TSTP Solution File: GRP257-1 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP257-1 : 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.gw2G0wSVzr true
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:50:56 EDT 2023
% Result : Unsatisfiable 1.22s 1.15s
% Output : Refutation 1.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP257-1 : TPTP v8.1.2. Released v2.5.0.
% 0.12/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.gw2G0wSVzr true
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 22:48:02 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.19/0.65 % Total configuration time : 435
% 0.19/0.65 % Estimated wc time : 1092
% 0.19/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.64/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.64/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.64/0.72 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.64/0.72 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.64/0.73 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.64/0.74 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.64/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 1.22/1.15 % Solved by fo/fo7.sh.
% 1.22/1.15 % done 1273 iterations in 0.403s
% 1.22/1.15 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.22/1.15 % SZS output start Refutation
% 1.22/1.15 thf(sk_c7_type, type, sk_c7: $i).
% 1.22/1.15 thf(sk_c9_type, type, sk_c9: $i).
% 1.22/1.15 thf(sk_c2_type, type, sk_c2: $i).
% 1.22/1.15 thf(sk_c8_type, type, sk_c8: $i).
% 1.22/1.15 thf(sk_c5_type, type, sk_c5: $i).
% 1.22/1.15 thf(identity_type, type, identity: $i).
% 1.22/1.15 thf(multiply_type, type, multiply: $i > $i > $i).
% 1.22/1.15 thf(sk_c10_type, type, sk_c10: $i).
% 1.22/1.15 thf(inverse_type, type, inverse: $i > $i).
% 1.22/1.15 thf(sk_c3_type, type, sk_c3: $i).
% 1.22/1.15 thf(sk_c6_type, type, sk_c6: $i).
% 1.22/1.15 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 1.22/1.15 thf(zip_derived_cl1, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.22/1.15 inference('cnf', [status(esa)], [left_inverse])).
% 1.22/1.15 thf(zip_derived_cl1, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.22/1.15 inference('cnf', [status(esa)], [left_inverse])).
% 1.22/1.15 thf(associativity, axiom,
% 1.22/1.15 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 1.22/1.15 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 1.22/1.15 thf(zip_derived_cl2, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.22/1.15 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.22/1.15 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.22/1.15 inference('cnf', [status(esa)], [associativity])).
% 1.22/1.15 thf(zip_derived_cl131, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i]:
% 1.22/1.15 ((multiply @ identity @ X0)
% 1.22/1.15 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 1.22/1.15 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 1.22/1.15 thf(zip_derived_cl0, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.22/1.15 inference('cnf', [status(esa)], [left_identity])).
% 1.22/1.15 thf(zip_derived_cl163, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i]:
% 1.22/1.15 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.22/1.15 inference('demod', [status(thm)], [zip_derived_cl131, zip_derived_cl0])).
% 1.22/1.15 thf(zip_derived_cl179, plain,
% 1.22/1.15 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl163])).
% 1.22/1.15 thf(zip_derived_cl163, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i]:
% 1.22/1.15 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.22/1.15 inference('demod', [status(thm)], [zip_derived_cl131, zip_derived_cl0])).
% 1.22/1.15 thf(zip_derived_cl163, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i]:
% 1.22/1.15 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.22/1.15 inference('demod', [status(thm)], [zip_derived_cl131, zip_derived_cl0])).
% 1.22/1.15 thf(zip_derived_cl176, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i]:
% 1.22/1.15 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl163, zip_derived_cl163])).
% 1.22/1.15 thf(zip_derived_cl1281, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl179, zip_derived_cl176])).
% 1.22/1.15 thf(zip_derived_cl179, plain,
% 1.22/1.15 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl163])).
% 1.22/1.15 thf(zip_derived_cl1327, plain,
% 1.22/1.15 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl1281, zip_derived_cl179])).
% 1.22/1.15 thf(zip_derived_cl1327, plain,
% 1.22/1.15 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl1281, zip_derived_cl179])).
% 1.22/1.15 thf(zip_derived_cl1327, plain,
% 1.22/1.15 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl1281, zip_derived_cl179])).
% 1.22/1.15 thf(prove_this_43, conjecture,
% 1.22/1.15 (~( ( ( inverse @ X7 ) != ( sk_c8 ) ) |
% 1.22/1.15 ( ( multiply @ X7 @ sk_c8 ) != ( X3 ) ) |
% 1.22/1.15 ( ( multiply @ sk_c8 @ X3 ) != ( sk_c9 ) ) |
% 1.22/1.15 ( ( inverse @ X2 ) != ( sk_c8 ) ) |
% 1.22/1.15 ( ( multiply @ X2 @ sk_c8 ) != ( sk_c9 ) ) |
% 1.22/1.15 ( ( inverse @ X1 ) != ( sk_c10 ) ) |
% 1.22/1.15 ( ( multiply @ X1 @ sk_c10 ) != ( sk_c9 ) ) |
% 1.22/1.15 ( ( multiply @ X6 @ sk_c9 ) != ( sk_c8 ) ) |
% 1.22/1.15 ( ( inverse @ X6 ) != ( sk_c8 ) ) |
% 1.22/1.15 ( ( inverse @ X5 ) != ( sk_c9 ) ) |
% 1.22/1.15 ( ( multiply @ X5 @ sk_c9 ) != ( sk_c8 ) ) |
% 1.22/1.15 ( ( inverse @ X4 ) != ( sk_c10 ) ) |
% 1.22/1.15 ( ( multiply @ X4 @ sk_c10 ) != ( sk_c9 ) ) ))).
% 1.22/1.15 thf(zf_stmt_0, negated_conjecture,
% 1.22/1.15 (( ( inverse @ X7 ) != ( sk_c8 ) ) |
% 1.22/1.15 ( ( multiply @ X7 @ sk_c8 ) != ( X3 ) ) |
% 1.22/1.15 ( ( multiply @ sk_c8 @ X3 ) != ( sk_c9 ) ) |
% 1.22/1.15 ( ( inverse @ X2 ) != ( sk_c8 ) ) |
% 1.22/1.15 ( ( multiply @ X2 @ sk_c8 ) != ( sk_c9 ) ) |
% 1.22/1.15 ( ( inverse @ X1 ) != ( sk_c10 ) ) |
% 1.22/1.15 ( ( multiply @ X1 @ sk_c10 ) != ( sk_c9 ) ) |
% 1.22/1.15 ( ( multiply @ X6 @ sk_c9 ) != ( sk_c8 ) ) |
% 1.22/1.15 ( ( inverse @ X6 ) != ( sk_c8 ) ) | ( ( inverse @ X5 ) != ( sk_c9 ) ) |
% 1.22/1.15 ( ( multiply @ X5 @ sk_c9 ) != ( sk_c8 ) ) |
% 1.22/1.15 ( ( inverse @ X4 ) != ( sk_c10 ) ) |
% 1.22/1.15 ( ( multiply @ X4 @ sk_c10 ) != ( sk_c9 ) )),
% 1.22/1.15 inference('cnf.neg', [status(esa)], [prove_this_43])).
