) = (sk_c10))) &
% 114.17/17.08 (![X6 : $i]:
% 114.17/17.08 (((inverse @ X6) != (sk_c10))
% 114.17/17.08 | ((multiply @ X6 @ sk_c10) != (sk_c12)))))),
% 114.17/17.08 inference('simplify', [status(thm)], [zip_derived_cl392])).
% 114.17/17.08 thf(zip_derived_cl558, plain,
% 114.17/17.08 ((((sk_c12) != (sk_c12)))
% 114.17/17.08 <= ((((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c3) = (sk_c10))) &
% 114.17/17.08 (![X6 : $i]:
% 114.17/17.08 (((inverse @ X6) != (sk_c10))
% 114.17/17.08 | ((multiply @ X6 @ sk_c10) != (sk_c12)))))),
% 114.17/17.08 inference('s_sup-', [status(thm)], [zip_derived_cl174, zip_derived_cl395])).
% 114.17/17.08 thf('44', plain,
% 114.17/17.08 (~
% 114.17/17.08 (![X6 : $i]:
% 114.17/17.08 (((inverse @ X6) != (sk_c10))
% 114.17/17.08 | ((multiply @ X6 @ sk_c10) != (sk_c12)))) |
% 114.17/17.08 ~ (((multiply @ sk_c3 @ sk_c10) = (sk_c12))) |
% 114.17/17.08 ~ (((inverse @ sk_c3) = (sk_c10)))),
% 114.17/17.08 inference('simplify', [status(thm)], [zip_derived_cl558])).
% 114.17/17.08 thf('45', plain,
% 114.17/17.08 ((((multiply @ sk_c1 @ sk_c12) = (sk_c11))) |
% 114.17/17.08 (((multiply @ sk_c6 @ sk_c9) = (sk_c12)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl7])).
% 114.17/17.08 thf(prove_this_15, conjecture,
% 114.17/17.08 (~( ( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c12 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c1 ) = ( sk_c12 ) ) ))).
% 114.17/17.08 thf(zf_stmt_46, negated_conjecture,
% 114.17/17.08 (( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c12 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c1 ) = ( sk_c12 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_15])).
% 114.17/17.08 thf(zip_derived_cl17, plain,
% 114.17/17.08 ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))
% 114.17/17.08 | ((inverse @ sk_c1) = (sk_c12)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_46])).
% 114.17/17.08 thf('46', plain,
% 114.17/17.08 ((((inverse @ sk_c1) = (sk_c12))) |
% 114.17/17.08 (((multiply @ sk_c6 @ sk_c9) = (sk_c12)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl17])).
% 114.17/17.08 thf(prove_this_13, conjecture,
% 114.17/17.08 (~( ( ( multiply @ sk_c5 @ sk_c11 ) = ( sk_c10 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c1 ) = ( sk_c12 ) ) ))).
% 114.17/17.08 thf(zf_stmt_47, negated_conjecture,
% 114.17/17.08 (( ( multiply @ sk_c5 @ sk_c11 ) = ( sk_c10 ) ) |
% 114.17/17.08 ( ( inverse @ sk_c1 ) = ( sk_c12 ) )),
% 114.17/17.08 inference('cnf.neg', [status(esa)], [prove_this_13])).
% 114.17/17.08 thf(zip_derived_cl15, plain,
% 114.17/17.08 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))
% 114.17/17.08 | ((inverse @ sk_c1) = (sk_c12)))),
% 114.17/17.08 inference('cnf', [status(esa)], [zf_stmt_47])).
% 114.17/17.08 thf('47', plain,
% 114.17/17.08 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))) |
% 114.17/17.08 (((inverse @ sk_c1) = (sk_c12)))),
% 114.17/17.08 inference('split', [status(esa)], [zip_derived_cl15])).
% 114.17/17.08 thf(zip_derived_cl1760, plain,
% 114.17/17.08 ((((identity) = (sk_c12)))
% 114.17/17.08 <= ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))) &
% 114.17/17.08 (((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.08 inference('s_sup+', [status(thm)], [zip_derived_cl1726, zip_derived_cl82])).
% 114.17/17.09 thf(zip_derived_cl1850, plain,
% 114.17/17.09 ((((sk_c12) = (sk_c11)))
% 114.17/17.09 <= ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.09 (((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.09 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.09 inference('demod', [status(thm)], [zip_derived_cl1810, zip_derived_cl0])).
% 114.17/17.09 thf(zip_derived_cl1103, plain,
% 114.17/17.09 ((((multiply @ sk_c4 @ sk_c12) = (identity)))
% 114.17/17.09 <= ((((inverse @ sk_c4) = (sk_c12))))),
% 114.17/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl682, zip_derived_cl1])).
% 114.17/17.09 thf(zip_derived_cl76, plain,
% 114.17/17.09 ((((inverse @ sk_c4) = (sk_c12))) <= ((((inverse @ sk_c4) = (sk_c12))))),
% 114.17/17.09 inference('split', [status(esa)], [zip_derived_cl4])).
% 114.17/17.09 thf(zip_derived_cl214, plain,
% 114.17/17.09 ((![X8 : $i]:
% 114.17/17.09 (((inverse @ X8) != (sk_c12))
% 114.17/17.09 | ((multiply @ X8 @ sk_c12) != (sk_c11))))
% 114.17/17.09 <= ((![X8 : $i]:
% 114.17/17.09 (((inverse @ X8) != (sk_c12))
% 114.17/17.09 | ((multiply @ X8 @ sk_c12) != (sk_c11)))))),
% 114.17/17.09 inference('split', [status(esa)], [zip_derived_cl73])).
% 114.17/17.09 thf(zip_derived_cl221, plain,
% 114.17/17.09 (((((sk_c12) != (sk_c12)) | ((multiply @ sk_c4 @ sk_c12) != (sk_c11))))
% 114.17/17.09 <= ((((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.09 (![X8 : $i]:
% 114.17/17.09 (((inverse @ X8) != (sk_c12))
% 114.17/17.09 | ((multiply @ X8 @ sk_c12) != (sk_c11)))))),
% 114.17/17.09 inference('s_sup-', [status(thm)], [zip_derived_cl76, zip_derived_cl214])).
% 114.17/17.09 thf(zip_derived_cl225, plain,
% 114.17/17.09 ((((multiply @ sk_c4 @ sk_c12) != (sk_c11)))
% 114.17/17.09 <= ((((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.09 (![X8 : $i]:
% 114.17/17.09 (((inverse @ X8) != (sk_c12))
% 114.17/17.09 | ((multiply @ X8 @ sk_c12) != (sk_c11)))))),
% 114.17/17.09 inference('simplify', [status(thm)], [zip_derived_cl221])).
% 114.17/17.09 thf(zip_derived_cl1117, plain,
% 114.17/17.09 ((((identity) != (sk_c11)))
% 114.17/17.09 <= ((((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.09 (![X8 : $i]:
% 114.17/17.09 (((inverse @ X8) != (sk_c12))
% 114.17/17.09 | ((multiply @ X8 @ sk_c12) != (sk_c11)))))),
% 114.17/17.09 inference('s_sup-', [status(thm)],
% 114.17/17.09 [zip_derived_cl1103, zip_derived_cl225])).
% 114.17/17.09 thf(zip_derived_cl1960, plain,
% 114.17/17.09 ((((identity) != (sk_c12)))
% 114.17/17.09 <= ((((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.09 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.09 (((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.09 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))) &
% 114.17/17.09 (![X8 : $i]:
% 114.17/17.09 (((inverse @ X8) != (sk_c12))
% 114.17/17.09 | ((multiply @ X8 @ sk_c12) != (sk_c11)))))),
% 114.17/17.09 inference('s_sup-', [status(thm)],
% 114.17/17.09 [zip_derived_cl1850, zip_derived_cl1117])).
% 114.17/17.09 thf(zip_derived_cl42756, plain,
% 114.17/17.09 ((((identity) != (identity)))
% 114.17/17.09 <= ((((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.09 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.09 (((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.09 (((multiply @ sk_c6 @ sk_c9) = (sk_c12))) &
% 114.17/17.09 (((inverse @ sk_c6) = (sk_c9))) &
% 114.17/17.09 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))) &
% 114.17/17.09 (![X8 : $i]:
% 114.17/17.09 (((inverse @ X8) != (sk_c12))
% 114.17/17.09 | ((multiply @ X8 @ sk_c12) != (sk_c11)))))),
% 114.17/17.09 inference('s_sup-', [status(thm)],
% 114.17/17.09 [zip_derived_cl1760, zip_derived_cl1960])).
% 114.17/17.09 thf('48', plain,
% 114.17/17.09 (~
% 114.17/17.09 (![X8 : $i]:
% 114.17/17.09 (((inverse @ X8) != (sk_c12))
% 114.17/17.09 | ((multiply @ X8 @ sk_c12) != (sk_c11)))) |
% 114.17/17.09 ~ (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) |
% 114.17/17.09 ~ (((inverse @ sk_c6) = (sk_c9))) |
% 114.17/17.09 ~ (((inverse @ sk_c5) = (sk_c11))) |
% 114.17/17.09 ~ (((multiply @ sk_c10 @ sk_c12) = (sk_c11))) |
% 114.17/17.09 ~ (((multiply @ sk_c6 @ sk_c9) = (sk_c12))) |
% 114.17/17.09 ~ (((inverse @ sk_c4) = (sk_c12)))),
% 114.17/17.09 inference('simplify', [status(thm)], [zip_derived_cl42756])).
% 114.17/17.09 thf('49', plain,
% 114.17/17.09 ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) |
% 114.17/17.09 (((multiply @ sk_c1 @ sk_c12) = (sk_c11)))),
% 114.17/17.09 inference('split', [status(esa)], [zip_derived_cl3])).
% 114.17/17.09 thf('50', plain,
% 114.17/17.09 ((((inverse @ sk_c4) = (sk_c12))) |
% 114.17/17.09 (((multiply @ sk_c1 @ sk_c12) = (sk_c11)))),
% 114.17/17.09 inference('split', [status(esa)], [zip_derived_cl4])).
% 114.17/17.09 thf('51', plain,
% 114.17/17.09 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))) |
% 114.17/17.09 (((multiply @ sk_c1 @ sk_c12) = (sk_c11)))),
% 114.17/17.09 inference('split', [status(esa)], [zip_derived_cl5])).
% 114.17/17.09 thf('52', plain,
% 114.17/17.09 ((((multiply @ sk_c1 @ sk_c12) = (sk_c11))) |
% 114.17/17.09 (((inverse @ sk_c5) = (sk_c11)))),
% 114.17/17.09 inference('split', [status(esa)], [zip_derived_cl6])).
% 114.17/17.09 thf(zip_derived_cl1760, plain,
% 114.17/17.09 ((((identity) = (sk_c12)))
% 114.17/17.09 <= ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))) &
% 114.17/17.09 (((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl1726, zip_derived_cl82])).
% 114.17/17.09 thf(zip_derived_cl1116, plain,
% 114.17/17.09 ((((identity) = (sk_c11)))
% 114.17/17.09 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.09 (((inverse @ sk_c4) = (sk_c12))))),
% 114.17/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl1103, zip_derived_cl75])).
% 114.17/17.09 thf(zip_derived_cl1256, plain,
% 114.17/17.09 ((((identity) = (sk_c10)))
% 114.17/17.09 <= ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.09 (((inverse @ sk_c5) = (sk_c11))))),
% 114.17/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl1171, zip_derived_cl78])).
% 114.17/17.09 thf(zip_derived_cl220, plain,
% 114.17/17.09 ((((multiply @ sk_c10 @ sk_c12) != (sk_c11)))
% 114.17/17.09 <= (~ (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.09 inference('split', [status(esa)], [zip_derived_cl73])).
% 114.17/17.09 thf(zip_derived_cl1812, plain,
% 114.17/17.09 ((((multiply @ identity @ sk_c12) != (sk_c11)))
% 114.17/17.09 <= (~ (((multiply @ sk_c10 @ sk_c12) = (sk_c11))) &
% 114.17/17.09 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.09 (((inverse @ sk_c5) = (sk_c11))))),
% 114.17/17.09 inference('s_sup-', [status(thm)],
% 114.17/17.09 [zip_derived_cl1256, zip_derived_cl220])).
% 114.17/17.09 thf(zip_derived_cl0, plain,
% 114.17/17.09 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 114.17/17.09 inference('cnf', [status(esa)], [left_identity])).
% 114.17/17.09 thf(zip_derived_cl1851, plain,
% 114.17/17.09 ((((sk_c12) != (sk_c11)))
% 114.17/17.09 <= (~ (((multiply @ sk_c10 @ sk_c12) = (sk_c11))) &
% 114.17/17.09 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.09 (((inverse @ sk_c5) = (sk_c11))))),
% 114.17/17.09 inference('demod', [status(thm)], [zip_derived_cl1812, zip_derived_cl0])).
