TSTP Solution File: GRP263-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP263-1 : 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.qo6tbdgJek true
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:50:57 EDT 2023
% Result : Unsatisfiable 259.22s 38.02s
% Output : Refutation 259.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP263-1 : TPTP v8.1.2. Released v2.5.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.qo6tbdgJek true
% 0.14/0.36 % Computer : n005.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Aug 29 01:10:08 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.14/0.37 % Running portfolio for 300 s
% 0.14/0.37 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.37 % Number of cores: 8
% 0.14/0.37 % Python version: Python 3.6.8
% 0.14/0.37 % Running in FO mode
% 0.22/0.62 % Total configuration time : 435
% 0.22/0.62 % Estimated wc time : 1092
% 0.22/0.62 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.69 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.77 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.77 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.22/0.77 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 259.22/38.02 % Solved by fo/fo1_av.sh.
% 259.22/38.02 % done 21407 iterations in 37.181s
% 259.22/38.02 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 259.22/38.02 % SZS output start Refutation
% 259.22/38.02 thf(sk_c5_type, type, sk_c5: $i).
% 259.22/38.02 thf(sk_c10_type, type, sk_c10: $i).
% 259.22/38.02 thf(sk_c7_type, type, sk_c7: $i).
% 259.22/38.02 thf(sk_c9_type, type, sk_c9: $i).
% 259.22/38.02 thf(sk_c4_type, type, sk_c4: $i).
% 259.22/38.02 thf(identity_type, type, identity: $i).
% 259.22/38.02 thf(multiply_type, type, multiply: $i > $i > $i).
% 259.22/38.02 thf(sk_c11_type, type, sk_c11: $i).
% 259.22/38.02 thf(sk_c2_type, type, sk_c2: $i).
% 259.22/38.02 thf(inverse_type, type, inverse: $i > $i).
% 259.22/38.02 thf(sk_c3_type, type, sk_c3: $i).
% 259.22/38.02 thf(sk_c6_type, type, sk_c6: $i).
% 259.22/38.02 thf(sk_c8_type, type, sk_c8: $i).
% 259.22/38.02 thf(sk_c1_type, type, sk_c1: $i).
% 259.22/38.02 thf(prove_this_4, conjecture,
% 259.22/38.02 (~( ( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 259.22/38.02 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 259.22/38.02 thf(zf_stmt_0, negated_conjecture,
% 259.22/38.02 (( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 259.22/38.02 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) )),
% 259.22/38.02 inference('cnf.neg', [status(esa)], [prove_this_4])).
% 259.22/38.02 thf(zip_derived_cl6, plain,
% 259.22/38.02 ((((inverse @ sk_c4) = (sk_c10))
% 259.22/38.02 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 259.22/38.02 inference('cnf', [status(esa)], [zf_stmt_0])).
% 259.22/38.02 thf(zip_derived_cl60, plain,
% 259.22/38.02 ((((inverse @ sk_c4) = (sk_c10))) <= ((((inverse @ sk_c4) = (sk_c10))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl6])).
% 259.22/38.02 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 259.22/38.02 thf(zip_derived_cl1, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_inverse])).
% 259.22/38.02 thf(zip_derived_cl179, plain,
% 259.22/38.02 ((((multiply @ sk_c10 @ sk_c4) = (identity)))
% 259.22/38.02 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl60, zip_derived_cl1])).
% 259.22/38.02 thf(associativity, axiom,
% 259.22/38.02 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 259.22/38.02 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 259.22/38.02 thf(zip_derived_cl2, plain,
% 259.22/38.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 259.22/38.02 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 259.22/38.02 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 259.22/38.02 inference('cnf', [status(esa)], [associativity])).
% 259.22/38.02 thf(zip_derived_cl441, plain,
% 259.22/38.02 ((![X0 : $i]:
% 259.22/38.02 ((multiply @ identity @ X0)
% 259.22/38.02 = (multiply @ sk_c10 @ (multiply @ sk_c4 @ X0))))
% 259.22/38.02 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl179, zip_derived_cl2])).
% 259.22/38.02 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 259.22/38.02 thf(zip_derived_cl0, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_identity])).
% 259.22/38.02 thf(zip_derived_cl442, plain,
% 259.22/38.02 ((![X0 : $i]: ((X0) = (multiply @ sk_c10 @ (multiply @ sk_c4 @ X0))))
% 259.22/38.02 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl441, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl1, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_inverse])).
% 259.22/38.02 thf(zip_derived_cl2, plain,
% 259.22/38.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 259.22/38.02 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 259.22/38.02 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 259.22/38.02 inference('cnf', [status(esa)], [associativity])).
% 259.22/38.02 thf(zip_derived_cl194, plain,
% 259.22/38.02 (![X0 : $i, X1 : $i]:
% 259.22/38.02 ((multiply @ identity @ X0)
% 259.22/38.02 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 259.22/38.02 thf(zip_derived_cl0, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_identity])).
% 259.22/38.02 thf(zip_derived_cl196, plain,
% 259.22/38.02 (![X0 : $i, X1 : $i]:
% 259.22/38.02 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl504, plain,
% 259.22/38.02 ((![X0 : $i]:
% 259.22/38.02 ((multiply @ sk_c4 @ X0) = (multiply @ (inverse @ sk_c10) @ X0)))
% 259.22/38.02 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl442, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl1, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_inverse])).
% 259.22/38.02 thf(zip_derived_cl1059, plain,
% 259.22/38.02 ((((multiply @ sk_c4 @ sk_c10) = (identity)))
% 259.22/38.02 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl504, zip_derived_cl1])).
% 259.22/38.02 thf(prove_this_3, conjecture,
% 259.22/38.02 (~( ( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 259.22/38.02 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 259.22/38.02 thf(zf_stmt_1, negated_conjecture,
% 259.22/38.02 (( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 259.22/38.02 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) )),
% 259.22/38.02 inference('cnf.neg', [status(esa)], [prove_this_3])).
% 259.22/38.02 thf(zip_derived_cl5, plain,
% 259.22/38.02 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))
% 259.22/38.02 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 259.22/38.02 inference('cnf', [status(esa)], [zf_stmt_1])).
% 259.22/38.02 thf(zip_derived_cl58, plain,
% 259.22/38.02 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9)))
% 259.22/38.02 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl5])).
% 259.22/38.02 thf(zip_derived_cl1073, plain,
% 259.22/38.02 ((((identity) = (sk_c9)))
% 259.22/38.02 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl1059, zip_derived_cl58])).
% 259.22/38.02 thf(prove_this_2, conjecture,
% 259.22/38.02 (~( ( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 259.22/38.02 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 259.22/38.02 thf(zf_stmt_2, negated_conjecture,
% 259.22/38.02 (( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 259.22/38.02 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) )),
% 259.22/38.02 inference('cnf.neg', [status(esa)], [prove_this_2])).
% 259.22/38.02 thf(zip_derived_cl4, plain,
% 259.22/38.02 ((((inverse @ sk_c3) = (sk_c11))
% 259.22/38.02 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 259.22/38.02 inference('cnf', [status(esa)], [zf_stmt_2])).
% 259.22/38.02 thf(zip_derived_cl56, plain,
% 259.22/38.02 ((((inverse @ sk_c3) = (sk_c11))) <= ((((inverse @ sk_c3) = (sk_c11))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl4])).
% 259.22/38.02 thf(zip_derived_cl1, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_inverse])).
% 259.22/38.02 thf(zip_derived_cl178, plain,
% 259.22/38.02 ((((multiply @ sk_c11 @ sk_c3) = (identity)))
% 259.22/38.02 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl56, zip_derived_cl1])).
% 259.22/38.02 thf(zip_derived_cl2, plain,
% 259.22/38.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 259.22/38.02 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 259.22/38.02 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 259.22/38.02 inference('cnf', [status(esa)], [associativity])).
% 259.22/38.02 thf(zip_derived_cl431, plain,
% 259.22/38.02 ((![X0 : $i]:
% 259.22/38.02 ((multiply @ identity @ X0)
% 259.22/38.02 = (multiply @ sk_c11 @ (multiply @ sk_c3 @ X0))))
% 259.22/38.02 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl178, zip_derived_cl2])).
% 259.22/38.02 thf(zip_derived_cl0, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_identity])).
% 259.22/38.02 thf(zip_derived_cl432, plain,
% 259.22/38.02 ((![X0 : $i]: ((X0) = (multiply @ sk_c11 @ (multiply @ sk_c3 @ X0))))
% 259.22/38.02 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl431, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl196, plain,
% 259.22/38.02 (![X0 : $i, X1 : $i]:
% 259.22/38.02 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl501, plain,
% 259.22/38.02 ((![X0 : $i]:
% 259.22/38.02 ((multiply @ sk_c3 @ X0) = (multiply @ (inverse @ sk_c11) @ X0)))
% 259.22/38.02 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl432, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl1, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_inverse])).
% 259.22/38.02 thf(zip_derived_cl918, plain,
% 259.22/38.02 ((((multiply @ sk_c3 @ sk_c11) = (identity)))
% 259.22/38.02 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl501, zip_derived_cl1])).
% 259.22/38.02 thf(prove_this_1, conjecture,
% 259.22/38.02 (~( ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 259.22/38.02 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 259.22/38.02 thf(zf_stmt_3, negated_conjecture,
% 259.22/38.02 (( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 259.22/38.02 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) )),
% 259.22/38.02 inference('cnf.neg', [status(esa)], [prove_this_1])).
% 259.22/38.02 thf(zip_derived_cl3, plain,
% 259.22/38.02 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))
% 259.22/38.02 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 259.22/38.02 inference('cnf', [status(esa)], [zf_stmt_3])).
% 259.22/38.02 thf(zip_derived_cl55, plain,
% 259.22/38.02 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl3])).
% 259.22/38.02 thf(zip_derived_cl1002, plain,
% 259.22/38.02 ((((identity) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl918, zip_derived_cl55])).
% 259.22/38.02 thf(prove_this_51, conjecture,
% 259.22/38.02 (~( ( ( multiply @ X7 @ X6 ) != ( X8 ) ) |
% 259.22/38.02 ( ( inverse @ X8 ) != ( X6 ) ) | ( ( inverse @ X7 ) != ( X8 ) ) |
% 259.22/38.02 ( ( multiply @ X6 @ sk_c10 ) != ( sk_c11 ) ) |
% 259.22/38.02 ( ( inverse @ X5 ) != ( X6 ) ) |
% 259.22/38.02 ( ( multiply @ X5 @ X6 ) != ( sk_c11 ) ) |
% 259.22/38.02 ( ( inverse @ X2 ) != ( sk_c10 ) ) |
% 259.22/38.02 ( ( multiply @ X2 @ sk_c10 ) != ( sk_c9 ) ) |
% 259.22/38.02 ( ( inverse @ X1 ) != ( sk_c11 ) ) |
% 259.22/38.02 ( ( multiply @ X1 @ sk_c11 ) != ( sk_c10 ) ) |
% 259.22/38.02 ( ( multiply @ sk_c9 @ sk_c10 ) != ( sk_c11 ) ) |
% 259.22/38.02 ( ( inverse @ X4 ) != ( sk_c10 ) ) |
% 259.22/38.02 ( ( multiply @ X4 @ sk_c10 ) != ( sk_c9 ) ) |
% 259.22/38.02 ( ( inverse @ X3 ) != ( sk_c11 ) ) |
% 259.22/38.02 ( ( multiply @ X3 @ sk_c11 ) != ( sk_c10 ) ) ))).
% 259.22/38.02 thf(zf_stmt_4, negated_conjecture,
% 259.22/38.02 (( ( multiply @ X7 @ X6 ) != ( X8 ) ) | ( ( inverse @ X8 ) != ( X6 ) ) |
% 259.22/38.02 ( ( inverse @ X7 ) != ( X8 ) ) |
% 259.22/38.02 ( ( multiply @ X6 @ sk_c10 ) != ( sk_c11 ) ) |
% 259.22/38.02 ( ( inverse @ X5 ) != ( X6 ) ) |
% 259.22/38.02 ( ( multiply @ X5 @ X6 ) != ( sk_c11 ) ) |
% 259.22/38.02 ( ( inverse @ X2 ) != ( sk_c10 ) ) |
% 259.22/38.02 ( ( multiply @ X2 @ sk_c10 ) != ( sk_c9 ) ) |
% 259.22/38.02 ( ( inverse @ X1 ) != ( sk_c11 ) ) |
% 259.22/38.02 ( ( multiply @ X1 @ sk_c11 ) != ( sk_c10 ) ) |
% 259.22/38.02 ( ( multiply @ sk_c9 @ sk_c10 ) != ( sk_c11 ) ) |
% 259.22/38.02 ( ( inverse @ X4 ) != ( sk_c10 ) ) |
% 259.22/38.02 ( ( multiply @ X4 @ sk_c10 ) != ( sk_c9 ) ) |
% 259.22/38.02 ( ( inverse @ X3 ) != ( sk_c11 ) ) |
% 259.22/38.02 ( ( multiply @ X3 @ sk_c11 ) != ( sk_c10 ) )),
% 259.22/38.02 inference('cnf.neg', [status(esa)], [prove_this_51])).
% 259.22/38.02 thf(zip_derived_cl53, plain,
% 259.22/38.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 259.22/38.02 (((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X0) != (X2))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11))
% 259.22/38.02 | ((inverse @ X4) != (sk_c10))
% 259.22/38.02 | ((multiply @ X4 @ sk_c10) != (sk_c9))
% 259.22/38.02 | ((inverse @ X5) != (sk_c11))
% 259.22/38.02 | ((multiply @ X5 @ sk_c11) != (sk_c10))
% 259.22/38.02 | ((multiply @ sk_c9 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X6) != (sk_c10))
% 259.22/38.02 | ((multiply @ X6 @ sk_c10) != (sk_c9))
% 259.22/38.02 | ((inverse @ X7) != (sk_c11))
% 259.22/38.02 | ((multiply @ X7 @ sk_c11) != (sk_c10)))),
% 259.22/38.02 inference('cnf', [status(esa)], [zf_stmt_4])).
% 259.22/38.02 thf(zip_derived_cl159, plain,
% 259.22/38.02 ((((multiply @ sk_c9 @ sk_c10) != (sk_c11)))
% 259.22/38.02 <= (~ (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl53])).
% 259.22/38.02 thf(zip_derived_cl1892, plain,
% 259.22/38.02 ((((multiply @ sk_c9 @ identity) != (sk_c11)))
% 259.22/38.02 <= (~ (((multiply @ sk_c9 @ sk_c10) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))))),
% 259.22/38.02 inference('s_sup-', [status(thm)],
% 259.22/38.02 [zip_derived_cl1002, zip_derived_cl159])).
% 259.22/38.02 thf(zip_derived_cl57661, plain,
% 259.22/38.02 ((((multiply @ identity @ identity) != (sk_c11)))
% 259.22/38.02 <= (~ (((multiply @ sk_c9 @ sk_c10) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))))),
% 259.22/38.02 inference('s_sup-', [status(thm)],
% 259.22/38.02 [zip_derived_cl1073, zip_derived_cl1892])).
% 259.22/38.02 thf(zip_derived_cl0, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_identity])).
% 259.22/38.02 thf(zip_derived_cl57676, plain,
% 259.22/38.02 ((((identity) != (sk_c11)))
% 259.22/38.02 <= (~ (((multiply @ sk_c9 @ sk_c10) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl57661, zip_derived_cl0])).
% 259.22/38.02 thf(prove_this_6, conjecture,
% 259.22/38.02 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 259.22/38.02 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 259.22/38.02 thf(zf_stmt_5, negated_conjecture,
% 259.22/38.02 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 259.22/38.02 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) )),
% 259.22/38.02 inference('cnf.neg', [status(esa)], [prove_this_6])).
% 259.22/38.02 thf(zip_derived_cl8, plain,
% 259.22/38.02 ((((inverse @ sk_c5) = (sk_c8))
% 259.22/38.02 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 259.22/38.02 inference('cnf', [status(esa)], [zf_stmt_5])).
% 259.22/38.02 thf(zip_derived_cl64, plain,
% 259.22/38.02 ((((inverse @ sk_c5) = (sk_c8))) <= ((((inverse @ sk_c5) = (sk_c8))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl8])).
% 259.22/38.02 thf(prove_this_5, conjecture,
% 259.22/38.02 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 259.22/38.02 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 259.22/38.02 thf(zf_stmt_6, negated_conjecture,
% 259.22/38.02 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 259.22/38.02 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) )),
% 259.22/38.02 inference('cnf.neg', [status(esa)], [prove_this_5])).
% 259.22/38.02 thf(zip_derived_cl7, plain,
% 259.22/38.02 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))
% 259.22/38.02 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 259.22/38.02 inference('cnf', [status(esa)], [zf_stmt_6])).
% 259.22/38.02 thf(zip_derived_cl62, plain,
% 259.22/38.02 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl7])).
% 259.22/38.02 thf(zip_derived_cl196, plain,
% 259.22/38.02 (![X0 : $i, X1 : $i]:
% 259.22/38.02 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl510, plain,
% 259.22/38.02 ((((sk_c8) = (multiply @ (inverse @ sk_c5) @ sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl62, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl614, plain,
% 259.22/38.02 ((((sk_c8) = (multiply @ sk_c8 @ sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c5) = (sk_c8))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl64, zip_derived_cl510])).
% 259.22/38.02 thf(zip_derived_cl196, plain,
% 259.22/38.02 (![X0 : $i, X1 : $i]:
% 259.22/38.02 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl5602, plain,
% 259.22/38.02 ((((sk_c11) = (multiply @ (inverse @ sk_c8) @ sk_c8)))
% 259.22/38.02 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c5) = (sk_c8))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl614, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl1, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_inverse])).
% 259.22/38.02 thf(zip_derived_cl5616, plain,
% 259.22/38.02 ((((sk_c11) = (identity)))
% 259.22/38.02 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c5) = (sk_c8))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl5602, zip_derived_cl1])).
% 259.22/38.02 thf(prove_this_11, conjecture,
% 259.22/38.02 (~( ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 259.22/38.02 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 259.22/38.02 thf(zf_stmt_7, negated_conjecture,
% 259.22/38.02 (( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 259.22/38.02 ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 259.22/38.02 inference('cnf.neg', [status(esa)], [prove_this_11])).
% 259.22/38.02 thf(zip_derived_cl13, plain,
% 259.22/38.02 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))
% 259.22/38.02 | ((inverse @ sk_c1) = (sk_c11)))),
% 259.22/38.02 inference('cnf', [status(esa)], [zf_stmt_7])).
% 259.22/38.02 thf(zip_derived_cl74, plain,
% 259.22/38.02 ((((inverse @ sk_c1) = (sk_c11))) <= ((((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl13])).
% 259.22/38.02 thf(zip_derived_cl1, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_inverse])).
% 259.22/38.02 thf(zip_derived_cl177, plain,
% 259.22/38.02 ((((multiply @ sk_c11 @ sk_c1) = (identity)))
% 259.22/38.02 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl74, zip_derived_cl1])).
% 259.22/38.02 thf(zip_derived_cl2, plain,
% 259.22/38.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 259.22/38.02 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 259.22/38.02 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 259.22/38.02 inference('cnf', [status(esa)], [associativity])).
% 259.22/38.02 thf(zip_derived_cl428, plain,
% 259.22/38.02 ((![X0 : $i]:
% 259.22/38.02 ((multiply @ identity @ X0)
% 259.22/38.02 = (multiply @ sk_c11 @ (multiply @ sk_c1 @ X0))))
% 259.22/38.02 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl177, zip_derived_cl2])).
% 259.22/38.02 thf(zip_derived_cl0, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_identity])).
% 259.22/38.02 thf(zip_derived_cl429, plain,
% 259.22/38.02 ((![X0 : $i]: ((X0) = (multiply @ sk_c11 @ (multiply @ sk_c1 @ X0))))
% 259.22/38.02 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl428, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl196, plain,
% 259.22/38.02 (![X0 : $i, X1 : $i]:
% 259.22/38.02 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl500, plain,
% 259.22/38.02 ((![X0 : $i]:
% 259.22/38.02 ((multiply @ sk_c1 @ X0) = (multiply @ (inverse @ sk_c11) @ X0)))
% 259.22/38.02 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl429, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl1, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_inverse])).
% 259.22/38.02 thf(zip_derived_cl807, plain,
% 259.22/38.02 ((((multiply @ sk_c1 @ sk_c11) = (identity)))
% 259.22/38.02 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl500, zip_derived_cl1])).
% 259.22/38.02 thf(zip_derived_cl54, plain,
% 259.22/38.02 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl3])).
% 259.22/38.02 thf(zip_derived_cl819, plain,
% 259.22/38.02 ((((identity) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl807, zip_derived_cl54])).
% 259.22/38.02 thf(zip_derived_cl179, plain,
% 259.22/38.02 ((((multiply @ sk_c10 @ sk_c4) = (identity)))
% 259.22/38.02 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl60, zip_derived_cl1])).
% 259.22/38.02 thf(zip_derived_cl196, plain,
% 259.22/38.02 (![X0 : $i, X1 : $i]:
% 259.22/38.02 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl505, plain,
% 259.22/38.02 ((((sk_c4) = (multiply @ (inverse @ sk_c10) @ identity)))
% 259.22/38.02 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl179, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl958, plain,
% 259.22/38.02 ((((sk_c4) = (multiply @ (inverse @ identity) @ identity)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl819, zip_derived_cl505])).
% 259.22/38.02 thf(zip_derived_cl1, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_inverse])).
% 259.22/38.02 thf(zip_derived_cl973, plain,
% 259.22/38.02 ((((sk_c4) = (identity)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl958, zip_derived_cl1])).
% 259.22/38.02 thf(zip_derived_cl60, plain,
% 259.22/38.02 ((((inverse @ sk_c4) = (sk_c10))) <= ((((inverse @ sk_c4) = (sk_c10))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl6])).
% 259.22/38.02 thf(zip_derived_cl1597, plain,
% 259.22/38.02 ((((inverse @ identity) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl973, zip_derived_cl60])).
% 259.22/38.02 thf(zip_derived_cl819, plain,
% 259.22/38.02 ((((identity) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl807, zip_derived_cl54])).
% 259.22/38.02 thf(zip_derived_cl1630, plain,
% 259.22/38.02 ((((inverse @ identity) = (identity)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl1597, zip_derived_cl819])).
% 259.22/38.02 thf(zip_derived_cl178, plain,
% 259.22/38.02 ((((multiply @ sk_c11 @ sk_c3) = (identity)))
% 259.22/38.02 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl56, zip_derived_cl1])).
% 259.22/38.02 thf(zip_derived_cl196, plain,
% 259.22/38.02 (![X0 : $i, X1 : $i]:
% 259.22/38.02 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl503, plain,
% 259.22/38.02 ((((sk_c3) = (multiply @ (inverse @ sk_c11) @ identity)))
% 259.22/38.02 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl178, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl177, plain,
% 259.22/38.02 ((((multiply @ sk_c11 @ sk_c1) = (identity)))
% 259.22/38.02 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl74, zip_derived_cl1])).