% 1.22/1.15 thf(zip_derived_cl45, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 1.22/1.15 (((inverse @ X0) != (sk_c8))
% 1.22/1.15 | ((multiply @ X0 @ sk_c8) != (X1))
% 1.22/1.15 | ((multiply @ sk_c8 @ X1) != (sk_c9))
% 1.22/1.15 | ((inverse @ X2) != (sk_c8))
% 1.22/1.15 | ((multiply @ X2 @ sk_c8) != (sk_c9))
% 1.22/1.15 | ((inverse @ X3) != (sk_c10))
% 1.22/1.15 | ((multiply @ X3 @ sk_c10) != (sk_c9))
% 1.22/1.15 | ((multiply @ X4 @ sk_c9) != (sk_c8))
% 1.22/1.15 | ((inverse @ X4) != (sk_c8))
% 1.22/1.15 | ((inverse @ X5) != (sk_c9))
% 1.22/1.15 | ((multiply @ X5 @ sk_c9) != (sk_c8))
% 1.22/1.15 | ((inverse @ X6) != (sk_c10))
% 1.22/1.15 | ((multiply @ X6 @ sk_c10) != (sk_c9)))),
% 1.22/1.15 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.22/1.15 thf(zip_derived_cl1514, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 1.22/1.15 (((X0) != (sk_c8))
% 1.22/1.15 | ((multiply @ X1 @ sk_c10) != (sk_c9))
% 1.22/1.15 | ((inverse @ X1) != (sk_c10))
% 1.22/1.15 | ((multiply @ X2 @ sk_c9) != (sk_c8))
% 1.22/1.15 | ((inverse @ X2) != (sk_c9))
% 1.22/1.15 | ((inverse @ X3) != (sk_c8))
% 1.22/1.15 | ((multiply @ X3 @ sk_c9) != (sk_c8))
% 1.22/1.15 | ((multiply @ X4 @ sk_c10) != (sk_c9))
% 1.22/1.15 | ((inverse @ X4) != (sk_c10))
% 1.22/1.15 | ((multiply @ X5 @ sk_c8) != (sk_c9))
% 1.22/1.15 | ((inverse @ X5) != (sk_c8))
% 1.22/1.15 | ((multiply @ sk_c8 @ X6) != (sk_c9))
% 1.22/1.15 | ((multiply @ (inverse @ X0) @ sk_c8) != (X6)))),
% 1.22/1.15 inference('sup-', [status(thm)], [zip_derived_cl1327, zip_derived_cl45])).
% 1.22/1.15 thf(zip_derived_cl1662, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 1.22/1.15 (((multiply @ (inverse @ sk_c8) @ sk_c8) != (X0))
% 1.22/1.15 | ((multiply @ sk_c8 @ X0) != (sk_c9))
% 1.22/1.15 | ((inverse @ X1) != (sk_c8))
% 1.22/1.15 | ((multiply @ X1 @ sk_c8) != (sk_c9))
% 1.22/1.15 | ((inverse @ X2) != (sk_c10))
% 1.22/1.15 | ((multiply @ X2 @ sk_c10) != (sk_c9))
% 1.22/1.15 | ((multiply @ X3 @ sk_c9) != (sk_c8))
% 1.22/1.15 | ((inverse @ X3) != (sk_c8))
% 1.22/1.15 | ((inverse @ X4) != (sk_c9))
% 1.22/1.15 | ((multiply @ X4 @ sk_c9) != (sk_c8))
% 1.22/1.15 | ((inverse @ X5) != (sk_c10))
% 1.22/1.15 | ((multiply @ X5 @ sk_c10) != (sk_c9)))),
% 1.22/1.15 inference('eq_res', [status(thm)], [zip_derived_cl1514])).
% 1.22/1.15 thf(zip_derived_cl1, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.22/1.15 inference('cnf', [status(esa)], [left_inverse])).
% 1.22/1.15 thf(zip_derived_cl1663, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 1.22/1.15 (((identity) != (X0))
% 1.22/1.15 | ((multiply @ sk_c8 @ X0) != (sk_c9))
% 1.22/1.15 | ((inverse @ X1) != (sk_c8))
% 1.22/1.15 | ((multiply @ X1 @ sk_c8) != (sk_c9))
% 1.22/1.15 | ((inverse @ X2) != (sk_c10))
% 1.22/1.15 | ((multiply @ X2 @ sk_c10) != (sk_c9))
% 1.22/1.15 | ((multiply @ X3 @ sk_c9) != (sk_c8))
% 1.22/1.15 | ((inverse @ X3) != (sk_c8))
% 1.22/1.15 | ((inverse @ X4) != (sk_c9))
% 1.22/1.15 | ((multiply @ X4 @ sk_c9) != (sk_c8))
% 1.22/1.15 | ((inverse @ X5) != (sk_c10))
% 1.22/1.15 | ((multiply @ X5 @ sk_c10) != (sk_c9)))),
% 1.22/1.15 inference('demod', [status(thm)], [zip_derived_cl1662, zip_derived_cl1])).
% 1.22/1.15 thf(zip_derived_cl1664, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.22/1.15 (((multiply @ X0 @ sk_c10) != (sk_c9))
% 1.22/1.15 | ((inverse @ X0) != (sk_c10))
% 1.22/1.15 | ((multiply @ X1 @ sk_c9) != (sk_c8))
% 1.22/1.15 | ((inverse @ X1) != (sk_c9))
% 1.22/1.15 | ((inverse @ X2) != (sk_c8))
% 1.22/1.15 | ((multiply @ X2 @ sk_c9) != (sk_c8))
% 1.22/1.15 | ((multiply @ X3 @ sk_c10) != (sk_c9))
% 1.22/1.15 | ((inverse @ X3) != (sk_c10))
% 1.22/1.15 | ((multiply @ X4 @ sk_c8) != (sk_c9))
% 1.22/1.15 | ((inverse @ X4) != (sk_c8))
% 1.22/1.15 | ((multiply @ sk_c8 @ identity) != (sk_c9)))),
% 1.22/1.15 inference('eq_res', [status(thm)], [zip_derived_cl1663])).
% 1.22/1.15 thf(zip_derived_cl1281, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl179, zip_derived_cl176])).
% 1.22/1.15 thf(zip_derived_cl1665, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.22/1.15 (((multiply @ X0 @ sk_c10) != (sk_c9))
% 1.22/1.15 | ((inverse @ X0) != (sk_c10))
% 1.22/1.15 | ((multiply @ X1 @ sk_c9) != (sk_c8))
% 1.22/1.15 | ((inverse @ X1) != (sk_c9))
% 1.22/1.15 | ((inverse @ X2) != (sk_c8))
% 1.22/1.15 | ((multiply @ X2 @ sk_c9) != (sk_c8))
% 1.22/1.15 | ((multiply @ X3 @ sk_c10) != (sk_c9))
% 1.22/1.15 | ((inverse @ X3) != (sk_c10))
% 1.22/1.15 | ((multiply @ X4 @ sk_c8) != (sk_c9))
% 1.22/1.15 | ((inverse @ X4) != (sk_c8))
% 1.22/1.15 | ((sk_c8) != (sk_c9)))),
% 1.22/1.15 inference('demod', [status(thm)],
% 1.22/1.15 [zip_derived_cl1664, zip_derived_cl1281])).