% 114.17/17.09 thf(zip_derived_cl2051, plain,
% 114.17/17.09 ((((sk_c12) != (identity)))
% 114.17/17.09 <= (~ (((multiply @ sk_c10 @ sk_c12) = (sk_c11))) &
% 114.17/17.09 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.09 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.09 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.09 (((inverse @ sk_c5) = (sk_c11))))),
% 114.17/17.09 inference('s_sup-', [status(thm)],
% 114.17/17.09 [zip_derived_cl1116, zip_derived_cl1851])).
% 114.17/17.09 thf(zip_derived_cl42760, plain,
% 114.17/17.09 ((((identity) != (identity)))
% 114.17/17.09 <= (~ (((multiply @ sk_c10 @ sk_c12) = (sk_c11))) &
% 114.17/17.09 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.17/17.09 (((inverse @ sk_c4) = (sk_c12))) &
% 114.17/17.09 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 114.17/17.09 (((inverse @ sk_c5) = (sk_c11))) &
% 114.17/17.09 (((multiply @ sk_c6 @ sk_c9) = (sk_c12))) &
% 114.17/17.09 (((inverse @ sk_c6) = (sk_c9))))),
% 114.17/17.09 inference('s_sup-', [status(thm)],
% 114.17/17.09 [zip_derived_cl1760, zip_derived_cl2051])).
% 114.17/17.09 thf('53', plain,
% 114.17/17.09 (~ (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) |
% 114.17/17.09 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))) |
% 114.17/17.09 ~ (((inverse @ sk_c6) = (sk_c9))) |
% 114.17/17.09 ~ (((multiply @ sk_c6 @ sk_c9) = (sk_c12))) |
% 114.17/17.09 ~ (((inverse @ sk_c5) = (sk_c11))) |
% 114.17/17.09 ~ (((inverse @ sk_c4) = (sk_c12))) |
% 114.17/17.09 ~ (((multiply @ sk_c4 @ sk_c12) = (sk_c11)))),
% 114.17/17.09 inference('simplify', [status(thm)], [zip_derived_cl42760])).
% 114.17/17.09 thf(prove_this_16, conjecture,
% 114.17/17.09 (~( ( ( inverse @ sk_c6 ) = ( sk_c9 ) ) |
% 114.17/17.09 ( ( inverse @ sk_c1 ) = ( sk_c12 ) ) ))).
% 114.17/17.09 thf(zf_stmt_48, negated_conjecture,
% 114.17/17.09 (( ( inverse @ sk_c6 ) = ( sk_c9 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c12 ) )),
% 114.17/17.09 inference('cnf.neg', [status(esa)], [prove_this_16])).
% 114.17/17.09 thf(zip_derived_cl18, plain,
% 114.17/17.09 ((((inverse @ sk_c6) = (sk_c9)) | ((inverse @ sk_c1) = (sk_c12)))),
% 114.17/17.09 inference('cnf', [status(esa)], [zf_stmt_48])).
% 114.17/17.09 thf('54', plain,
% 114.17/17.09 ((((inverse @ sk_c1) = (sk_c12))) | (((inverse @ sk_c6) = (sk_c9)))),
% 114.17/17.09 inference('split', [status(esa)], [zip_derived_cl18])).
% 114.17/17.09 thf(zip_derived_cl74, plain,
% 114.17/17.09 ((((multiply @ sk_c1 @ sk_c12) = (sk_c11)))
% 114.17/17.09 <= ((((multiply @ sk_c1 @ sk_c12) = (sk_c11))))),
% 114.17/17.09 inference('split', [status(esa)], [zip_derived_cl3])).
% 114.17/17.09 thf(prove_this_11, conjecture,
% 114.17/17.09 (~( ( ( multiply @ sk_c4 @ sk_c12 ) = ( sk_c11 ) ) |
% 114.17/17.09 ( ( inverse @ sk_c1 ) = ( sk_c12 ) ) ))).
% 114.17/17.09 thf(zf_stmt_49, negated_conjecture,
% 114.17/17.09 (( ( multiply @ sk_c4 @ sk_c12 ) = ( sk_c11 ) ) |
% 114.17/17.09 ( ( inverse @ sk_c1 ) = ( sk_c12 ) )),
% 114.17/17.09 inference('cnf.neg', [status(esa)], [prove_this_11])).
% 114.17/17.09 thf(zip_derived_cl13, plain,
% 114.17/17.09 ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))
% 114.17/17.09 | ((inverse @ sk_c1) = (sk_c12)))),
% 114.17/17.09 inference('cnf', [status(esa)], [zf_stmt_49])).
% 114.17/17.09 thf(zip_derived_cl94, plain,
% 114.17/17.09 ((((inverse @ sk_c1) = (sk_c12))) <= ((((inverse @ sk_c1) = (sk_c12))))),
% 114.17/17.09 inference('split', [status(esa)], [zip_derived_cl13])).
% 114.17/17.09 thf(zip_derived_cl214, plain,
% 114.17/17.09 ((![X8 : $i]:
% 114.17/17.09 (((inverse @ X8) != (sk_c12))
% 114.17/17.09 | ((multiply @ X8 @ sk_c12) != (sk_c11))))
% 114.17/17.09 <= ((![X8 : $i]:
% 114.17/17.09 (((inverse @ X8) != (sk_c12))
% 114.17/17.09 | ((multiply @ X8 @ sk_c12) != (sk_c11)))))),
% 114.17/17.09 inference('split', [status(esa)], [zip_derived_cl73])).
% 114.17/17.09 thf(zip_derived_cl250, plain,
% 114.17/17.09 (((((sk_c12) != (sk_c12)) | ((multiply @ sk_c1 @ sk_c12) != (sk_c11))))
% 114.17/17.09 <= ((((inverse @ sk_c1) = (sk_c12))) &
% 114.17/17.09 (![X8 : $i]:
% 114.17/17.09 (((inverse @ X8) != (sk_c12))
% 114.17/17.09 | ((multiply @ X8 @ sk_c12) != (sk_c11)))))),
% 114.17/17.09 inference('s_sup-', [status(thm)], [zip_derived_cl94, zip_derived_cl214])).
% 114.17/17.09 thf(zip_derived_cl251, plain,
% 114.17/17.09 ((((multiply @ sk_c1 @ sk_c12) != (sk_c11)))
% 114.17/17.09 <= ((((inverse @ sk_c1) = (sk_c12))) &
% 114.17/17.09 (![X8 : $i]:
% 114.17/17.09 (((inverse @ X8) != (sk_c12))
% 114.17/17.09 | ((multiply @ X8 @ sk_c12) != (sk_c11)))))),
% 114.17/17.09 inference('simplify', [status(thm)], [zip_derived_cl250])).
% 114.17/17.09 thf(zip_derived_cl274, plain,
% 114.17/17.09 ((((sk_c11) != (sk_c11)))
% 114.17/17.09 <= ((((multiply @ sk_c1 @ sk_c12) = (sk_c11))) &
% 114.17/17.09 (((inverse @ sk_c1) = (sk_c12))) &
% 114.17/17.09 (![X8 : $i]:
% 114.17/17.09 (((inverse @ X8) != (sk_c12))
% 114.17/17.09 | ((multiply @ X8 @ sk_c12) != (sk_c11)))))),
% 114.17/17.09 inference('s_sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl251])).
% 114.17/17.09 thf('55', plain,
% 114.17/17.09 (~
% 114.17/17.09 (![X8 : $i]:
% 114.17/17.09 (((inverse @ X8) != (sk_c12))
% 114.17/17.09 | ((multiply @ X8 @ sk_c12) != (sk_c11)))) |
% 114.17/17.09 ~ (((inverse @ sk_c1) = (sk_c12))) |
% 114.17/17.09 ~ (((multiply @ sk_c1 @ sk_c12) = (sk_c11)))),
% 114.17/17.09 inference('simplify', [status(thm)], [zip_derived_cl274])).
% 114.17/17.09 thf(zip_derived_cl1442, plain,
% 114.17/17.09 ((((multiply @ sk_c2 @ sk_c11) = (identity)))
% 114.17/17.09 <= ((((inverse @ sk_c2) = (sk_c11))))),
% 114.17/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl771, zip_derived_cl1])).
% 114.17/17.09 thf(prove_this_21, conjecture,
% 114.17/17.09 (~( ( ( multiply @ sk_c4 @ sk_c12 ) = ( sk_c11 ) ) |
% 114.17/17.09 ( ( multiply @ sk_c2 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 114.17/17.09 thf(zf_stmt_50, negated_conjecture,
% 114.17/17.09 (( ( multiply @ sk_c4 @ sk_c12 ) = ( sk_c11 ) ) |
% 114.17/17.09 ( ( multiply @ sk_c2 @ sk_c11 ) = ( sk_c10 ) )),
% 114.17/17.09 inference('cnf.neg', [status(esa)], [prove_this_21])).
% 114.17/17.09 thf(zip_derived_cl23, plain,
% 114.17/17.09 ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))
% 114.17/17.09 | ((multiply @ sk_c2 @ sk_c11) = (sk_c10)))),
% 114.17/17.09 inference('cnf', [status(esa)], [zf_stmt_50])).
% 114.17/17.09 thf(zip_derived_cl114, plain,
% 114.17/17.09 ((((multiply @ sk_c2 @ sk_c11) = (sk_c10)))
% 114.17/17.09 <= ((((multiply @ sk_c2 @ sk_c11) = (sk_c10))))),
% 114.17/17.09 inference('split', [status(esa)], [zip_derived_cl23])).
% 114.17/17.09 thf(zip_derived_cl1537, plain,
% 114.17/17.09 ((((identity) = (sk_c10)))
% 114.17/17.09 <= ((((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 114.17/17.09 (((inverse @ sk_c2) = (sk_c11))))),
% 114.17/17.09 inference('s_sup+', [status(thm)],
% 114.17/17.09 [zip_derived_cl1442, zip_derived_cl114])).
% 114.17/17.09 thf(zip_derived_cl154, plain,
% 114.17/17.09 ((((multiply @ sk_c10 @ sk_c12) = (sk_c11)))
% 114.17/17.09 <= ((((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.09 inference('split', [status(esa)], [zip_derived_cl43])).
% 114.17/17.09 thf(zip_derived_cl34824, plain,
% 114.17/17.09 ((((multiply @ identity @ sk_c12) = (sk_c11)))
% 114.17/17.09 <= ((((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 114.17/17.09 (((inverse @ sk_c2) = (sk_c11))) &
% 114.17/17.09 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.09 inference('s_sup+', [status(thm)],
% 114.17/17.09 [zip_derived_cl1537, zip_derived_cl154])).
% 114.17/17.09 thf(zip_derived_cl0, plain,
% 114.17/17.09 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 114.17/17.09 inference('cnf', [status(esa)], [left_identity])).
% 114.17/17.09 thf(zip_derived_cl34945, plain,
% 114.17/17.09 ((((sk_c12) = (sk_c11)))
% 114.17/17.09 <= ((((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 114.17/17.09 (((inverse @ sk_c2) = (sk_c11))) &
% 114.17/17.09 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.09 inference('demod', [status(thm)], [zip_derived_cl34824, zip_derived_cl0])).
% 114.17/17.09 thf(zip_derived_cl174, plain,
% 114.17/17.09 ((((multiply @ sk_c3 @ sk_c10) = (sk_c12)))
% 114.17/17.09 <= ((((multiply @ sk_c3 @ sk_c10) = (sk_c12))))),
% 114.17/17.09 inference('split', [status(esa)], [zip_derived_cl53])).
% 114.17/17.09 thf(zip_derived_cl219, plain,
% 114.17/17.09 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.17/17.09 (((inverse @ X0) != (X2))
% 114.17/17.09 | ((multiply @ X1 @ X2) != (X0))
% 114.17/17.09 | ((inverse @ X1) != (X0))
% 114.17/17.09 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.17/17.09 | ((inverse @ X3) != (X2))
% 114.17/17.09 | ((multiply @ X3 @ X2) != (sk_c12))))
% 114.17/17.09 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.17/17.09 (((inverse @ X0) != (X2))
% 114.17/17.09 | ((multiply @ X1 @ X2) != (X0))
% 114.17/17.09 | ((inverse @ X1) != (X0))
% 114.17/17.09 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.17/17.09 | ((inverse @ X3) != (X2))
% 114.17/17.09 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 114.17/17.09 inference('split', [status(esa)], [zip_derived_cl73])).
% 114.17/17.09 thf(zip_derived_cl556, plain,
% 114.17/17.09 ((![X0 : $i, X1 : $i]:
% 114.17/17.09 (((inverse @ X0) != (sk_c10))
% 114.17/17.09 | ((sk_c12) != (X0))
% 114.17/17.09 | ((inverse @ sk_c3) != (X0))
% 114.17/17.09 | ((multiply @ sk_c10 @ sk_c11) != (sk_c12))
% 114.17/17.09 | ((inverse @ X1) != (sk_c10))
% 114.17/17.09 | ((multiply @ X1 @ sk_c10) != (sk_c12))))
% 114.17/17.09 <= ((((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.17/17.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.17/17.09 (((inverse @ X0) != (X2))
% 114.17/17.09 | ((multiply @ X1 @ X2) != (X0))
% 114.17/17.09 | ((inverse @ X1) != (X0))
% 114.17/17.09 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.17/17.09 | ((inverse @ X3) != (X2))
% 114.17/17.09 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 114.17/17.09 inference('s_sup-', [status(thm)], [zip_derived_cl174, zip_derived_cl219])).