% 259.22/38.02 thf(zip_derived_cl196, plain,
% 259.22/38.02 (![X0 : $i, X1 : $i]:
% 259.22/38.02 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl502, plain,
% 259.22/38.02 ((((sk_c1) = (multiply @ (inverse @ sk_c11) @ identity)))
% 259.22/38.02 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl177, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl538, plain,
% 259.22/38.02 ((((sk_c1) = (sk_c3)))
% 259.22/38.02 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl503, zip_derived_cl502])).
% 259.22/38.02 thf(zip_derived_cl55, plain,
% 259.22/38.02 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl3])).
% 259.22/38.02 thf(zip_derived_cl541, plain,
% 259.22/38.02 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl538, zip_derived_cl55])).
% 259.22/38.02 thf(zip_derived_cl807, plain,
% 259.22/38.02 ((((multiply @ sk_c1 @ sk_c11) = (identity)))
% 259.22/38.02 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl500, zip_derived_cl1])).
% 259.22/38.02 thf(zip_derived_cl1139, plain,
% 259.22/38.02 ((((identity) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl541, zip_derived_cl807])).
% 259.22/38.02 thf(zip_derived_cl505, plain,
% 259.22/38.02 ((((sk_c4) = (multiply @ (inverse @ sk_c10) @ identity)))
% 259.22/38.02 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl179, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl1174, plain,
% 259.22/38.02 ((((sk_c4) = (multiply @ (inverse @ identity) @ identity)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)],
% 259.22/38.02 [zip_derived_cl1139, zip_derived_cl505])).
% 259.22/38.02 thf(zip_derived_cl1, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_inverse])).
% 259.22/38.02 thf(zip_derived_cl1198, plain,
% 259.22/38.02 ((((sk_c4) = (identity)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl1174, zip_derived_cl1])).
% 259.22/38.02 thf(zip_derived_cl58, plain,
% 259.22/38.02 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9)))
% 259.22/38.02 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl5])).
% 259.22/38.02 thf(zip_derived_cl1467, plain,
% 259.22/38.02 ((((multiply @ identity @ sk_c10) = (sk_c9)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl1198, zip_derived_cl58])).
% 259.22/38.02 thf(zip_derived_cl1139, plain,
% 259.22/38.02 ((((identity) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl541, zip_derived_cl807])).
% 259.22/38.02 thf(zip_derived_cl0, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_identity])).
% 259.22/38.02 thf(zip_derived_cl1500, plain,
% 259.22/38.02 ((((identity) = (sk_c9)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)],
% 259.22/38.02 [zip_derived_cl1467, zip_derived_cl1139, zip_derived_cl0])).
% 259.22/38.02 thf(prove_this_41, conjecture,
% 259.22/38.02 (~( ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 259.22/38.02 ( ( multiply @ sk_c9 @ sk_c10 ) = ( sk_c11 ) ) ))).
% 259.22/38.02 thf(zf_stmt_8, negated_conjecture,
% 259.22/38.02 (( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 259.22/38.02 ( ( multiply @ sk_c9 @ sk_c10 ) = ( sk_c11 ) )),
% 259.22/38.02 inference('cnf.neg', [status(esa)], [prove_this_41])).
% 259.22/38.02 thf(zip_derived_cl43, plain,
% 259.22/38.02 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))
% 259.22/38.02 | ((multiply @ sk_c9 @ sk_c10) = (sk_c11)))),
% 259.22/38.02 inference('cnf', [status(esa)], [zf_stmt_8])).
% 259.22/38.02 thf(zip_derived_cl134, plain,
% 259.22/38.02 ((((multiply @ sk_c9 @ sk_c10) = (sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl43])).
% 259.22/38.02 thf(zip_derived_cl1994, plain,
% 259.22/38.02 ((((multiply @ identity @ sk_c10) = (sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)],
% 259.22/38.02 [zip_derived_cl1500, zip_derived_cl134])).
% 259.22/38.02 thf(zip_derived_cl1002, plain,
% 259.22/38.02 ((((identity) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl918, zip_derived_cl55])).
% 259.22/38.02 thf(zip_derived_cl0, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_identity])).
% 259.22/38.02 thf(zip_derived_cl2010, plain,
% 259.22/38.02 ((((identity) = (sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)],
% 259.22/38.02 [zip_derived_cl1994, zip_derived_cl1002, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl54, plain,
% 259.22/38.02 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl3])).
% 259.22/38.02 thf(zip_derived_cl2121, plain,
% 259.22/38.02 ((((multiply @ sk_c1 @ identity) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl2010, zip_derived_cl54])).
% 259.22/38.02 thf(zip_derived_cl502, plain,
% 259.22/38.02 ((((sk_c1) = (multiply @ (inverse @ sk_c11) @ identity)))
% 259.22/38.02 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl177, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl500, plain,
% 259.22/38.02 ((![X0 : $i]:
% 259.22/38.02 ((multiply @ sk_c1 @ X0) = (multiply @ (inverse @ sk_c11) @ X0)))
% 259.22/38.02 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl429, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl809, plain,
% 259.22/38.02 ((((multiply @ sk_c1 @ identity) = (sk_c1)))
% 259.22/38.02 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl502, zip_derived_cl500])).
% 259.22/38.02 thf(zip_derived_cl1002, plain,
% 259.22/38.02 ((((identity) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl918, zip_derived_cl55])).
% 259.22/38.02 thf(zip_derived_cl2192, plain,
% 259.22/38.02 ((((sk_c1) = (identity)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)],
% 259.22/38.02 [zip_derived_cl2121, zip_derived_cl809, zip_derived_cl1002])).
% 259.22/38.02 thf(zip_derived_cl54, plain,
% 259.22/38.02 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl3])).
% 259.22/38.02 thf(zip_derived_cl196, plain,
% 259.22/38.02 (![X0 : $i, X1 : $i]:
% 259.22/38.02 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl499, plain,
% 259.22/38.02 ((((sk_c11) = (multiply @ (inverse @ sk_c1) @ sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl54, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl158, plain,
% 259.22/38.02 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11))))
% 259.22/38.02 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl53])).
% 259.22/38.02 thf(zip_derived_cl526, plain,
% 259.22/38.02 ((![X0 : $i, X1 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c10))
% 259.22/38.02 | ((sk_c11) != (X0))
% 259.22/38.02 | ((inverse @ (inverse @ sk_c1)) != (X0))
% 259.22/38.02 | ((multiply @ sk_c10 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X1) != (sk_c10))
% 259.22/38.02 | ((multiply @ X1 @ sk_c10) != (sk_c11))))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.02 inference('s_sup-', [status(thm)], [zip_derived_cl499, zip_derived_cl158])).
% 259.22/38.02 thf(zip_derived_cl2874, plain,
% 259.22/38.02 ((![X0 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c10))
% 259.22/38.02 | ((sk_c11) != (X0))
% 259.22/38.02 | ((inverse @ (inverse @ sk_c1)) != (X0))))
% 259.22/38.02 <= ((![X0 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c10))
% 259.22/38.02 | ((sk_c11) != (X0))
% 259.22/38.02 | ((inverse @ (inverse @ sk_c1)) != (X0)))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl526])).
% 259.22/38.02 thf(zip_derived_cl2925, plain,
% 259.22/38.02 ((![X0 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c10))
% 259.22/38.02 | ((sk_c11) != (X0))
% 259.22/38.02 | ((inverse @ (inverse @ identity)) != (X0))))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))) &
% 259.22/38.02 (![X0 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c10))
% 259.22/38.02 | ((sk_c11) != (X0))
% 259.22/38.02 | ((inverse @ (inverse @ sk_c1)) != (X0)))))),
% 259.22/38.02 inference('s_sup-', [status(thm)],
% 259.22/38.02 [zip_derived_cl2192, zip_derived_cl2874])).
% 259.22/38.02 thf(zip_derived_cl1002, plain,
% 259.22/38.02 ((((identity) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl918, zip_derived_cl55])).
% 259.22/38.02 thf(zip_derived_cl2010, plain,
% 259.22/38.02 ((((identity) = (sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)],
% 259.22/38.02 [zip_derived_cl1994, zip_derived_cl1002, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl2970, plain,
% 259.22/38.02 ((![X0 : $i]:
% 259.22/38.02 (((inverse @ X0) != (identity))
% 259.22/38.02 | ((identity) != (X0))
% 259.22/38.02 | ((inverse @ (inverse @ identity)) != (X0))))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))) &
% 259.22/38.02 (![X0 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c10))
% 259.22/38.02 | ((sk_c11) != (X0))
% 259.22/38.02 | ((inverse @ (inverse @ sk_c1)) != (X0)))))),
% 259.22/38.02 inference('demod', [status(thm)],
% 259.22/38.02 [zip_derived_cl2925, zip_derived_cl1002, zip_derived_cl2010])).
% 259.22/38.02 thf(zip_derived_cl3105, plain,
% 259.22/38.02 (((((identity) != (inverse @ (inverse @ identity)))
% 259.22/38.02 | ((inverse @ (inverse @ (inverse @ identity))) != (identity))))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))) &
% 259.22/38.02 (![X0 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c10))
% 259.22/38.02 | ((sk_c11) != (X0))
% 259.22/38.02 | ((inverse @ (inverse @ sk_c1)) != (X0)))))),
% 259.22/38.02 inference('eq_res', [status(thm)], [zip_derived_cl2970])).
% 259.22/38.02 thf(zip_derived_cl3107, plain,
% 259.22/38.02 ((((identity) != (inverse @ (inverse @ identity))))
% 259.22/38.02 <= (~ (((identity) = (inverse @ (inverse @ identity)))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl3105])).
% 259.22/38.02 thf(zip_derived_cl46837, plain,
% 259.22/38.02 ((((identity) != (inverse @ identity)))
% 259.22/38.02 <= (~ (((identity) = (inverse @ (inverse @ identity)))) &
% 259.22/38.02 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup-', [status(thm)],
% 259.22/38.02 [zip_derived_cl1630, zip_derived_cl3107])).
% 259.22/38.02 thf(zip_derived_cl1630, plain,
% 259.22/38.02 ((((inverse @ identity) = (identity)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl1597, zip_derived_cl819])).
% 259.22/38.02 thf(zip_derived_cl47332, plain,
% 259.22/38.02 ((((identity) != (identity)))
% 259.22/38.02 <= (~ (((identity) = (inverse @ (inverse @ identity)))) &
% 259.22/38.02 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)],
% 259.22/38.02 [zip_derived_cl46837, zip_derived_cl1630])).
% 259.22/38.02 thf('0', plain,
% 259.22/38.02 ((((identity) = (inverse @ (inverse @ identity)))) |
% 259.22/38.02 ~ (((inverse @ sk_c1) = (sk_c11))) |
% 259.22/38.02 ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 259.22/38.02 ~ (((inverse @ sk_c4) = (sk_c10)))),
% 259.22/38.02 inference('simplify', [status(thm)], [zip_derived_cl47332])).
% 259.22/38.02 thf(zip_derived_cl1630, plain,
% 259.22/38.02 ((((inverse @ identity) = (identity)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl1597, zip_derived_cl819])).
% 259.22/38.02 thf(zip_derived_cl1, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_inverse])).
% 259.22/38.02 thf(zip_derived_cl196, plain,
% 259.22/38.02 (![X0 : $i, X1 : $i]:
% 259.22/38.02 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl497, plain,
% 259.22/38.02 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl0, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_identity])).
% 259.22/38.02 thf(zip_derived_cl158, plain,
% 259.22/38.02 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11))))
% 259.22/38.02 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl53])).
% 259.22/38.02 thf(zip_derived_cl219, plain,
% 259.22/38.02 ((![X0 : $i, X1 : $i, X2 : $i]:
% 259.22/38.02 (((inverse @ X1) != (X0))
% 259.22/38.02 | ((X0) != (X1))
% 259.22/38.02 | ((inverse @ identity) != (X1))
% 259.22/38.02 | ((multiply @ X0 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X2) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ X0) != (sk_c11))))
% 259.22/38.02 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.02 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl158])).
% 259.22/38.02 thf(zip_derived_cl729, plain,
% 259.22/38.02 ((![X0 : $i, X1 : $i]:
% 259.22/38.02 (((multiply @ X1 @ X0) != (sk_c11))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X0 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ identity) != (X0))
% 259.22/38.02 | ((inverse @ X0) != (X0))))
% 259.22/38.02 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.02 inference('eq_res', [status(thm)], [zip_derived_cl219])).
% 259.22/38.02 thf(zip_derived_cl2855, plain,
% 259.22/38.02 ((![X0 : $i]:
% 259.22/38.02 (((X0) != (sk_c11))
% 259.22/38.02 | ((inverse @ (inverse @ (inverse @ X0))) != (identity))
% 259.22/38.02 | ((multiply @ identity @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ identity) != (identity))
% 259.22/38.02 | ((inverse @ identity) != (identity))))
% 259.22/38.02 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.02 inference('s_sup-', [status(thm)], [zip_derived_cl497, zip_derived_cl729])).
% 259.22/38.02 thf(zip_derived_cl0, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_identity])).
% 259.22/38.02 thf(zip_derived_cl2869, plain,
% 259.22/38.02 ((![X0 : $i]:
% 259.22/38.02 (((X0) != (sk_c11))
% 259.22/38.02 | ((inverse @ (inverse @ (inverse @ X0))) != (identity))
% 259.22/38.02 | ((sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ identity) != (identity))
% 259.22/38.02 | ((inverse @ identity) != (identity))))
% 259.22/38.02 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl2855, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl2870, plain,
% 259.22/38.02 ((![X0 : $i]:
% 259.22/38.02 (((inverse @ identity) != (identity))
% 259.22/38.02 | ((sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ (inverse @ (inverse @ X0))) != (identity))
% 259.22/38.02 | ((X0) != (sk_c11))))
% 259.22/38.02 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.02 inference('simplify', [status(thm)], [zip_derived_cl2869])).
% 259.22/38.02 thf(zip_derived_cl3027, plain,
% 259.22/38.02 ((((inverse @ identity) != (identity)))
% 259.22/38.02 <= (~ (((inverse @ identity) = (identity))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl2870])).
% 259.22/38.02 thf(zip_derived_cl46835, plain,
% 259.22/38.02 ((((identity) != (identity)))
% 259.22/38.02 <= (~ (((inverse @ identity) = (identity))) &
% 259.22/38.02 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup-', [status(thm)],
% 259.22/38.02 [zip_derived_cl1630, zip_derived_cl3027])).
% 259.22/38.02 thf('1', plain,
% 259.22/38.02 ((((inverse @ identity) = (identity))) |
% 259.22/38.02 ~ (((inverse @ sk_c1) = (sk_c11))) |
% 259.22/38.02 ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 259.22/38.02 ~ (((inverse @ sk_c4) = (sk_c10)))),
% 259.22/38.02 inference('simplify', [status(thm)], [zip_derived_cl46835])).
% 259.22/38.02 thf(prove_this_31, conjecture,
% 259.22/38.02 (~( ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 259.22/38.02 ( ( inverse @ sk_c2 ) = ( sk_c10 ) ) ))).
% 259.22/38.02 thf(zf_stmt_9, negated_conjecture,
% 259.22/38.02 (( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 259.22/38.02 ( ( inverse @ sk_c2 ) = ( sk_c10 ) )),
% 259.22/38.02 inference('cnf.neg', [status(esa)], [prove_this_31])).
% 259.22/38.02 thf(zip_derived_cl33, plain,
% 259.22/38.02 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))
% 259.22/38.02 | ((inverse @ sk_c2) = (sk_c10)))),
% 259.22/38.02 inference('cnf', [status(esa)], [zf_stmt_9])).
% 259.22/38.02 thf(zip_derived_cl114, plain,
% 259.22/38.02 ((((inverse @ sk_c2) = (sk_c10))) <= ((((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl33])).
% 259.22/38.02 thf(zip_derived_cl1, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_inverse])).
% 259.22/38.02 thf(zip_derived_cl212, plain,
% 259.22/38.02 ((((multiply @ sk_c10 @ sk_c2) = (identity)))
% 259.22/38.02 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl114, zip_derived_cl1])).
% 259.22/38.02 thf(zip_derived_cl196, plain,
% 259.22/38.02 (![X0 : $i, X1 : $i]:
% 259.22/38.02 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl506, plain,
% 259.22/38.02 ((((sk_c2) = (multiply @ (inverse @ sk_c10) @ identity)))
% 259.22/38.02 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl212, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl505, plain,
% 259.22/38.02 ((((sk_c4) = (multiply @ (inverse @ sk_c10) @ identity)))
% 259.22/38.02 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl179, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl584, plain,
% 259.22/38.02 ((((sk_c4) = (sk_c2)))
% 259.22/38.02 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl506, zip_derived_cl505])).
% 259.22/38.02 thf(prove_this_21, conjecture,
% 259.22/38.02 (~( ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 259.22/38.02 ( ( multiply @ sk_c2 @ sk_c10 ) = ( sk_c9 ) ) ))).
% 259.22/38.02 thf(zf_stmt_10, negated_conjecture,
% 259.22/38.02 (( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 259.22/38.02 ( ( multiply @ sk_c2 @ sk_c10 ) = ( sk_c9 ) )),
% 259.22/38.02 inference('cnf.neg', [status(esa)], [prove_this_21])).
% 259.22/38.02 thf(zip_derived_cl23, plain,
% 259.22/38.02 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))
% 259.22/38.02 | ((multiply @ sk_c2 @ sk_c10) = (sk_c9)))),
% 259.22/38.02 inference('cnf', [status(esa)], [zf_stmt_10])).
% 259.22/38.02 thf(zip_derived_cl94, plain,
% 259.22/38.02 ((((multiply @ sk_c2 @ sk_c10) = (sk_c9)))
% 259.22/38.02 <= ((((multiply @ sk_c2 @ sk_c10) = (sk_c9))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl23])).
% 259.22/38.02 thf(zip_derived_cl623, plain,
% 259.22/38.02 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9)))
% 259.22/38.02 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl584, zip_derived_cl94])).
% 259.22/38.02 thf(zip_derived_cl1059, plain,
% 259.22/38.02 ((((multiply @ sk_c4 @ sk_c10) = (identity)))
% 259.22/38.02 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl504, zip_derived_cl1])).
% 259.22/38.02 thf(zip_derived_cl5800, plain,
% 259.22/38.02 ((((identity) = (sk_c9)))
% 259.22/38.02 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl623, zip_derived_cl1059])).
% 259.22/38.02 thf(zip_derived_cl134, plain,
% 259.22/38.02 ((((multiply @ sk_c9 @ sk_c10) = (sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl43])).
% 259.22/38.02 thf(zip_derived_cl196, plain,
% 259.22/38.02 (![X0 : $i, X1 : $i]:
% 259.22/38.02 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl509, plain,
% 259.22/38.02 ((((sk_c10) = (multiply @ (inverse @ sk_c9) @ sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl134, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl5811, plain,
% 259.22/38.02 ((((sk_c10) = (multiply @ (inverse @ identity) @ sk_c11)))
% 259.22/38.02 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)],
% 259.22/38.02 [zip_derived_cl5800, zip_derived_cl509])).
% 259.22/38.02 thf(zip_derived_cl0, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_identity])).
% 259.22/38.02 thf(zip_derived_cl196, plain,
% 259.22/38.02 (![X0 : $i, X1 : $i]:
% 259.22/38.02 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl496, plain,
% 259.22/38.02 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl5829, plain,
% 259.22/38.02 ((((sk_c10) = (sk_c11)))
% 259.22/38.02 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl5811, zip_derived_cl496])).
% 259.22/38.02 thf(zip_derived_cl60, plain,
% 259.22/38.02 ((((inverse @ sk_c4) = (sk_c10))) <= ((((inverse @ sk_c4) = (sk_c10))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl6])).
% 259.22/38.02 thf(zip_derived_cl154, plain,
% 259.22/38.02 ((![X7 : $i]:
% 259.22/38.02 (((inverse @ X7) != (sk_c11))
% 259.22/38.02 | ((multiply @ X7 @ sk_c11) != (sk_c10))))
% 259.22/38.02 <= ((![X7 : $i]:
% 259.22/38.02 (((inverse @ X7) != (sk_c11))
% 259.22/38.02 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl53])).
% 259.22/38.02 thf(zip_derived_cl161, plain,
% 259.22/38.02 (((((sk_c10) != (sk_c11)) | ((multiply @ sk_c4 @ sk_c11) != (sk_c10))))
% 259.22/38.02 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (![X7 : $i]:
% 259.22/38.02 (((inverse @ X7) != (sk_c11))
% 259.22/38.02 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 259.22/38.02 inference('s_sup-', [status(thm)], [zip_derived_cl60, zip_derived_cl154])).
% 259.22/38.02 thf(zip_derived_cl176, plain,
% 259.22/38.02 ((((sk_c10) != (sk_c11))) <= (~ (((sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl161])).
% 259.22/38.02 thf(zip_derived_cl7336, plain,
% 259.22/38.02 ((((sk_c11) != (sk_c11)))
% 259.22/38.02 <= (~ (((sk_c10) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('s_sup-', [status(thm)],
% 259.22/38.02 [zip_derived_cl5829, zip_derived_cl176])).
% 259.22/38.02 thf('2', plain,
% 259.22/38.02 ((((sk_c10) = (sk_c11))) | ~ (((inverse @ sk_c2) = (sk_c10))) |
% 259.22/38.02 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 259.22/38.02 ~ (((multiply @ sk_c2 @ sk_c10) = (sk_c9))) |
% 259.22/38.02 ~ (((multiply @ sk_c9 @ sk_c10) = (sk_c11)))),
% 259.22/38.02 inference('simplify', [status(thm)], [zip_derived_cl7336])).
% 259.22/38.02 thf('3', plain,
% 259.22/38.02 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9)))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl5])).
% 259.22/38.02 thf(prove_this_43, conjecture,
% 259.22/38.02 (~( ( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 259.22/38.02 ( ( multiply @ sk_c9 @ sk_c10 ) = ( sk_c11 ) ) ))).
% 259.22/38.02 thf(zf_stmt_11, negated_conjecture,
% 259.22/38.02 (( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 259.22/38.02 ( ( multiply @ sk_c9 @ sk_c10 ) = ( sk_c11 ) )),
% 259.22/38.02 inference('cnf.neg', [status(esa)], [prove_this_43])).
% 259.22/38.02 thf(zip_derived_cl45, plain,
% 259.22/38.02 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))
% 259.22/38.02 | ((multiply @ sk_c9 @ sk_c10) = (sk_c11)))),
% 259.22/38.02 inference('cnf', [status(esa)], [zf_stmt_11])).
% 259.22/38.02 thf('4', plain,
% 259.22/38.02 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11)))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl45])).
% 259.22/38.02 thf(zip_derived_cl1500, plain,
% 259.22/38.02 ((((identity) = (sk_c9)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)],
% 259.22/38.02 [zip_derived_cl1467, zip_derived_cl1139, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl60, plain,
% 259.22/38.02 ((((inverse @ sk_c4) = (sk_c10))) <= ((((inverse @ sk_c4) = (sk_c10))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl6])).