% 1.22/1.15 thf(zip_derived_cl1666, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.22/1.15 (((multiply @ X0 @ sk_c10) != (sk_c9))
% 1.22/1.15 | ((inverse @ X0) != (sk_c10))
% 1.22/1.15 | ((multiply @ X1 @ sk_c9) != (sk_c9))
% 1.22/1.15 | ((inverse @ X1) != (sk_c9))
% 1.22/1.15 | ((inverse @ X2) != (sk_c9))
% 1.22/1.15 | ((multiply @ X2 @ sk_c9) != (sk_c9))
% 1.22/1.15 | ((multiply @ X3 @ sk_c10) != (sk_c9))
% 1.22/1.15 | ((inverse @ X3) != (sk_c10))
% 1.22/1.15 | ((multiply @ X4 @ sk_c9) != (sk_c9))
% 1.22/1.15 | ((inverse @ X4) != (sk_c9))
% 1.22/1.15 | ((sk_c8) != (sk_c9)))),
% 1.22/1.15 inference('local_rewriting', [status(thm)], [zip_derived_cl1665])).
% 1.22/1.15 thf(prove_this_28, conjecture,
% 1.22/1.15 (~( ( ( inverse @ sk_c6 ) = ( sk_c8 ) ) |
% 1.22/1.15 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 1.22/1.15 thf(zf_stmt_1, negated_conjecture,
% 1.22/1.15 (( ( inverse @ sk_c6 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 1.22/1.15 inference('cnf.neg', [status(esa)], [prove_this_28])).
% 1.22/1.15 thf(zip_derived_cl30, plain,
% 1.22/1.15 ((((inverse @ sk_c6) = (sk_c8)) | ((inverse @ sk_c2) = (sk_c9)))),
% 1.22/1.15 inference('cnf', [status(esa)], [zf_stmt_1])).
% 1.22/1.15 thf(zip_derived_cl1, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.22/1.15 inference('cnf', [status(esa)], [left_inverse])).
% 1.22/1.15 thf(zip_derived_cl65, plain,
% 1.22/1.15 ((((multiply @ sk_c9 @ sk_c2) = (identity))
% 1.22/1.15 | ((inverse @ sk_c6) = (sk_c8)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl1])).
% 1.22/1.15 thf(zip_derived_cl163, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i]:
% 1.22/1.15 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.22/1.15 inference('demod', [status(thm)], [zip_derived_cl131, zip_derived_cl0])).
% 1.22/1.15 thf(zip_derived_cl186, plain,
% 1.22/1.15 ((((sk_c2) = (multiply @ (inverse @ sk_c9) @ identity))
% 1.22/1.15 | ((inverse @ sk_c6) = (sk_c8)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl65, zip_derived_cl163])).
% 1.22/1.15 thf(prove_this_21, conjecture,
% 1.22/1.15 (~( ( ( inverse @ sk_c6 ) = ( sk_c8 ) ) |
% 1.22/1.15 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 1.22/1.15 thf(zf_stmt_2, negated_conjecture,
% 1.22/1.15 (( ( inverse @ sk_c6 ) = ( sk_c8 ) ) |
% 1.22/1.15 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) )),
% 1.22/1.15 inference('cnf.neg', [status(esa)], [prove_this_21])).
% 1.22/1.15 thf(zip_derived_cl23, plain,
% 1.22/1.15 ((((inverse @ sk_c6) = (sk_c8)) | ((multiply @ sk_c2 @ sk_c9) = (sk_c8)))),
% 1.22/1.15 inference('cnf', [status(esa)], [zf_stmt_2])).
% 1.22/1.15 thf(zip_derived_cl378, plain,
% 1.22/1.15 ((((multiply @ (multiply @ (inverse @ sk_c9) @ identity) @ sk_c9)
% 1.22/1.15 = (sk_c8))
% 1.22/1.15 | ((inverse @ sk_c6) = (sk_c8))
% 1.22/1.15 | ((inverse @ sk_c6) = (sk_c8)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl186, zip_derived_cl23])).
% 1.22/1.15 thf(zip_derived_cl2, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.22/1.15 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.22/1.15 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.22/1.15 inference('cnf', [status(esa)], [associativity])).
% 1.22/1.15 thf(zip_derived_cl0, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.22/1.15 inference('cnf', [status(esa)], [left_identity])).
% 1.22/1.15 thf(zip_derived_cl1, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.22/1.15 inference('cnf', [status(esa)], [left_inverse])).
% 1.22/1.15 thf(zip_derived_cl395, plain,
% 1.22/1.15 ((((identity) = (sk_c8))
% 1.22/1.15 | ((inverse @ sk_c6) = (sk_c8))
% 1.22/1.15 | ((inverse @ sk_c6) = (sk_c8)))),
% 1.22/1.15 inference('demod', [status(thm)],
% 1.22/1.15 [zip_derived_cl378, zip_derived_cl2, zip_derived_cl0,
% 1.22/1.15 zip_derived_cl1])).
% 1.22/1.15 thf(zip_derived_cl396, plain,
% 1.22/1.15 ((((inverse @ sk_c6) = (sk_c8)) | ((identity) = (sk_c8)))),
% 1.22/1.15 inference('simplify', [status(thm)], [zip_derived_cl395])).
% 1.22/1.15 thf(zip_derived_cl1, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.22/1.15 inference('cnf', [status(esa)], [left_inverse])).
% 1.22/1.15 thf(zip_derived_cl404, plain,
% 1.22/1.15 ((((multiply @ sk_c8 @ sk_c6) = (identity)) | ((identity) = (sk_c8)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl396, zip_derived_cl1])).
% 1.22/1.15 thf(zip_derived_cl163, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i]:
% 1.22/1.15 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.22/1.15 inference('demod', [status(thm)], [zip_derived_cl131, zip_derived_cl0])).
% 1.22/1.15 thf(zip_derived_cl576, plain,
% 1.22/1.15 ((((sk_c6) = (multiply @ (inverse @ sk_c8) @ identity))
% 1.22/1.15 | ((identity) = (sk_c8)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl404, zip_derived_cl163])).
% 1.22/1.15 thf(zip_derived_cl1281, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl179, zip_derived_cl176])).
% 1.22/1.15 thf(zip_derived_cl1316, plain,
% 1.22/1.15 ((((sk_c6) = (inverse @ sk_c8)) | ((identity) = (sk_c8)))),
% 1.22/1.15 inference('demod', [status(thm)], [zip_derived_cl576, zip_derived_cl1281])).
% 1.22/1.15 thf(prove_this_27, conjecture,
% 1.22/1.15 (~( ( ( multiply @ sk_c6 @ sk_c8 ) = ( sk_c7 ) ) |
% 1.22/1.15 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 1.22/1.15 thf(zf_stmt_3, negated_conjecture,
% 1.22/1.15 (( ( multiply @ sk_c6 @ sk_c8 ) = ( sk_c7 ) ) |
% 1.22/1.15 ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 1.22/1.15 inference('cnf.neg', [status(esa)], [prove_this_27])).
% 1.22/1.15 thf(zip_derived_cl29, plain,
% 1.22/1.15 ((((multiply @ sk_c6 @ sk_c8) = (sk_c7)) | ((inverse @ sk_c2) = (sk_c9)))),
% 1.22/1.15 inference('cnf', [status(esa)], [zf_stmt_3])).
% 1.22/1.15 thf(zip_derived_cl1327, plain,
% 1.22/1.15 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl1281, zip_derived_cl179])).
% 1.22/1.15 thf(zip_derived_cl1530, plain,
% 1.22/1.15 ((((sk_c2) = (inverse @ sk_c9)) | ((multiply @ sk_c6 @ sk_c8) = (sk_c7)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl29, zip_derived_cl1327])).