% 114.17/17.09 thf(zip_derived_cl1578, plain,
% 114.17/17.09 ((((multiply @ sk_c10 @ sk_c11) != (sk_c12)))
% 114.17/17.09 <= (~ (((multiply @ sk_c10 @ sk_c11) = (sk_c12))))),
% 114.17/17.09 inference('split', [status(esa)], [zip_derived_cl556])).
% 114.17/17.09 thf(zip_derived_cl79901, plain,
% 114.17/17.09 ((((multiply @ sk_c10 @ sk_c12) != (sk_c12)))
% 114.17/17.09 <= (~ (((multiply @ sk_c10 @ sk_c11) = (sk_c12))) &
% 114.17/17.09 (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 114.17/17.09 (((inverse @ sk_c2) = (sk_c11))) &
% 114.17/17.09 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.09 inference('s_sup-', [status(thm)],
% 114.17/17.09 [zip_derived_cl34945, zip_derived_cl1578])).
% 114.17/17.09 thf(zip_derived_cl1537, plain,
% 114.17/17.09 ((((identity) = (sk_c10)))
% 114.17/17.09 <= ((((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 114.17/17.09 (((inverse @ sk_c2) = (sk_c11))))),
% 114.17/17.09 inference('s_sup+', [status(thm)],
% 114.17/17.09 [zip_derived_cl1442, zip_derived_cl114])).
% 114.17/17.09 thf(zip_derived_cl0, plain,
% 114.17/17.09 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 114.17/17.09 inference('cnf', [status(esa)], [left_identity])).
% 114.17/17.09 thf(zip_derived_cl80120, plain,
% 114.17/17.09 ((((sk_c12) != (sk_c12)))
% 114.17/17.09 <= (~ (((multiply @ sk_c10 @ sk_c11) = (sk_c12))) &
% 114.17/17.09 (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 114.17/17.09 (((inverse @ sk_c2) = (sk_c11))) &
% 114.17/17.09 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.09 inference('demod', [status(thm)],
% 114.17/17.09 [zip_derived_cl79901, zip_derived_cl1537, zip_derived_cl0])).
% 114.17/17.09 thf('56', plain,
% 114.17/17.09 ((((multiply @ sk_c10 @ sk_c11) = (sk_c12))) |
% 114.17/17.09 ~ (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) |
% 114.17/17.09 ~ (((inverse @ sk_c2) = (sk_c11))) |
% 114.17/17.09 ~ (((multiply @ sk_c10 @ sk_c12) = (sk_c11)))),
% 114.17/17.09 inference('simplify', [status(thm)], [zip_derived_cl80120])).
% 114.17/17.09 thf(zip_derived_cl34945, plain,
% 114.17/17.09 ((((sk_c12) = (sk_c11)))
% 114.17/17.09 <= ((((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 114.17/17.09 (((inverse @ sk_c2) = (sk_c11))) &
% 114.17/17.09 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.17/17.09 inference('demod', [status(thm)], [zip_derived_cl34824, zip_derived_cl0])).
% 114.17/17.09 thf(zip_derived_cl194, plain,
% 114.17/17.09 ((((inverse @ sk_c3) = (sk_c10))) <= ((((inverse @ sk_c3) = (sk_c10))))),
% 114.17/17.09 inference('split', [status(esa)], [zip_derived_cl63])).
% 114.17/17.09 thf(zip_derived_cl174, plain,
% 114.17/17.09 ((((multiply @ sk_c3 @ sk_c10) = (sk_c12)))
% 114.17/17.09 <= ((((multiply @ sk_c3 @ sk_c10) = (sk_c12))))),
% 114.17/17.09 inference('split', [status(esa)], [zip_derived_cl53])).
% 114.17/17.09 thf(zip_derived_cl263, plain,
% 114.17/17.09 (![X0 : $i, X1 : $i]:
% 114.17/17.09 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.17/17.09 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.17/17.09 thf(zip_derived_cl699, plain,
% 114.17/17.09 ((((sk_c10) = (multiply @ (inverse @ sk_c3) @ sk_c12)))
% 114.17/17.09 <= ((((multiply @ sk_c3 @ sk_c10) = (sk_c12))))),
% 114.17/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl174, zip_derived_cl263])).
% 114.17/17.09 thf(zip_derived_cl925, plain,
% 114.17/17.09 ((((sk_c10) = (multiply @ sk_c10 @ sk_c12)))
% 114.17/17.09 <= ((((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.17/17.09 (((inverse @ sk_c3) = (sk_c10))))),
% 114.17/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl194, zip_derived_cl699])).
% 114.73/17.09 thf(zip_derived_cl154, plain,
% 114.73/17.09 ((((multiply @ sk_c10 @ sk_c12) = (sk_c11)))
% 114.73/17.09 <= ((((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl43])).
% 114.73/17.09 thf(zip_derived_cl12308, plain,
% 114.73/17.09 ((((sk_c10) = (sk_c11)))
% 114.73/17.09 <= ((((multiply @ sk_c10 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c3) = (sk_c10))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl925, zip_derived_cl154])).
% 114.73/17.09 thf(zip_derived_cl194, plain,
% 114.73/17.09 ((((inverse @ sk_c3) = (sk_c10))) <= ((((inverse @ sk_c3) = (sk_c10))))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl63])).
% 114.73/17.09 thf(zip_derived_cl0, plain,
% 114.73/17.09 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 114.73/17.09 inference('cnf', [status(esa)], [left_identity])).
% 114.73/17.09 thf(zip_derived_cl174, plain,
% 114.73/17.09 ((((multiply @ sk_c3 @ sk_c10) = (sk_c12)))
% 114.73/17.09 <= ((((multiply @ sk_c3 @ sk_c10) = (sk_c12))))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl53])).
% 114.73/17.09 thf(zip_derived_cl2, plain,
% 114.73/17.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 114.73/17.09 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 114.73/17.09 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 114.73/17.09 inference('cnf', [status(esa)], [associativity])).
% 114.73/17.09 thf(zip_derived_cl219, plain,
% 114.73/17.09 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.73/17.09 (((inverse @ X0) != (X2))
% 114.73/17.09 | ((multiply @ X1 @ X2) != (X0))
% 114.73/17.09 | ((inverse @ X1) != (X0))
% 114.73/17.09 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ X3) != (X2))
% 114.73/17.09 | ((multiply @ X3 @ X2) != (sk_c12))))
% 114.73/17.09 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.73/17.09 (((inverse @ X0) != (X2))
% 114.73/17.09 | ((multiply @ X1 @ X2) != (X0))
% 114.73/17.09 | ((inverse @ X1) != (X0))
% 114.73/17.09 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ X3) != (X2))
% 114.73/17.09 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl73])).
% 114.73/17.09 thf(zip_derived_cl291, plain,
% 114.73/17.09 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 114.73/17.09 (((inverse @ X3) != (X0))
% 114.73/17.09 | ((multiply @ X2 @ (multiply @ X1 @ X0)) != (X3))
% 114.73/17.09 | ((inverse @ (multiply @ X2 @ X1)) != (X3))
% 114.73/17.09 | ((multiply @ X0 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ X4) != (X0))
% 114.73/17.09 | ((multiply @ X4 @ X0) != (sk_c12))))
% 114.73/17.09 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.73/17.09 (((inverse @ X0) != (X2))
% 114.73/17.09 | ((multiply @ X1 @ X2) != (X0))
% 114.73/17.09 | ((inverse @ X1) != (X0))
% 114.73/17.09 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ X3) != (X2))
% 114.73/17.09 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 114.73/17.09 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl219])).
% 114.73/17.09 thf(zip_derived_cl866, plain,
% 114.73/17.09 ((![X0 : $i, X1 : $i, X2 : $i]:
% 114.73/17.09 (((inverse @ X0) != (sk_c10))
% 114.73/17.09 | ((multiply @ X1 @ sk_c12) != (X0))
% 114.73/17.09 | ((inverse @ (multiply @ X1 @ sk_c3)) != (X0))
% 114.73/17.09 | ((multiply @ sk_c10 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ X2) != (sk_c10))
% 114.73/17.09 | ((multiply @ X2 @ sk_c10) != (sk_c12))))
% 114.73/17.09 <= ((((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.73/17.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.73/17.09 (((inverse @ X0) != (X2))
% 114.73/17.09 | ((multiply @ X1 @ X2) != (X0))
% 114.73/17.09 | ((inverse @ X1) != (X0))
% 114.73/17.09 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ X3) != (X2))
% 114.73/17.09 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 114.73/17.09 inference('s_sup-', [status(thm)], [zip_derived_cl174, zip_derived_cl291])).
% 114.73/17.09 thf(zip_derived_cl9252, plain,
% 114.73/17.09 ((![X0 : $i, X1 : $i]:
% 114.73/17.09 (((inverse @ X0) != (sk_c10))
% 114.73/17.09 | ((multiply @ X1 @ sk_c12) != (X0))
% 114.73/17.09 | ((inverse @ (multiply @ X1 @ sk_c3)) != (X0))))
% 114.73/17.09 <= ((![X0 : $i, X1 : $i]:
% 114.73/17.09 (((inverse @ X0) != (sk_c10))
% 114.73/17.09 | ((multiply @ X1 @ sk_c12) != (X0))
% 114.73/17.09 | ((inverse @ (multiply @ X1 @ sk_c3)) != (X0)))))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl866])).
% 114.73/17.09 thf(zip_derived_cl9261, plain,
% 114.73/17.09 ((![X0 : $i]:
% 114.73/17.09 (((multiply @ X0 @ sk_c12) != (inverse @ (multiply @ X0 @ sk_c3)))
% 114.73/17.09 | ((inverse @ (inverse @ (multiply @ X0 @ sk_c3))) != (sk_c10))))
% 114.73/17.09 <= ((![X0 : $i, X1 : $i]:
% 114.73/17.09 (((inverse @ X0) != (sk_c10))
% 114.73/17.09 | ((multiply @ X1 @ sk_c12) != (X0))
% 114.73/17.09 | ((inverse @ (multiply @ X1 @ sk_c3)) != (X0)))))),
% 114.73/17.09 inference('eq_res', [status(thm)], [zip_derived_cl9252])).
% 114.73/17.09 thf(zip_derived_cl13847, plain,
% 114.73/17.09 (((((multiply @ identity @ sk_c12) != (inverse @ sk_c3))
% 114.73/17.09 | ((inverse @ (inverse @ sk_c3)) != (sk_c10))))
% 114.73/17.09 <= ((![X0 : $i, X1 : $i]:
% 114.73/17.09 (((inverse @ X0) != (sk_c10))
% 114.73/17.09 | ((multiply @ X1 @ sk_c12) != (X0))
% 114.73/17.09 | ((inverse @ (multiply @ X1 @ sk_c3)) != (X0)))))),
% 114.73/17.09 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl9261])).
% 114.73/17.09 thf(zip_derived_cl0, plain,
% 114.73/17.09 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 114.73/17.09 inference('cnf', [status(esa)], [left_identity])).
% 114.73/17.09 thf(zip_derived_cl13854, plain,
% 114.73/17.09 (((((sk_c12) != (inverse @ sk_c3))
% 114.73/17.09 | ((inverse @ (inverse @ sk_c3)) != (sk_c10))))
% 114.73/17.09 <= ((![X0 : $i, X1 : $i]:
% 114.73/17.09 (((inverse @ X0) != (sk_c10))
% 114.73/17.09 | ((multiply @ X1 @ sk_c12) != (X0))
% 114.73/17.09 | ((inverse @ (multiply @ X1 @ sk_c3)) != (X0)))))),
% 114.73/17.09 inference('demod', [status(thm)], [zip_derived_cl13847, zip_derived_cl0])).
% 114.73/17.09 thf(zip_derived_cl13876, plain,
% 114.73/17.09 ((((sk_c12) != (inverse @ sk_c3)))
% 114.73/17.09 <= (~ (((sk_c12) = (inverse @ sk_c3))))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl13854])).
% 114.73/17.09 thf(zip_derived_cl13877, plain,
% 114.73/17.09 ((((sk_c12) != (sk_c10)))
% 114.73/17.09 <= (~ (((sk_c12) = (inverse @ sk_c3))) &
% 114.73/17.09 (((inverse @ sk_c3) = (sk_c10))))),
% 114.73/17.09 inference('s_sup-', [status(thm)],
% 114.73/17.09 [zip_derived_cl194, zip_derived_cl13876])).
% 114.73/17.09 thf(zip_derived_cl15782, plain,
% 114.73/17.09 ((((sk_c12) != (sk_c11)))
% 114.73/17.09 <= (~ (((sk_c12) = (inverse @ sk_c3))) &
% 114.73/17.09 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c3) = (sk_c10))))),
% 114.73/17.09 inference('s_sup-', [status(thm)],
% 114.73/17.09 [zip_derived_cl12308, zip_derived_cl13877])).