% 259.22/38.02 thf(zip_derived_cl58, plain,
% 259.22/38.02 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9)))
% 259.22/38.02 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl5])).
% 259.22/38.02 thf(zip_derived_cl158, plain,
% 259.22/38.02 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11))))
% 259.22/38.02 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl53])).
% 259.22/38.02 thf(zip_derived_cl238, plain,
% 259.22/38.02 ((![X0 : $i, X1 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c10))
% 259.22/38.02 | ((sk_c9) != (X0))
% 259.22/38.02 | ((inverse @ sk_c4) != (X0))
% 259.22/38.02 | ((multiply @ sk_c10 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X1) != (sk_c10))
% 259.22/38.02 | ((multiply @ X1 @ sk_c10) != (sk_c11))))
% 259.22/38.02 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.02 inference('s_sup-', [status(thm)], [zip_derived_cl58, zip_derived_cl158])).
% 259.22/38.02 thf(zip_derived_cl334, plain,
% 259.22/38.02 ((![X0 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c10))
% 259.22/38.02 | ((sk_c9) != (X0))
% 259.22/38.02 | ((inverse @ sk_c4) != (X0))))
% 259.22/38.02 <= ((![X0 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c10))
% 259.22/38.02 | ((sk_c9) != (X0))
% 259.22/38.02 | ((inverse @ sk_c4) != (X0)))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl238])).
% 259.22/38.02 thf(zip_derived_cl347, plain,
% 259.22/38.02 (((((sk_c10) != (sk_c10)) | ((sk_c9) != (sk_c4)) | ((sk_c10) != (sk_c4))))
% 259.22/38.02 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (![X0 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c10))
% 259.22/38.02 | ((sk_c9) != (X0))
% 259.22/38.02 | ((inverse @ sk_c4) != (X0)))))),
% 259.22/38.02 inference('s_sup-', [status(thm)], [zip_derived_cl60, zip_derived_cl334])).
% 259.22/38.02 thf(zip_derived_cl352, plain,
% 259.22/38.02 (((((sk_c10) != (sk_c4)) | ((sk_c9) != (sk_c4))))
% 259.22/38.02 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (![X0 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c10))
% 259.22/38.02 | ((sk_c9) != (X0))
% 259.22/38.02 | ((inverse @ sk_c4) != (X0)))))),
% 259.22/38.02 inference('simplify', [status(thm)], [zip_derived_cl347])).
% 259.22/38.02 thf(zip_derived_cl354, plain,
% 259.22/38.02 ((((sk_c9) != (sk_c4))) <= (~ (((sk_c9) = (sk_c4))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl352])).
% 259.22/38.02 thf(zip_derived_cl1996, plain,
% 259.22/38.02 ((((identity) != (sk_c4)))
% 259.22/38.02 <= (~ (((sk_c9) = (sk_c4))) &
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup-', [status(thm)],
% 259.22/38.02 [zip_derived_cl1500, zip_derived_cl354])).
% 259.22/38.02 thf(zip_derived_cl1198, plain,
% 259.22/38.02 ((((sk_c4) = (identity)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl1174, zip_derived_cl1])).
% 259.22/38.02 thf(zip_derived_cl2012, plain,
% 259.22/38.02 ((((identity) != (identity)))
% 259.22/38.02 <= (~ (((sk_c9) = (sk_c4))) &
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)],
% 259.22/38.02 [zip_derived_cl1996, zip_derived_cl1198])).
% 259.22/38.02 thf('5', plain,
% 259.22/38.02 ((((sk_c9) = (sk_c4))) | ~ (((inverse @ sk_c1) = (sk_c11))) |
% 259.22/38.02 ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 259.22/38.02 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 259.22/38.02 ~ (((inverse @ sk_c3) = (sk_c11))) |
% 259.22/38.02 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c10)))),
% 259.22/38.02 inference('simplify', [status(thm)], [zip_derived_cl2012])).
% 259.22/38.02 thf(zip_derived_cl1198, plain,
% 259.22/38.02 ((((sk_c4) = (identity)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl1174, zip_derived_cl1])).
% 259.22/38.02 thf(zip_derived_cl60, plain,
% 259.22/38.02 ((((inverse @ sk_c4) = (sk_c10))) <= ((((inverse @ sk_c4) = (sk_c10))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl6])).
% 259.22/38.02 thf(zip_derived_cl55, plain,
% 259.22/38.02 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl3])).
% 259.22/38.02 thf(zip_derived_cl158, plain,
% 259.22/38.02 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11))))
% 259.22/38.02 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl53])).
% 259.22/38.02 thf(zip_derived_cl222, plain,
% 259.22/38.02 ((![X0 : $i, X1 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c11))
% 259.22/38.02 | ((sk_c10) != (X0))
% 259.22/38.02 | ((inverse @ sk_c3) != (X0))
% 259.22/38.02 | ((multiply @ sk_c11 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X1) != (sk_c11))
% 259.22/38.02 | ((multiply @ X1 @ sk_c11) != (sk_c11))))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.02 inference('s_sup-', [status(thm)], [zip_derived_cl55, zip_derived_cl158])).
% 259.22/38.02 thf(zip_derived_cl253, plain,
% 259.22/38.02 ((![X0 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c11))
% 259.22/38.02 | ((sk_c10) != (X0))
% 259.22/38.02 | ((inverse @ sk_c3) != (X0))))
% 259.22/38.02 <= ((![X0 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c11))
% 259.22/38.02 | ((sk_c10) != (X0))
% 259.22/38.02 | ((inverse @ sk_c3) != (X0)))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl222])).
% 259.22/38.02 thf(zip_derived_cl257, plain,
% 259.22/38.02 (((((sk_c10) != (sk_c11))
% 259.22/38.02 | ((sk_c10) != (sk_c4))
% 259.22/38.02 | ((inverse @ sk_c3) != (sk_c4))))
% 259.22/38.02 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (![X0 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c11))
% 259.22/38.02 | ((sk_c10) != (X0))
% 259.22/38.02 | ((inverse @ sk_c3) != (X0)))))),
% 259.22/38.02 inference('s_sup-', [status(thm)], [zip_derived_cl60, zip_derived_cl253])).
% 259.22/38.02 thf(zip_derived_cl272, plain,
% 259.22/38.02 ((((sk_c10) != (sk_c4))) <= (~ (((sk_c10) = (sk_c4))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl257])).
% 259.22/38.02 thf(zip_derived_cl1473, plain,
% 259.22/38.02 ((((sk_c10) != (identity)))
% 259.22/38.02 <= (~ (((sk_c10) = (sk_c4))) &
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup-', [status(thm)],
% 259.22/38.02 [zip_derived_cl1198, zip_derived_cl272])).
% 259.22/38.02 thf(zip_derived_cl1139, plain,
% 259.22/38.02 ((((identity) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl541, zip_derived_cl807])).
% 259.22/38.02 thf(zip_derived_cl1507, plain,
% 259.22/38.02 ((((identity) != (identity)))
% 259.22/38.02 <= (~ (((sk_c10) = (sk_c4))) &
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)],
% 259.22/38.02 [zip_derived_cl1473, zip_derived_cl1139])).
% 259.22/38.02 thf('6', plain,
% 259.22/38.02 ((((sk_c10) = (sk_c4))) | ~ (((inverse @ sk_c1) = (sk_c11))) |
% 259.22/38.02 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 259.22/38.02 ~ (((inverse @ sk_c3) = (sk_c11))) |
% 259.22/38.02 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c10)))),
% 259.22/38.02 inference('simplify', [status(thm)], [zip_derived_cl1507])).
% 259.22/38.02 thf('7', plain,
% 259.22/38.02 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 259.22/38.02 (((multiply @ sk_c5 @ sk_c8) = (sk_c11)))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl7])).
% 259.22/38.02 thf('8', plain,
% 259.22/38.02 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 259.22/38.02 (((inverse @ sk_c5) = (sk_c8)))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl8])).
% 259.22/38.02 thf(zip_derived_cl819, plain,
% 259.22/38.02 ((((identity) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl807, zip_derived_cl54])).
% 259.22/38.02 thf(zip_derived_cl58, plain,
% 259.22/38.02 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9)))
% 259.22/38.02 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl5])).
% 259.22/38.02 thf(zip_derived_cl196, plain,
% 259.22/38.02 (![X0 : $i, X1 : $i]:
% 259.22/38.02 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl508, plain,
% 259.22/38.02 ((((sk_c10) = (multiply @ (inverse @ sk_c4) @ sk_c9)))
% 259.22/38.02 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl58, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl196, plain,
% 259.22/38.02 (![X0 : $i, X1 : $i]:
% 259.22/38.02 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl595, plain,
% 259.22/38.02 ((((sk_c9) = (multiply @ (inverse @ (inverse @ sk_c4)) @ sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl508, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl3201, plain,
% 259.22/38.02 ((((sk_c9) = (multiply @ (inverse @ (inverse @ sk_c4)) @ identity)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl819, zip_derived_cl595])).
% 259.22/38.02 thf(zip_derived_cl497, plain,
% 259.22/38.02 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl3206, plain,
% 259.22/38.02 ((((sk_c9) = (sk_c4)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl3201, zip_derived_cl497])).
% 259.22/38.02 thf(zip_derived_cl509, plain,
% 259.22/38.02 ((((sk_c10) = (multiply @ (inverse @ sk_c9) @ sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl134, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl196, plain,
% 259.22/38.02 (![X0 : $i, X1 : $i]:
% 259.22/38.02 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl610, plain,
% 259.22/38.02 ((((sk_c11) = (multiply @ (inverse @ (inverse @ sk_c9)) @ sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl509, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl3290, plain,
% 259.22/38.02 ((((sk_c11) = (multiply @ (inverse @ (inverse @ sk_c4)) @ sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)],
% 259.22/38.02 [zip_derived_cl3206, zip_derived_cl610])).
% 259.22/38.02 thf(zip_derived_cl819, plain,
% 259.22/38.02 ((((identity) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl807, zip_derived_cl54])).
% 259.22/38.02 thf(zip_derived_cl497, plain,
% 259.22/38.02 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl3307, plain,
% 259.22/38.02 ((((sk_c11) = (sk_c4)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)],
% 259.22/38.02 [zip_derived_cl3290, zip_derived_cl819, zip_derived_cl497])).
% 259.22/38.02 thf(zip_derived_cl74, plain,
% 259.22/38.02 ((((inverse @ sk_c1) = (sk_c11))) <= ((((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl13])).
% 259.22/38.02 thf(zip_derived_cl60, plain,
% 259.22/38.02 ((((inverse @ sk_c4) = (sk_c10))) <= ((((inverse @ sk_c4) = (sk_c10))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl6])).
% 259.22/38.02 thf(zip_derived_cl54, plain,
% 259.22/38.02 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl3])).
% 259.22/38.02 thf(zip_derived_cl158, plain,
% 259.22/38.02 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11))))
% 259.22/38.02 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl53])).
% 259.22/38.02 thf(zip_derived_cl221, plain,
% 259.22/38.02 ((![X0 : $i, X1 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c11))
% 259.22/38.02 | ((sk_c10) != (X0))
% 259.22/38.02 | ((inverse @ sk_c1) != (X0))
% 259.22/38.02 | ((multiply @ sk_c11 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X1) != (sk_c11))
% 259.22/38.02 | ((multiply @ X1 @ sk_c11) != (sk_c11))))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.02 inference('s_sup-', [status(thm)], [zip_derived_cl54, zip_derived_cl158])).
% 259.22/38.02 thf(zip_derived_cl225, plain,
% 259.22/38.02 ((![X0 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c11))
% 259.22/38.02 | ((sk_c10) != (X0))
% 259.22/38.02 | ((inverse @ sk_c1) != (X0))))
% 259.22/38.02 <= ((![X0 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c11))
% 259.22/38.02 | ((sk_c10) != (X0))
% 259.22/38.02 | ((inverse @ sk_c1) != (X0)))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl221])).
% 259.22/38.02 thf(zip_derived_cl281, plain,
% 259.22/38.02 (((((sk_c10) != (sk_c11))
% 259.22/38.02 | ((sk_c10) != (sk_c4))
% 259.22/38.02 | ((inverse @ sk_c1) != (sk_c4))))
% 259.22/38.02 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (![X0 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c11))
% 259.22/38.02 | ((sk_c10) != (X0))
% 259.22/38.02 | ((inverse @ sk_c1) != (X0)))))),
% 259.22/38.02 inference('s_sup-', [status(thm)], [zip_derived_cl60, zip_derived_cl225])).
% 259.22/38.02 thf(zip_derived_cl313, plain,
% 259.22/38.02 ((((inverse @ sk_c1) != (sk_c4))) <= (~ (((inverse @ sk_c1) = (sk_c4))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl281])).
% 259.22/38.02 thf(zip_derived_cl316, plain,
% 259.22/38.02 ((((sk_c11) != (sk_c4)))
% 259.22/38.02 <= (~ (((inverse @ sk_c1) = (sk_c4))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl313])).
% 259.22/38.02 thf(zip_derived_cl4313, plain,
% 259.22/38.02 ((((sk_c11) != (sk_c11)))
% 259.22/38.02 <= (~ (((inverse @ sk_c1) = (sk_c4))) &
% 259.22/38.02 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('s_sup-', [status(thm)],
% 259.22/38.02 [zip_derived_cl3307, zip_derived_cl316])).
% 259.22/38.02 thf('9', plain,
% 259.22/38.02 (~ (((inverse @ sk_c1) = (sk_c11))) | (((inverse @ sk_c1) = (sk_c4))) |
% 259.22/38.02 ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 259.22/38.02 ~ (((multiply @ sk_c9 @ sk_c10) = (sk_c11))) |
% 259.22/38.02 ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 259.22/38.02 inference('simplify', [status(thm)], [zip_derived_cl4313])).
% 259.22/38.02 thf('10', plain,
% 259.22/38.02 ((((multiply @ sk_c2 @ sk_c10) = (sk_c9))) |
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10)))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl23])).
% 259.22/38.02 thf('11', plain,
% 259.22/38.02 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) |
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10)))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl33])).
% 259.22/38.02 thf('12', plain,
% 259.22/38.02 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) |
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11)))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl43])).
% 259.22/38.02 thf(zip_derived_cl1002, plain,
% 259.22/38.02 ((((identity) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl918, zip_derived_cl55])).
% 259.22/38.02 thf(zip_derived_cl595, plain,
% 259.22/38.02 ((((sk_c9) = (multiply @ (inverse @ (inverse @ sk_c4)) @ sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl508, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl3202, plain,
% 259.22/38.02 ((((sk_c9) = (multiply @ (inverse @ (inverse @ sk_c4)) @ identity)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))))),
% 259.22/38.02 inference('s_sup+', [status(thm)],
% 259.22/38.02 [zip_derived_cl1002, zip_derived_cl595])).
% 259.22/38.02 thf(zip_derived_cl497, plain,
% 259.22/38.02 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl3207, plain,
% 259.22/38.02 ((((sk_c9) = (sk_c4)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl3202, zip_derived_cl497])).
% 259.22/38.02 thf(zip_derived_cl610, plain,
% 259.22/38.02 ((((sk_c11) = (multiply @ (inverse @ (inverse @ sk_c9)) @ sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl509, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl3664, plain,
% 259.22/38.02 ((((sk_c11) = (multiply @ (inverse @ (inverse @ sk_c4)) @ sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)],
% 259.22/38.02 [zip_derived_cl3207, zip_derived_cl610])).
% 259.22/38.02 thf(zip_derived_cl1002, plain,
% 259.22/38.02 ((((identity) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl918, zip_derived_cl55])).
% 259.22/38.02 thf(zip_derived_cl497, plain,
% 259.22/38.02 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl3680, plain,
% 259.22/38.02 ((((sk_c11) = (sk_c4)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)],
% 259.22/38.02 [zip_derived_cl3664, zip_derived_cl1002, zip_derived_cl497])).
% 259.22/38.02 thf(zip_derived_cl60, plain,
% 259.22/38.02 ((((inverse @ sk_c4) = (sk_c10))) <= ((((inverse @ sk_c4) = (sk_c10))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl6])).
% 259.22/38.02 thf(zip_derived_cl333, plain,
% 259.22/38.02 ((![X1 : $i]:
% 259.22/38.02 (((inverse @ X1) != (sk_c10))
% 259.22/38.02 | ((multiply @ X1 @ sk_c10) != (sk_c11))))
% 259.22/38.02 <= ((![X1 : $i]:
% 259.22/38.02 (((inverse @ X1) != (sk_c10))
% 259.22/38.02 | ((multiply @ X1 @ sk_c10) != (sk_c11)))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl238])).
% 259.22/38.02 thf(zip_derived_cl338, plain,
% 259.22/38.02 (((((sk_c10) != (sk_c10)) | ((multiply @ sk_c4 @ sk_c10) != (sk_c11))))
% 259.22/38.02 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (![X1 : $i]:
% 259.22/38.02 (((inverse @ X1) != (sk_c10))
% 259.22/38.02 | ((multiply @ X1 @ sk_c10) != (sk_c11)))))),
% 259.22/38.02 inference('s_sup-', [status(thm)], [zip_derived_cl60, zip_derived_cl333])).
% 259.22/38.02 thf(zip_derived_cl343, plain,
% 259.22/38.02 ((((multiply @ sk_c4 @ sk_c10) != (sk_c11)))
% 259.22/38.02 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (![X1 : $i]:
% 259.22/38.02 (((inverse @ X1) != (sk_c10))
% 259.22/38.02 | ((multiply @ X1 @ sk_c10) != (sk_c11)))))),
% 259.22/38.02 inference('simplify', [status(thm)], [zip_derived_cl338])).
% 259.22/38.02 thf(zip_derived_cl4988, plain,
% 259.22/38.02 ((((multiply @ sk_c11 @ sk_c10) != (sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))) &
% 259.22/38.02 (![X1 : $i]:
% 259.22/38.02 (((inverse @ X1) != (sk_c10))
% 259.22/38.02 | ((multiply @ X1 @ sk_c10) != (sk_c11)))))),
% 259.22/38.02 inference('s_sup-', [status(thm)],
% 259.22/38.02 [zip_derived_cl3680, zip_derived_cl343])).
% 259.22/38.02 thf(zip_derived_cl1002, plain,
% 259.22/38.02 ((((identity) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl918, zip_derived_cl55])).
% 259.22/38.02 thf(zip_derived_cl918, plain,
% 259.22/38.02 ((((multiply @ sk_c3 @ sk_c11) = (identity)))
% 259.22/38.02 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl501, zip_derived_cl1])).
% 259.22/38.02 thf(zip_derived_cl432, plain,
% 259.22/38.02 ((![X0 : $i]: ((X0) = (multiply @ sk_c11 @ (multiply @ sk_c3 @ X0))))
% 259.22/38.02 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl431, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl1001, plain,
% 259.22/38.02 ((((sk_c11) = (multiply @ sk_c11 @ identity)))
% 259.22/38.02 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl918, zip_derived_cl432])).
% 259.22/38.02 thf(zip_derived_cl5040, plain,
% 259.22/38.02 ((((sk_c11) != (sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))) &
% 259.22/38.02 (![X1 : $i]:
% 259.22/38.02 (((inverse @ X1) != (sk_c10))
% 259.22/38.02 | ((multiply @ X1 @ sk_c10) != (sk_c11)))))),
% 259.22/38.02 inference('demod', [status(thm)],
% 259.22/38.02 [zip_derived_cl4988, zip_derived_cl1002, zip_derived_cl1001])).
% 259.22/38.02 thf('13', plain,
% 259.22/38.02 (~
% 259.22/38.02 (![X1 : $i]:
% 259.22/38.02 (((inverse @ X1) != (sk_c10))
% 259.22/38.02 | ((multiply @ X1 @ sk_c10) != (sk_c11)))) |
% 259.22/38.02 ~ (((inverse @ sk_c3) = (sk_c11))) |
% 259.22/38.02 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 259.22/38.02 ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 259.22/38.02 ~ (((multiply @ sk_c9 @ sk_c10) = (sk_c11))) |
% 259.22/38.02 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c10)))),
% 259.22/38.02 inference('simplify', [status(thm)], [zip_derived_cl5040])).
% 259.22/38.02 thf(zip_derived_cl2010, plain,
% 259.22/38.02 ((((identity) = (sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)],
% 259.22/38.02 [zip_derived_cl1994, zip_derived_cl1002, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl1139, plain,
% 259.22/38.02 ((((identity) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl541, zip_derived_cl807])).
% 259.22/38.02 thf(zip_derived_cl335, plain,
% 259.22/38.02 ((((multiply @ sk_c10 @ sk_c10) != (sk_c11)))
% 259.22/38.02 <= (~ (((multiply @ sk_c10 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl238])).
% 259.22/38.02 thf(zip_derived_cl1159, plain,
% 259.22/38.02 ((((multiply @ identity @ identity) != (sk_c11)))
% 259.22/38.02 <= (~ (((multiply @ sk_c10 @ sk_c10) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup-', [status(thm)],
% 259.22/38.02 [zip_derived_cl1139, zip_derived_cl335])).
% 259.22/38.02 thf(zip_derived_cl0, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_identity])).
% 259.22/38.02 thf(zip_derived_cl1192, plain,
% 259.22/38.02 ((((identity) != (sk_c11)))
% 259.22/38.02 <= (~ (((multiply @ sk_c10 @ sk_c10) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl1159, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl2172, plain,
% 259.22/38.02 ((((identity) != (identity)))
% 259.22/38.02 <= (~ (((multiply @ sk_c10 @ sk_c10) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('s_sup-', [status(thm)],
% 259.22/38.02 [zip_derived_cl2010, zip_derived_cl1192])).
% 259.22/38.02 thf('14', plain,
% 259.22/38.02 ((((multiply @ sk_c10 @ sk_c10) = (sk_c11))) |
% 259.22/38.02 ~ (((inverse @ sk_c3) = (sk_c11))) |
% 259.22/38.02 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 259.22/38.02 ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 259.22/38.02 ~ (((inverse @ sk_c1) = (sk_c11))) |
% 259.22/38.02 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) |
% 259.22/38.02 ~ (((multiply @ sk_c9 @ sk_c10) = (sk_c11)))),
% 259.22/38.02 inference('simplify', [status(thm)], [zip_derived_cl2172])).
% 259.22/38.02 thf(prove_this_32, conjecture,
% 259.22/38.02 (~( ( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 259.22/38.02 ( ( inverse @ sk_c2 ) = ( sk_c10 ) ) ))).
% 259.22/38.02 thf(zf_stmt_12, negated_conjecture,
% 259.22/38.02 (( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 259.22/38.02 ( ( inverse @ sk_c2 ) = ( sk_c10 ) )),
% 259.22/38.02 inference('cnf.neg', [status(esa)], [prove_this_32])).
% 259.22/38.02 thf(zip_derived_cl34, plain,
% 259.22/38.02 ((((inverse @ sk_c3) = (sk_c11)) | ((inverse @ sk_c2) = (sk_c10)))),
% 259.22/38.02 inference('cnf', [status(esa)], [zf_stmt_12])).