% 1.22/1.15 thf(prove_this_20, conjecture,
% 1.22/1.15 (~( ( ( multiply @ sk_c6 @ sk_c8 ) = ( sk_c7 ) ) |
% 1.22/1.15 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 1.22/1.15 thf(zf_stmt_4, negated_conjecture,
% 1.22/1.15 (( ( multiply @ sk_c6 @ sk_c8 ) = ( sk_c7 ) ) |
% 1.22/1.15 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) )),
% 1.22/1.15 inference('cnf.neg', [status(esa)], [prove_this_20])).
% 1.22/1.15 thf(zip_derived_cl22, plain,
% 1.22/1.15 ((((multiply @ sk_c6 @ sk_c8) = (sk_c7))
% 1.22/1.15 | ((multiply @ sk_c2 @ sk_c9) = (sk_c8)))),
% 1.22/1.15 inference('cnf', [status(esa)], [zf_stmt_4])).
% 1.22/1.15 thf(zip_derived_cl2673, plain,
% 1.22/1.15 ((((multiply @ (inverse @ sk_c9) @ sk_c9) = (sk_c8))
% 1.22/1.15 | ((multiply @ sk_c6 @ sk_c8) = (sk_c7))
% 1.22/1.15 | ((multiply @ sk_c6 @ sk_c8) = (sk_c7)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl1530, zip_derived_cl22])).
% 1.22/1.15 thf(zip_derived_cl1, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.22/1.15 inference('cnf', [status(esa)], [left_inverse])).
% 1.22/1.15 thf(zip_derived_cl2690, plain,
% 1.22/1.15 ((((identity) = (sk_c8))
% 1.22/1.15 | ((multiply @ sk_c6 @ sk_c8) = (sk_c7))
% 1.22/1.15 | ((multiply @ sk_c6 @ sk_c8) = (sk_c7)))),
% 1.22/1.15 inference('demod', [status(thm)], [zip_derived_cl2673, zip_derived_cl1])).
% 1.22/1.15 thf(zip_derived_cl2691, plain,
% 1.22/1.15 ((((multiply @ sk_c6 @ sk_c8) = (sk_c7)) | ((identity) = (sk_c8)))),
% 1.22/1.15 inference('simplify', [status(thm)], [zip_derived_cl2690])).
% 1.22/1.15 thf(zip_derived_cl3240, plain,
% 1.22/1.15 ((((multiply @ (inverse @ sk_c8) @ sk_c8) = (sk_c7))
% 1.22/1.15 | ((identity) = (sk_c8))
% 1.22/1.15 | ((identity) = (sk_c8)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl1316, zip_derived_cl2691])).
% 1.22/1.15 thf(zip_derived_cl1, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.22/1.15 inference('cnf', [status(esa)], [left_inverse])).
% 1.22/1.15 thf(zip_derived_cl3248, plain,
% 1.22/1.15 ((((identity) = (sk_c7))
% 1.22/1.15 | ((identity) = (sk_c8))
% 1.22/1.15 | ((identity) = (sk_c8)))),
% 1.22/1.15 inference('demod', [status(thm)], [zip_derived_cl3240, zip_derived_cl1])).
% 1.22/1.15 thf(zip_derived_cl3249, plain,
% 1.22/1.15 ((((identity) = (sk_c8)) | ((identity) = (sk_c7)))),
% 1.22/1.15 inference('simplify', [status(thm)], [zip_derived_cl3248])).
% 1.22/1.15 thf(prove_this_26, conjecture,
% 1.22/1.15 (~( ( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c9 ) ) |
% 1.22/1.15 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 1.22/1.15 thf(zf_stmt_5, negated_conjecture,
% 1.22/1.15 (( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c9 ) ) |
% 1.22/1.15 ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 1.22/1.15 inference('cnf.neg', [status(esa)], [prove_this_26])).
% 1.22/1.15 thf(zip_derived_cl28, plain,
% 1.22/1.15 ((((multiply @ sk_c8 @ sk_c7) = (sk_c9)) | ((inverse @ sk_c2) = (sk_c9)))),
% 1.22/1.15 inference('cnf', [status(esa)], [zf_stmt_5])).
% 1.22/1.15 thf(zip_derived_cl1327, plain,
% 1.22/1.15 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl1281, zip_derived_cl179])).
% 1.22/1.15 thf(zip_derived_cl1529, plain,
% 1.22/1.15 ((((sk_c2) = (inverse @ sk_c9)) | ((multiply @ sk_c8 @ sk_c7) = (sk_c9)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl28, zip_derived_cl1327])).
% 1.22/1.15 thf(prove_this_19, conjecture,
% 1.22/1.15 (~( ( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c9 ) ) |
% 1.22/1.15 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 1.22/1.15 thf(zf_stmt_6, negated_conjecture,
% 1.22/1.15 (( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c9 ) ) |
% 1.22/1.15 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) )),
% 1.22/1.15 inference('cnf.neg', [status(esa)], [prove_this_19])).
% 1.22/1.15 thf(zip_derived_cl21, plain,
% 1.22/1.15 ((((multiply @ sk_c8 @ sk_c7) = (sk_c9))
% 1.22/1.15 | ((multiply @ sk_c2 @ sk_c9) = (sk_c8)))),
% 1.22/1.15 inference('cnf', [status(esa)], [zf_stmt_6])).
% 1.22/1.15 thf(zip_derived_cl3051, plain,
% 1.22/1.15 ((((multiply @ (inverse @ sk_c9) @ sk_c9) = (sk_c8))
% 1.22/1.15 | ((multiply @ sk_c8 @ sk_c7) = (sk_c9))
% 1.22/1.15 | ((multiply @ sk_c8 @ sk_c7) = (sk_c9)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl1529, zip_derived_cl21])).
% 1.22/1.15 thf(zip_derived_cl1, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.22/1.15 inference('cnf', [status(esa)], [left_inverse])).
% 1.22/1.15 thf(zip_derived_cl3068, plain,
% 1.22/1.15 ((((identity) = (sk_c8))
% 1.22/1.15 | ((multiply @ sk_c8 @ sk_c7) = (sk_c9))
% 1.22/1.15 | ((multiply @ sk_c8 @ sk_c7) = (sk_c9)))),
% 1.22/1.15 inference('demod', [status(thm)], [zip_derived_cl3051, zip_derived_cl1])).
% 1.22/1.15 thf(zip_derived_cl3069, plain,
% 1.22/1.15 ((((multiply @ sk_c8 @ sk_c7) = (sk_c9)) | ((identity) = (sk_c8)))),
% 1.22/1.15 inference('simplify', [status(thm)], [zip_derived_cl3068])).
% 1.22/1.15 thf(zip_derived_cl3537, plain,
% 1.22/1.15 ((((multiply @ sk_c8 @ identity) = (sk_c9))
% 1.22/1.15 | ((identity) = (sk_c8))
% 1.22/1.15 | ((identity) = (sk_c8)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl3249, zip_derived_cl3069])).
% 1.22/1.15 thf(zip_derived_cl3555, plain,
% 1.22/1.15 ((((identity) = (sk_c8)) | ((multiply @ sk_c8 @ identity) = (sk_c9)))),
% 1.22/1.15 inference('simplify', [status(thm)], [zip_derived_cl3537])).
% 1.22/1.15 thf(zip_derived_cl1281, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl179, zip_derived_cl176])).