% 114.73/17.09 thf(zip_derived_cl79979, plain,
% 114.73/17.09 ((((sk_c12) != (sk_c12)))
% 114.73/17.09 <= (~ (((sk_c12) = (inverse @ sk_c3))) &
% 114.73/17.09 (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 114.73/17.09 (((inverse @ sk_c2) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c3) = (sk_c10))))),
% 114.73/17.09 inference('s_sup-', [status(thm)],
% 114.73/17.09 [zip_derived_cl34945, zip_derived_cl15782])).
% 114.73/17.09 thf(zip_derived_cl1627, plain,
% 114.73/17.09 ((((identity) = (sk_c12)))
% 114.73/17.09 <= ((((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c3) = (sk_c10))))),
% 114.73/17.09 inference('s_sup+', [status(thm)],
% 114.73/17.09 [zip_derived_cl1595, zip_derived_cl174])).
% 114.73/17.09 thf(zip_derived_cl1627, plain,
% 114.73/17.09 ((((identity) = (sk_c12)))
% 114.73/17.09 <= ((((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c3) = (sk_c10))))),
% 114.73/17.09 inference('s_sup+', [status(thm)],
% 114.73/17.09 [zip_derived_cl1595, zip_derived_cl174])).
% 114.73/17.09 thf(zip_derived_cl80143, plain,
% 114.73/17.09 ((((identity) != (identity)))
% 114.73/17.09 <= (~ (((sk_c12) = (inverse @ sk_c3))) &
% 114.73/17.09 (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 114.73/17.09 (((inverse @ sk_c2) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c3) = (sk_c10))))),
% 114.73/17.09 inference('demod', [status(thm)],
% 114.73/17.09 [zip_derived_cl79979, zip_derived_cl1627, zip_derived_cl1627])).
% 114.73/17.09 thf('57', plain,
% 114.73/17.09 ((((sk_c12) = (inverse @ sk_c3))) |
% 114.73/17.09 ~ (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) |
% 114.73/17.09 ~ (((multiply @ sk_c3 @ sk_c10) = (sk_c12))) |
% 114.73/17.09 ~ (((inverse @ sk_c2) = (sk_c11))) |
% 114.73/17.09 ~ (((multiply @ sk_c10 @ sk_c12) = (sk_c11))) |
% 114.73/17.09 ~ (((inverse @ sk_c3) = (sk_c10)))),
% 114.73/17.09 inference('simplify', [status(thm)], [zip_derived_cl80143])).
% 114.73/17.09 thf(prove_this_14, conjecture,
% 114.73/17.09 (~( ( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 114.73/17.09 ( ( inverse @ sk_c1 ) = ( sk_c12 ) ) ))).
% 114.73/17.09 thf(zf_stmt_51, negated_conjecture,
% 114.73/17.09 (( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 114.73/17.09 ( ( inverse @ sk_c1 ) = ( sk_c12 ) )),
% 114.73/17.09 inference('cnf.neg', [status(esa)], [prove_this_14])).
% 114.73/17.09 thf(zip_derived_cl16, plain,
% 114.73/17.09 ((((inverse @ sk_c5) = (sk_c11)) | ((inverse @ sk_c1) = (sk_c12)))),
% 114.73/17.09 inference('cnf', [status(esa)], [zf_stmt_51])).
% 114.73/17.09 thf('58', plain,
% 114.73/17.09 ((((inverse @ sk_c1) = (sk_c12))) | (((inverse @ sk_c5) = (sk_c11)))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl16])).
% 114.73/17.09 thf(prove_this_24, conjecture,
% 114.73/17.09 (~( ( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 114.73/17.09 ( ( multiply @ sk_c2 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 114.73/17.09 thf(zf_stmt_52, negated_conjecture,
% 114.73/17.09 (( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 114.73/17.09 ( ( multiply @ sk_c2 @ sk_c11 ) = ( sk_c10 ) )),
% 114.73/17.09 inference('cnf.neg', [status(esa)], [prove_this_24])).
% 114.73/17.09 thf(zip_derived_cl26, plain,
% 114.73/17.09 ((((inverse @ sk_c5) = (sk_c11))
% 114.73/17.09 | ((multiply @ sk_c2 @ sk_c11) = (sk_c10)))),
% 114.73/17.09 inference('cnf', [status(esa)], [zf_stmt_52])).
% 114.73/17.09 thf('59', plain,
% 114.73/17.09 ((((multiply @ sk_c2 @ sk_c11) = (sk_c10))) |
% 114.73/17.09 (((inverse @ sk_c5) = (sk_c11)))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl26])).
% 114.73/17.09 thf(prove_this_12, conjecture,
% 114.73/17.09 (~( ( ( inverse @ sk_c4 ) = ( sk_c12 ) ) |
% 114.73/17.09 ( ( inverse @ sk_c1 ) = ( sk_c12 ) ) ))).
% 114.73/17.09 thf(zf_stmt_53, negated_conjecture,
% 114.73/17.09 (( ( inverse @ sk_c4 ) = ( sk_c12 ) ) |
% 114.73/17.09 ( ( inverse @ sk_c1 ) = ( sk_c12 ) )),
% 114.73/17.09 inference('cnf.neg', [status(esa)], [prove_this_12])).
% 114.73/17.09 thf(zip_derived_cl14, plain,
% 114.73/17.09 ((((inverse @ sk_c4) = (sk_c12)) | ((inverse @ sk_c1) = (sk_c12)))),
% 114.73/17.09 inference('cnf', [status(esa)], [zf_stmt_53])).
% 114.73/17.09 thf('60', plain,
% 114.73/17.09 ((((inverse @ sk_c1) = (sk_c12))) | (((inverse @ sk_c4) = (sk_c12)))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl14])).
% 114.73/17.09 thf(prove_this_22, conjecture,
% 114.73/17.09 (~( ( ( inverse @ sk_c4 ) = ( sk_c12 ) ) |
% 114.73/17.09 ( ( multiply @ sk_c2 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 114.73/17.09 thf(zf_stmt_54, negated_conjecture,
% 114.73/17.09 (( ( inverse @ sk_c4 ) = ( sk_c12 ) ) |
% 114.73/17.09 ( ( multiply @ sk_c2 @ sk_c11 ) = ( sk_c10 ) )),
% 114.73/17.09 inference('cnf.neg', [status(esa)], [prove_this_22])).
% 114.73/17.09 thf(zip_derived_cl24, plain,
% 114.73/17.09 ((((inverse @ sk_c4) = (sk_c12))
% 114.73/17.09 | ((multiply @ sk_c2 @ sk_c11) = (sk_c10)))),
% 114.73/17.09 inference('cnf', [status(esa)], [zf_stmt_54])).
% 114.73/17.09 thf('61', plain,
% 114.73/17.09 ((((multiply @ sk_c2 @ sk_c11) = (sk_c10))) |
% 114.73/17.09 (((inverse @ sk_c4) = (sk_c12)))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl24])).
% 114.73/17.09 thf(zip_derived_cl1116, plain,
% 114.73/17.09 ((((identity) = (sk_c11)))
% 114.73/17.09 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((inverse @ sk_c4) = (sk_c12))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl1103, zip_derived_cl75])).
% 114.73/17.09 thf(zip_derived_cl687, plain,
% 114.73/17.09 ((((sk_c2) = (multiply @ (inverse @ sk_c11) @ identity)))
% 114.73/17.09 <= ((((inverse @ sk_c2) = (sk_c11))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl314, zip_derived_cl263])).
% 114.73/17.09 thf(zip_derived_cl1214, plain,
% 114.73/17.09 ((((sk_c2) = (multiply @ (inverse @ identity) @ identity)))
% 114.73/17.09 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((inverse @ sk_c4) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c2) = (sk_c11))))),
% 114.73/17.09 inference('s_sup+', [status(thm)],
% 114.73/17.09 [zip_derived_cl1116, zip_derived_cl687])).
% 114.73/17.09 thf(zip_derived_cl1, plain,
% 114.73/17.09 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 114.73/17.09 inference('cnf', [status(esa)], [left_inverse])).
% 114.73/17.09 thf(zip_derived_cl1230, plain,
% 114.73/17.09 ((((sk_c2) = (identity)))
% 114.73/17.09 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((inverse @ sk_c4) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c2) = (sk_c11))))),
% 114.73/17.09 inference('demod', [status(thm)], [zip_derived_cl1214, zip_derived_cl1])).
% 114.73/17.09 thf(zip_derived_cl134, plain,
% 114.73/17.09 ((((inverse @ sk_c2) = (sk_c11))) <= ((((inverse @ sk_c2) = (sk_c11))))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl33])).
% 114.73/17.09 thf(zip_derived_cl1656, plain,
% 114.73/17.09 ((((inverse @ identity) = (sk_c11)))
% 114.73/17.09 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((inverse @ sk_c4) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c2) = (sk_c11))))),
% 114.73/17.09 inference('s_sup+', [status(thm)],
% 114.73/17.09 [zip_derived_cl1230, zip_derived_cl134])).
% 114.73/17.09 thf(zip_derived_cl1116, plain,
% 114.73/17.09 ((((identity) = (sk_c11)))
% 114.73/17.09 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((inverse @ sk_c4) = (sk_c12))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl1103, zip_derived_cl75])).
% 114.73/17.09 thf(zip_derived_cl1682, plain,
% 114.73/17.09 ((((inverse @ identity) = (identity)))
% 114.73/17.09 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((inverse @ sk_c4) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c2) = (sk_c11))))),
% 114.73/17.09 inference('demod', [status(thm)],
% 114.73/17.09 [zip_derived_cl1656, zip_derived_cl1116])).
% 114.73/17.09 thf(zip_derived_cl0, plain,
% 114.73/17.09 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 114.73/17.09 inference('cnf', [status(esa)], [left_identity])).
% 114.73/17.09 thf(zip_derived_cl263, plain,
% 114.73/17.09 (![X0 : $i, X1 : $i]:
% 114.73/17.09 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.73/17.09 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.73/17.09 thf(zip_derived_cl263, plain,
% 114.73/17.09 (![X0 : $i, X1 : $i]:
% 114.73/17.09 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.73/17.09 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.73/17.09 thf(zip_derived_cl676, plain,
% 114.73/17.09 (![X0 : $i, X1 : $i]:
% 114.73/17.09 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl263, zip_derived_cl263])).
% 114.73/17.09 thf(zip_derived_cl1171, plain,
% 114.73/17.09 ((((multiply @ sk_c5 @ sk_c11) = (identity)))
% 114.73/17.09 <= ((((inverse @ sk_c5) = (sk_c11))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl685, zip_derived_cl1])).
% 114.73/17.09 thf(zip_derived_cl291, plain,
% 114.73/17.09 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 114.73/17.09 (((inverse @ X3) != (X0))
% 114.73/17.09 | ((multiply @ X2 @ (multiply @ X1 @ X0)) != (X3))
% 114.73/17.09 | ((inverse @ (multiply @ X2 @ X1)) != (X3))
% 114.73/17.09 | ((multiply @ X0 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ X4) != (X0))
% 114.73/17.09 | ((multiply @ X4 @ X0) != (sk_c12))))
% 114.73/17.09 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.73/17.09 (((inverse @ X0) != (X2))
% 114.73/17.09 | ((multiply @ X1 @ X2) != (X0))
% 114.73/17.09 | ((inverse @ X1) != (X0))
% 114.73/17.09 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ X3) != (X2))
% 114.73/17.09 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 114.73/17.09 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl219])).
% 114.73/17.09 thf(zip_derived_cl1253, plain,
% 114.73/17.09 ((![X0 : $i, X1 : $i, X2 : $i]:
% 114.73/17.09 (((inverse @ X0) != (sk_c11))
% 114.73/17.09 | ((multiply @ X1 @ identity) != (X0))
% 114.73/17.09 | ((inverse @ (multiply @ X1 @ sk_c5)) != (X0))
% 114.73/17.09 | ((multiply @ sk_c11 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ X2) != (sk_c11))
% 114.73/17.09 | ((multiply @ X2 @ sk_c11) != (sk_c12))))
% 114.73/17.09 <= ((((inverse @ sk_c5) = (sk_c11))) &
% 114.73/17.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.73/17.09 (((inverse @ X0) != (X2))
% 114.73/17.09 | ((multiply @ X1 @ X2) != (X0))
% 114.73/17.09 | ((inverse @ X1) != (X0))
% 114.73/17.09 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ X3) != (X2))
% 114.73/17.09 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 114.73/17.09 inference('s_sup-', [status(thm)],
% 114.73/17.09 [zip_derived_cl1171, zip_derived_cl291])).