% 259.22/38.02 thf('15', plain,
% 259.22/38.02 ((((inverse @ sk_c3) = (sk_c11))) | (((inverse @ sk_c2) = (sk_c10)))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl34])).
% 259.22/38.02 thf(prove_this_35, conjecture,
% 259.22/38.02 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 259.22/38.02 ( ( inverse @ sk_c2 ) = ( sk_c10 ) ) ))).
% 259.22/38.02 thf(zf_stmt_13, negated_conjecture,
% 259.22/38.02 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 259.22/38.02 ( ( inverse @ sk_c2 ) = ( sk_c10 ) )),
% 259.22/38.02 inference('cnf.neg', [status(esa)], [prove_this_35])).
% 259.22/38.02 thf(zip_derived_cl37, plain,
% 259.22/38.02 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))
% 259.22/38.02 | ((inverse @ sk_c2) = (sk_c10)))),
% 259.22/38.02 inference('cnf', [status(esa)], [zf_stmt_13])).
% 259.22/38.02 thf('16', plain,
% 259.22/38.02 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) |
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10)))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl37])).
% 259.22/38.02 thf(prove_this_36, conjecture,
% 259.22/38.02 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 259.22/38.02 ( ( inverse @ sk_c2 ) = ( sk_c10 ) ) ))).
% 259.22/38.02 thf(zf_stmt_14, negated_conjecture,
% 259.22/38.02 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c10 ) )),
% 259.22/38.02 inference('cnf.neg', [status(esa)], [prove_this_36])).
% 259.22/38.02 thf(zip_derived_cl38, plain,
% 259.22/38.02 ((((inverse @ sk_c5) = (sk_c8)) | ((inverse @ sk_c2) = (sk_c10)))),
% 259.22/38.02 inference('cnf', [status(esa)], [zf_stmt_14])).
% 259.22/38.02 thf('17', plain,
% 259.22/38.02 ((((inverse @ sk_c5) = (sk_c8))) | (((inverse @ sk_c2) = (sk_c10)))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl38])).
% 259.22/38.02 thf('18', plain,
% 259.22/38.02 (~
% 259.22/38.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11)))) |
% 259.22/38.02 (![X0 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c11))
% 259.22/38.02 | ((sk_c10) != (X0))
% 259.22/38.02 | ((inverse @ sk_c1) != (X0)))) |
% 259.22/38.02 ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 259.22/38.02 ~ (((multiply @ sk_c11 @ sk_c10) = (sk_c11))) |
% 259.22/38.02 (![X1 : $i]:
% 259.22/38.02 (((inverse @ X1) != (sk_c11))
% 259.22/38.02 | ((multiply @ X1 @ sk_c11) != (sk_c11))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl221])).
% 259.22/38.02 thf(zip_derived_cl3307, plain,
% 259.22/38.02 ((((sk_c11) = (sk_c4)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)],
% 259.22/38.02 [zip_derived_cl3290, zip_derived_cl819, zip_derived_cl497])).
% 259.22/38.02 thf(zip_derived_cl584, plain,
% 259.22/38.02 ((((sk_c4) = (sk_c2)))
% 259.22/38.02 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl506, zip_derived_cl505])).
% 259.22/38.02 thf(zip_derived_cl74, plain,
% 259.22/38.02 ((((inverse @ sk_c1) = (sk_c11))) <= ((((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl13])).
% 259.22/38.02 thf(zip_derived_cl114, plain,
% 259.22/38.02 ((((inverse @ sk_c2) = (sk_c10))) <= ((((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl33])).
% 259.22/38.02 thf(zip_derived_cl225, plain,
% 259.22/38.02 ((![X0 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c11))
% 259.22/38.02 | ((sk_c10) != (X0))
% 259.22/38.02 | ((inverse @ sk_c1) != (X0))))
% 259.22/38.02 <= ((![X0 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c11))
% 259.22/38.02 | ((sk_c10) != (X0))
% 259.22/38.02 | ((inverse @ sk_c1) != (X0)))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl221])).
% 259.22/38.02 thf(zip_derived_cl285, plain,
% 259.22/38.02 (((((sk_c10) != (sk_c11))
% 259.22/38.02 | ((sk_c10) != (sk_c2))
% 259.22/38.02 | ((inverse @ sk_c1) != (sk_c2))))
% 259.22/38.02 <= ((((inverse @ sk_c2) = (sk_c10))) &
% 259.22/38.02 (![X0 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c11))
% 259.22/38.02 | ((sk_c10) != (X0))
% 259.22/38.02 | ((inverse @ sk_c1) != (X0)))))),
% 259.22/38.02 inference('s_sup-', [status(thm)], [zip_derived_cl114, zip_derived_cl225])).
% 259.22/38.02 thf(zip_derived_cl329, plain,
% 259.22/38.02 ((((inverse @ sk_c1) != (sk_c2))) <= (~ (((inverse @ sk_c1) = (sk_c2))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl285])).
% 259.22/38.02 thf(zip_derived_cl332, plain,
% 259.22/38.02 ((((sk_c11) != (sk_c2)))
% 259.22/38.02 <= (~ (((inverse @ sk_c1) = (sk_c2))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl329])).
% 259.22/38.02 thf(zip_derived_cl630, plain,
% 259.22/38.02 ((((sk_c11) != (sk_c4)))
% 259.22/38.02 <= (~ (((inverse @ sk_c1) = (sk_c2))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('s_sup-', [status(thm)], [zip_derived_cl584, zip_derived_cl332])).
% 259.22/38.02 thf(zip_derived_cl4331, plain,
% 259.22/38.02 ((((sk_c11) != (sk_c11)))
% 259.22/38.02 <= (~ (((inverse @ sk_c1) = (sk_c2))) &
% 259.22/38.02 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('s_sup-', [status(thm)],
% 259.22/38.02 [zip_derived_cl3307, zip_derived_cl630])).
% 259.22/38.02 thf('19', plain,
% 259.22/38.02 (~ (((inverse @ sk_c1) = (sk_c11))) | (((inverse @ sk_c1) = (sk_c2))) |
% 259.22/38.02 ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 259.22/38.02 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 259.22/38.02 ~ (((inverse @ sk_c2) = (sk_c10))) |
% 259.22/38.02 ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 259.22/38.02 ~ (((multiply @ sk_c9 @ sk_c10) = (sk_c11)))),
% 259.22/38.02 inference('simplify', [status(thm)], [zip_derived_cl4331])).
% 259.22/38.02 thf(zip_derived_cl1073, plain,
% 259.22/38.02 ((((identity) = (sk_c9)))
% 259.22/38.02 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl1059, zip_derived_cl58])).
% 259.22/38.02 thf(zip_derived_cl509, plain,
% 259.22/38.02 ((((sk_c10) = (multiply @ (inverse @ sk_c9) @ sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl134, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl7915, plain,
% 259.22/38.02 ((((sk_c10) = (multiply @ (inverse @ identity) @ sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)],
% 259.22/38.02 [zip_derived_cl1073, zip_derived_cl509])).
% 259.22/38.02 thf(zip_derived_cl496, plain,
% 259.22/38.02 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl7935, plain,
% 259.22/38.02 ((((sk_c10) = (sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl7915, zip_derived_cl496])).
% 259.22/38.02 thf(zip_derived_cl176, plain,
% 259.22/38.02 ((((sk_c10) != (sk_c11))) <= (~ (((sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl161])).
% 259.22/38.02 thf(zip_derived_cl8247, plain,
% 259.22/38.02 ((((sk_c11) != (sk_c11)))
% 259.22/38.02 <= (~ (((sk_c10) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('s_sup-', [status(thm)],
% 259.22/38.02 [zip_derived_cl7935, zip_derived_cl176])).
% 259.22/38.02 thf('20', plain,
% 259.22/38.02 ((((sk_c10) = (sk_c11))) | ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 259.22/38.02 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 259.22/38.02 ~ (((multiply @ sk_c9 @ sk_c10) = (sk_c11)))),
% 259.22/38.02 inference('simplify', [status(thm)], [zip_derived_cl8247])).
% 259.22/38.02 thf(zip_derived_cl506, plain,
% 259.22/38.02 ((((sk_c2) = (multiply @ (inverse @ sk_c10) @ identity)))
% 259.22/38.02 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl212, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl2, plain,
% 259.22/38.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 259.22/38.02 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 259.22/38.02 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 259.22/38.02 inference('cnf', [status(esa)], [associativity])).
% 259.22/38.02 thf(zip_derived_cl582, plain,
% 259.22/38.02 ((![X0 : $i]:
% 259.22/38.02 ((multiply @ sk_c2 @ X0)
% 259.22/38.02 = (multiply @ (inverse @ sk_c10) @ (multiply @ identity @ X0))))
% 259.22/38.02 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl506, zip_derived_cl2])).
% 259.22/38.02 thf(zip_derived_cl0, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_identity])).
% 259.22/38.02 thf(zip_derived_cl586, plain,
% 259.22/38.02 ((![X0 : $i]:
% 259.22/38.02 ((multiply @ sk_c2 @ X0) = (multiply @ (inverse @ sk_c10) @ X0)))
% 259.22/38.02 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl582, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl1, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_inverse])).
% 259.22/38.02 thf(zip_derived_cl1241, plain,
% 259.22/38.02 ((((multiply @ sk_c2 @ sk_c10) = (identity)))
% 259.22/38.02 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl586, zip_derived_cl1])).
% 259.22/38.02 thf(zip_derived_cl94, plain,
% 259.22/38.02 ((((multiply @ sk_c2 @ sk_c10) = (sk_c9)))
% 259.22/38.02 <= ((((multiply @ sk_c2 @ sk_c10) = (sk_c9))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl23])).
% 259.22/38.02 thf(zip_derived_cl1272, plain,
% 259.22/38.02 ((((identity) = (sk_c9)))
% 259.22/38.02 <= ((((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl1241, zip_derived_cl94])).
% 259.22/38.02 thf(zip_derived_cl509, plain,
% 259.22/38.02 ((((sk_c10) = (multiply @ (inverse @ sk_c9) @ sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl134, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl9109, plain,
% 259.22/38.02 ((((sk_c10) = (multiply @ (inverse @ identity) @ sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)],
% 259.22/38.02 [zip_derived_cl1272, zip_derived_cl509])).
% 259.22/38.02 thf(zip_derived_cl496, plain,
% 259.22/38.02 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl9129, plain,
% 259.22/38.02 ((((sk_c10) = (sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl9109, zip_derived_cl496])).
% 259.22/38.02 thf(zip_derived_cl54, plain,
% 259.22/38.02 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl3])).
% 259.22/38.02 thf(zip_derived_cl74, plain,
% 259.22/38.02 ((((inverse @ sk_c1) = (sk_c11))) <= ((((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl13])).
% 259.22/38.02 thf(zip_derived_cl224, plain,
% 259.22/38.02 ((![X1 : $i]:
% 259.22/38.02 (((inverse @ X1) != (sk_c11))
% 259.22/38.02 | ((multiply @ X1 @ sk_c11) != (sk_c11))))
% 259.22/38.02 <= ((![X1 : $i]:
% 259.22/38.02 (((inverse @ X1) != (sk_c11))
% 259.22/38.02 | ((multiply @ X1 @ sk_c11) != (sk_c11)))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl221])).
% 259.22/38.02 thf(zip_derived_cl227, plain,
% 259.22/38.02 (((((sk_c11) != (sk_c11)) | ((multiply @ sk_c1 @ sk_c11) != (sk_c11))))
% 259.22/38.02 <= ((((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (![X1 : $i]:
% 259.22/38.02 (((inverse @ X1) != (sk_c11))
% 259.22/38.02 | ((multiply @ X1 @ sk_c11) != (sk_c11)))))),
% 259.22/38.02 inference('s_sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl224])).
% 259.22/38.02 thf(zip_derived_cl234, plain,
% 259.22/38.02 ((((multiply @ sk_c1 @ sk_c11) != (sk_c11)))
% 259.22/38.02 <= ((((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (![X1 : $i]:
% 259.22/38.02 (((inverse @ X1) != (sk_c11))
% 259.22/38.02 | ((multiply @ X1 @ sk_c11) != (sk_c11)))))),
% 259.22/38.02 inference('simplify', [status(thm)], [zip_derived_cl227])).
% 259.22/38.02 thf(zip_derived_cl236, plain,
% 259.22/38.02 ((((sk_c10) != (sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (![X1 : $i]:
% 259.22/38.02 (((inverse @ X1) != (sk_c11))
% 259.22/38.02 | ((multiply @ X1 @ sk_c11) != (sk_c11)))))),
% 259.22/38.02 inference('s_sup-', [status(thm)], [zip_derived_cl54, zip_derived_cl234])).
% 259.22/38.02 thf(zip_derived_cl9200, plain,
% 259.22/38.02 ((((sk_c11) != (sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))) &
% 259.22/38.02 (![X1 : $i]:
% 259.22/38.02 (((inverse @ X1) != (sk_c11))
% 259.22/38.02 | ((multiply @ X1 @ sk_c11) != (sk_c11)))))),
% 259.22/38.02 inference('s_sup-', [status(thm)],
% 259.22/38.02 [zip_derived_cl9129, zip_derived_cl236])).
% 259.22/38.02 thf('21', plain,
% 259.22/38.02 (~
% 259.22/38.02 (![X1 : $i]:
% 259.22/38.02 (((inverse @ X1) != (sk_c11))
% 259.22/38.02 | ((multiply @ X1 @ sk_c11) != (sk_c11)))) |
% 259.22/38.02 ~ (((multiply @ sk_c9 @ sk_c10) = (sk_c11))) |
% 259.22/38.02 ~ (((inverse @ sk_c2) = (sk_c10))) |
% 259.22/38.02 ~ (((multiply @ sk_c2 @ sk_c10) = (sk_c9))) |
% 259.22/38.02 ~ (((inverse @ sk_c1) = (sk_c11))) |
% 259.22/38.02 ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 259.22/38.02 inference('simplify', [status(thm)], [zip_derived_cl9200])).
% 259.22/38.02 thf(prove_this_22, conjecture,
% 259.22/38.02 (~( ( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 259.22/38.02 ( ( multiply @ sk_c2 @ sk_c10 ) = ( sk_c9 ) ) ))).
% 259.22/38.02 thf(zf_stmt_15, negated_conjecture,
% 259.22/38.02 (( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 259.22/38.02 ( ( multiply @ sk_c2 @ sk_c10 ) = ( sk_c9 ) )),
% 259.22/38.02 inference('cnf.neg', [status(esa)], [prove_this_22])).
% 259.22/38.02 thf(zip_derived_cl24, plain,
% 259.22/38.02 ((((inverse @ sk_c3) = (sk_c11))
% 259.22/38.02 | ((multiply @ sk_c2 @ sk_c10) = (sk_c9)))),
% 259.22/38.02 inference('cnf', [status(esa)], [zf_stmt_15])).
% 259.22/38.02 thf('22', plain,
% 259.22/38.02 ((((multiply @ sk_c2 @ sk_c10) = (sk_c9))) |
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11)))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl24])).
% 259.22/38.02 thf(prove_this_42, conjecture,
% 259.22/38.02 (~( ( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 259.22/38.02 ( ( multiply @ sk_c9 @ sk_c10 ) = ( sk_c11 ) ) ))).
% 259.22/38.02 thf(zf_stmt_16, negated_conjecture,
% 259.22/38.02 (( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 259.22/38.02 ( ( multiply @ sk_c9 @ sk_c10 ) = ( sk_c11 ) )),
% 259.22/38.02 inference('cnf.neg', [status(esa)], [prove_this_42])).
% 259.22/38.02 thf(zip_derived_cl44, plain,
% 259.22/38.02 ((((inverse @ sk_c3) = (sk_c11))
% 259.22/38.02 | ((multiply @ sk_c9 @ sk_c10) = (sk_c11)))),
% 259.22/38.02 inference('cnf', [status(esa)], [zf_stmt_16])).
% 259.22/38.02 thf('23', plain,
% 259.22/38.02 ((((inverse @ sk_c3) = (sk_c11))) |
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11)))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl44])).
% 259.22/38.02 thf(prove_this_45, conjecture,
% 259.22/38.02 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 259.22/38.02 ( ( multiply @ sk_c9 @ sk_c10 ) = ( sk_c11 ) ) ))).
% 259.22/38.02 thf(zf_stmt_17, negated_conjecture,
% 259.22/38.02 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 259.22/38.02 ( ( multiply @ sk_c9 @ sk_c10 ) = ( sk_c11 ) )),
% 259.22/38.02 inference('cnf.neg', [status(esa)], [prove_this_45])).
% 259.22/38.02 thf(zip_derived_cl47, plain,
% 259.22/38.02 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))
% 259.22/38.02 | ((multiply @ sk_c9 @ sk_c10) = (sk_c11)))),
% 259.22/38.02 inference('cnf', [status(esa)], [zf_stmt_17])).
% 259.22/38.02 thf('24', plain,
% 259.22/38.02 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) |
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11)))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl47])).
% 259.22/38.02 thf(prove_this_46, conjecture,
% 259.22/38.02 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 259.22/38.02 ( ( multiply @ sk_c9 @ sk_c10 ) = ( sk_c11 ) ) ))).
% 259.22/38.02 thf(zf_stmt_18, negated_conjecture,
% 259.22/38.02 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 259.22/38.02 ( ( multiply @ sk_c9 @ sk_c10 ) = ( sk_c11 ) )),
% 259.22/38.02 inference('cnf.neg', [status(esa)], [prove_this_46])).
% 259.22/38.02 thf(zip_derived_cl48, plain,
% 259.22/38.02 ((((inverse @ sk_c5) = (sk_c8))
% 259.22/38.02 | ((multiply @ sk_c9 @ sk_c10) = (sk_c11)))),
% 259.22/38.02 inference('cnf', [status(esa)], [zf_stmt_18])).
% 259.22/38.02 thf('25', plain,
% 259.22/38.02 ((((inverse @ sk_c5) = (sk_c8))) |
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11)))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl48])).
% 259.22/38.02 thf(zip_derived_cl2010, plain,
% 259.22/38.02 ((((identity) = (sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)],
% 259.22/38.02 [zip_derived_cl1994, zip_derived_cl1002, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl819, plain,
% 259.22/38.02 ((((identity) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl807, zip_derived_cl54])).
% 259.22/38.02 thf(zip_derived_cl335, plain,
% 259.22/38.02 ((((multiply @ sk_c10 @ sk_c10) != (sk_c11)))
% 259.22/38.02 <= (~ (((multiply @ sk_c10 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl238])).
% 259.22/38.02 thf(zip_derived_cl944, plain,
% 259.22/38.02 ((((multiply @ identity @ identity) != (sk_c11)))
% 259.22/38.02 <= (~ (((multiply @ sk_c10 @ sk_c10) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup-', [status(thm)], [zip_derived_cl819, zip_derived_cl335])).
% 259.22/38.02 thf(zip_derived_cl0, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_identity])).
% 259.22/38.02 thf(zip_derived_cl969, plain,
% 259.22/38.02 ((((identity) != (sk_c11)))
% 259.22/38.02 <= (~ (((multiply @ sk_c10 @ sk_c10) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl944, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl2166, plain,
% 259.22/38.02 ((((identity) != (identity)))
% 259.22/38.02 <= (~ (((multiply @ sk_c10 @ sk_c10) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('s_sup-', [status(thm)],
% 259.22/38.02 [zip_derived_cl2010, zip_derived_cl969])).
% 259.22/38.02 thf('26', plain,
% 259.22/38.02 ((((multiply @ sk_c10 @ sk_c10) = (sk_c11))) |
% 259.22/38.02 ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 259.22/38.02 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 259.22/38.02 ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 259.22/38.02 ~ (((inverse @ sk_c1) = (sk_c11))) |
% 259.22/38.02 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) |
% 259.22/38.02 ~ (((multiply @ sk_c9 @ sk_c10) = (sk_c11))) |
% 259.22/38.02 ~ (((inverse @ sk_c3) = (sk_c11)))),
% 259.22/38.02 inference('simplify', [status(thm)], [zip_derived_cl2166])).
% 259.22/38.02 thf(zip_derived_cl2010, plain,
% 259.22/38.02 ((((identity) = (sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)],
% 259.22/38.02 [zip_derived_cl1994, zip_derived_cl1002, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl819, plain,
% 259.22/38.02 ((((identity) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl807, zip_derived_cl54])).
% 259.22/38.02 thf(zip_derived_cl506, plain,
% 259.22/38.02 ((((sk_c2) = (multiply @ (inverse @ sk_c10) @ identity)))
% 259.22/38.02 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl212, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl959, plain,
% 259.22/38.02 ((((sk_c2) = (multiply @ (inverse @ identity) @ identity)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl819, zip_derived_cl506])).
% 259.22/38.02 thf(zip_derived_cl1, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_inverse])).
% 259.22/38.02 thf(zip_derived_cl974, plain,
% 259.22/38.02 ((((sk_c2) = (identity)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl959, zip_derived_cl1])).
% 259.22/38.02 thf(zip_derived_cl586, plain,
% 259.22/38.02 ((![X0 : $i]:
% 259.22/38.02 ((multiply @ sk_c2 @ X0) = (multiply @ (inverse @ sk_c10) @ X0)))
% 259.22/38.02 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl582, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl506, plain,
% 259.22/38.02 ((((sk_c2) = (multiply @ (inverse @ sk_c10) @ identity)))
% 259.22/38.02 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl212, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl1245, plain,
% 259.22/38.02 ((((sk_c2) = (multiply @ sk_c2 @ identity)))
% 259.22/38.02 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl586, zip_derived_cl506])).
% 259.22/38.02 thf(zip_derived_cl1139, plain,
% 259.22/38.02 ((((identity) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl541, zip_derived_cl807])).
% 259.22/38.02 thf(zip_derived_cl114, plain,
% 259.22/38.02 ((((inverse @ sk_c2) = (sk_c10))) <= ((((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl33])).
% 259.22/38.02 thf(zip_derived_cl333, plain,
% 259.22/38.02 ((![X1 : $i]:
% 259.22/38.02 (((inverse @ X1) != (sk_c10))
% 259.22/38.02 | ((multiply @ X1 @ sk_c10) != (sk_c11))))
% 259.22/38.02 <= ((![X1 : $i]:
% 259.22/38.02 (((inverse @ X1) != (sk_c10))
% 259.22/38.02 | ((multiply @ X1 @ sk_c10) != (sk_c11)))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl238])).
% 259.22/38.02 thf(zip_derived_cl342, plain,
% 259.22/38.02 (((((sk_c10) != (sk_c10)) | ((multiply @ sk_c2 @ sk_c10) != (sk_c11))))
% 259.22/38.02 <= ((((inverse @ sk_c2) = (sk_c10))) &
% 259.22/38.02 (![X1 : $i]:
% 259.22/38.02 (((inverse @ X1) != (sk_c10))
% 259.22/38.02 | ((multiply @ X1 @ sk_c10) != (sk_c11)))))),
% 259.22/38.02 inference('s_sup-', [status(thm)], [zip_derived_cl114, zip_derived_cl333])).