% 1.22/1.15 thf(zip_derived_cl3631, plain,
% 1.22/1.15 ((((sk_c9) = (sk_c8)) | ((identity) = (sk_c8)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl3555, zip_derived_cl1281])).
% 1.22/1.15 thf(zip_derived_cl3715, plain,
% 1.22/1.15 ((((sk_c9) != (identity)) | ((identity) = (sk_c8)))),
% 1.22/1.15 inference('eq_fact', [status(thm)], [zip_derived_cl3631])).
% 1.22/1.15 thf(prove_this_25, conjecture,
% 1.22/1.15 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 1.22/1.15 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 1.22/1.15 thf(zf_stmt_7, negated_conjecture,
% 1.22/1.15 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 1.22/1.15 inference('cnf.neg', [status(esa)], [prove_this_25])).
% 1.22/1.15 thf(zip_derived_cl27, plain,
% 1.22/1.15 ((((inverse @ sk_c5) = (sk_c8)) | ((inverse @ sk_c2) = (sk_c9)))),
% 1.22/1.15 inference('cnf', [status(esa)], [zf_stmt_7])).
% 1.22/1.15 thf(zip_derived_cl1, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.22/1.15 inference('cnf', [status(esa)], [left_inverse])).
% 1.22/1.15 thf(zip_derived_cl52, plain,
% 1.22/1.15 ((((multiply @ sk_c9 @ sk_c2) = (identity))
% 1.22/1.15 | ((inverse @ sk_c5) = (sk_c8)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl1])).
% 1.22/1.15 thf(zip_derived_cl163, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i]:
% 1.22/1.15 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.22/1.15 inference('demod', [status(thm)], [zip_derived_cl131, zip_derived_cl0])).
% 1.22/1.15 thf(zip_derived_cl184, plain,
% 1.22/1.15 ((((sk_c2) = (multiply @ (inverse @ sk_c9) @ identity))
% 1.22/1.15 | ((inverse @ sk_c5) = (sk_c8)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl52, zip_derived_cl163])).
% 1.22/1.15 thf(prove_this_18, conjecture,
% 1.22/1.15 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 1.22/1.15 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 1.22/1.15 thf(zf_stmt_8, negated_conjecture,
% 1.22/1.15 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 1.22/1.15 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) )),
% 1.22/1.15 inference('cnf.neg', [status(esa)], [prove_this_18])).
% 1.22/1.15 thf(zip_derived_cl20, plain,
% 1.22/1.15 ((((inverse @ sk_c5) = (sk_c8)) | ((multiply @ sk_c2 @ sk_c9) = (sk_c8)))),
% 1.22/1.15 inference('cnf', [status(esa)], [zf_stmt_8])).
% 1.22/1.15 thf(zip_derived_cl260, plain,
% 1.22/1.15 ((((multiply @ (multiply @ (inverse @ sk_c9) @ identity) @ sk_c9)
% 1.22/1.15 = (sk_c8))
% 1.22/1.15 | ((inverse @ sk_c5) = (sk_c8))
% 1.22/1.15 | ((inverse @ sk_c5) = (sk_c8)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl184, zip_derived_cl20])).
% 1.22/1.15 thf(zip_derived_cl2, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.22/1.15 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.22/1.15 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.22/1.15 inference('cnf', [status(esa)], [associativity])).
% 1.22/1.15 thf(zip_derived_cl0, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.22/1.15 inference('cnf', [status(esa)], [left_identity])).
% 1.22/1.15 thf(zip_derived_cl1, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.22/1.15 inference('cnf', [status(esa)], [left_inverse])).
% 1.22/1.15 thf(zip_derived_cl277, plain,
% 1.22/1.15 ((((identity) = (sk_c8))
% 1.22/1.15 | ((inverse @ sk_c5) = (sk_c8))
% 1.22/1.15 | ((inverse @ sk_c5) = (sk_c8)))),
% 1.22/1.15 inference('demod', [status(thm)],
% 1.22/1.15 [zip_derived_cl260, zip_derived_cl2, zip_derived_cl0,
% 1.22/1.15 zip_derived_cl1])).
% 1.22/1.15 thf(zip_derived_cl278, plain,
% 1.22/1.15 ((((inverse @ sk_c5) = (sk_c8)) | ((identity) = (sk_c8)))),
% 1.22/1.15 inference('simplify', [status(thm)], [zip_derived_cl277])).
% 1.22/1.15 thf(prove_this_24, conjecture,
% 1.22/1.15 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c9 ) ) |
% 1.22/1.15 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 1.22/1.15 thf(zf_stmt_9, negated_conjecture,
% 1.22/1.15 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c9 ) ) |
% 1.22/1.15 ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 1.22/1.15 inference('cnf.neg', [status(esa)], [prove_this_24])).
% 1.22/1.15 thf(zip_derived_cl26, plain,
% 1.22/1.15 ((((multiply @ sk_c5 @ sk_c8) = (sk_c9)) | ((inverse @ sk_c2) = (sk_c9)))),
% 1.22/1.15 inference('cnf', [status(esa)], [zf_stmt_9])).
% 1.22/1.15 thf(zip_derived_cl1327, plain,
% 1.22/1.15 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl1281, zip_derived_cl179])).
% 1.22/1.15 thf(zip_derived_cl1527, plain,
% 1.22/1.15 ((((sk_c2) = (inverse @ sk_c9)) | ((multiply @ sk_c5 @ sk_c8) = (sk_c9)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl1327])).
% 1.22/1.15 thf(prove_this_17, conjecture,
% 1.22/1.15 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c9 ) ) |
% 1.22/1.15 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 1.22/1.15 thf(zf_stmt_10, negated_conjecture,
% 1.22/1.15 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c9 ) ) |
% 1.22/1.15 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) )),
% 1.22/1.15 inference('cnf.neg', [status(esa)], [prove_this_17])).
% 1.22/1.15 thf(zip_derived_cl19, plain,
% 1.22/1.15 ((((multiply @ sk_c5 @ sk_c8) = (sk_c9))
% 1.22/1.15 | ((multiply @ sk_c2 @ sk_c9) = (sk_c8)))),
% 1.22/1.15 inference('cnf', [status(esa)], [zf_stmt_10])).
% 1.22/1.15 thf(zip_derived_cl3013, plain,
% 1.22/1.15 ((((multiply @ (inverse @ sk_c9) @ sk_c9) = (sk_c8))
% 1.22/1.15 | ((multiply @ sk_c5 @ sk_c8) = (sk_c9))
% 1.22/1.15 | ((multiply @ sk_c5 @ sk_c8) = (sk_c9)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl1527, zip_derived_cl19])).
% 1.22/1.15 thf(zip_derived_cl1, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.22/1.15 inference('cnf', [status(esa)], [left_inverse])).
% 1.22/1.15 thf(zip_derived_cl3030, plain,
% 1.22/1.15 ((((identity) = (sk_c8))
% 1.22/1.15 | ((multiply @ sk_c5 @ sk_c8) = (sk_c9))
% 1.22/1.15 | ((multiply @ sk_c5 @ sk_c8) = (sk_c9)))),
% 1.22/1.15 inference('demod', [status(thm)], [zip_derived_cl3013, zip_derived_cl1])).
% 1.22/1.15 thf(zip_derived_cl3031, plain,
% 1.22/1.15 ((((multiply @ sk_c5 @ sk_c8) = (sk_c9)) | ((identity) = (sk_c8)))),
% 1.22/1.15 inference('simplify', [status(thm)], [zip_derived_cl3030])).