% 114.73/17.09 thf(zip_derived_cl23739, plain,
% 114.73/17.09 ((![X0 : $i, X1 : $i]:
% 114.73/17.09 (((inverse @ X0) != (sk_c11))
% 114.73/17.09 | ((multiply @ X1 @ identity) != (X0))
% 114.73/17.09 | ((inverse @ (multiply @ X1 @ sk_c5)) != (X0))))
% 114.73/17.09 <= ((![X0 : $i, X1 : $i]:
% 114.73/17.09 (((inverse @ X0) != (sk_c11))
% 114.73/17.09 | ((multiply @ X1 @ identity) != (X0))
% 114.73/17.09 | ((inverse @ (multiply @ X1 @ sk_c5)) != (X0)))))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl1253])).
% 114.73/17.09 thf(zip_derived_cl23745, plain,
% 114.73/17.09 ((![X0 : $i, X1 : $i]:
% 114.73/17.09 (((inverse @ X1) != (sk_c11))
% 114.73/17.09 | ((multiply @ (inverse @ (inverse @ X0)) @ identity) != (X1))
% 114.73/17.09 | ((inverse @ (multiply @ X0 @ sk_c5)) != (X1))))
% 114.73/17.09 <= ((![X0 : $i, X1 : $i]:
% 114.73/17.09 (((inverse @ X0) != (sk_c11))
% 114.73/17.09 | ((multiply @ X1 @ identity) != (X0))
% 114.73/17.09 | ((inverse @ (multiply @ X1 @ sk_c5)) != (X0)))))),
% 114.73/17.09 inference('s_sup-', [status(thm)],
% 114.73/17.09 [zip_derived_cl676, zip_derived_cl23739])).
% 114.73/17.09 thf(zip_derived_cl679, plain,
% 114.73/17.09 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl263])).
% 114.73/17.09 thf(zip_derived_cl23753, plain,
% 114.73/17.09 ((![X0 : $i, X1 : $i]:
% 114.73/17.09 (((inverse @ X1) != (sk_c11))
% 114.73/17.09 | ((X0) != (X1))
% 114.73/17.09 | ((inverse @ (multiply @ X0 @ sk_c5)) != (X1))))
% 114.73/17.09 <= ((![X0 : $i, X1 : $i]:
% 114.73/17.09 (((inverse @ X0) != (sk_c11))
% 114.73/17.09 | ((multiply @ X1 @ identity) != (X0))
% 114.73/17.09 | ((inverse @ (multiply @ X1 @ sk_c5)) != (X0)))))),
% 114.73/17.09 inference('demod', [status(thm)],
% 114.73/17.09 [zip_derived_cl23745, zip_derived_cl679])).
% 114.73/17.09 thf(zip_derived_cl23779, plain,
% 114.73/17.09 ((![X0 : $i]:
% 114.73/17.09 (((inverse @ (multiply @ X0 @ sk_c5)) != (X0))
% 114.73/17.09 | ((inverse @ X0) != (sk_c11))))
% 114.73/17.09 <= ((![X0 : $i, X1 : $i]:
% 114.73/17.09 (((inverse @ X0) != (sk_c11))
% 114.73/17.09 | ((multiply @ X1 @ identity) != (X0))
% 114.73/17.09 | ((inverse @ (multiply @ X1 @ sk_c5)) != (X0)))))),
% 114.73/17.09 inference('eq_res', [status(thm)], [zip_derived_cl23753])).
% 114.73/17.09 thf(zip_derived_cl23781, plain,
% 114.73/17.09 (((((inverse @ sk_c5) != (identity)) | ((inverse @ identity) != (sk_c11))))
% 114.73/17.09 <= ((![X0 : $i, X1 : $i]:
% 114.73/17.09 (((inverse @ X0) != (sk_c11))
% 114.73/17.09 | ((multiply @ X1 @ identity) != (X0))
% 114.73/17.09 | ((inverse @ (multiply @ X1 @ sk_c5)) != (X0)))))),
% 114.73/17.09 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl23779])).
% 114.73/17.09 thf(zip_derived_cl23802, plain,
% 114.73/17.09 ((((inverse @ identity) != (sk_c11)))
% 114.73/17.09 <= (~ (((inverse @ identity) = (sk_c11))))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl23781])).
% 114.73/17.09 thf(zip_derived_cl39779, plain,
% 114.73/17.09 ((((identity) != (sk_c11)))
% 114.73/17.09 <= (~ (((inverse @ identity) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((inverse @ sk_c4) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c2) = (sk_c11))))),
% 114.73/17.09 inference('s_sup-', [status(thm)],
% 114.73/17.09 [zip_derived_cl1682, zip_derived_cl23802])).
% 114.73/17.09 thf(zip_derived_cl1116, plain,
% 114.73/17.09 ((((identity) = (sk_c11)))
% 114.73/17.09 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((inverse @ sk_c4) = (sk_c12))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl1103, zip_derived_cl75])).
% 114.73/17.09 thf(zip_derived_cl40180, plain,
% 114.73/17.09 ((((identity) != (identity)))
% 114.73/17.09 <= (~ (((inverse @ identity) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((inverse @ sk_c4) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c2) = (sk_c11))))),
% 114.73/17.09 inference('demod', [status(thm)],
% 114.73/17.09 [zip_derived_cl39779, zip_derived_cl1116])).
% 114.73/17.09 thf('62', plain,
% 114.73/17.09 ((((inverse @ identity) = (sk_c11))) |
% 114.73/17.09 ~ (((inverse @ sk_c4) = (sk_c12))) |
% 114.73/17.09 ~ (((inverse @ sk_c2) = (sk_c11))) |
% 114.73/17.09 ~ (((multiply @ sk_c4 @ sk_c12) = (sk_c11)))),
% 114.73/17.09 inference('simplify', [status(thm)], [zip_derived_cl40180])).
% 114.73/17.09 thf(zip_derived_cl1627, plain,
% 114.73/17.09 ((((identity) = (sk_c12)))
% 114.73/17.09 <= ((((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c3) = (sk_c10))))),
% 114.73/17.09 inference('s_sup+', [status(thm)],
% 114.73/17.09 [zip_derived_cl1595, zip_derived_cl174])).
% 114.73/17.09 thf(zip_derived_cl1116, plain,
% 114.73/17.09 ((((identity) = (sk_c11)))
% 114.73/17.09 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((inverse @ sk_c4) = (sk_c12))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl1103, zip_derived_cl75])).
% 114.73/17.09 thf(zip_derived_cl375, plain,
% 114.73/17.09 ((((multiply @ sk_c11 @ sk_c11) != (sk_c12)))
% 114.73/17.09 <= (~ (((multiply @ sk_c11 @ sk_c11) = (sk_c12))))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl310])).
% 114.73/17.09 thf(zip_derived_cl1196, plain,
% 114.73/17.09 ((((multiply @ identity @ identity) != (sk_c12)))
% 114.73/17.09 <= (~ (((multiply @ sk_c11 @ sk_c11) = (sk_c12))) &
% 114.73/17.09 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((inverse @ sk_c4) = (sk_c12))))),
% 114.73/17.09 inference('s_sup-', [status(thm)],
% 114.73/17.09 [zip_derived_cl1116, zip_derived_cl375])).
% 114.73/17.09 thf(zip_derived_cl0, plain,
% 114.73/17.09 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 114.73/17.09 inference('cnf', [status(esa)], [left_identity])).
% 114.73/17.09 thf(zip_derived_cl1226, plain,
% 114.73/17.09 ((((identity) != (sk_c12)))
% 114.73/17.09 <= (~ (((multiply @ sk_c11 @ sk_c11) = (sk_c12))) &
% 114.73/17.09 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((inverse @ sk_c4) = (sk_c12))))),
% 114.73/17.09 inference('demod', [status(thm)], [zip_derived_cl1196, zip_derived_cl0])).
% 114.73/17.09 thf(zip_derived_cl38309, plain,
% 114.73/17.09 ((((identity) != (identity)))
% 114.73/17.09 <= (~ (((multiply @ sk_c11 @ sk_c11) = (sk_c12))) &
% 114.73/17.09 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((inverse @ sk_c4) = (sk_c12))) &
% 114.73/17.09 (((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c3) = (sk_c10))))),
% 114.73/17.09 inference('s_sup-', [status(thm)],
% 114.73/17.09 [zip_derived_cl1627, zip_derived_cl1226])).
% 114.73/17.09 thf('63', plain,
% 114.73/17.09 ((((multiply @ sk_c11 @ sk_c11) = (sk_c12))) |
% 114.73/17.09 ~ (((inverse @ sk_c4) = (sk_c12))) |
% 114.73/17.09 ~ (((inverse @ sk_c3) = (sk_c10))) |
% 114.73/17.09 ~ (((multiply @ sk_c3 @ sk_c10) = (sk_c12))) |
% 114.73/17.09 ~ (((multiply @ sk_c4 @ sk_c12) = (sk_c11)))),
% 114.73/17.09 inference('simplify', [status(thm)], [zip_derived_cl38309])).
% 114.73/17.09 thf(zip_derived_cl1116, plain,
% 114.73/17.09 ((((identity) = (sk_c11)))
% 114.73/17.09 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((inverse @ sk_c4) = (sk_c12))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl1103, zip_derived_cl75])).
% 114.73/17.09 thf(zip_derived_cl686, plain,
% 114.73/17.09 ((((sk_c5) = (multiply @ (inverse @ sk_c11) @ identity)))
% 114.73/17.09 <= ((((inverse @ sk_c5) = (sk_c11))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl243, zip_derived_cl263])).
% 114.73/17.09 thf(zip_derived_cl296, plain,
% 114.73/17.09 ((![X0 : $i, X1 : $i, X2 : $i]:
% 114.73/17.09 (((multiply @ X1 @ X0) != (sk_c12))
% 114.73/17.09 | ((inverse @ X1) != (X0))
% 114.73/17.09 | ((multiply @ X0 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ X2) != (multiply @ X2 @ X0))
% 114.73/17.09 | ((inverse @ (multiply @ X2 @ X0)) != (X0))))
% 114.73/17.09 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.73/17.09 (((inverse @ X0) != (X2))
% 114.73/17.09 | ((multiply @ X1 @ X2) != (X0))
% 114.73/17.09 | ((inverse @ X1) != (X0))
% 114.73/17.09 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ X3) != (X2))
% 114.73/17.09 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 114.73/17.09 inference('eq_res', [status(thm)], [zip_derived_cl219])).
% 114.73/17.09 thf(zip_derived_cl1036, plain,
% 114.73/17.09 ((![X0 : $i]:
% 114.73/17.09 (((multiply @ X0 @ identity) != (sk_c12))
% 114.73/17.09 | ((inverse @ X0) != (identity))
% 114.73/17.09 | ((multiply @ identity @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ (inverse @ sk_c11)) != (sk_c5))
% 114.73/17.09 | ((inverse @ sk_c5) != (identity))))
% 114.73/17.09 <= ((((inverse @ sk_c5) = (sk_c11))) &
% 114.73/17.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.73/17.09 (((inverse @ X0) != (X2))
% 114.73/17.09 | ((multiply @ X1 @ X2) != (X0))
% 114.73/17.09 | ((inverse @ X1) != (X0))
% 114.73/17.09 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ X3) != (X2))
% 114.73/17.09 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 114.73/17.09 inference('s_sup-', [status(thm)], [zip_derived_cl686, zip_derived_cl296])).
% 114.73/17.09 thf(zip_derived_cl0, plain,
% 114.73/17.09 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 114.73/17.09 inference('cnf', [status(esa)], [left_identity])).
% 114.73/17.09 thf(zip_derived_cl80, plain,
% 114.73/17.09 ((((inverse @ sk_c5) = (sk_c11))) <= ((((inverse @ sk_c5) = (sk_c11))))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl6])).
% 114.73/17.09 thf(zip_derived_cl1081, plain,
% 114.73/17.09 ((![X0 : $i]:
% 114.73/17.09 (((multiply @ X0 @ identity) != (sk_c12))
% 114.73/17.09 | ((inverse @ X0) != (identity))
% 114.73/17.09 | ((sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ (inverse @ sk_c11)) != (sk_c5))
% 114.73/17.09 | ((sk_c11) != (identity))))
% 114.73/17.09 <= ((((inverse @ sk_c5) = (sk_c11))) &
% 114.73/17.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.73/17.09 (((inverse @ X0) != (X2))
% 114.73/17.09 | ((multiply @ X1 @ X2) != (X0))
% 114.73/17.09 | ((inverse @ X1) != (X0))
% 114.73/17.09 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ X3) != (X2))
% 114.73/17.09 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 114.73/17.09 inference('demod', [status(thm)],
% 114.73/17.09 [zip_derived_cl1036, zip_derived_cl0, zip_derived_cl80])).
% 114.73/17.09 thf(zip_derived_cl686, plain,
% 114.73/17.09 ((((sk_c5) = (multiply @ (inverse @ sk_c11) @ identity)))
% 114.73/17.09 <= ((((inverse @ sk_c5) = (sk_c11))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl243, zip_derived_cl263])).
% 114.73/17.09 thf(zip_derived_cl263, plain,
% 114.73/17.09 (![X0 : $i, X1 : $i]:
% 114.73/17.09 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.73/17.09 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.73/17.09 thf(zip_derived_cl763, plain,
% 114.73/17.09 ((((identity) = (multiply @ (inverse @ (inverse @ sk_c11)) @ sk_c5)))
% 114.73/17.09 <= ((((inverse @ sk_c5) = (sk_c11))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl686, zip_derived_cl263])).