% 259.22/38.02 thf(zip_derived_cl344, plain,
% 259.22/38.02 ((((multiply @ sk_c2 @ sk_c10) != (sk_c11)))
% 259.22/38.02 <= ((((inverse @ sk_c2) = (sk_c10))) &
% 259.22/38.02 (![X1 : $i]:
% 259.22/38.02 (((inverse @ X1) != (sk_c10))
% 259.22/38.02 | ((multiply @ X1 @ sk_c10) != (sk_c11)))))),
% 259.22/38.02 inference('simplify', [status(thm)], [zip_derived_cl342])).
% 259.22/38.02 thf(zip_derived_cl1162, plain,
% 259.22/38.02 ((((multiply @ sk_c2 @ identity) != (sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))) &
% 259.22/38.02 (![X1 : $i]:
% 259.22/38.02 (((inverse @ X1) != (sk_c10))
% 259.22/38.02 | ((multiply @ X1 @ sk_c10) != (sk_c11)))))),
% 259.22/38.02 inference('s_sup-', [status(thm)],
% 259.22/38.02 [zip_derived_cl1139, zip_derived_cl344])).
% 259.22/38.02 thf(zip_derived_cl1288, plain,
% 259.22/38.02 ((((sk_c2) != (sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))) &
% 259.22/38.02 (![X1 : $i]:
% 259.22/38.02 (((inverse @ X1) != (sk_c10))
% 259.22/38.02 | ((multiply @ X1 @ sk_c10) != (sk_c11)))))),
% 259.22/38.02 inference('s_sup-', [status(thm)],
% 259.22/38.02 [zip_derived_cl1245, zip_derived_cl1162])).
% 259.22/38.02 thf(zip_derived_cl1796, plain,
% 259.22/38.02 ((((identity) != (sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))) &
% 259.22/38.02 (![X1 : $i]:
% 259.22/38.02 (((inverse @ X1) != (sk_c10))
% 259.22/38.02 | ((multiply @ X1 @ sk_c10) != (sk_c11)))))),
% 259.22/38.02 inference('s_sup-', [status(thm)],
% 259.22/38.02 [zip_derived_cl974, zip_derived_cl1288])).
% 259.22/38.02 thf(zip_derived_cl2190, plain,
% 259.22/38.02 ((((identity) != (identity)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))) &
% 259.22/38.02 (![X1 : $i]:
% 259.22/38.02 (((inverse @ X1) != (sk_c10))
% 259.22/38.02 | ((multiply @ X1 @ sk_c10) != (sk_c11)))))),
% 259.22/38.02 inference('s_sup-', [status(thm)],
% 259.22/38.02 [zip_derived_cl2010, zip_derived_cl1796])).
% 259.22/38.02 thf('27', plain,
% 259.22/38.02 (~
% 259.22/38.02 (![X1 : $i]:
% 259.22/38.02 (((inverse @ X1) != (sk_c10))
% 259.22/38.02 | ((multiply @ X1 @ sk_c10) != (sk_c11)))) |
% 259.22/38.02 ~ (((inverse @ sk_c2) = (sk_c10))) |
% 259.22/38.02 ~ (((inverse @ sk_c3) = (sk_c11))) |
% 259.22/38.02 ~ (((inverse @ sk_c1) = (sk_c11))) |
% 259.22/38.02 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 259.22/38.02 ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 259.22/38.02 ~ (((multiply @ sk_c9 @ sk_c10) = (sk_c11))) |
% 259.22/38.02 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) |
% 259.22/38.02 ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 259.22/38.02 inference('simplify', [status(thm)], [zip_derived_cl2190])).
% 259.22/38.02 thf(zip_derived_cl64, plain,
% 259.22/38.02 ((((inverse @ sk_c5) = (sk_c8))) <= ((((inverse @ sk_c5) = (sk_c8))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl8])).
% 259.22/38.02 thf(zip_derived_cl1, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_inverse])).
% 259.22/38.02 thf(zip_derived_cl180, plain,
% 259.22/38.02 ((((multiply @ sk_c8 @ sk_c5) = (identity)))
% 259.22/38.02 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl64, zip_derived_cl1])).
% 259.22/38.02 thf(zip_derived_cl196, plain,
% 259.22/38.02 (![X0 : $i, X1 : $i]:
% 259.22/38.02 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl512, plain,
% 259.22/38.02 ((((sk_c5) = (multiply @ (inverse @ sk_c8) @ identity)))
% 259.22/38.02 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl180, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl2, plain,
% 259.22/38.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 259.22/38.02 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 259.22/38.02 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 259.22/38.02 inference('cnf', [status(esa)], [associativity])).
% 259.22/38.02 thf(zip_derived_cl619, plain,
% 259.22/38.02 ((![X0 : $i]:
% 259.22/38.02 ((multiply @ sk_c5 @ X0)
% 259.22/38.02 = (multiply @ (inverse @ sk_c8) @ (multiply @ identity @ X0))))
% 259.22/38.02 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl512, zip_derived_cl2])).
% 259.22/38.02 thf(zip_derived_cl0, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_identity])).
% 259.22/38.02 thf(zip_derived_cl622, plain,
% 259.22/38.02 ((![X0 : $i]:
% 259.22/38.02 ((multiply @ sk_c5 @ X0) = (multiply @ (inverse @ sk_c8) @ X0)))
% 259.22/38.02 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl619, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl1, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_inverse])).
% 259.22/38.02 thf(zip_derived_cl1344, plain,
% 259.22/38.02 ((((multiply @ sk_c5 @ sk_c8) = (identity)))
% 259.22/38.02 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl622, zip_derived_cl1])).
% 259.22/38.02 thf(zip_derived_cl62, plain,
% 259.22/38.02 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl7])).
% 259.22/38.02 thf(zip_derived_cl1358, plain,
% 259.22/38.02 ((((identity) = (sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c5) = (sk_c8))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl1344, zip_derived_cl62])).
% 259.22/38.02 thf(zip_derived_cl1500, plain,
% 259.22/38.02 ((((identity) = (sk_c9)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)],
% 259.22/38.02 [zip_derived_cl1467, zip_derived_cl1139, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl159, plain,
% 259.22/38.02 ((((multiply @ sk_c9 @ sk_c10) != (sk_c11)))
% 259.22/38.02 <= (~ (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl53])).
% 259.22/38.02 thf(zip_derived_cl1995, plain,
% 259.22/38.02 ((((multiply @ identity @ sk_c10) != (sk_c11)))
% 259.22/38.02 <= (~ (((multiply @ sk_c9 @ sk_c10) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup-', [status(thm)],
% 259.22/38.02 [zip_derived_cl1500, zip_derived_cl159])).
% 259.22/38.02 thf(zip_derived_cl1002, plain,
% 259.22/38.02 ((((identity) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl918, zip_derived_cl55])).
% 259.22/38.02 thf(zip_derived_cl0, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_identity])).
% 259.22/38.02 thf(zip_derived_cl2011, plain,
% 259.22/38.02 ((((identity) != (sk_c11)))
% 259.22/38.02 <= (~ (((multiply @ sk_c9 @ sk_c10) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)],
% 259.22/38.02 [zip_derived_cl1995, zip_derived_cl1002, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl9827, plain,
% 259.22/38.02 ((((identity) != (identity)))
% 259.22/38.02 <= (~ (((multiply @ sk_c9 @ sk_c10) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c5) = (sk_c8))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup-', [status(thm)],
% 259.22/38.02 [zip_derived_cl1358, zip_derived_cl2011])).
% 259.22/38.02 thf('28', plain,
% 259.22/38.02 (~ (((inverse @ sk_c1) = (sk_c11))) |
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))) |
% 259.22/38.02 ~ (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) |
% 259.22/38.02 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 259.22/38.02 ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 259.22/38.02 ~ (((inverse @ sk_c3) = (sk_c11))) |
% 259.22/38.02 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) |
% 259.22/38.02 ~ (((inverse @ sk_c5) = (sk_c8)))),
% 259.22/38.02 inference('simplify', [status(thm)], [zip_derived_cl9827])).
% 259.22/38.02 thf(zip_derived_cl973, plain,
% 259.22/38.02 ((((sk_c4) = (identity)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl958, zip_derived_cl1])).
% 259.22/38.02 thf(zip_derived_cl584, plain,
% 259.22/38.02 ((((sk_c4) = (sk_c2)))
% 259.22/38.02 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl506, zip_derived_cl505])).
% 259.22/38.02 thf(zip_derived_cl114, plain,
% 259.22/38.02 ((((inverse @ sk_c2) = (sk_c10))) <= ((((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl33])).
% 259.22/38.02 thf(zip_derived_cl253, plain,
% 259.22/38.02 ((![X0 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c11))
% 259.22/38.02 | ((sk_c10) != (X0))
% 259.22/38.02 | ((inverse @ sk_c3) != (X0))))
% 259.22/38.02 <= ((![X0 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c11))
% 259.22/38.02 | ((sk_c10) != (X0))
% 259.22/38.02 | ((inverse @ sk_c3) != (X0)))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl222])).
% 259.22/38.02 thf(zip_derived_cl261, plain,
% 259.22/38.02 (((((sk_c10) != (sk_c11))
% 259.22/38.02 | ((sk_c10) != (sk_c2))
% 259.22/38.02 | ((inverse @ sk_c3) != (sk_c2))))
% 259.22/38.02 <= ((((inverse @ sk_c2) = (sk_c10))) &
% 259.22/38.02 (![X0 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c11))
% 259.22/38.02 | ((sk_c10) != (X0))
% 259.22/38.02 | ((inverse @ sk_c3) != (X0)))))),
% 259.22/38.02 inference('s_sup-', [status(thm)], [zip_derived_cl114, zip_derived_cl253])).
% 259.22/38.02 thf(zip_derived_cl306, plain,
% 259.22/38.02 ((((sk_c10) != (sk_c2))) <= (~ (((sk_c10) = (sk_c2))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl261])).
% 259.22/38.02 thf(zip_derived_cl628, plain,
% 259.22/38.02 ((((sk_c10) != (sk_c4)))
% 259.22/38.02 <= (~ (((sk_c10) = (sk_c2))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('s_sup-', [status(thm)], [zip_derived_cl584, zip_derived_cl306])).
% 259.22/38.02 thf(zip_derived_cl1618, plain,
% 259.22/38.02 ((((sk_c10) != (identity)))
% 259.22/38.02 <= (~ (((sk_c10) = (sk_c2))) &
% 259.22/38.02 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('s_sup-', [status(thm)], [zip_derived_cl973, zip_derived_cl628])).
% 259.22/38.02 thf(zip_derived_cl819, plain,
% 259.22/38.02 ((((identity) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl807, zip_derived_cl54])).
% 259.22/38.02 thf(zip_derived_cl1645, plain,
% 259.22/38.02 ((((identity) != (identity)))
% 259.22/38.02 <= (~ (((sk_c10) = (sk_c2))) &
% 259.22/38.02 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl1618, zip_derived_cl819])).
% 259.22/38.02 thf('29', plain,
% 259.22/38.02 ((((sk_c10) = (sk_c2))) | ~ (((inverse @ sk_c2) = (sk_c10))) |
% 259.22/38.02 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 259.22/38.02 ~ (((inverse @ sk_c1) = (sk_c11))) |
% 259.22/38.02 ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 259.22/38.02 inference('simplify', [status(thm)], [zip_derived_cl1645])).
% 259.22/38.02 thf('30', plain,
% 259.22/38.02 (~ (((inverse @ sk_c2) = (sk_c10))) |
% 259.22/38.02 ~ (((inverse @ sk_c1) = (sk_c2))) | ~ (((sk_c10) = (sk_c11))) |
% 259.22/38.02 ~
% 259.22/38.02 (![X0 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c11))
% 259.22/38.02 | ((sk_c10) != (X0))
% 259.22/38.02 | ((inverse @ sk_c1) != (X0)))) |
% 259.22/38.02 ~ (((sk_c10) = (sk_c2)))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl285])).
% 259.22/38.02 thf('31', plain,
% 259.22/38.02 (~
% 259.22/38.02 (![X0 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c10))
% 259.22/38.02 | ((sk_c9) != (X0))
% 259.22/38.02 | ((inverse @ sk_c4) != (X0)))) |
% 259.22/38.02 ~ (((sk_c10) = (sk_c4))) | ~ (((inverse @ sk_c4) = (sk_c10))) |
% 259.22/38.02 ~ (((sk_c9) = (sk_c4)))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl352])).
% 259.22/38.02 thf(zip_derived_cl3206, plain,
% 259.22/38.02 ((((sk_c9) = (sk_c4)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl3201, zip_derived_cl497])).
% 259.22/38.02 thf(zip_derived_cl354, plain,
% 259.22/38.02 ((((sk_c9) != (sk_c4))) <= (~ (((sk_c9) = (sk_c4))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl352])).
% 259.22/38.02 thf(zip_derived_cl3280, plain,
% 259.22/38.02 ((((sk_c4) != (sk_c4)))
% 259.22/38.02 <= (~ (((sk_c9) = (sk_c4))) &
% 259.22/38.02 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup-', [status(thm)],
% 259.22/38.02 [zip_derived_cl3206, zip_derived_cl354])).
% 259.22/38.02 thf('32', plain,
% 259.22/38.02 ((((sk_c9) = (sk_c4))) | ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 259.22/38.02 ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 259.22/38.02 ~ (((inverse @ sk_c1) = (sk_c11)))),
% 259.22/38.02 inference('simplify', [status(thm)], [zip_derived_cl3280])).
% 259.22/38.02 thf(zip_derived_cl973, plain,
% 259.22/38.02 ((((sk_c4) = (identity)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl958, zip_derived_cl1])).
% 259.22/38.02 thf(zip_derived_cl272, plain,
% 259.22/38.02 ((((sk_c10) != (sk_c4))) <= (~ (((sk_c10) = (sk_c4))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl257])).
% 259.22/38.02 thf(zip_derived_cl1602, plain,
% 259.22/38.02 ((((sk_c10) != (identity)))
% 259.22/38.02 <= (~ (((sk_c10) = (sk_c4))) &
% 259.22/38.02 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup-', [status(thm)], [zip_derived_cl973, zip_derived_cl272])).
% 259.22/38.02 thf(zip_derived_cl819, plain,
% 259.22/38.02 ((((identity) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl807, zip_derived_cl54])).
% 259.22/38.02 thf(zip_derived_cl1636, plain,
% 259.22/38.02 ((((identity) != (identity)))
% 259.22/38.02 <= (~ (((sk_c10) = (sk_c4))) &
% 259.22/38.02 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl1602, zip_derived_cl819])).
% 259.22/38.02 thf('33', plain,
% 259.22/38.02 ((((sk_c10) = (sk_c4))) | ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 259.22/38.02 ~ (((inverse @ sk_c4) = (sk_c10))) | ~ (((inverse @ sk_c1) = (sk_c11)))),
% 259.22/38.02 inference('simplify', [status(thm)], [zip_derived_cl1636])).
% 259.22/38.02 thf(zip_derived_cl819, plain,
% 259.22/38.02 ((((identity) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl807, zip_derived_cl54])).
% 259.22/38.02 thf(zip_derived_cl226, plain,
% 259.22/38.02 ((((multiply @ sk_c11 @ sk_c10) != (sk_c11)))
% 259.22/38.02 <= (~ (((multiply @ sk_c11 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl221])).
% 259.22/38.02 thf(zip_derived_cl940, plain,
% 259.22/38.02 ((((multiply @ sk_c11 @ identity) != (sk_c11)))
% 259.22/38.02 <= (~ (((multiply @ sk_c11 @ sk_c10) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup-', [status(thm)], [zip_derived_cl819, zip_derived_cl226])).
% 259.22/38.02 thf(zip_derived_cl807, plain,
% 259.22/38.02 ((((multiply @ sk_c1 @ sk_c11) = (identity)))
% 259.22/38.02 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl500, zip_derived_cl1])).
% 259.22/38.02 thf(zip_derived_cl429, plain,
% 259.22/38.02 ((![X0 : $i]: ((X0) = (multiply @ sk_c11 @ (multiply @ sk_c1 @ X0))))
% 259.22/38.02 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl428, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl818, plain,
% 259.22/38.02 ((((sk_c11) = (multiply @ sk_c11 @ identity)))
% 259.22/38.02 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl807, zip_derived_cl429])).
% 259.22/38.02 thf(zip_derived_cl967, plain,
% 259.22/38.02 ((((sk_c11) != (sk_c11)))
% 259.22/38.02 <= (~ (((multiply @ sk_c11 @ sk_c10) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl940, zip_derived_cl818])).
% 259.22/38.02 thf('34', plain,
% 259.22/38.02 ((((multiply @ sk_c11 @ sk_c10) = (sk_c11))) |
% 259.22/38.02 ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 259.22/38.02 ~ (((inverse @ sk_c1) = (sk_c11)))),
% 259.22/38.02 inference('simplify', [status(thm)], [zip_derived_cl967])).
% 259.22/38.02 thf('35', plain,
% 259.22/38.02 (~
% 259.22/38.02 (![X0 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c11))
% 259.22/38.02 | ((sk_c10) != (X0))
% 259.22/38.02 | ((inverse @ sk_c1) != (X0)))) |
% 259.22/38.02 ~ (((inverse @ sk_c1) = (sk_c4))) |
% 259.22/38.02 ~ (((inverse @ sk_c4) = (sk_c10))) | ~ (((sk_c10) = (sk_c11))) |
% 259.22/38.02 ~ (((sk_c10) = (sk_c4)))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl281])).
% 259.22/38.02 thf('36', plain,
% 259.22/38.02 (~
% 259.22/38.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11)))) |
% 259.22/38.02 (![X0 : $i]:
% 259.22/38.02 (((inverse @ X0) != (sk_c10))
% 259.22/38.02 | ((sk_c9) != (X0))
% 259.22/38.02 | ((inverse @ sk_c4) != (X0)))) |
% 259.22/38.02 ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 259.22/38.02 ~ (((multiply @ sk_c10 @ sk_c10) = (sk_c11))) |
% 259.22/38.02 (![X1 : $i]:
% 259.22/38.02 (((inverse @ X1) != (sk_c10))
% 259.22/38.02 | ((multiply @ X1 @ sk_c10) != (sk_c11))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl238])).
% 259.22/38.02 thf(zip_derived_cl974, plain,
% 259.22/38.02 ((((sk_c2) = (identity)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl959, zip_derived_cl1])).
% 259.22/38.02 thf(zip_derived_cl114, plain,
% 259.22/38.02 ((((inverse @ sk_c2) = (sk_c10))) <= ((((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl33])).
% 259.22/38.02 thf(zip_derived_cl1774, plain,
% 259.22/38.02 ((((inverse @ identity) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl974, zip_derived_cl114])).
% 259.22/38.02 thf(zip_derived_cl819, plain,
% 259.22/38.02 ((((identity) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl807, zip_derived_cl54])).
% 259.22/38.02 thf(zip_derived_cl1798, plain,
% 259.22/38.02 ((((inverse @ identity) = (identity)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl1774, zip_derived_cl819])).
% 259.22/38.02 thf(zip_derived_cl3107, plain,
% 259.22/38.02 ((((identity) != (inverse @ (inverse @ identity))))
% 259.22/38.02 <= (~ (((identity) = (inverse @ (inverse @ identity)))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl3105])).
% 259.22/38.02 thf(zip_derived_cl54206, plain,
% 259.22/38.02 ((((identity) != (inverse @ identity)))
% 259.22/38.02 <= (~ (((identity) = (inverse @ (inverse @ identity)))) &
% 259.22/38.02 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('s_sup-', [status(thm)],
% 259.22/38.02 [zip_derived_cl1798, zip_derived_cl3107])).
% 259.22/38.02 thf(zip_derived_cl1798, plain,
% 259.22/38.02 ((((inverse @ identity) = (identity)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl1774, zip_derived_cl819])).
% 259.22/38.02 thf(zip_derived_cl54760, plain,
% 259.22/38.02 ((((identity) != (identity)))
% 259.22/38.02 <= (~ (((identity) = (inverse @ (inverse @ identity)))) &
% 259.22/38.02 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('demod', [status(thm)],
% 259.22/38.02 [zip_derived_cl54206, zip_derived_cl1798])).
% 259.22/38.02 thf('37', plain,
% 259.22/38.02 ((((identity) = (inverse @ (inverse @ identity)))) |
% 259.22/38.02 ~ (((inverse @ sk_c1) = (sk_c11))) |
% 259.22/38.02 ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 259.22/38.02 ~ (((inverse @ sk_c2) = (sk_c10)))),
% 259.22/38.02 inference('simplify', [status(thm)], [zip_derived_cl54760])).
% 259.22/38.02 thf(zip_derived_cl1798, plain,
% 259.22/38.02 ((((inverse @ identity) = (identity)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl1774, zip_derived_cl819])).
% 259.22/38.02 thf(zip_derived_cl3027, plain,
% 259.22/38.02 ((((inverse @ identity) != (identity)))
% 259.22/38.02 <= (~ (((inverse @ identity) = (identity))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl2870])).
% 259.22/38.02 thf(zip_derived_cl54204, plain,
% 259.22/38.02 ((((identity) != (identity)))
% 259.22/38.02 <= (~ (((inverse @ identity) = (identity))) &
% 259.22/38.02 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('s_sup-', [status(thm)],
% 259.22/38.02 [zip_derived_cl1798, zip_derived_cl3027])).
% 259.22/38.02 thf('38', plain,
% 259.22/38.02 ((((inverse @ identity) = (identity))) |
% 259.22/38.02 ~ (((inverse @ sk_c1) = (sk_c11))) |
% 259.22/38.02 ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 259.22/38.02 ~ (((inverse @ sk_c2) = (sk_c10)))),
% 259.22/38.02 inference('simplify', [status(thm)], [zip_derived_cl54204])).
% 259.22/38.02 thf(zip_derived_cl974, plain,
% 259.22/38.02 ((((sk_c2) = (identity)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl959, zip_derived_cl1])).
% 259.22/38.02 thf(zip_derived_cl94, plain,
% 259.22/38.02 ((((multiply @ sk_c2 @ sk_c10) = (sk_c9)))
% 259.22/38.02 <= ((((multiply @ sk_c2 @ sk_c10) = (sk_c9))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl23])).
% 259.22/38.02 thf(zip_derived_cl196, plain,
% 259.22/38.02 (![X0 : $i, X1 : $i]:
% 259.22/38.02 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl516, plain,
% 259.22/38.02 ((((sk_c10) = (multiply @ (inverse @ sk_c2) @ sk_c9)))
% 259.22/38.02 <= ((((multiply @ sk_c2 @ sk_c10) = (sk_c9))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl94, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl2, plain,
% 259.22/38.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 259.22/38.02 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 259.22/38.02 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 259.22/38.02 inference('cnf', [status(esa)], [associativity])).
% 259.22/38.02 thf(zip_derived_cl723, plain,
% 259.22/38.02 ((![X0 : $i]:
% 259.22/38.02 ((multiply @ sk_c10 @ X0)
% 259.22/38.02 = (multiply @ (inverse @ sk_c2) @ (multiply @ sk_c9 @ X0))))
% 259.22/38.02 <= ((((multiply @ sk_c2 @ sk_c10) = (sk_c9))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl516, zip_derived_cl2])).