% 1.22/1.15 thf(zip_derived_cl3354, plain,
% 1.22/1.15 ((((multiply @ sk_c5 @ (inverse @ sk_c5)) = (sk_c9))
% 1.22/1.15 | ((identity) = (sk_c8))
% 1.22/1.15 | ((identity) = (sk_c8)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl278, zip_derived_cl3031])).
% 1.22/1.15 thf(zip_derived_cl1327, plain,
% 1.22/1.15 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl1281, zip_derived_cl179])).
% 1.22/1.15 thf(zip_derived_cl1, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.22/1.15 inference('cnf', [status(esa)], [left_inverse])).
% 1.22/1.15 thf(zip_derived_cl1513, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl1327, zip_derived_cl1])).
% 1.22/1.15 thf(zip_derived_cl3368, plain,
% 1.22/1.15 ((((identity) = (sk_c9))
% 1.22/1.15 | ((identity) = (sk_c8))
% 1.22/1.15 | ((identity) = (sk_c8)))),
% 1.22/1.15 inference('demod', [status(thm)],
% 1.22/1.15 [zip_derived_cl3354, zip_derived_cl1513])).
% 1.22/1.15 thf(zip_derived_cl3369, plain,
% 1.22/1.15 ((((identity) = (sk_c8)) | ((identity) = (sk_c9)))),
% 1.22/1.15 inference('simplify', [status(thm)], [zip_derived_cl3368])).
% 1.22/1.15 thf(zip_derived_cl3734, plain, (((identity) = (sk_c8))),
% 1.22/1.15 inference('clc', [status(thm)], [zip_derived_cl3715, zip_derived_cl3369])).
% 1.22/1.15 thf(zip_derived_cl3809, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.22/1.15 (((multiply @ X0 @ sk_c10) != (sk_c9))
% 1.22/1.15 | ((inverse @ X0) != (sk_c10))
% 1.22/1.15 | ((multiply @ X1 @ sk_c9) != (sk_c9))
% 1.22/1.15 | ((inverse @ X1) != (sk_c9))
% 1.22/1.15 | ((inverse @ X2) != (sk_c9))
% 1.22/1.15 | ((multiply @ X2 @ sk_c9) != (sk_c9))
% 1.22/1.15 | ((multiply @ X3 @ sk_c10) != (sk_c9))
% 1.22/1.15 | ((inverse @ X3) != (sk_c10))
% 1.22/1.15 | ((multiply @ X4 @ sk_c9) != (sk_c9))
% 1.22/1.15 | ((inverse @ X4) != (sk_c9))
% 1.22/1.15 | ((identity) != (sk_c9)))),
% 1.22/1.15 inference('demod', [status(thm)],
% 1.22/1.15 [zip_derived_cl1666, zip_derived_cl3734])).
% 1.22/1.15 thf(zip_derived_cl3810, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.22/1.15 (((multiply @ X0 @ sk_c10) != (identity))
% 1.22/1.15 | ((inverse @ X0) != (sk_c10))
% 1.22/1.15 | ((multiply @ X1 @ identity) != (identity))
% 1.22/1.15 | ((inverse @ X1) != (identity))
% 1.22/1.15 | ((inverse @ X2) != (identity))
% 1.22/1.15 | ((multiply @ X2 @ identity) != (identity))
% 1.22/1.15 | ((multiply @ X3 @ sk_c10) != (identity))
% 1.22/1.15 | ((inverse @ X3) != (sk_c10))
% 1.22/1.15 | ((multiply @ X4 @ identity) != (identity))
% 1.22/1.15 | ((inverse @ X4) != (identity))
% 1.22/1.15 | ((identity) != (sk_c9)))),
% 1.22/1.15 inference('local_rewriting', [status(thm)], [zip_derived_cl3809])).
% 1.22/1.15 thf(zip_derived_cl1281, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl179, zip_derived_cl176])).
% 1.22/1.15 thf(zip_derived_cl1281, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl179, zip_derived_cl176])).
% 1.22/1.15 thf(zip_derived_cl1281, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl179, zip_derived_cl176])).
% 1.22/1.15 thf(zip_derived_cl3811, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.22/1.15 (((multiply @ X0 @ sk_c10) != (identity))
% 1.22/1.15 | ((inverse @ X0) != (sk_c10))
% 1.22/1.15 | ((X1) != (identity))
% 1.22/1.15 | ((inverse @ X1) != (identity))
% 1.22/1.15 | ((inverse @ X2) != (identity))
% 1.22/1.15 | ((X2) != (identity))
% 1.22/1.15 | ((multiply @ X3 @ sk_c10) != (identity))
% 1.22/1.15 | ((inverse @ X3) != (sk_c10))
% 1.22/1.15 | ((X4) != (identity))
% 1.22/1.15 | ((inverse @ X4) != (identity))
% 1.22/1.15 | ((identity) != (sk_c9)))),
% 1.22/1.15 inference('demod', [status(thm)],
% 1.22/1.15 [zip_derived_cl3810, zip_derived_cl1281, zip_derived_cl1281,
% 1.22/1.15 zip_derived_cl1281])).
% 1.22/1.15 thf(prove_this_32, conjecture,
% 1.22/1.15 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 1.22/1.15 ( ( inverse @ sk_c3 ) = ( sk_c8 ) ) ))).
% 1.22/1.15 thf(zf_stmt_11, negated_conjecture,
% 1.22/1.15 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c3 ) = ( sk_c8 ) )),
% 1.22/1.15 inference('cnf.neg', [status(esa)], [prove_this_32])).
% 1.22/1.15 thf(zip_derived_cl34, plain,
% 1.22/1.15 ((((inverse @ sk_c5) = (sk_c8)) | ((inverse @ sk_c3) = (sk_c8)))),
% 1.22/1.15 inference('cnf', [status(esa)], [zf_stmt_11])).
% 1.22/1.15 thf(zip_derived_cl3734, plain, (((identity) = (sk_c8))),
% 1.22/1.15 inference('clc', [status(thm)], [zip_derived_cl3715, zip_derived_cl3369])).
% 1.22/1.15 thf(zip_derived_cl3734, plain, (((identity) = (sk_c8))),
% 1.22/1.15 inference('clc', [status(thm)], [zip_derived_cl3715, zip_derived_cl3369])).
% 1.22/1.15 thf(zip_derived_cl3760, plain,
% 1.22/1.15 ((((inverse @ sk_c5) = (identity)) | ((inverse @ sk_c3) = (identity)))),
% 1.22/1.15 inference('demod', [status(thm)],
% 1.22/1.15 [zip_derived_cl34, zip_derived_cl3734, zip_derived_cl3734])).
% 1.22/1.15 thf(zip_derived_cl1327, plain,
% 1.22/1.15 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl1281, zip_derived_cl179])).
% 1.22/1.15 thf(zip_derived_cl163, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i]:
% 1.22/1.15 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.22/1.15 inference('demod', [status(thm)], [zip_derived_cl131, zip_derived_cl0])).
% 1.22/1.15 thf(zip_derived_cl1516, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i]:
% 1.22/1.15 ((X1) = (multiply @ X0 @ (multiply @ (inverse @ X0) @ X1)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl1327, zip_derived_cl163])).