% 114.73/17.09 thf(zip_derived_cl263, plain,
% 114.73/17.09 (![X0 : $i, X1 : $i]:
% 114.73/17.09 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.73/17.09 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.73/17.09 thf(zip_derived_cl3831, plain,
% 114.73/17.09 ((((sk_c5)
% 114.73/17.09 = (multiply @ (inverse @ (inverse @ (inverse @ sk_c11))) @ identity)))
% 114.73/17.09 <= ((((inverse @ sk_c5) = (sk_c11))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl763, zip_derived_cl263])).
% 114.73/17.09 thf(zip_derived_cl679, plain,
% 114.73/17.09 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl263])).
% 114.73/17.09 thf(zip_derived_cl5682, plain,
% 114.73/17.09 ((((inverse @ sk_c11) = (sk_c5))) <= ((((inverse @ sk_c5) = (sk_c11))))),
% 114.73/17.09 inference('s_sup+', [status(thm)],
% 114.73/17.09 [zip_derived_cl3831, zip_derived_cl679])).
% 114.73/17.09 thf(zip_derived_cl80, plain,
% 114.73/17.09 ((((inverse @ sk_c5) = (sk_c11))) <= ((((inverse @ sk_c5) = (sk_c11))))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl6])).
% 114.73/17.09 thf(zip_derived_cl17623, plain,
% 114.73/17.09 ((![X0 : $i]:
% 114.73/17.09 (((multiply @ X0 @ identity) != (sk_c12))
% 114.73/17.09 | ((inverse @ X0) != (identity))
% 114.73/17.09 | ((sk_c11) != (sk_c12))
% 114.73/17.09 | ((sk_c11) != (sk_c5))
% 114.73/17.09 | ((sk_c11) != (identity))))
% 114.73/17.09 <= ((((inverse @ sk_c5) = (sk_c11))) &
% 114.73/17.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.73/17.09 (((inverse @ X0) != (X2))
% 114.73/17.09 | ((multiply @ X1 @ X2) != (X0))
% 114.73/17.09 | ((inverse @ X1) != (X0))
% 114.73/17.09 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ X3) != (X2))
% 114.73/17.09 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 114.73/17.09 inference('demod', [status(thm)],
% 114.73/17.09 [zip_derived_cl1081, zip_derived_cl5682, zip_derived_cl80])).
% 114.73/17.09 thf(zip_derived_cl17627, plain,
% 114.73/17.09 ((((sk_c11) != (identity))) <= (~ (((sk_c11) = (identity))))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl17623])).
% 114.73/17.09 thf(zip_derived_cl17628, plain,
% 114.73/17.09 ((((identity) != (identity)))
% 114.73/17.09 <= (~ (((sk_c11) = (identity))) &
% 114.73/17.09 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((inverse @ sk_c4) = (sk_c12))))),
% 114.73/17.09 inference('s_sup-', [status(thm)],
% 114.73/17.09 [zip_derived_cl1116, zip_derived_cl17627])).
% 114.73/17.09 thf('64', plain,
% 114.73/17.09 ((((sk_c11) = (identity))) | ~ (((inverse @ sk_c4) = (sk_c12))) |
% 114.73/17.09 ~ (((multiply @ sk_c4 @ sk_c12) = (sk_c11)))),
% 114.73/17.09 inference('simplify', [status(thm)], [zip_derived_cl17628])).
% 114.73/17.09 thf(zip_derived_cl12308, plain,
% 114.73/17.09 ((((sk_c10) = (sk_c11)))
% 114.73/17.09 <= ((((multiply @ sk_c10 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c3) = (sk_c10))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl925, zip_derived_cl154])).
% 114.73/17.09 thf(zip_derived_cl1116, plain,
% 114.73/17.09 ((((identity) = (sk_c11)))
% 114.73/17.09 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((inverse @ sk_c4) = (sk_c12))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl1103, zip_derived_cl75])).
% 114.73/17.09 thf(zip_derived_cl230, plain,
% 114.73/17.09 ((((multiply @ sk_c5 @ sk_c11) != (sk_c10)))
% 114.73/17.09 <= ((((inverse @ sk_c5) = (sk_c11))) &
% 114.73/17.09 (![X7 : $i]:
% 114.73/17.09 (((inverse @ X7) != (sk_c11))
% 114.73/17.09 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 114.73/17.09 inference('simplify', [status(thm)], [zip_derived_cl227])).
% 114.73/17.09 thf(zip_derived_cl1181, plain,
% 114.73/17.09 ((((multiply @ sk_c5 @ identity) != (sk_c10)))
% 114.73/17.09 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((inverse @ sk_c4) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c5) = (sk_c11))) &
% 114.73/17.09 (![X7 : $i]:
% 114.73/17.09 (((inverse @ X7) != (sk_c11))
% 114.73/17.09 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 114.73/17.09 inference('s_sup-', [status(thm)],
% 114.73/17.09 [zip_derived_cl1116, zip_derived_cl230])).
% 114.73/17.09 thf(zip_derived_cl686, plain,
% 114.73/17.09 ((((sk_c5) = (multiply @ (inverse @ sk_c11) @ identity)))
% 114.73/17.09 <= ((((inverse @ sk_c5) = (sk_c11))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl243, zip_derived_cl263])).
% 114.73/17.09 thf(zip_derived_cl685, plain,
% 114.73/17.09 ((![X0 : $i]:
% 114.73/17.09 ((multiply @ sk_c5 @ X0) = (multiply @ (inverse @ sk_c11) @ X0)))
% 114.73/17.09 <= ((((inverse @ sk_c5) = (sk_c11))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl614, zip_derived_cl263])).
% 114.73/17.09 thf(zip_derived_cl1173, plain,
% 114.73/17.09 ((((multiply @ sk_c5 @ identity) = (sk_c5)))
% 114.73/17.09 <= ((((inverse @ sk_c5) = (sk_c11))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl686, zip_derived_cl685])).
% 114.73/17.09 thf(zip_derived_cl1287, plain,
% 114.73/17.09 ((((sk_c5) != (sk_c10)))
% 114.73/17.09 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((inverse @ sk_c4) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c5) = (sk_c11))) &
% 114.73/17.09 (![X7 : $i]:
% 114.73/17.09 (((inverse @ X7) != (sk_c11))
% 114.73/17.09 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 114.73/17.09 inference('demod', [status(thm)],
% 114.73/17.09 [zip_derived_cl1181, zip_derived_cl1173])).
% 114.73/17.09 thf(zip_derived_cl14433, plain,
% 114.73/17.09 ((((sk_c5) != (sk_c11)))
% 114.73/17.09 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((inverse @ sk_c4) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c5) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c3) = (sk_c10))) &
% 114.73/17.09 (![X7 : $i]:
% 114.73/17.09 (((inverse @ X7) != (sk_c11))
% 114.73/17.09 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 114.73/17.09 inference('s_sup-', [status(thm)],
% 114.73/17.09 [zip_derived_cl12308, zip_derived_cl1287])).
% 114.73/17.09 thf(zip_derived_cl1229, plain,
% 114.73/17.09 ((((sk_c5) = (identity)))
% 114.73/17.09 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((inverse @ sk_c4) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c5) = (sk_c11))))),
% 114.73/17.09 inference('demod', [status(thm)], [zip_derived_cl1213, zip_derived_cl1])).
% 114.73/17.09 thf(zip_derived_cl1116, plain,
% 114.73/17.09 ((((identity) = (sk_c11)))
% 114.73/17.09 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((inverse @ sk_c4) = (sk_c12))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl1103, zip_derived_cl75])).
% 114.73/17.09 thf(zip_derived_cl14489, plain,
% 114.73/17.09 ((((identity) != (identity)))
% 114.73/17.09 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((inverse @ sk_c4) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c5) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c3) = (sk_c10))) &
% 114.73/17.09 (![X7 : $i]:
% 114.73/17.09 (((inverse @ X7) != (sk_c11))
% 114.73/17.09 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 114.73/17.09 inference('demod', [status(thm)],
% 114.73/17.09 [zip_derived_cl14433, zip_derived_cl1229, zip_derived_cl1116])).
% 114.73/17.09 thf('65', plain,
% 114.73/17.09 (~
% 114.73/17.09 (![X7 : $i]:
% 114.73/17.09 (((inverse @ X7) != (sk_c11))
% 114.73/17.09 | ((multiply @ X7 @ sk_c11) != (sk_c10)))) |
% 114.73/17.09 ~ (((inverse @ sk_c4) = (sk_c12))) |
% 114.73/17.09 ~ (((multiply @ sk_c3 @ sk_c10) = (sk_c12))) |
% 114.73/17.09 ~ (((multiply @ sk_c10 @ sk_c12) = (sk_c11))) |
% 114.73/17.09 ~ (((inverse @ sk_c3) = (sk_c10))) |
% 114.73/17.09 ~ (((inverse @ sk_c5) = (sk_c11))) |
% 114.73/17.09 ~ (((multiply @ sk_c4 @ sk_c12) = (sk_c11)))),
% 114.73/17.09 inference('simplify', [status(thm)], [zip_derived_cl14489])).
% 114.73/17.09 thf(zip_derived_cl1171, plain,
% 114.73/17.09 ((((multiply @ sk_c5 @ sk_c11) = (identity)))
% 114.73/17.09 <= ((((inverse @ sk_c5) = (sk_c11))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl685, zip_derived_cl1])).
% 114.73/17.09 thf(zip_derived_cl296, plain,
% 114.73/17.09 ((![X0 : $i, X1 : $i, X2 : $i]:
% 114.73/17.09 (((multiply @ X1 @ X0) != (sk_c12))
% 114.73/17.09 | ((inverse @ X1) != (X0))
% 114.73/17.09 | ((multiply @ X0 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ X2) != (multiply @ X2 @ X0))
% 114.73/17.09 | ((inverse @ (multiply @ X2 @ X0)) != (X0))))
% 114.73/17.09 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.73/17.09 (((inverse @ X0) != (X2))
% 114.73/17.09 | ((multiply @ X1 @ X2) != (X0))
% 114.73/17.09 | ((inverse @ X1) != (X0))
% 114.73/17.09 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ X3) != (X2))
% 114.73/17.09 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 114.73/17.09 inference('eq_res', [status(thm)], [zip_derived_cl219])).
% 114.73/17.09 thf(zip_derived_cl1254, plain,
% 114.73/17.09 ((![X0 : $i]:
% 114.73/17.09 (((multiply @ X0 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ X0) != (sk_c11))
% 114.73/17.09 | ((multiply @ sk_c11 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ sk_c5) != (identity))
% 114.73/17.09 | ((inverse @ identity) != (sk_c11))))
% 114.73/17.09 <= ((((inverse @ sk_c5) = (sk_c11))) &
% 114.73/17.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.73/17.09 (((inverse @ X0) != (X2))
% 114.73/17.09 | ((multiply @ X1 @ X2) != (X0))
% 114.73/17.09 | ((inverse @ X1) != (X0))
% 114.73/17.09 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ X3) != (X2))
% 114.73/17.09 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 114.73/17.09 inference('s_sup-', [status(thm)],
% 114.73/17.09 [zip_derived_cl1171, zip_derived_cl296])).
% 114.73/17.09 thf(zip_derived_cl80, plain,
% 114.73/17.09 ((((inverse @ sk_c5) = (sk_c11))) <= ((((inverse @ sk_c5) = (sk_c11))))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl6])).
% 114.73/17.09 thf(zip_derived_cl1263, plain,
% 114.73/17.09 ((![X0 : $i]:
% 114.73/17.09 (((multiply @ X0 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ X0) != (sk_c11))
% 114.73/17.09 | ((multiply @ sk_c11 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((sk_c11) != (identity))
% 114.73/17.09 | ((inverse @ identity) != (sk_c11))))
% 114.73/17.09 <= ((((inverse @ sk_c5) = (sk_c11))) &
% 114.73/17.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.73/17.09 (((inverse @ X0) != (X2))
% 114.73/17.09 | ((multiply @ X1 @ X2) != (X0))
% 114.73/17.09 | ((inverse @ X1) != (X0))
% 114.73/17.09 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ X3) != (X2))
% 114.73/17.09 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 114.73/17.09 inference('demod', [status(thm)], [zip_derived_cl1254, zip_derived_cl80])).
% 114.73/17.09 thf('66', plain,
% 114.73/17.09 (~ (((multiply @ sk_c11 @ sk_c11) = (sk_c12))) |
% 114.73/17.09 ~ (((sk_c11) = (identity))) | ~ (((inverse @ sk_c5) = (sk_c11))) |
% 114.73/17.09 ~
% 114.73/17.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.73/17.09 (((inverse @ X0) != (X2))
% 114.73/17.09 | ((multiply @ X1 @ X2) != (X0))
% 114.73/17.09 | ((inverse @ X1) != (X0))
% 114.73/17.09 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ X3) != (X2))
% 114.73/17.09 | ((multiply @ X3 @ X2) != (sk_c12)))) |
% 114.73/17.09 ~ (((inverse @ identity) = (sk_c11))) |
% 114.73/17.09 (![X1 : $i]:
% 114.73/17.09 (((inverse @ X1) != (sk_c11))
% 114.73/17.09 | ((multiply @ X1 @ sk_c11) != (sk_c12))))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl1263])).