% 259.22/38.02 thf(zip_derived_cl2010, plain,
% 259.22/38.02 ((((identity) = (sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)],
% 259.22/38.02 [zip_derived_cl1994, zip_derived_cl1002, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl54, plain,
% 259.22/38.02 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl3])).
% 259.22/38.02 thf(zip_derived_cl2, plain,
% 259.22/38.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 259.22/38.02 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 259.22/38.02 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 259.22/38.02 inference('cnf', [status(esa)], [associativity])).
% 259.22/38.02 thf(zip_derived_cl206, plain,
% 259.22/38.02 ((![X0 : $i]:
% 259.22/38.02 ((multiply @ sk_c10 @ X0)
% 259.22/38.02 = (multiply @ sk_c1 @ (multiply @ sk_c11 @ X0))))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl54, zip_derived_cl2])).
% 259.22/38.02 thf(zip_derived_cl158, plain,
% 259.22/38.02 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11))))
% 259.22/38.02 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl53])).
% 259.22/38.02 thf(zip_derived_cl566, plain,
% 259.22/38.02 ((![X0 : $i, X1 : $i, X2 : $i]:
% 259.22/38.02 (((inverse @ X1) != (multiply @ sk_c11 @ X0))
% 259.22/38.02 | ((multiply @ sk_c10 @ X0) != (X1))
% 259.22/38.02 | ((inverse @ sk_c1) != (X1))
% 259.22/38.02 | ((multiply @ (multiply @ sk_c11 @ X0) @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X2) != (multiply @ sk_c11 @ X0))
% 259.22/38.02 | ((multiply @ X2 @ (multiply @ sk_c11 @ X0)) != (sk_c11))))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.02 inference('s_sup-', [status(thm)], [zip_derived_cl206, zip_derived_cl158])).
% 259.22/38.02 thf(zip_derived_cl2, plain,
% 259.22/38.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 259.22/38.02 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 259.22/38.02 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 259.22/38.02 inference('cnf', [status(esa)], [associativity])).
% 259.22/38.02 thf(zip_derived_cl574, plain,
% 259.22/38.02 ((![X0 : $i, X1 : $i, X2 : $i]:
% 259.22/38.02 (((inverse @ X1) != (multiply @ sk_c11 @ X0))
% 259.22/38.02 | ((multiply @ sk_c10 @ X0) != (X1))
% 259.22/38.02 | ((inverse @ sk_c1) != (X1))
% 259.22/38.02 | ((multiply @ sk_c11 @ (multiply @ X0 @ sk_c10)) != (sk_c11))
% 259.22/38.02 | ((inverse @ X2) != (multiply @ sk_c11 @ X0))
% 259.22/38.02 | ((multiply @ X2 @ (multiply @ sk_c11 @ X0)) != (sk_c11))))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl566, zip_derived_cl2])).
% 259.22/38.02 thf(zip_derived_cl3829, plain,
% 259.22/38.02 ((![X0 : $i, X1 : $i, X2 : $i]:
% 259.22/38.02 (((inverse @ X1) != (multiply @ identity @ X0))
% 259.22/38.02 | ((multiply @ sk_c10 @ X0) != (X1))
% 259.22/38.02 | ((inverse @ sk_c1) != (X1))
% 259.22/38.02 | ((multiply @ identity @ (multiply @ X0 @ sk_c10)) != (identity))
% 259.22/38.02 | ((inverse @ X2) != (multiply @ identity @ X0))
% 259.22/38.02 | ((multiply @ X2 @ (multiply @ identity @ X0)) != (identity))))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))) &
% 259.22/38.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.02 inference('s_sup-', [status(thm)],
% 259.22/38.02 [zip_derived_cl2010, zip_derived_cl574])).
% 259.22/38.02 thf(zip_derived_cl0, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_identity])).
% 259.22/38.02 thf(zip_derived_cl1002, plain,
% 259.22/38.02 ((((identity) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl918, zip_derived_cl55])).
% 259.22/38.02 thf(zip_derived_cl0, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_identity])).
% 259.22/38.02 thf(zip_derived_cl2192, plain,
% 259.22/38.02 ((((sk_c1) = (identity)))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)],
% 259.22/38.02 [zip_derived_cl2121, zip_derived_cl809, zip_derived_cl1002])).
% 259.22/38.02 thf(zip_derived_cl1002, plain,
% 259.22/38.02 ((((identity) = (sk_c10)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl918, zip_derived_cl55])).
% 259.22/38.02 thf(zip_derived_cl0, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_identity])).
% 259.22/38.02 thf(zip_derived_cl0, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_identity])).
% 259.22/38.02 thf(zip_derived_cl0, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_identity])).
% 259.22/38.02 thf(zip_derived_cl3840, plain,
% 259.22/38.02 ((![X0 : $i, X1 : $i, X2 : $i]:
% 259.22/38.02 (((inverse @ X1) != (X0))
% 259.22/38.02 | ((X0) != (X1))
% 259.22/38.02 | ((inverse @ identity) != (X1))
% 259.22/38.02 | ((multiply @ X0 @ identity) != (identity))
% 259.22/38.02 | ((inverse @ X2) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ X0) != (identity))))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))) &
% 259.22/38.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.02 inference('demod', [status(thm)],
% 259.22/38.02 [zip_derived_cl3829, zip_derived_cl0, zip_derived_cl1002,
% 259.22/38.02 zip_derived_cl0, zip_derived_cl2192, zip_derived_cl1002,
% 259.22/38.02 zip_derived_cl0, zip_derived_cl0, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl3923, plain,
% 259.22/38.02 ((![X0 : $i, X1 : $i]:
% 259.22/38.02 (((multiply @ X1 @ X0) != (identity))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X0 @ identity) != (identity))
% 259.22/38.02 | ((inverse @ identity) != (X0))
% 259.22/38.02 | ((inverse @ X0) != (X0))))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))) &
% 259.22/38.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.02 inference('eq_res', [status(thm)], [zip_derived_cl3840])).
% 259.22/38.02 thf(zip_derived_cl11032, plain,
% 259.22/38.02 ((![X0 : $i]:
% 259.22/38.02 (((multiply @ sk_c10 @ X0) != (identity))
% 259.22/38.02 | ((inverse @ (inverse @ sk_c2)) != (multiply @ sk_c9 @ X0))
% 259.22/38.02 | ((multiply @ (multiply @ sk_c9 @ X0) @ identity) != (identity))
% 259.22/38.02 | ((inverse @ identity) != (multiply @ sk_c9 @ X0))
% 259.22/38.02 | ((inverse @ (multiply @ sk_c9 @ X0)) != (multiply @ sk_c9 @ X0))))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))) &
% 259.22/38.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.02 inference('s_sup-', [status(thm)],
% 259.22/38.02 [zip_derived_cl723, zip_derived_cl3923])).
% 259.22/38.02 thf(zip_derived_cl7935, plain,
% 259.22/38.02 ((((sk_c10) = (sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl7915, zip_derived_cl496])).
% 259.22/38.02 thf(zip_derived_cl2010, plain,
% 259.22/38.02 ((((identity) = (sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)],
% 259.22/38.02 [zip_derived_cl1994, zip_derived_cl1002, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl0, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_identity])).
% 259.22/38.02 thf(zip_derived_cl1073, plain,
% 259.22/38.02 ((((identity) = (sk_c9)))
% 259.22/38.02 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl1059, zip_derived_cl58])).
% 259.22/38.02 thf(zip_derived_cl0, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_identity])).
% 259.22/38.02 thf(zip_derived_cl1073, plain,
% 259.22/38.02 ((((identity) = (sk_c9)))
% 259.22/38.02 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl1059, zip_derived_cl58])).
% 259.22/38.02 thf(zip_derived_cl0, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_identity])).
% 259.22/38.02 thf(zip_derived_cl1073, plain,
% 259.22/38.02 ((((identity) = (sk_c9)))
% 259.22/38.02 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl1059, zip_derived_cl58])).
% 259.22/38.02 thf(zip_derived_cl0, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_identity])).
% 259.22/38.02 thf(zip_derived_cl1073, plain,
% 259.22/38.02 ((((identity) = (sk_c9)))
% 259.22/38.02 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl1059, zip_derived_cl58])).
% 259.22/38.02 thf(zip_derived_cl0, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_identity])).
% 259.22/38.02 thf(zip_derived_cl1073, plain,
% 259.22/38.02 ((((identity) = (sk_c9)))
% 259.22/38.02 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl1059, zip_derived_cl58])).
% 259.22/38.02 thf(zip_derived_cl0, plain,
% 259.22/38.02 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 259.22/38.02 inference('cnf', [status(esa)], [left_identity])).
% 259.22/38.02 thf(zip_derived_cl11069, plain,
% 259.22/38.02 ((![X0 : $i]:
% 259.22/38.02 (((X0) != (identity))
% 259.22/38.02 | ((inverse @ (inverse @ sk_c2)) != (X0))
% 259.22/38.02 | ((multiply @ X0 @ identity) != (identity))
% 259.22/38.02 | ((inverse @ identity) != (X0))
% 259.22/38.02 | ((inverse @ X0) != (X0))))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))) &
% 259.22/38.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.02 inference('demod', [status(thm)],
% 259.22/38.02 [zip_derived_cl11032, zip_derived_cl7935, zip_derived_cl2010,
% 259.22/38.02 zip_derived_cl0, zip_derived_cl1073, zip_derived_cl0,
% 259.22/38.02 zip_derived_cl1073, zip_derived_cl0, zip_derived_cl1073,
% 259.22/38.02 zip_derived_cl0, zip_derived_cl1073, zip_derived_cl0,
% 259.22/38.02 zip_derived_cl1073, zip_derived_cl0])).
% 259.22/38.02 thf(zip_derived_cl11406, plain,
% 259.22/38.02 (((((inverse @ (inverse @ (inverse @ sk_c2)))
% 259.22/38.02 != (inverse @ (inverse @ sk_c2)))
% 259.22/38.02 | ((inverse @ identity) != (inverse @ (inverse @ sk_c2)))
% 259.22/38.02 | ((multiply @ (inverse @ (inverse @ sk_c2)) @ identity) != (identity))
% 259.22/38.02 | ((inverse @ (inverse @ sk_c2)) != (identity))))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))) &
% 259.22/38.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.02 inference('eq_res', [status(thm)], [zip_derived_cl11069])).
% 259.22/38.02 thf(zip_derived_cl497, plain,
% 259.22/38.02 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 259.22/38.02 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl196])).
% 259.22/38.02 thf(zip_derived_cl11407, plain,
% 259.22/38.02 (((((inverse @ (inverse @ (inverse @ sk_c2)))
% 259.22/38.02 != (inverse @ (inverse @ sk_c2)))
% 259.22/38.02 | ((inverse @ identity) != (inverse @ (inverse @ sk_c2)))
% 259.22/38.02 | ((sk_c2) != (identity))
% 259.22/38.02 | ((inverse @ (inverse @ sk_c2)) != (identity))))
% 259.22/38.02 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))) &
% 259.22/38.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.02 (((inverse @ X0) != (X2))
% 259.22/38.02 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.02 | ((inverse @ X1) != (X0))
% 259.22/38.02 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.02 | ((inverse @ X3) != (X2))
% 259.22/38.02 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.02 inference('demod', [status(thm)],
% 259.22/38.02 [zip_derived_cl11406, zip_derived_cl497])).
% 259.22/38.02 thf(zip_derived_cl11512, plain,
% 259.22/38.02 ((((sk_c2) != (identity))) <= (~ (((sk_c2) = (identity))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl11407])).
% 259.22/38.02 thf(zip_derived_cl11537, plain,
% 259.22/38.02 ((((identity) != (identity)))
% 259.22/38.02 <= (~ (((sk_c2) = (identity))) &
% 259.22/38.02 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.02 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.02 inference('s_sup-', [status(thm)],
% 259.22/38.02 [zip_derived_cl974, zip_derived_cl11512])).
% 259.22/38.02 thf('39', plain,
% 259.22/38.02 ((((sk_c2) = (identity))) | ~ (((inverse @ sk_c1) = (sk_c11))) |
% 259.22/38.02 ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 259.22/38.02 ~ (((inverse @ sk_c2) = (sk_c10)))),
% 259.22/38.02 inference('simplify', [status(thm)], [zip_derived_cl11537])).
% 259.22/38.02 thf(zip_derived_cl9129, plain,
% 259.22/38.02 ((((sk_c10) = (sk_c11)))
% 259.22/38.02 <= ((((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 259.22/38.02 (((inverse @ sk_c2) = (sk_c10))) &
% 259.22/38.02 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('demod', [status(thm)], [zip_derived_cl9109, zip_derived_cl496])).
% 259.22/38.02 thf(zip_derived_cl176, plain,
% 259.22/38.02 ((((sk_c10) != (sk_c11))) <= (~ (((sk_c10) = (sk_c11))))),
% 259.22/38.02 inference('split', [status(esa)], [zip_derived_cl161])).
% 259.22/38.02 thf(zip_derived_cl9191, plain,
% 259.22/38.02 ((((sk_c11) != (sk_c11)))
% 259.22/38.02 <= (~ (((sk_c10) = (sk_c11))) &
% 259.22/38.02 (((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 259.22/38.03 (((inverse @ sk_c2) = (sk_c10))) &
% 259.22/38.03 (((multiply @ sk_c9 @ sk_c10) = (sk_c11))))),
% 259.22/38.03 inference('s_sup-', [status(thm)],
% 259.22/38.03 [zip_derived_cl9129, zip_derived_cl176])).
% 259.22/38.03 thf('40', plain,
% 259.22/38.03 ((((sk_c10) = (sk_c11))) | ~ (((multiply @ sk_c2 @ sk_c10) = (sk_c9))) |
% 259.22/38.03 ~ (((inverse @ sk_c2) = (sk_c10))) |
% 259.22/38.03 ~ (((multiply @ sk_c9 @ sk_c10) = (sk_c11)))),
% 259.22/38.03 inference('simplify', [status(thm)], [zip_derived_cl9191])).
% 259.22/38.03 thf('41', plain,
% 259.22/38.03 (~ (((multiply @ sk_c9 @ sk_c10) = (sk_c11))) |
% 259.22/38.03 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.03 (((inverse @ X0) != (X2))
% 259.22/38.03 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.03 | ((inverse @ X1) != (X0))
% 259.22/38.03 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.03 | ((inverse @ X3) != (X2))
% 259.22/38.03 | ((multiply @ X3 @ X2) != (sk_c11)))) |
% 259.22/38.03 (![X6 : $i]:
% 259.22/38.03 (((inverse @ X6) != (sk_c10)) | ((multiply @ X6 @ sk_c10) != (sk_c9)))) |
% 259.22/38.03 (![X7 : $i]:
% 259.22/38.03 (((inverse @ X7) != (sk_c11))
% 259.22/38.03 | ((multiply @ X7 @ sk_c11) != (sk_c10))))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl53])).
% 259.22/38.03 thf(zip_derived_cl58, plain,
% 259.22/38.03 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9)))
% 259.22/38.03 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl5])).
% 259.22/38.03 thf(zip_derived_cl60, plain,
% 259.22/38.03 ((((inverse @ sk_c4) = (sk_c10))) <= ((((inverse @ sk_c4) = (sk_c10))))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl6])).
% 259.22/38.03 thf(zip_derived_cl155, plain,
% 259.22/38.03 ((![X6 : $i]:
% 259.22/38.03 (((inverse @ X6) != (sk_c10)) | ((multiply @ X6 @ sk_c10) != (sk_c9))))
% 259.22/38.03 <= ((![X6 : $i]:
% 259.22/38.03 (((inverse @ X6) != (sk_c10))
% 259.22/38.03 | ((multiply @ X6 @ sk_c10) != (sk_c9)))))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl53])).
% 259.22/38.03 thf(zip_derived_cl166, plain,
% 259.22/38.03 (((((sk_c10) != (sk_c10)) | ((multiply @ sk_c4 @ sk_c10) != (sk_c9))))
% 259.22/38.03 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.03 (![X6 : $i]:
% 259.22/38.03 (((inverse @ X6) != (sk_c10))
% 259.22/38.03 | ((multiply @ X6 @ sk_c10) != (sk_c9)))))),
% 259.22/38.03 inference('s_sup-', [status(thm)], [zip_derived_cl60, zip_derived_cl155])).
% 259.22/38.03 thf(zip_derived_cl169, plain,
% 259.22/38.03 ((((multiply @ sk_c4 @ sk_c10) != (sk_c9)))
% 259.22/38.03 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.03 (![X6 : $i]:
% 259.22/38.03 (((inverse @ X6) != (sk_c10))
% 259.22/38.03 | ((multiply @ X6 @ sk_c10) != (sk_c9)))))),
% 259.22/38.03 inference('simplify', [status(thm)], [zip_derived_cl166])).
% 259.22/38.03 thf(zip_derived_cl240, plain,
% 259.22/38.03 ((((sk_c9) != (sk_c9)))
% 259.22/38.03 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.03 (((inverse @ sk_c4) = (sk_c10))) &
% 259.22/38.03 (![X6 : $i]:
% 259.22/38.03 (((inverse @ X6) != (sk_c10))
% 259.22/38.03 | ((multiply @ X6 @ sk_c10) != (sk_c9)))))),
% 259.22/38.03 inference('s_sup-', [status(thm)], [zip_derived_cl58, zip_derived_cl169])).
% 259.22/38.03 thf('42', plain,
% 259.22/38.03 (~
% 259.22/38.03 (![X6 : $i]:
% 259.22/38.03 (((inverse @ X6) != (sk_c10)) | ((multiply @ X6 @ sk_c10) != (sk_c9)))) |
% 259.22/38.03 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 259.22/38.03 ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9)))),
% 259.22/38.03 inference('simplify', [status(thm)], [zip_derived_cl240])).
% 259.22/38.03 thf(prove_this_23, conjecture,
% 259.22/38.03 (~( ( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 259.22/38.03 ( ( multiply @ sk_c2 @ sk_c10 ) = ( sk_c9 ) ) ))).
% 259.22/38.03 thf(zf_stmt_19, negated_conjecture,
% 259.22/38.03 (( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 259.22/38.03 ( ( multiply @ sk_c2 @ sk_c10 ) = ( sk_c9 ) )),
% 259.22/38.03 inference('cnf.neg', [status(esa)], [prove_this_23])).
% 259.22/38.03 thf(zip_derived_cl25, plain,
% 259.22/38.03 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))
% 259.22/38.03 | ((multiply @ sk_c2 @ sk_c10) = (sk_c9)))),
% 259.22/38.03 inference('cnf', [status(esa)], [zf_stmt_19])).
% 259.22/38.03 thf('43', plain,
% 259.22/38.03 ((((multiply @ sk_c2 @ sk_c10) = (sk_c9))) |
% 259.22/38.03 (((multiply @ sk_c4 @ sk_c10) = (sk_c9)))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl25])).
% 259.22/38.03 thf(prove_this_33, conjecture,
% 259.22/38.03 (~( ( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 259.22/38.03 ( ( inverse @ sk_c2 ) = ( sk_c10 ) ) ))).
% 259.22/38.03 thf(zf_stmt_20, negated_conjecture,
% 259.22/38.03 (( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 259.22/38.03 ( ( inverse @ sk_c2 ) = ( sk_c10 ) )),
% 259.22/38.03 inference('cnf.neg', [status(esa)], [prove_this_33])).
% 259.22/38.03 thf(zip_derived_cl35, plain,
% 259.22/38.03 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))
% 259.22/38.03 | ((inverse @ sk_c2) = (sk_c10)))),
% 259.22/38.03 inference('cnf', [status(esa)], [zf_stmt_20])).
% 259.22/38.03 thf('44', plain,
% 259.22/38.03 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 259.22/38.03 (((inverse @ sk_c2) = (sk_c10)))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl35])).
% 259.22/38.03 thf(zip_derived_cl94, plain,
% 259.22/38.03 ((((multiply @ sk_c2 @ sk_c10) = (sk_c9)))
% 259.22/38.03 <= ((((multiply @ sk_c2 @ sk_c10) = (sk_c9))))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl23])).
% 259.22/38.03 thf(zip_derived_cl114, plain,
% 259.22/38.03 ((((inverse @ sk_c2) = (sk_c10))) <= ((((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl33])).
% 259.22/38.03 thf(zip_derived_cl155, plain,
% 259.22/38.03 ((![X6 : $i]:
% 259.22/38.03 (((inverse @ X6) != (sk_c10)) | ((multiply @ X6 @ sk_c10) != (sk_c9))))
% 259.22/38.03 <= ((![X6 : $i]:
% 259.22/38.03 (((inverse @ X6) != (sk_c10))
% 259.22/38.03 | ((multiply @ X6 @ sk_c10) != (sk_c9)))))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl53])).
% 259.22/38.03 thf(zip_derived_cl213, plain,
% 259.22/38.03 (((((sk_c10) != (sk_c10)) | ((multiply @ sk_c2 @ sk_c10) != (sk_c9))))
% 259.22/38.03 <= ((((inverse @ sk_c2) = (sk_c10))) &
% 259.22/38.03 (![X6 : $i]:
% 259.22/38.03 (((inverse @ X6) != (sk_c10))
% 259.22/38.03 | ((multiply @ X6 @ sk_c10) != (sk_c9)))))),
% 259.22/38.03 inference('s_sup-', [status(thm)], [zip_derived_cl114, zip_derived_cl155])).
% 259.22/38.03 thf(zip_derived_cl215, plain,
% 259.22/38.03 ((((multiply @ sk_c2 @ sk_c10) != (sk_c9)))
% 259.22/38.03 <= ((((inverse @ sk_c2) = (sk_c10))) &
% 259.22/38.03 (![X6 : $i]:
% 259.22/38.03 (((inverse @ X6) != (sk_c10))
% 259.22/38.03 | ((multiply @ X6 @ sk_c10) != (sk_c9)))))),
% 259.22/38.03 inference('simplify', [status(thm)], [zip_derived_cl213])).
% 259.22/38.03 thf(zip_derived_cl311, plain,
% 259.22/38.03 ((((sk_c9) != (sk_c9)))
% 259.22/38.03 <= ((((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 259.22/38.03 (((inverse @ sk_c2) = (sk_c10))) &
% 259.22/38.03 (![X6 : $i]:
% 259.22/38.03 (((inverse @ X6) != (sk_c10))
% 259.22/38.03 | ((multiply @ X6 @ sk_c10) != (sk_c9)))))),
% 259.22/38.03 inference('s_sup-', [status(thm)], [zip_derived_cl94, zip_derived_cl215])).
% 259.22/38.03 thf('45', plain,
% 259.22/38.03 (~
% 259.22/38.03 (![X6 : $i]:
% 259.22/38.03 (((inverse @ X6) != (sk_c10)) | ((multiply @ X6 @ sk_c10) != (sk_c9)))) |
% 259.22/38.03 ~ (((multiply @ sk_c2 @ sk_c10) = (sk_c9))) |
% 259.22/38.03 ~ (((inverse @ sk_c2) = (sk_c10)))),
% 259.22/38.03 inference('simplify', [status(thm)], [zip_derived_cl311])).