% 1.22/1.15 thf(zip_derived_cl5606, plain,
% 1.22/1.15 (![X0 : $i]:
% 1.22/1.15 (((X0) = (multiply @ sk_c3 @ (multiply @ identity @ X0)))
% 1.22/1.15 | ((inverse @ sk_c5) = (identity)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl3760, zip_derived_cl1516])).
% 1.22/1.15 thf(zip_derived_cl0, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.22/1.15 inference('cnf', [status(esa)], [left_identity])).
% 1.22/1.15 thf(zip_derived_cl5627, plain,
% 1.22/1.15 (![X0 : $i]:
% 1.22/1.15 (((X0) = (multiply @ sk_c3 @ X0)) | ((inverse @ sk_c5) = (identity)))),
% 1.22/1.15 inference('demod', [status(thm)], [zip_derived_cl5606, zip_derived_cl0])).
% 1.22/1.15 thf(prove_this_39, conjecture,
% 1.22/1.15 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 1.22/1.15 ( ( multiply @ sk_c3 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 1.22/1.15 thf(zf_stmt_12, negated_conjecture,
% 1.22/1.15 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 1.22/1.15 ( ( multiply @ sk_c3 @ sk_c9 ) = ( sk_c8 ) )),
% 1.22/1.15 inference('cnf.neg', [status(esa)], [prove_this_39])).
% 1.22/1.15 thf(zip_derived_cl41, plain,
% 1.22/1.15 ((((inverse @ sk_c5) = (sk_c8)) | ((multiply @ sk_c3 @ sk_c9) = (sk_c8)))),
% 1.22/1.15 inference('cnf', [status(esa)], [zf_stmt_12])).
% 1.22/1.15 thf(zip_derived_cl3734, plain, (((identity) = (sk_c8))),
% 1.22/1.15 inference('clc', [status(thm)], [zip_derived_cl3715, zip_derived_cl3369])).
% 1.22/1.15 thf(zip_derived_cl3734, plain, (((identity) = (sk_c8))),
% 1.22/1.15 inference('clc', [status(thm)], [zip_derived_cl3715, zip_derived_cl3369])).
% 1.22/1.15 thf(zip_derived_cl3767, plain,
% 1.22/1.15 ((((inverse @ sk_c5) = (identity))
% 1.22/1.15 | ((multiply @ sk_c3 @ sk_c9) = (identity)))),
% 1.22/1.15 inference('demod', [status(thm)],
% 1.22/1.15 [zip_derived_cl41, zip_derived_cl3734, zip_derived_cl3734])).
% 1.22/1.15 thf(zip_derived_cl6834, plain,
% 1.22/1.15 ((((sk_c9) = (identity))
% 1.22/1.15 | ((inverse @ sk_c5) = (identity))
% 1.22/1.15 | ((inverse @ sk_c5) = (identity)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl5627, zip_derived_cl3767])).
% 1.22/1.15 thf(zip_derived_cl6846, plain,
% 1.22/1.15 ((((inverse @ sk_c5) = (identity)) | ((sk_c9) = (identity)))),
% 1.22/1.15 inference('simplify', [status(thm)], [zip_derived_cl6834])).
% 1.22/1.15 thf(zip_derived_cl1327, plain,
% 1.22/1.15 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl1281, zip_derived_cl179])).
% 1.22/1.15 thf(zip_derived_cl6858, plain,
% 1.22/1.15 ((((sk_c5) = (inverse @ identity)) | ((sk_c9) = (identity)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl6846, zip_derived_cl1327])).
% 1.22/1.15 thf(zip_derived_cl0, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.22/1.15 inference('cnf', [status(esa)], [left_identity])).
% 1.22/1.15 thf(zip_derived_cl163, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i]:
% 1.22/1.15 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.22/1.15 inference('demod', [status(thm)], [zip_derived_cl131, zip_derived_cl0])).
% 1.22/1.15 thf(zip_derived_cl178, plain,
% 1.22/1.15 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl163])).
% 1.22/1.15 thf(zip_derived_cl163, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i]:
% 1.22/1.15 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.22/1.15 inference('demod', [status(thm)], [zip_derived_cl131, zip_derived_cl0])).
% 1.22/1.15 thf(zip_derived_cl231, plain,
% 1.22/1.15 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ identity)) @ X0))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl178, zip_derived_cl163])).
% 1.22/1.15 thf(zip_derived_cl1, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.22/1.15 inference('cnf', [status(esa)], [left_inverse])).
% 1.22/1.15 thf(zip_derived_cl1161, plain, (((inverse @ identity) = (identity))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl231, zip_derived_cl1])).
% 1.22/1.15 thf(zip_derived_cl6889, plain,
% 1.22/1.15 ((((sk_c5) = (identity)) | ((sk_c9) = (identity)))),
% 1.22/1.15 inference('demod', [status(thm)],
% 1.22/1.15 [zip_derived_cl6858, zip_derived_cl1161])).
% 1.22/1.15 thf(prove_this_31, conjecture,
% 1.22/1.15 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c9 ) ) |
% 1.22/1.15 ( ( inverse @ sk_c3 ) = ( sk_c8 ) ) ))).
% 1.22/1.15 thf(zf_stmt_13, negated_conjecture,
% 1.22/1.15 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c9 ) ) |
% 1.22/1.15 ( ( inverse @ sk_c3 ) = ( sk_c8 ) )),
% 1.22/1.15 inference('cnf.neg', [status(esa)], [prove_this_31])).
% 1.22/1.15 thf(zip_derived_cl33, plain,
% 1.22/1.15 ((((multiply @ sk_c5 @ sk_c8) = (sk_c9)) | ((inverse @ sk_c3) = (sk_c8)))),
% 1.22/1.15 inference('cnf', [status(esa)], [zf_stmt_13])).
% 1.22/1.15 thf(zip_derived_cl1327, plain,
% 1.22/1.15 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl1281, zip_derived_cl179])).
% 1.22/1.15 thf(zip_derived_cl1534, plain,
% 1.22/1.15 ((((sk_c3) = (inverse @ sk_c8)) | ((multiply @ sk_c5 @ sk_c8) = (sk_c9)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl33, zip_derived_cl1327])).
% 1.22/1.15 thf(zip_derived_cl3734, plain, (((identity) = (sk_c8))),
% 1.22/1.15 inference('clc', [status(thm)], [zip_derived_cl3715, zip_derived_cl3369])).
% 1.22/1.15 thf(zip_derived_cl1161, plain, (((inverse @ identity) = (identity))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl231, zip_derived_cl1])).
% 1.22/1.15 thf(zip_derived_cl3734, plain, (((identity) = (sk_c8))),
% 1.22/1.15 inference('clc', [status(thm)], [zip_derived_cl3715, zip_derived_cl3369])).
% 1.22/1.15 thf(zip_derived_cl1281, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl179, zip_derived_cl176])).
% 1.22/1.15 thf(zip_derived_cl3805, plain,
% 1.22/1.15 ((((sk_c3) = (identity)) | ((sk_c5) = (sk_c9)))),
% 1.22/1.15 inference('demod', [status(thm)],
% 1.22/1.15 [zip_derived_cl1534, zip_derived_cl3734, zip_derived_cl1161,
% 1.22/1.15 zip_derived_cl3734, zip_derived_cl1281])).