% 114.73/17.09 thf('67', plain,
% 114.73/17.09 ((![X6 : $i]:
% 114.73/17.09 (((inverse @ X6) != (sk_c10))
% 114.73/17.09 | ((multiply @ X6 @ sk_c10) != (sk_c12)))) |
% 114.73/17.09 (![X7 : $i]:
% 114.73/17.09 (((inverse @ X7) != (sk_c11))
% 114.73/17.09 | ((multiply @ X7 @ sk_c11) != (sk_c10)))) |
% 114.73/17.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.73/17.09 (((inverse @ X0) != (X2))
% 114.73/17.09 | ((multiply @ X1 @ X2) != (X0))
% 114.73/17.09 | ((inverse @ X1) != (X0))
% 114.73/17.09 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ X3) != (X2))
% 114.73/17.09 | ((multiply @ X3 @ X2) != (sk_c12)))) |
% 114.73/17.09 (![X8 : $i]:
% 114.73/17.09 (((inverse @ X8) != (sk_c12))
% 114.73/17.09 | ((multiply @ X8 @ sk_c12) != (sk_c11)))) |
% 114.73/17.09 ~ (((multiply @ sk_c10 @ sk_c12) = (sk_c11)))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl73])).
% 114.73/17.09 thf(zip_derived_cl1627, plain,
% 114.73/17.09 ((((identity) = (sk_c12)))
% 114.73/17.09 <= ((((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c3) = (sk_c10))))),
% 114.73/17.09 inference('s_sup+', [status(thm)],
% 114.73/17.09 [zip_derived_cl1595, zip_derived_cl174])).
% 114.73/17.09 thf(zip_derived_cl74, plain,
% 114.73/17.09 ((((multiply @ sk_c1 @ sk_c12) = (sk_c11)))
% 114.73/17.09 <= ((((multiply @ sk_c1 @ sk_c12) = (sk_c11))))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl3])).
% 114.73/17.09 thf(zip_derived_cl263, plain,
% 114.73/17.09 (![X0 : $i, X1 : $i]:
% 114.73/17.09 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.73/17.09 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.73/17.09 thf(zip_derived_cl681, plain,
% 114.73/17.09 ((((sk_c12) = (multiply @ (inverse @ sk_c1) @ sk_c11)))
% 114.73/17.09 <= ((((multiply @ sk_c1 @ sk_c12) = (sk_c11))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl74, zip_derived_cl263])).
% 114.73/17.09 thf(zip_derived_cl263, plain,
% 114.73/17.09 (![X0 : $i, X1 : $i]:
% 114.73/17.09 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.73/17.09 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.73/17.09 thf(zip_derived_cl712, plain,
% 114.73/17.09 ((((sk_c11) = (multiply @ (inverse @ (inverse @ sk_c1)) @ sk_c12)))
% 114.73/17.09 <= ((((multiply @ sk_c1 @ sk_c12) = (sk_c11))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl681, zip_derived_cl263])).
% 114.73/17.09 thf(zip_derived_cl38287, plain,
% 114.73/17.09 ((((sk_c11) = (multiply @ (inverse @ (inverse @ sk_c1)) @ identity)))
% 114.73/17.09 <= ((((multiply @ sk_c1 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c3) = (sk_c10))))),
% 114.73/17.09 inference('s_sup+', [status(thm)],
% 114.73/17.09 [zip_derived_cl1627, zip_derived_cl712])).
% 114.73/17.09 thf(zip_derived_cl679, plain,
% 114.73/17.09 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl263])).
% 114.73/17.09 thf(zip_derived_cl38508, plain,
% 114.73/17.09 ((((sk_c11) = (sk_c1)))
% 114.73/17.09 <= ((((multiply @ sk_c1 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c3) = (sk_c10))))),
% 114.73/17.09 inference('demod', [status(thm)],
% 114.73/17.09 [zip_derived_cl38287, zip_derived_cl679])).
% 114.73/17.09 thf(zip_derived_cl12308, plain,
% 114.73/17.09 ((((sk_c10) = (sk_c11)))
% 114.73/17.09 <= ((((multiply @ sk_c10 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c3) = (sk_c10))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl925, zip_derived_cl154])).
% 114.73/17.09 thf(zip_derived_cl94, plain,
% 114.73/17.09 ((((inverse @ sk_c1) = (sk_c12))) <= ((((inverse @ sk_c1) = (sk_c12))))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl13])).
% 114.73/17.09 thf(zip_derived_cl1, plain,
% 114.73/17.09 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 114.73/17.09 inference('cnf', [status(esa)], [left_inverse])).
% 114.73/17.09 thf(zip_derived_cl247, plain,
% 114.73/17.09 ((((multiply @ sk_c12 @ sk_c1) = (identity)))
% 114.73/17.09 <= ((((inverse @ sk_c1) = (sk_c12))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl94, zip_derived_cl1])).
% 114.73/17.09 thf(zip_derived_cl263, plain,
% 114.73/17.09 (![X0 : $i, X1 : $i]:
% 114.73/17.09 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.73/17.09 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.73/17.09 thf(zip_derived_cl683, plain,
% 114.73/17.09 ((((sk_c1) = (multiply @ (inverse @ sk_c12) @ identity)))
% 114.73/17.09 <= ((((inverse @ sk_c1) = (sk_c12))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl247, zip_derived_cl263])).
% 114.73/17.09 thf(zip_derived_cl263, plain,
% 114.73/17.09 (![X0 : $i, X1 : $i]:
% 114.73/17.09 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.73/17.09 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.73/17.09 thf(zip_derived_cl716, plain,
% 114.73/17.09 ((((identity) = (multiply @ (inverse @ (inverse @ sk_c12)) @ sk_c1)))
% 114.73/17.09 <= ((((inverse @ sk_c1) = (sk_c12))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl683, zip_derived_cl263])).
% 114.73/17.09 thf(zip_derived_cl263, plain,
% 114.73/17.09 (![X0 : $i, X1 : $i]:
% 114.73/17.09 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 114.73/17.09 inference('demod', [status(thm)], [zip_derived_cl261, zip_derived_cl0])).
% 114.73/17.09 thf(zip_derived_cl3204, plain,
% 114.73/17.09 ((((sk_c1)
% 114.73/17.09 = (multiply @ (inverse @ (inverse @ (inverse @ sk_c12))) @ identity)))
% 114.73/17.09 <= ((((inverse @ sk_c1) = (sk_c12))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl716, zip_derived_cl263])).
% 114.73/17.09 thf(zip_derived_cl679, plain,
% 114.73/17.09 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl263])).
% 114.73/17.09 thf(zip_derived_cl5091, plain,
% 114.73/17.09 ((((inverse @ sk_c12) = (sk_c1))) <= ((((inverse @ sk_c1) = (sk_c12))))),
% 114.73/17.09 inference('s_sup+', [status(thm)],
% 114.73/17.09 [zip_derived_cl3204, zip_derived_cl679])).
% 114.73/17.09 thf(zip_derived_cl174, plain,
% 114.73/17.09 ((((multiply @ sk_c3 @ sk_c10) = (sk_c12)))
% 114.73/17.09 <= ((((multiply @ sk_c3 @ sk_c10) = (sk_c12))))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl53])).
% 114.73/17.09 thf(zip_derived_cl296, plain,
% 114.73/17.09 ((![X0 : $i, X1 : $i, X2 : $i]:
% 114.73/17.09 (((multiply @ X1 @ X0) != (sk_c12))
% 114.73/17.09 | ((inverse @ X1) != (X0))
% 114.73/17.09 | ((multiply @ X0 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ X2) != (multiply @ X2 @ X0))
% 114.73/17.09 | ((inverse @ (multiply @ X2 @ X0)) != (X0))))
% 114.73/17.09 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.73/17.09 (((inverse @ X0) != (X2))
% 114.73/17.09 | ((multiply @ X1 @ X2) != (X0))
% 114.73/17.09 | ((inverse @ X1) != (X0))
% 114.73/17.09 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ X3) != (X2))
% 114.73/17.09 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 114.73/17.09 inference('eq_res', [status(thm)], [zip_derived_cl219])).
% 114.73/17.09 thf(zip_derived_cl1077, plain,
% 114.73/17.09 ((![X0 : $i]:
% 114.73/17.09 (((multiply @ X0 @ sk_c10) != (sk_c12))
% 114.73/17.09 | ((inverse @ X0) != (sk_c10))
% 114.73/17.09 | ((multiply @ sk_c10 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ sk_c3) != (sk_c12))
% 114.73/17.09 | ((inverse @ sk_c12) != (sk_c10))))
% 114.73/17.09 <= ((((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.73/17.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.73/17.09 (((inverse @ X0) != (X2))
% 114.73/17.09 | ((multiply @ X1 @ X2) != (X0))
% 114.73/17.09 | ((inverse @ X1) != (X0))
% 114.73/17.09 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ X3) != (X2))
% 114.73/17.09 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 114.73/17.09 inference('s_sup-', [status(thm)], [zip_derived_cl174, zip_derived_cl296])).
% 114.73/17.09 thf(zip_derived_cl17072, plain,
% 114.73/17.09 ((((inverse @ sk_c12) != (sk_c10)))
% 114.73/17.09 <= (~ (((inverse @ sk_c12) = (sk_c10))))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl1077])).
% 114.73/17.09 thf(zip_derived_cl17075, plain,
% 114.73/17.09 ((((sk_c1) != (sk_c10)))
% 114.73/17.09 <= (~ (((inverse @ sk_c12) = (sk_c10))) &
% 114.73/17.09 (((inverse @ sk_c1) = (sk_c12))))),
% 114.73/17.09 inference('s_sup-', [status(thm)],
% 114.73/17.09 [zip_derived_cl5091, zip_derived_cl17072])).
% 114.73/17.09 thf(zip_derived_cl20521, plain,
% 114.73/17.09 ((((sk_c1) != (sk_c11)))
% 114.73/17.09 <= (~ (((inverse @ sk_c12) = (sk_c10))) &
% 114.73/17.09 (((inverse @ sk_c1) = (sk_c12))) &
% 114.73/17.09 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c3) = (sk_c10))))),
% 114.73/17.09 inference('s_sup-', [status(thm)],
% 114.73/17.09 [zip_derived_cl12308, zip_derived_cl17075])).
% 114.73/17.09 thf(zip_derived_cl101207, plain,
% 114.73/17.09 ((((sk_c1) != (sk_c1)))
% 114.73/17.09 <= (~ (((inverse @ sk_c12) = (sk_c10))) &
% 114.73/17.09 (((multiply @ sk_c1 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((inverse @ sk_c1) = (sk_c12))) &
% 114.73/17.09 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c3) = (sk_c10))))),
% 114.73/17.09 inference('s_sup-', [status(thm)],
% 114.73/17.09 [zip_derived_cl38508, zip_derived_cl20521])).
% 114.73/17.09 thf('68', plain,
% 114.73/17.09 ((((inverse @ sk_c12) = (sk_c10))) |
% 114.73/17.09 ~ (((inverse @ sk_c1) = (sk_c12))) |
% 114.73/17.09 ~ (((multiply @ sk_c3 @ sk_c10) = (sk_c12))) |
% 114.73/17.09 ~ (((multiply @ sk_c10 @ sk_c12) = (sk_c11))) |
% 114.73/17.09 ~ (((multiply @ sk_c1 @ sk_c12) = (sk_c11))) |
% 114.73/17.09 ~ (((inverse @ sk_c3) = (sk_c10)))),
% 114.73/17.09 inference('simplify', [status(thm)], [zip_derived_cl101207])).
% 114.73/17.09 thf(zip_derived_cl687, plain,
% 114.73/17.09 ((((sk_c2) = (multiply @ (inverse @ sk_c11) @ identity)))
% 114.73/17.09 <= ((((inverse @ sk_c2) = (sk_c11))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl314, zip_derived_cl263])).
% 114.73/17.09 thf(zip_derived_cl686, plain,
% 114.73/17.09 ((((sk_c5) = (multiply @ (inverse @ sk_c11) @ identity)))
% 114.73/17.09 <= ((((inverse @ sk_c5) = (sk_c11))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl243, zip_derived_cl263])).
% 114.73/17.09 thf(zip_derived_cl769, plain,
% 114.73/17.09 ((((sk_c5) = (sk_c2)))
% 114.73/17.09 <= ((((inverse @ sk_c5) = (sk_c11))) &
% 114.73/17.09 (((inverse @ sk_c2) = (sk_c11))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl687, zip_derived_cl686])).
% 114.73/17.09 thf(zip_derived_cl114, plain,
% 114.73/17.09 ((((multiply @ sk_c2 @ sk_c11) = (sk_c10)))
% 114.73/17.09 <= ((((multiply @ sk_c2 @ sk_c11) = (sk_c10))))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl23])).