% 259.22/38.03 thf('46', plain,
% 259.22/38.03 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 259.22/38.03 (((inverse @ sk_c4) = (sk_c10)))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl6])).
% 259.22/38.03 thf(prove_this_24, conjecture,
% 259.22/38.03 (~( ( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 259.22/38.03 ( ( multiply @ sk_c2 @ sk_c10 ) = ( sk_c9 ) ) ))).
% 259.22/38.03 thf(zf_stmt_21, negated_conjecture,
% 259.22/38.03 (( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 259.22/38.03 ( ( multiply @ sk_c2 @ sk_c10 ) = ( sk_c9 ) )),
% 259.22/38.03 inference('cnf.neg', [status(esa)], [prove_this_24])).
% 259.22/38.03 thf(zip_derived_cl26, plain,
% 259.22/38.03 ((((inverse @ sk_c4) = (sk_c10))
% 259.22/38.03 | ((multiply @ sk_c2 @ sk_c10) = (sk_c9)))),
% 259.22/38.03 inference('cnf', [status(esa)], [zf_stmt_21])).
% 259.22/38.03 thf('47', plain,
% 259.22/38.03 ((((multiply @ sk_c2 @ sk_c10) = (sk_c9))) |
% 259.22/38.03 (((inverse @ sk_c4) = (sk_c10)))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl26])).
% 259.22/38.03 thf(prove_this_34, conjecture,
% 259.22/38.03 (~( ( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 259.22/38.03 ( ( inverse @ sk_c2 ) = ( sk_c10 ) ) ))).
% 259.22/38.03 thf(zf_stmt_22, negated_conjecture,
% 259.22/38.03 (( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 259.22/38.03 ( ( inverse @ sk_c2 ) = ( sk_c10 ) )),
% 259.22/38.03 inference('cnf.neg', [status(esa)], [prove_this_34])).
% 259.22/38.03 thf(zip_derived_cl36, plain,
% 259.22/38.03 ((((inverse @ sk_c4) = (sk_c10)) | ((inverse @ sk_c2) = (sk_c10)))),
% 259.22/38.03 inference('cnf', [status(esa)], [zf_stmt_22])).
% 259.22/38.03 thf('48', plain,
% 259.22/38.03 ((((inverse @ sk_c4) = (sk_c10))) | (((inverse @ sk_c2) = (sk_c10)))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl36])).
% 259.22/38.03 thf(prove_this_44, conjecture,
% 259.22/38.03 (~( ( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 259.22/38.03 ( ( multiply @ sk_c9 @ sk_c10 ) = ( sk_c11 ) ) ))).
% 259.22/38.03 thf(zf_stmt_23, negated_conjecture,
% 259.22/38.03 (( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 259.22/38.03 ( ( multiply @ sk_c9 @ sk_c10 ) = ( sk_c11 ) )),
% 259.22/38.03 inference('cnf.neg', [status(esa)], [prove_this_44])).
% 259.22/38.03 thf(zip_derived_cl46, plain,
% 259.22/38.03 ((((inverse @ sk_c4) = (sk_c10))
% 259.22/38.03 | ((multiply @ sk_c9 @ sk_c10) = (sk_c11)))),
% 259.22/38.03 inference('cnf', [status(esa)], [zf_stmt_23])).
% 259.22/38.03 thf('49', plain,
% 259.22/38.03 ((((inverse @ sk_c4) = (sk_c10))) |
% 259.22/38.03 (((multiply @ sk_c9 @ sk_c10) = (sk_c11)))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl46])).
% 259.22/38.03 thf(zip_derived_cl54, plain,
% 259.22/38.03 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10)))
% 259.22/38.03 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl3])).
% 259.22/38.03 thf(zip_derived_cl74, plain,
% 259.22/38.03 ((((inverse @ sk_c1) = (sk_c11))) <= ((((inverse @ sk_c1) = (sk_c11))))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl13])).
% 259.22/38.03 thf(zip_derived_cl154, plain,
% 259.22/38.03 ((![X7 : $i]:
% 259.22/38.03 (((inverse @ X7) != (sk_c11))
% 259.22/38.03 | ((multiply @ X7 @ sk_c11) != (sk_c10))))
% 259.22/38.03 <= ((![X7 : $i]:
% 259.22/38.03 (((inverse @ X7) != (sk_c11))
% 259.22/38.03 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl53])).
% 259.22/38.03 thf(zip_derived_cl173, plain,
% 259.22/38.03 (((((sk_c11) != (sk_c11)) | ((multiply @ sk_c1 @ sk_c11) != (sk_c10))))
% 259.22/38.03 <= ((((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.03 (![X7 : $i]:
% 259.22/38.03 (((inverse @ X7) != (sk_c11))
% 259.22/38.03 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 259.22/38.03 inference('s_sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl154])).
% 259.22/38.03 thf(zip_derived_cl174, plain,
% 259.22/38.03 ((((multiply @ sk_c1 @ sk_c11) != (sk_c10)))
% 259.22/38.03 <= ((((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.03 (![X7 : $i]:
% 259.22/38.03 (((inverse @ X7) != (sk_c11))
% 259.22/38.03 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 259.22/38.03 inference('simplify', [status(thm)], [zip_derived_cl173])).
% 259.22/38.03 thf(zip_derived_cl207, plain,
% 259.22/38.03 ((((sk_c10) != (sk_c10)))
% 259.22/38.03 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 259.22/38.03 (((inverse @ sk_c1) = (sk_c11))) &
% 259.22/38.03 (![X7 : $i]:
% 259.22/38.03 (((inverse @ X7) != (sk_c11))
% 259.22/38.03 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 259.22/38.03 inference('s_sup-', [status(thm)], [zip_derived_cl54, zip_derived_cl174])).
% 259.22/38.03 thf('50', plain,
% 259.22/38.03 (~
% 259.22/38.03 (![X7 : $i]:
% 259.22/38.03 (((inverse @ X7) != (sk_c11))
% 259.22/38.03 | ((multiply @ X7 @ sk_c11) != (sk_c10)))) |
% 259.22/38.03 ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 259.22/38.03 ~ (((inverse @ sk_c1) = (sk_c11)))),
% 259.22/38.03 inference('simplify', [status(thm)], [zip_derived_cl207])).
% 259.22/38.03 thf(zip_derived_cl55, plain,
% 259.22/38.03 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10)))
% 259.22/38.03 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl3])).
% 259.22/38.03 thf(zip_derived_cl56, plain,
% 259.22/38.03 ((((inverse @ sk_c3) = (sk_c11))) <= ((((inverse @ sk_c3) = (sk_c11))))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl4])).
% 259.22/38.03 thf(zip_derived_cl154, plain,
% 259.22/38.03 ((![X7 : $i]:
% 259.22/38.03 (((inverse @ X7) != (sk_c11))
% 259.22/38.03 | ((multiply @ X7 @ sk_c11) != (sk_c10))))
% 259.22/38.03 <= ((![X7 : $i]:
% 259.22/38.03 (((inverse @ X7) != (sk_c11))
% 259.22/38.03 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl53])).
% 259.22/38.03 thf(zip_derived_cl160, plain,
% 259.22/38.03 (((((sk_c11) != (sk_c11)) | ((multiply @ sk_c3 @ sk_c11) != (sk_c10))))
% 259.22/38.03 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.03 (![X7 : $i]:
% 259.22/38.03 (((inverse @ X7) != (sk_c11))
% 259.22/38.03 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 259.22/38.03 inference('s_sup-', [status(thm)], [zip_derived_cl56, zip_derived_cl154])).
% 259.22/38.03 thf(zip_derived_cl164, plain,
% 259.22/38.03 ((((multiply @ sk_c3 @ sk_c11) != (sk_c10)))
% 259.22/38.03 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.03 (![X7 : $i]:
% 259.22/38.03 (((inverse @ X7) != (sk_c11))
% 259.22/38.03 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 259.22/38.03 inference('simplify', [status(thm)], [zip_derived_cl160])).
% 259.22/38.03 thf(zip_derived_cl210, plain,
% 259.22/38.03 ((((sk_c10) != (sk_c10)))
% 259.22/38.03 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.03 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.03 (![X7 : $i]:
% 259.22/38.03 (((inverse @ X7) != (sk_c11))
% 259.22/38.03 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 259.22/38.03 inference('s_sup-', [status(thm)], [zip_derived_cl55, zip_derived_cl164])).
% 259.22/38.03 thf('51', plain,
% 259.22/38.03 (~
% 259.22/38.03 (![X7 : $i]:
% 259.22/38.03 (((inverse @ X7) != (sk_c11))
% 259.22/38.03 | ((multiply @ X7 @ sk_c11) != (sk_c10)))) |
% 259.22/38.03 ~ (((inverse @ sk_c3) = (sk_c11))) |
% 259.22/38.03 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c10)))),
% 259.22/38.03 inference('simplify', [status(thm)], [zip_derived_cl210])).
% 259.22/38.03 thf('52', plain,
% 259.22/38.03 ((((inverse @ sk_c3) = (sk_c11))) |
% 259.22/38.03 (((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl4])).
% 259.22/38.03 thf('53', plain,
% 259.22/38.03 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) |
% 259.22/38.03 (((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl3])).
% 259.22/38.03 thf(zip_derived_cl1241, plain,
% 259.22/38.03 ((((multiply @ sk_c2 @ sk_c10) = (identity)))
% 259.22/38.03 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.03 inference('s_sup+', [status(thm)], [zip_derived_cl586, zip_derived_cl1])).
% 259.22/38.03 thf(zip_derived_cl212, plain,
% 259.22/38.03 ((((multiply @ sk_c10 @ sk_c2) = (identity)))
% 259.22/38.03 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.03 inference('s_sup+', [status(thm)], [zip_derived_cl114, zip_derived_cl1])).
% 259.22/38.03 thf(zip_derived_cl2, plain,
% 259.22/38.03 (![X0 : $i, X1 : $i, X2 : $i]:
% 259.22/38.03 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 259.22/38.03 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 259.22/38.03 inference('cnf', [status(esa)], [associativity])).
% 259.22/38.03 thf(zip_derived_cl453, plain,
% 259.22/38.03 ((![X0 : $i]:
% 259.22/38.03 ((multiply @ identity @ X0)
% 259.22/38.03 = (multiply @ sk_c10 @ (multiply @ sk_c2 @ X0))))
% 259.22/38.03 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.03 inference('s_sup+', [status(thm)], [zip_derived_cl212, zip_derived_cl2])).
% 259.22/38.03 thf(zip_derived_cl0, plain,
% 259.22/38.03 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 259.22/38.03 inference('cnf', [status(esa)], [left_identity])).
% 259.22/38.03 thf(zip_derived_cl454, plain,
% 259.22/38.03 ((![X0 : $i]: ((X0) = (multiply @ sk_c10 @ (multiply @ sk_c2 @ X0))))
% 259.22/38.03 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.03 inference('demod', [status(thm)], [zip_derived_cl453, zip_derived_cl0])).
% 259.22/38.03 thf(zip_derived_cl1271, plain,
% 259.22/38.03 ((((sk_c10) = (multiply @ sk_c10 @ identity)))
% 259.22/38.03 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.03 inference('s_sup+', [status(thm)],
% 259.22/38.03 [zip_derived_cl1241, zip_derived_cl454])).
% 259.22/38.03 thf(zip_derived_cl496, plain,
% 259.22/38.03 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 259.22/38.03 inference('s_sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl196])).
% 259.22/38.03 thf(zip_derived_cl158, plain,
% 259.22/38.03 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.03 (((inverse @ X0) != (X2))
% 259.22/38.03 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.03 | ((inverse @ X1) != (X0))
% 259.22/38.03 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.03 | ((inverse @ X3) != (X2))
% 259.22/38.03 | ((multiply @ X3 @ X2) != (sk_c11))))
% 259.22/38.03 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.03 (((inverse @ X0) != (X2))
% 259.22/38.03 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.03 | ((inverse @ X1) != (X0))
% 259.22/38.03 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.03 | ((inverse @ X3) != (X2))
% 259.22/38.03 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl53])).
% 259.22/38.03 thf(zip_derived_cl223, plain,
% 259.22/38.03 ((![X0 : $i, X1 : $i, X2 : $i]:
% 259.22/38.03 (((multiply @ X1 @ X0) != (sk_c11))
% 259.22/38.03 | ((inverse @ X1) != (X0))
% 259.22/38.03 | ((multiply @ X0 @ sk_c10) != (sk_c11))
% 259.22/38.03 | ((inverse @ X2) != (multiply @ X2 @ X0))
% 259.22/38.03 | ((inverse @ (multiply @ X2 @ X0)) != (X0))))
% 259.22/38.03 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.03 (((inverse @ X0) != (X2))
% 259.22/38.03 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.03 | ((inverse @ X1) != (X0))
% 259.22/38.03 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.03 | ((inverse @ X3) != (X2))
% 259.22/38.03 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.03 inference('eq_res', [status(thm)], [zip_derived_cl158])).
% 259.22/38.03 thf(zip_derived_cl2842, plain,
% 259.22/38.03 ((![X0 : $i, X1 : $i]:
% 259.22/38.03 (((multiply @ X1 @ X0) != (sk_c11))
% 259.22/38.03 | ((inverse @ X1) != (X0))
% 259.22/38.03 | ((multiply @ X0 @ sk_c10) != (sk_c11))
% 259.22/38.03 | ((inverse @ (inverse @ identity)) != (X0))
% 259.22/38.03 | ((inverse @ X0) != (X0))))
% 259.22/38.03 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.03 (((inverse @ X0) != (X2))
% 259.22/38.03 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.03 | ((inverse @ X1) != (X0))
% 259.22/38.03 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.03 | ((inverse @ X3) != (X2))
% 259.22/38.03 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.03 inference('s_sup-', [status(thm)], [zip_derived_cl496, zip_derived_cl223])).
% 259.22/38.03 thf(zip_derived_cl3507, plain,
% 259.22/38.03 (((((sk_c10) != (sk_c11))
% 259.22/38.03 | ((inverse @ sk_c10) != (identity))
% 259.22/38.03 | ((multiply @ identity @ sk_c10) != (sk_c11))
% 259.22/38.03 | ((inverse @ (inverse @ identity)) != (identity))
% 259.22/38.03 | ((inverse @ identity) != (identity))))
% 259.22/38.03 <= ((((inverse @ sk_c2) = (sk_c10))) &
% 259.22/38.03 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.03 (((inverse @ X0) != (X2))
% 259.22/38.03 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.03 | ((inverse @ X1) != (X0))
% 259.22/38.03 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.03 | ((inverse @ X3) != (X2))
% 259.22/38.03 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.03 inference('s_sup-', [status(thm)],
% 259.22/38.03 [zip_derived_cl1271, zip_derived_cl2842])).
% 259.22/38.03 thf(zip_derived_cl0, plain,
% 259.22/38.03 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 259.22/38.03 inference('cnf', [status(esa)], [left_identity])).
% 259.22/38.03 thf(zip_derived_cl3598, plain,
% 259.22/38.03 (((((sk_c10) != (sk_c11))
% 259.22/38.03 | ((inverse @ sk_c10) != (identity))
% 259.22/38.03 | ((sk_c10) != (sk_c11))
% 259.22/38.03 | ((inverse @ (inverse @ identity)) != (identity))
% 259.22/38.03 | ((inverse @ identity) != (identity))))
% 259.22/38.03 <= ((((inverse @ sk_c2) = (sk_c10))) &
% 259.22/38.03 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.03 (((inverse @ X0) != (X2))
% 259.22/38.03 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.03 | ((inverse @ X1) != (X0))
% 259.22/38.03 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.03 | ((inverse @ X3) != (X2))
% 259.22/38.03 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.03 inference('demod', [status(thm)], [zip_derived_cl3507, zip_derived_cl0])).
% 259.22/38.03 thf(zip_derived_cl3599, plain,
% 259.22/38.03 (((((inverse @ identity) != (identity))
% 259.22/38.03 | ((inverse @ (inverse @ identity)) != (identity))
% 259.22/38.03 | ((inverse @ sk_c10) != (identity))
% 259.22/38.03 | ((sk_c10) != (sk_c11))))
% 259.22/38.03 <= ((((inverse @ sk_c2) = (sk_c10))) &
% 259.22/38.03 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.03 (((inverse @ X0) != (X2))
% 259.22/38.03 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.03 | ((inverse @ X1) != (X0))
% 259.22/38.03 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.03 | ((inverse @ X3) != (X2))
% 259.22/38.03 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.03 inference('simplify', [status(thm)], [zip_derived_cl3598])).
% 259.22/38.03 thf(zip_derived_cl196, plain,
% 259.22/38.03 (![X0 : $i, X1 : $i]:
% 259.22/38.03 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 259.22/38.03 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 259.22/38.03 thf(zip_derived_cl196, plain,
% 259.22/38.03 (![X0 : $i, X1 : $i]:
% 259.22/38.03 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 259.22/38.03 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 259.22/38.03 thf(zip_derived_cl494, plain,
% 259.22/38.03 (![X0 : $i, X1 : $i]:
% 259.22/38.03 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 259.22/38.03 inference('s_sup+', [status(thm)], [zip_derived_cl196, zip_derived_cl196])).
% 259.22/38.03 thf(zip_derived_cl1, plain,
% 259.22/38.03 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 259.22/38.03 inference('cnf', [status(esa)], [left_inverse])).
% 259.22/38.03 thf(zip_derived_cl2436, plain,
% 259.22/38.03 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 259.22/38.03 inference('s_sup+', [status(thm)], [zip_derived_cl494, zip_derived_cl1])).
% 259.22/38.03 thf(zip_derived_cl586, plain,
% 259.22/38.03 ((![X0 : $i]:
% 259.22/38.03 ((multiply @ sk_c2 @ X0) = (multiply @ (inverse @ sk_c10) @ X0)))
% 259.22/38.03 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.03 inference('demod', [status(thm)], [zip_derived_cl582, zip_derived_cl0])).
% 259.22/38.03 thf(zip_derived_cl196, plain,
% 259.22/38.03 (![X0 : $i, X1 : $i]:
% 259.22/38.03 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 259.22/38.03 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 259.22/38.03 thf(zip_derived_cl1243, plain,
% 259.22/38.03 ((![X0 : $i]: ((X0) = (multiply @ sk_c2 @ (multiply @ sk_c10 @ X0))))
% 259.22/38.03 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.03 inference('s_sup+', [status(thm)], [zip_derived_cl586, zip_derived_cl196])).
% 259.22/38.03 thf(zip_derived_cl78117, plain,
% 259.22/38.03 ((((inverse @ sk_c10) = (multiply @ sk_c2 @ identity)))
% 259.22/38.03 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.03 inference('s_sup+', [status(thm)],
% 259.22/38.03 [zip_derived_cl2436, zip_derived_cl1243])).
% 259.22/38.03 thf(zip_derived_cl1245, plain,
% 259.22/38.03 ((((sk_c2) = (multiply @ sk_c2 @ identity)))
% 259.22/38.03 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.03 inference('s_sup+', [status(thm)], [zip_derived_cl586, zip_derived_cl506])).
% 259.22/38.03 thf(zip_derived_cl78342, plain,
% 259.22/38.03 ((((inverse @ sk_c10) = (sk_c2))) <= ((((inverse @ sk_c2) = (sk_c10))))),
% 259.22/38.03 inference('demod', [status(thm)],
% 259.22/38.03 [zip_derived_cl78117, zip_derived_cl1245])).
% 259.22/38.03 thf(zip_derived_cl146474, plain,
% 259.22/38.03 (((((inverse @ identity) != (identity))
% 259.22/38.03 | ((inverse @ (inverse @ identity)) != (identity))
% 259.22/38.03 | ((sk_c2) != (identity))
% 259.22/38.03 | ((sk_c10) != (sk_c11))))
% 259.22/38.03 <= ((((inverse @ sk_c2) = (sk_c10))) &
% 259.22/38.03 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.03 (((inverse @ X0) != (X2))
% 259.22/38.03 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.03 | ((inverse @ X1) != (X0))
% 259.22/38.03 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.03 | ((inverse @ X3) != (X2))
% 259.22/38.03 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.03 inference('demod', [status(thm)],
% 259.22/38.03 [zip_derived_cl3599, zip_derived_cl78342])).
% 259.22/38.03 thf('54', plain,
% 259.22/38.03 (~
% 259.22/38.03 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.03 (((inverse @ X0) != (X2))
% 259.22/38.03 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.03 | ((inverse @ X1) != (X0))
% 259.22/38.03 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.03 | ((inverse @ X3) != (X2))
% 259.22/38.03 | ((multiply @ X3 @ X2) != (sk_c11)))) |
% 259.22/38.03 ~ (((inverse @ identity) = (identity))) | ~ (((sk_c2) = (identity))) |
% 259.22/38.03 ~ (((sk_c10) = (sk_c11))) |
% 259.22/38.03 ~ (((identity) = (inverse @ (inverse @ identity)))) |
% 259.22/38.03 ~ (((inverse @ sk_c2) = (sk_c10)))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl146474])).
% 259.22/38.03 thf(prove_this_15, conjecture,
% 259.22/38.03 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 259.22/38.03 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 259.22/38.03 thf(zf_stmt_24, negated_conjecture,
% 259.22/38.03 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 259.22/38.03 ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 259.22/38.03 inference('cnf.neg', [status(esa)], [prove_this_15])).
% 259.22/38.03 thf(zip_derived_cl17, plain,
% 259.22/38.03 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))
% 259.22/38.03 | ((inverse @ sk_c1) = (sk_c11)))),
% 259.22/38.03 inference('cnf', [status(esa)], [zf_stmt_24])).
% 259.22/38.03 thf('55', plain,
% 259.22/38.03 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) |
% 259.22/38.03 (((inverse @ sk_c1) = (sk_c11)))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl17])).
% 259.22/38.03 thf('56', plain, ((((multiply @ sk_c5 @ sk_c8) = (sk_c11)))),
% 259.22/38.03 inference('sat_resolution*', [status(thm)],
% 259.22/38.03 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 259.22/38.03 '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
% 259.22/38.03 '22', '23', '24', '25', '26', '27', '28', '29', '30', '31',
% 259.22/38.03 '32', '33', '34', '35', '36', '37', '38', '39', '40', '41',
% 259.22/38.03 '42', '43', '44', '45', '46', '47', '48', '49', '50', '51',
% 259.22/38.03 '52', '53', '54', '55'])).
% 259.22/38.03 thf(prove_this_16, conjecture,
% 259.22/38.03 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 259.22/38.03 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 259.22/38.03 thf(zf_stmt_25, negated_conjecture,
% 259.22/38.03 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 259.22/38.03 inference('cnf.neg', [status(esa)], [prove_this_16])).
% 259.22/38.03 thf(zip_derived_cl18, plain,
% 259.22/38.03 ((((inverse @ sk_c5) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c11)))),
% 259.22/38.03 inference('cnf', [status(esa)], [zf_stmt_25])).
% 259.22/38.03 thf('57', plain,
% 259.22/38.03 ((((inverse @ sk_c5) = (sk_c8))) | (((inverse @ sk_c1) = (sk_c11)))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl18])).
% 259.22/38.03 thf('58', plain, ((((inverse @ sk_c5) = (sk_c8)))),
% 259.22/38.03 inference('sat_resolution*', [status(thm)],
% 259.22/38.03 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 259.22/38.03 '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
% 259.22/38.03 '22', '23', '24', '25', '26', '27', '28', '29', '30', '31',
% 259.22/38.03 '32', '33', '34', '35', '36', '37', '38', '39', '40', '41',
% 259.22/38.03 '42', '43', '44', '45', '46', '47', '48', '49', '50', '51',
% 259.22/38.03 '52', '53', '54', '57'])).
% 259.22/38.03 thf(zip_derived_cl168080, plain, (((sk_c11) = (identity))),
% 259.22/38.03 inference('simpl_trail', [status(thm)], [zip_derived_cl5616, '56', '58'])).
% 259.22/38.03 thf(zip_derived_cl178639, plain,
% 259.22/38.03 ((((identity) != (identity)))
% 259.22/38.03 <= (~ (((multiply @ sk_c9 @ sk_c10) = (sk_c11))) &
% 259.22/38.03 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.03 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.03 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.03 (((inverse @ sk_c4) = (sk_c10))))),
% 259.22/38.03 inference('demod', [status(thm)],
% 259.22/38.03 [zip_derived_cl57676, zip_derived_cl168080])).
% 259.22/38.03 thf(zip_derived_cl178640, plain,
% 259.22/38.03 (($false)
% 259.22/38.03 <= (~ (((multiply @ sk_c9 @ sk_c10) = (sk_c11))) &
% 259.22/38.03 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 259.22/38.03 (((inverse @ sk_c3) = (sk_c11))) &
% 259.22/38.03 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 259.22/38.03 (((inverse @ sk_c4) = (sk_c10))))),
% 259.22/38.03 inference('simplify', [status(thm)], [zip_derived_cl178639])).
% 259.22/38.03 thf('59', plain,
% 259.22/38.03 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) |
% 259.22/38.03 (((inverse @ sk_c1) = (sk_c11)))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl13])).
% 259.22/38.03 thf(prove_this_12, conjecture,
% 259.22/38.03 (~( ( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 259.22/38.03 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 259.22/38.03 thf(zf_stmt_26, negated_conjecture,
% 259.22/38.03 (( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 259.22/38.03 ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 259.22/38.03 inference('cnf.neg', [status(esa)], [prove_this_12])).
% 259.22/38.03 thf(zip_derived_cl14, plain,
% 259.22/38.03 ((((inverse @ sk_c3) = (sk_c11)) | ((inverse @ sk_c1) = (sk_c11)))),
% 259.22/38.03 inference('cnf', [status(esa)], [zf_stmt_26])).
% 259.22/38.03 thf('60', plain,
% 259.22/38.03 ((((inverse @ sk_c3) = (sk_c11))) | (((inverse @ sk_c1) = (sk_c11)))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl14])).
% 259.22/38.03 thf(prove_this_18, conjecture,
% 259.22/38.03 (~( ( ( inverse @ sk_c7 ) = ( sk_c6 ) ) |
% 259.22/38.03 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 259.22/38.03 thf(zf_stmt_27, negated_conjecture,
% 259.22/38.03 (( ( inverse @ sk_c7 ) = ( sk_c6 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 259.22/38.03 inference('cnf.neg', [status(esa)], [prove_this_18])).
% 259.22/38.03 thf(zip_derived_cl20, plain,
% 259.22/38.03 ((((inverse @ sk_c7) = (sk_c6)) | ((inverse @ sk_c1) = (sk_c11)))),
% 259.22/38.03 inference('cnf', [status(esa)], [zf_stmt_27])).
% 259.22/38.03 thf('61', plain,
% 259.22/38.03 ((((inverse @ sk_c7) = (sk_c6))) | (((inverse @ sk_c1) = (sk_c11)))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl20])).
% 259.22/38.03 thf(prove_this_17, conjecture,
% 259.22/38.03 (~( ( ( multiply @ sk_c8 @ sk_c10 ) = ( sk_c11 ) ) |
% 259.22/38.03 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 259.22/38.03 thf(zf_stmt_28, negated_conjecture,
% 259.22/38.03 (( ( multiply @ sk_c8 @ sk_c10 ) = ( sk_c11 ) ) |
% 259.22/38.03 ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 259.22/38.03 inference('cnf.neg', [status(esa)], [prove_this_17])).
% 259.22/38.03 thf(zip_derived_cl19, plain,
% 259.22/38.03 ((((multiply @ sk_c8 @ sk_c10) = (sk_c11))
% 259.22/38.03 | ((inverse @ sk_c1) = (sk_c11)))),
% 259.22/38.03 inference('cnf', [status(esa)], [zf_stmt_28])).
% 259.22/38.03 thf('62', plain,
% 259.22/38.03 ((((multiply @ sk_c8 @ sk_c10) = (sk_c11))) |
% 259.22/38.03 (((inverse @ sk_c1) = (sk_c11)))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl19])).
% 259.22/38.03 thf(prove_this_20, conjecture,
% 259.22/38.03 (~( ( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c6 ) ) |
% 259.22/38.03 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 259.22/38.03 thf(zf_stmt_29, negated_conjecture,
% 259.22/38.03 (( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c6 ) ) |
% 259.22/38.03 ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 259.22/38.03 inference('cnf.neg', [status(esa)], [prove_this_20])).
% 259.22/38.03 thf(zip_derived_cl22, plain,
% 259.22/38.03 ((((multiply @ sk_c7 @ sk_c8) = (sk_c6)) | ((inverse @ sk_c1) = (sk_c11)))),
% 259.22/38.03 inference('cnf', [status(esa)], [zf_stmt_29])).
% 259.22/38.03 thf('63', plain,
% 259.22/38.03 ((((multiply @ sk_c7 @ sk_c8) = (sk_c6))) |
% 259.22/38.03 (((inverse @ sk_c1) = (sk_c11)))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl22])).
% 259.22/38.03 thf(prove_this_19, conjecture,
% 259.22/38.03 (~( ( ( inverse @ sk_c6 ) = ( sk_c8 ) ) |
% 259.22/38.03 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 259.22/38.03 thf(zf_stmt_30, negated_conjecture,
% 259.22/38.03 (( ( inverse @ sk_c6 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 259.22/38.03 inference('cnf.neg', [status(esa)], [prove_this_19])).
% 259.22/38.03 thf(zip_derived_cl21, plain,
% 259.22/38.03 ((((inverse @ sk_c6) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c11)))),
% 259.22/38.03 inference('cnf', [status(esa)], [zf_stmt_30])).
% 259.22/38.03 thf('64', plain,
% 259.22/38.03 ((((inverse @ sk_c6) = (sk_c8))) | (((inverse @ sk_c1) = (sk_c11)))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl21])).
% 259.22/38.03 thf('65', plain,
% 259.22/38.03 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 259.22/38.03 (((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl5])).
% 259.22/38.03 thf('66', plain,
% 259.22/38.03 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) |
% 259.22/38.03 (((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl7])).
% 259.22/38.03 thf('67', plain,
% 259.22/38.03 ((((inverse @ sk_c5) = (sk_c8))) |
% 259.22/38.03 (((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl8])).
% 259.22/38.03 thf('68', plain,
% 259.22/38.03 (~ (((inverse @ sk_c1) = (sk_c4))) |
% 259.22/38.03 ~
% 259.22/38.03 (![X0 : $i]:
% 259.22/38.03 (((inverse @ X0) != (sk_c11))
% 259.22/38.03 | ((sk_c10) != (X0))
% 259.22/38.03 | ((inverse @ sk_c1) != (X0)))) |
% 259.22/38.03 ~ (((inverse @ sk_c4) = (sk_c10))) | ~ (((sk_c10) = (sk_c11))) |
% 259.22/38.03 ~ (((sk_c10) = (sk_c4)))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl281])).
% 259.22/38.03 thf('69', plain,
% 259.22/38.03 ((((inverse @ sk_c4) = (sk_c10))) |
% 259.22/38.03 (((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl6])).
% 259.22/38.03 thf(zip_derived_cl62, plain,
% 259.22/38.03 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11)))
% 259.22/38.03 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl7])).
% 259.22/38.03 thf(zip_derived_cl64, plain,
% 259.22/38.03 ((((inverse @ sk_c5) = (sk_c8))) <= ((((inverse @ sk_c5) = (sk_c8))))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl8])).
% 259.22/38.03 thf(zip_derived_cl62, plain,
% 259.22/38.03 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11)))
% 259.22/38.03 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl7])).
% 259.22/38.03 thf(zip_derived_cl158, plain,
% 259.22/38.03 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.03 (((inverse @ X0) != (X2))
% 259.22/38.03 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.03 | ((inverse @ X1) != (X0))
% 259.22/38.03 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.03 | ((inverse @ X3) != (X2))
% 259.22/38.03 | ((multiply @ X3 @ X2) != (sk_c11))))
% 259.22/38.03 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.03 (((inverse @ X0) != (X2))
% 259.22/38.03 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.03 | ((inverse @ X1) != (X0))
% 259.22/38.03 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.03 | ((inverse @ X3) != (X2))
% 259.22/38.03 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl53])).
% 259.22/38.03 thf(zip_derived_cl269, plain,
% 259.22/38.03 ((![X0 : $i, X1 : $i]:
% 259.22/38.03 (((inverse @ X0) != (sk_c8))
% 259.22/38.03 | ((sk_c11) != (X0))
% 259.22/38.03 | ((inverse @ sk_c5) != (X0))
% 259.22/38.03 | ((multiply @ sk_c8 @ sk_c10) != (sk_c11))
% 259.22/38.03 | ((inverse @ X1) != (sk_c8))
% 259.22/38.03 | ((multiply @ X1 @ sk_c8) != (sk_c11))))
% 259.22/38.03 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 259.22/38.03 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.03 (((inverse @ X0) != (X2))
% 259.22/38.03 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.03 | ((inverse @ X1) != (X0))
% 259.22/38.03 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.03 | ((inverse @ X3) != (X2))
% 259.22/38.03 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.03 inference('s_sup-', [status(thm)], [zip_derived_cl62, zip_derived_cl158])).
% 259.22/38.03 thf(zip_derived_cl395, plain,
% 259.22/38.03 ((![X1 : $i]:
% 259.22/38.03 (((inverse @ X1) != (sk_c8)) | ((multiply @ X1 @ sk_c8) != (sk_c11))))
% 259.22/38.03 <= ((![X1 : $i]:
% 259.22/38.03 (((inverse @ X1) != (sk_c8))
% 259.22/38.03 | ((multiply @ X1 @ sk_c8) != (sk_c11)))))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl269])).
% 259.22/38.03 thf(zip_derived_cl401, plain,
% 259.22/38.03 (((((sk_c8) != (sk_c8)) | ((multiply @ sk_c5 @ sk_c8) != (sk_c11))))
% 259.22/38.03 <= ((((inverse @ sk_c5) = (sk_c8))) &
% 259.22/38.03 (![X1 : $i]:
% 259.22/38.03 (((inverse @ X1) != (sk_c8))
% 259.22/38.03 | ((multiply @ X1 @ sk_c8) != (sk_c11)))))),
% 259.22/38.03 inference('s_sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl395])).
% 259.22/38.03 thf(zip_derived_cl405, plain,
% 259.22/38.03 ((((multiply @ sk_c5 @ sk_c8) != (sk_c11)))
% 259.22/38.03 <= ((((inverse @ sk_c5) = (sk_c8))) &
% 259.22/38.03 (![X1 : $i]:
% 259.22/38.03 (((inverse @ X1) != (sk_c8))
% 259.22/38.03 | ((multiply @ X1 @ sk_c8) != (sk_c11)))))),
% 259.22/38.03 inference('simplify', [status(thm)], [zip_derived_cl401])).
% 259.22/38.03 thf(zip_derived_cl407, plain,
% 259.22/38.03 ((((sk_c11) != (sk_c11)))
% 259.22/38.03 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 259.22/38.03 (((inverse @ sk_c5) = (sk_c8))) &
% 259.22/38.03 (![X1 : $i]:
% 259.22/38.03 (((inverse @ X1) != (sk_c8))
% 259.22/38.03 | ((multiply @ X1 @ sk_c8) != (sk_c11)))))),
% 259.22/38.03 inference('s_sup-', [status(thm)], [zip_derived_cl62, zip_derived_cl405])).
% 259.22/38.03 thf('70', plain,
% 259.22/38.03 (~
% 259.22/38.03 (![X1 : $i]:
% 259.22/38.03 (((inverse @ X1) != (sk_c8)) | ((multiply @ X1 @ sk_c8) != (sk_c11)))) |
% 259.22/38.03 ~ (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) |
% 259.22/38.03 ~ (((inverse @ sk_c5) = (sk_c8)))),
% 259.22/38.03 inference('simplify', [status(thm)], [zip_derived_cl407])).
% 259.22/38.03 thf(prove_this_10, conjecture,
% 259.22/38.03 (~( ( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c6 ) ) |
% 259.22/38.03 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 259.22/38.03 thf(zf_stmt_31, negated_conjecture,
% 259.22/38.03 (( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c6 ) ) |
% 259.22/38.03 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) )),
% 259.22/38.03 inference('cnf.neg', [status(esa)], [prove_this_10])).
% 259.22/38.03 thf(zip_derived_cl12, plain,
% 259.22/38.03 ((((multiply @ sk_c7 @ sk_c8) = (sk_c6))
% 259.22/38.03 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 259.22/38.03 inference('cnf', [status(esa)], [zf_stmt_31])).
% 259.22/38.03 thf(zip_derived_cl72, plain,
% 259.22/38.03 ((((multiply @ sk_c7 @ sk_c8) = (sk_c6)))
% 259.22/38.03 <= ((((multiply @ sk_c7 @ sk_c8) = (sk_c6))))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl12])).
% 259.22/38.03 thf(zip_derived_cl223, plain,
% 259.22/38.03 ((![X0 : $i, X1 : $i, X2 : $i]:
% 259.22/38.03 (((multiply @ X1 @ X0) != (sk_c11))
% 259.22/38.03 | ((inverse @ X1) != (X0))
% 259.22/38.03 | ((multiply @ X0 @ sk_c10) != (sk_c11))
% 259.22/38.03 | ((inverse @ X2) != (multiply @ X2 @ X0))
% 259.22/38.03 | ((inverse @ (multiply @ X2 @ X0)) != (X0))))
% 259.22/38.03 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.03 (((inverse @ X0) != (X2))
% 259.22/38.03 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.03 | ((inverse @ X1) != (X0))
% 259.22/38.03 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.03 | ((inverse @ X3) != (X2))
% 259.22/38.03 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.03 inference('eq_res', [status(thm)], [zip_derived_cl158])).
% 259.22/38.03 thf(zip_derived_cl888, plain,
% 259.22/38.03 ((![X0 : $i]:
% 259.22/38.03 (((multiply @ X0 @ sk_c8) != (sk_c11))
% 259.22/38.03 | ((inverse @ X0) != (sk_c8))
% 259.22/38.03 | ((multiply @ sk_c8 @ sk_c10) != (sk_c11))
% 259.22/38.03 | ((inverse @ sk_c7) != (sk_c6))
% 259.22/38.03 | ((inverse @ sk_c6) != (sk_c8))))
% 259.22/38.03 <= ((((multiply @ sk_c7 @ sk_c8) = (sk_c6))) &
% 259.22/38.03 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.03 (((inverse @ X0) != (X2))
% 259.22/38.03 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.03 | ((inverse @ X1) != (X0))
% 259.22/38.03 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.03 | ((inverse @ X3) != (X2))
% 259.22/38.03 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 259.22/38.03 inference('s_sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl223])).
% 259.22/38.03 thf('71', plain,
% 259.22/38.03 (~
% 259.22/38.03 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 259.22/38.03 (((inverse @ X0) != (X2))
% 259.22/38.03 | ((multiply @ X1 @ X2) != (X0))
% 259.22/38.03 | ((inverse @ X1) != (X0))
% 259.22/38.03 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 259.22/38.03 | ((inverse @ X3) != (X2))
% 259.22/38.03 | ((multiply @ X3 @ X2) != (sk_c11)))) |
% 259.22/38.03 (![X1 : $i]:
% 259.22/38.03 (((inverse @ X1) != (sk_c8)) | ((multiply @ X1 @ sk_c8) != (sk_c11)))) |
% 259.22/38.03 ~ (((inverse @ sk_c6) = (sk_c8))) |
% 259.22/38.03 ~ (((multiply @ sk_c7 @ sk_c8) = (sk_c6))) |
% 259.22/38.03 ~ (((multiply @ sk_c8 @ sk_c10) = (sk_c11))) |
% 259.22/38.03 ~ (((inverse @ sk_c7) = (sk_c6)))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl888])).
% 259.22/38.03 thf('72', plain, (~ (((multiply @ sk_c9 @ sk_c10) = (sk_c11)))),
% 259.22/38.03 inference('sat_resolution*', [status(thm)],
% 259.22/38.03 ['59', '60', '61', '62', '63', '64', '57', '0', '1', '2',
% 259.22/38.03 '65', '4', '5', '6', '66', '67', '9', '10', '11', '12', '13',
% 259.22/38.03 '14', '15', '16', '17', '18', '19', '20', '21', '22', '23',
% 259.22/38.03 '24', '25', '26', '27', '28', '29', '30', '31', '32', '33',
% 259.22/38.03 '34', '68', '36', '37', '38', '39', '40', '42', '43', '44',
% 259.22/38.03 '45', '69', '47', '48', '49', '50', '51', '52', '53', '54',
% 259.22/38.03 '55', '70', '71', '41'])).
% 259.22/38.03 thf('73', plain, ((((multiply @ sk_c3 @ sk_c11) = (sk_c10)))),
% 259.22/38.03 inference('sat_resolution*', [status(thm)],
% 259.22/38.03 ['0', '1', '2', '65', '4', '5', '6', '66', '67', '9', '10',
% 259.22/38.03 '11', '12', '13', '14', '15', '16', '17', '18', '19', '20',
% 259.22/38.03 '21', '22', '23', '24', '25', '26', '27', '28', '29', '30',
% 259.22/38.03 '31', '32', '33', '34', '68', '36', '37', '38', '39', '40',
% 259.22/38.03 '41', '42', '43', '44', '45', '69', '47', '48', '49', '50',
% 259.22/38.03 '51', '52', '53', '54', '59'])).
% 259.22/38.03 thf('74', plain, ((((inverse @ sk_c3) = (sk_c11)))),
% 259.22/38.03 inference('sat_resolution*', [status(thm)],
% 259.22/38.03 ['0', '1', '2', '65', '4', '5', '6', '66', '67', '9', '10',
% 259.22/38.03 '11', '12', '13', '14', '15', '16', '17', '18', '19', '20',
% 259.22/38.03 '21', '22', '23', '24', '25', '26', '27', '28', '29', '30',
% 259.22/38.03 '31', '32', '33', '34', '68', '36', '37', '38', '39', '40',
% 259.22/38.03 '41', '42', '43', '44', '45', '69', '47', '48', '49', '50',
% 259.22/38.03 '51', '52', '53', '54', '60'])).
% 259.22/38.03 thf(prove_this_13, conjecture,
% 259.22/38.03 (~( ( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 259.22/38.03 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 259.22/38.03 thf(zf_stmt_32, negated_conjecture,
% 259.22/38.03 (( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 259.22/38.03 ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 259.22/38.03 inference('cnf.neg', [status(esa)], [prove_this_13])).
% 259.22/38.03 thf(zip_derived_cl15, plain,
% 259.22/38.03 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))
% 259.22/38.03 | ((inverse @ sk_c1) = (sk_c11)))),
% 259.22/38.03 inference('cnf', [status(esa)], [zf_stmt_32])).
% 259.22/38.03 thf('75', plain,
% 259.22/38.03 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 259.22/38.03 (((inverse @ sk_c1) = (sk_c11)))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl15])).
% 259.22/38.03 thf('76', plain, ((((multiply @ sk_c4 @ sk_c10) = (sk_c9)))),
% 259.22/38.03 inference('sat_resolution*', [status(thm)],
% 259.22/38.03 ['0', '1', '2', '65', '4', '5', '6', '66', '67', '9', '10',
% 259.22/38.03 '11', '12', '13', '14', '15', '16', '17', '18', '19', '20',
% 259.22/38.03 '21', '22', '23', '24', '25', '26', '27', '28', '29', '30',
% 259.22/38.03 '31', '32', '33', '34', '68', '36', '37', '38', '39', '40',
% 259.22/38.03 '41', '42', '43', '44', '45', '69', '47', '48', '49', '50',
% 259.22/38.03 '51', '52', '53', '54', '75'])).
% 259.22/38.03 thf(prove_this_14, conjecture,
% 259.22/38.03 (~( ( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 259.22/38.03 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 259.22/38.03 thf(zf_stmt_33, negated_conjecture,
% 259.22/38.03 (( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 259.22/38.03 ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 259.22/38.03 inference('cnf.neg', [status(esa)], [prove_this_14])).
% 259.22/38.03 thf(zip_derived_cl16, plain,
% 259.22/38.03 ((((inverse @ sk_c4) = (sk_c10)) | ((inverse @ sk_c1) = (sk_c11)))),
% 259.22/38.03 inference('cnf', [status(esa)], [zf_stmt_33])).
% 259.22/38.03 thf('77', plain,
% 259.22/38.03 ((((inverse @ sk_c4) = (sk_c10))) | (((inverse @ sk_c1) = (sk_c11)))),
% 259.22/38.03 inference('split', [status(esa)], [zip_derived_cl16])).
% 259.22/38.03 thf('78', plain, ((((inverse @ sk_c4) = (sk_c10)))),
% 259.22/38.03 inference('sat_resolution*', [status(thm)],
% 259.22/38.03 ['0', '1', '2', '65', '4', '5', '6', '66', '67', '9', '10',
% 259.22/38.03 '11', '12', '13', '14', '15', '16', '17', '18', '19', '20',
% 259.22/38.03 '21', '22', '23', '24', '25', '26', '27', '28', '29', '30',
% 259.22/38.03 '31', '32', '33', '34', '68', '36', '37', '38', '39', '40',
% 259.22/38.03 '41', '42', '43', '44', '45', '69', '47', '48', '49', '50',
% 259.22/38.03 '51', '52', '53', '54', '77'])).
% 259.22/38.03 thf(zip_derived_cl178641, plain, ($false),
% 259.22/38.03 inference('simpl_trail', [status(thm)],
% 259.22/38.03 [zip_derived_cl178640, '72', '73', '74', '76', '78'])).
% 259.22/38.03
% 259.22/38.03 % SZS output end Refutation
% 259.22/38.03
% 259.22/38.03
% 259.22/38.03 % Terminating...
% 260.22/38.17 % Runner terminated.
% 260.22/38.19 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------