% 114.73/17.09 thf(zip_derived_cl807, plain,
% 114.73/17.09 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10)))
% 114.73/17.09 <= ((((inverse @ sk_c5) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 114.73/17.09 (((inverse @ sk_c2) = (sk_c11))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl769, zip_derived_cl114])).
% 114.73/17.09 thf(zip_derived_cl1171, plain,
% 114.73/17.09 ((((multiply @ sk_c5 @ sk_c11) = (identity)))
% 114.73/17.09 <= ((((inverse @ sk_c5) = (sk_c11))))),
% 114.73/17.09 inference('s_sup+', [status(thm)], [zip_derived_cl685, zip_derived_cl1])).
% 114.73/17.09 thf(zip_derived_cl6472, plain,
% 114.73/17.09 ((((identity) = (sk_c10)))
% 114.73/17.09 <= ((((inverse @ sk_c5) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 114.73/17.09 (((inverse @ sk_c2) = (sk_c11))))),
% 114.73/17.09 inference('demod', [status(thm)], [zip_derived_cl807, zip_derived_cl1171])).
% 114.73/17.09 thf(zip_derived_cl154, plain,
% 114.73/17.09 ((((multiply @ sk_c10 @ sk_c12) = (sk_c11)))
% 114.73/17.09 <= ((((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl43])).
% 114.73/17.09 thf(zip_derived_cl6473, plain,
% 114.73/17.09 ((((multiply @ identity @ sk_c12) = (sk_c11)))
% 114.73/17.09 <= ((((inverse @ sk_c5) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 114.73/17.09 (((inverse @ sk_c2) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.73/17.09 inference('s_sup+', [status(thm)],
% 114.73/17.09 [zip_derived_cl6472, zip_derived_cl154])).
% 114.73/17.09 thf(zip_derived_cl0, plain,
% 114.73/17.09 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 114.73/17.09 inference('cnf', [status(esa)], [left_identity])).
% 114.73/17.09 thf(zip_derived_cl6530, plain,
% 114.73/17.09 ((((sk_c12) = (sk_c11)))
% 114.73/17.09 <= ((((inverse @ sk_c5) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 114.73/17.09 (((inverse @ sk_c2) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.73/17.09 inference('demod', [status(thm)], [zip_derived_cl6473, zip_derived_cl0])).
% 114.73/17.09 thf(zip_derived_cl15782, plain,
% 114.73/17.09 ((((sk_c12) != (sk_c11)))
% 114.73/17.09 <= (~ (((sk_c12) = (inverse @ sk_c3))) &
% 114.73/17.09 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c3) = (sk_c10))))),
% 114.73/17.09 inference('s_sup-', [status(thm)],
% 114.73/17.09 [zip_derived_cl12308, zip_derived_cl13877])).
% 114.73/17.09 thf(zip_derived_cl19874, plain,
% 114.73/17.09 ((((sk_c12) != (sk_c12)))
% 114.73/17.09 <= (~ (((sk_c12) = (inverse @ sk_c3))) &
% 114.73/17.09 (((inverse @ sk_c5) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 114.73/17.09 (((inverse @ sk_c2) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c3 @ sk_c10) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c3) = (sk_c10))))),
% 114.73/17.09 inference('s_sup-', [status(thm)],
% 114.73/17.09 [zip_derived_cl6530, zip_derived_cl15782])).
% 114.73/17.09 thf('69', plain,
% 114.73/17.09 ((((sk_c12) = (inverse @ sk_c3))) |
% 114.73/17.09 ~ (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) |
% 114.73/17.09 ~ (((multiply @ sk_c10 @ sk_c12) = (sk_c11))) |
% 114.73/17.09 ~ (((inverse @ sk_c2) = (sk_c11))) |
% 114.73/17.09 ~ (((inverse @ sk_c5) = (sk_c11))) |
% 114.73/17.09 ~ (((inverse @ sk_c3) = (sk_c10))) |
% 114.73/17.09 ~ (((multiply @ sk_c3 @ sk_c10) = (sk_c12)))),
% 114.73/17.09 inference('simplify', [status(thm)], [zip_derived_cl19874])).
% 114.73/17.09 thf(zip_derived_cl6530, plain,
% 114.73/17.09 ((((sk_c12) = (sk_c11)))
% 114.73/17.09 <= ((((inverse @ sk_c5) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 114.73/17.09 (((inverse @ sk_c2) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.73/17.09 inference('demod', [status(thm)], [zip_derived_cl6473, zip_derived_cl0])).
% 114.73/17.09 thf(zip_derived_cl1578, plain,
% 114.73/17.09 ((((multiply @ sk_c10 @ sk_c11) != (sk_c12)))
% 114.73/17.09 <= (~ (((multiply @ sk_c10 @ sk_c11) = (sk_c12))))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl556])).
% 114.73/17.09 thf(zip_derived_cl8780, plain,
% 114.73/17.09 ((((multiply @ sk_c10 @ sk_c12) != (sk_c12)))
% 114.73/17.09 <= (~ (((multiply @ sk_c10 @ sk_c11) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c5) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 114.73/17.09 (((inverse @ sk_c2) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.73/17.09 inference('s_sup-', [status(thm)],
% 114.73/17.09 [zip_derived_cl6530, zip_derived_cl1578])).
% 114.73/17.09 thf(zip_derived_cl6472, plain,
% 114.73/17.09 ((((identity) = (sk_c10)))
% 114.73/17.09 <= ((((inverse @ sk_c5) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 114.73/17.09 (((inverse @ sk_c2) = (sk_c11))))),
% 114.73/17.09 inference('demod', [status(thm)], [zip_derived_cl807, zip_derived_cl1171])).
% 114.73/17.09 thf(zip_derived_cl0, plain,
% 114.73/17.09 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 114.73/17.09 inference('cnf', [status(esa)], [left_identity])).
% 114.73/17.09 thf(zip_derived_cl8830, plain,
% 114.73/17.09 ((((sk_c12) != (sk_c12)))
% 114.73/17.09 <= (~ (((multiply @ sk_c10 @ sk_c11) = (sk_c12))) &
% 114.73/17.09 (((inverse @ sk_c5) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 114.73/17.09 (((inverse @ sk_c2) = (sk_c11))) &
% 114.73/17.09 (((multiply @ sk_c10 @ sk_c12) = (sk_c11))))),
% 114.73/17.09 inference('demod', [status(thm)],
% 114.73/17.09 [zip_derived_cl8780, zip_derived_cl6472, zip_derived_cl0])).
% 114.73/17.09 thf('70', plain,
% 114.73/17.09 ((((multiply @ sk_c10 @ sk_c11) = (sk_c12))) |
% 114.73/17.09 ~ (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) |
% 114.73/17.09 ~ (((inverse @ sk_c2) = (sk_c11))) |
% 114.73/17.09 ~ (((multiply @ sk_c10 @ sk_c12) = (sk_c11))) |
% 114.73/17.09 ~ (((inverse @ sk_c5) = (sk_c11)))),
% 114.73/17.09 inference('simplify', [status(thm)], [zip_derived_cl8830])).
% 114.73/17.09 thf(zip_derived_cl114, plain,
% 114.73/17.09 ((((multiply @ sk_c2 @ sk_c11) = (sk_c10)))
% 114.73/17.09 <= ((((multiply @ sk_c2 @ sk_c11) = (sk_c10))))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl23])).
% 114.73/17.09 thf(zip_derived_cl134, plain,
% 114.73/17.09 ((((inverse @ sk_c2) = (sk_c11))) <= ((((inverse @ sk_c2) = (sk_c11))))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl33])).
% 114.73/17.09 thf(zip_derived_cl215, plain,
% 114.73/17.09 ((![X7 : $i]:
% 114.73/17.09 (((inverse @ X7) != (sk_c11))
% 114.73/17.09 | ((multiply @ X7 @ sk_c11) != (sk_c10))))
% 114.73/17.09 <= ((![X7 : $i]:
% 114.73/17.09 (((inverse @ X7) != (sk_c11))
% 114.73/17.09 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl73])).
% 114.73/17.09 thf(zip_derived_cl317, plain,
% 114.73/17.09 (((((sk_c11) != (sk_c11)) | ((multiply @ sk_c2 @ sk_c11) != (sk_c10))))
% 114.73/17.09 <= ((((inverse @ sk_c2) = (sk_c11))) &
% 114.73/17.09 (![X7 : $i]:
% 114.73/17.09 (((inverse @ X7) != (sk_c11))
% 114.73/17.09 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 114.73/17.09 inference('s_sup-', [status(thm)], [zip_derived_cl134, zip_derived_cl215])).
% 114.73/17.09 thf(zip_derived_cl319, plain,
% 114.73/17.09 ((((multiply @ sk_c2 @ sk_c11) != (sk_c10)))
% 114.73/17.09 <= ((((inverse @ sk_c2) = (sk_c11))) &
% 114.73/17.09 (![X7 : $i]:
% 114.73/17.09 (((inverse @ X7) != (sk_c11))
% 114.73/17.09 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 114.73/17.09 inference('simplify', [status(thm)], [zip_derived_cl317])).
% 114.73/17.09 thf(zip_derived_cl486, plain,
% 114.73/17.09 ((((sk_c10) != (sk_c10)))
% 114.73/17.09 <= ((((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 114.73/17.09 (((inverse @ sk_c2) = (sk_c11))) &
% 114.73/17.09 (![X7 : $i]:
% 114.73/17.09 (((inverse @ X7) != (sk_c11))
% 114.73/17.09 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 114.73/17.09 inference('s_sup-', [status(thm)], [zip_derived_cl114, zip_derived_cl319])).
% 114.73/17.09 thf('71', plain,
% 114.73/17.09 (~
% 114.73/17.09 (![X7 : $i]:
% 114.73/17.09 (((inverse @ X7) != (sk_c11))
% 114.73/17.09 | ((multiply @ X7 @ sk_c11) != (sk_c10)))) |
% 114.73/17.09 ~ (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) |
% 114.73/17.09 ~ (((inverse @ sk_c2) = (sk_c11)))),
% 114.73/17.09 inference('simplify', [status(thm)], [zip_derived_cl486])).
% 114.73/17.09 thf('72', plain,
% 114.73/17.09 ((((inverse @ sk_c1) = (sk_c12))) |
% 114.73/17.09 (((multiply @ sk_c4 @ sk_c12) = (sk_c11)))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl13])).
% 114.73/17.09 thf('73', plain,
% 114.73/17.09 ((((multiply @ sk_c2 @ sk_c11) = (sk_c10))) |
% 114.73/17.09 (((multiply @ sk_c4 @ sk_c12) = (sk_c11)))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl23])).
% 114.73/17.09 thf('74', plain,
% 114.73/17.09 (~ (((inverse @ sk_c12) = (sk_c10))) |
% 114.73/17.09 ~ (((sk_c12) = (inverse @ sk_c3))) |
% 114.73/17.09 ~ (((multiply @ sk_c10 @ sk_c11) = (sk_c12))) |
% 114.73/17.09 ~
% 114.73/17.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 114.73/17.09 (((inverse @ X0) != (X2))
% 114.73/17.09 | ((multiply @ X1 @ X2) != (X0))
% 114.73/17.09 | ((inverse @ X1) != (X0))
% 114.73/17.09 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 114.73/17.09 | ((inverse @ X3) != (X2))
% 114.73/17.09 | ((multiply @ X3 @ X2) != (sk_c12)))) |
% 114.73/17.09 ~ (((multiply @ sk_c3 @ sk_c10) = (sk_c12))) |
% 114.73/17.09 (![X6 : $i]:
% 114.73/17.09 (((inverse @ X6) != (sk_c10))
% 114.73/17.09 | ((multiply @ X6 @ sk_c10) != (sk_c12))))),
% 114.73/17.09 inference('split', [status(esa)], [zip_derived_cl1077])).
% 114.73/17.09 thf(zip_derived_cl102211, plain, ($false),
% 114.73/17.09 inference('sat_resolution*', [status(thm)],
% 114.73/17.09 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 114.73/17.09 '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
% 114.73/17.09 '22', '23', '24', '25', '26', '27', '28', '29', '30', '31',
% 114.73/17.09 '32', '33', '34', '35', '36', '37', '38', '39', '40', '41',
% 114.73/17.09 '42', '43', '44', '45', '46', '47', '48', '49', '50', '51',
% 114.73/17.09 '52', '53', '54', '55', '56', '57', '58', '59', '60', '61',
% 114.73/17.09 '62', '63', '64', '65', '66', '67', '68', '69', '70', '71',
% 114.73/17.09 '72', '73', '74'])).
% 114.73/17.09
% 114.73/17.09 % SZS output end Refutation
% 114.73/17.09
% 114.73/17.09
% 114.73/17.09 % /export/starexec/sandbox/solver/bin/fo/fo1_lcnf.sh running for 50s
% 114.73/17.09 % Terminating...
% 115.32/17.23 % Runner terminated.
% 115.32/17.25 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------