% 1.22/1.15 thf(prove_this_38, conjecture,
% 1.22/1.15 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c9 ) ) |
% 1.22/1.15 ( ( multiply @ sk_c3 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 1.22/1.15 thf(zf_stmt_14, negated_conjecture,
% 1.22/1.15 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c9 ) ) |
% 1.22/1.15 ( ( multiply @ sk_c3 @ sk_c9 ) = ( sk_c8 ) )),
% 1.22/1.15 inference('cnf.neg', [status(esa)], [prove_this_38])).
% 1.22/1.15 thf(zip_derived_cl40, plain,
% 1.22/1.15 ((((multiply @ sk_c5 @ sk_c8) = (sk_c9))
% 1.22/1.15 | ((multiply @ sk_c3 @ sk_c9) = (sk_c8)))),
% 1.22/1.15 inference('cnf', [status(esa)], [zf_stmt_14])).
% 1.22/1.15 thf(zip_derived_cl3734, plain, (((identity) = (sk_c8))),
% 1.22/1.15 inference('clc', [status(thm)], [zip_derived_cl3715, zip_derived_cl3369])).
% 1.22/1.15 thf(zip_derived_cl1281, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl179, zip_derived_cl176])).
% 1.22/1.15 thf(zip_derived_cl3734, plain, (((identity) = (sk_c8))),
% 1.22/1.15 inference('clc', [status(thm)], [zip_derived_cl3715, zip_derived_cl3369])).
% 1.22/1.15 thf(zip_derived_cl3766, plain,
% 1.22/1.15 ((((sk_c5) = (sk_c9)) | ((multiply @ sk_c3 @ sk_c9) = (identity)))),
% 1.22/1.15 inference('demod', [status(thm)],
% 1.22/1.15 [zip_derived_cl40, zip_derived_cl3734, zip_derived_cl1281,
% 1.22/1.15 zip_derived_cl3734])).
% 1.22/1.15 thf(zip_derived_cl4457, plain,
% 1.22/1.15 ((((multiply @ identity @ sk_c9) = (identity))
% 1.22/1.15 | ((sk_c5) = (sk_c9))
% 1.22/1.15 | ((sk_c5) = (sk_c9)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl3805, zip_derived_cl3766])).
% 1.22/1.15 thf(zip_derived_cl0, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.22/1.15 inference('cnf', [status(esa)], [left_identity])).
% 1.22/1.15 thf(zip_derived_cl4465, plain,
% 1.22/1.15 ((((sk_c9) = (identity)) | ((sk_c5) = (sk_c9)) | ((sk_c5) = (sk_c9)))),
% 1.22/1.15 inference('demod', [status(thm)], [zip_derived_cl4457, zip_derived_cl0])).
% 1.22/1.15 thf(zip_derived_cl4466, plain,
% 1.22/1.15 ((((sk_c5) = (sk_c9)) | ((sk_c9) = (identity)))),
% 1.22/1.15 inference('simplify', [status(thm)], [zip_derived_cl4465])).
% 1.22/1.15 thf(zip_derived_cl6931, plain,
% 1.22/1.15 ((((identity) = (sk_c9))
% 1.22/1.15 | ((sk_c9) = (identity))
% 1.22/1.15 | ((sk_c9) = (identity)))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl6889, zip_derived_cl4466])).
% 1.22/1.15 thf(zip_derived_cl6971, plain, (((identity) = (sk_c9))),
% 1.22/1.15 inference('simplify', [status(thm)], [zip_derived_cl6931])).
% 1.22/1.15 thf(zip_derived_cl7067, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.22/1.15 (((multiply @ X0 @ sk_c10) != (identity))
% 1.22/1.15 | ((inverse @ X0) != (sk_c10))
% 1.22/1.15 | ((X1) != (identity))
% 1.22/1.15 | ((inverse @ X1) != (identity))
% 1.22/1.15 | ((inverse @ X2) != (identity))
% 1.22/1.15 | ((X2) != (identity))
% 1.22/1.15 | ((multiply @ X3 @ sk_c10) != (identity))
% 1.22/1.15 | ((inverse @ X3) != (sk_c10))
% 1.22/1.15 | ((X4) != (identity))
% 1.22/1.15 | ((inverse @ X4) != (identity))
% 1.22/1.15 | ((identity) != (identity)))),
% 1.22/1.15 inference('demod', [status(thm)],
% 1.22/1.15 [zip_derived_cl3811, zip_derived_cl6971])).
% 1.22/1.15 thf(zip_derived_cl7068, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.22/1.15 (((inverse @ X4) != (identity))
% 1.22/1.15 | ((X4) != (identity))
% 1.22/1.15 | ((inverse @ X3) != (sk_c10))
% 1.22/1.15 | ((multiply @ X3 @ sk_c10) != (identity))
% 1.22/1.15 | ((X2) != (identity))
% 1.22/1.15 | ((inverse @ X2) != (identity))
% 1.22/1.15 | ((inverse @ X1) != (identity))
% 1.22/1.15 | ((X1) != (identity))
% 1.22/1.15 | ((inverse @ X0) != (sk_c10))
% 1.22/1.15 | ((multiply @ X0 @ sk_c10) != (identity)))),
% 1.22/1.15 inference('simplify', [status(thm)], [zip_derived_cl7067])).
% 1.22/1.15 thf(zip_derived_cl7106, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.22/1.15 (((multiply @ X0 @ sk_c10) != (identity))
% 1.22/1.15 | ((inverse @ X0) != (sk_c10))
% 1.22/1.15 | ((X1) != (identity))
% 1.22/1.15 | ((inverse @ X1) != (identity))
% 1.22/1.15 | ((inverse @ X2) != (identity))
% 1.22/1.15 | ((X2) != (identity))
% 1.22/1.15 | ((multiply @ X3 @ sk_c10) != (identity))
% 1.22/1.15 | ((inverse @ X3) != (sk_c10))
% 1.22/1.15 | ((inverse @ identity) != (identity)))),
% 1.22/1.15 inference('eq_res', [status(thm)], [zip_derived_cl7068])).
% 1.22/1.15 thf(zip_derived_cl1161, plain, (((inverse @ identity) = (identity))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl231, zip_derived_cl1])).
% 1.22/1.15 thf(zip_derived_cl7107, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.22/1.15 (((multiply @ X0 @ sk_c10) != (identity))
% 1.22/1.15 | ((inverse @ X0) != (sk_c10))
% 1.22/1.15 | ((X1) != (identity))
% 1.22/1.15 | ((inverse @ X1) != (identity))
% 1.22/1.15 | ((inverse @ X2) != (identity))
% 1.22/1.15 | ((X2) != (identity))
% 1.22/1.15 | ((multiply @ X3 @ sk_c10) != (identity))
% 1.22/1.15 | ((inverse @ X3) != (sk_c10))
% 1.22/1.15 | ((identity) != (identity)))),
% 1.22/1.15 inference('demod', [status(thm)],
% 1.22/1.15 [zip_derived_cl7106, zip_derived_cl1161])).
% 1.22/1.15 thf(zip_derived_cl7108, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.22/1.15 (((inverse @ X3) != (sk_c10))
% 1.22/1.15 | ((multiply @ X3 @ sk_c10) != (identity))
% 1.22/1.15 | ((X2) != (identity))
% 1.22/1.15 | ((inverse @ X2) != (identity))
% 1.22/1.15 | ((inverse @ X1) != (identity))
% 1.22/1.15 | ((X1) != (identity))
% 1.22/1.15 | ((inverse @ X0) != (sk_c10))
% 1.22/1.15 | ((multiply @ X0 @ sk_c10) != (identity)))),
% 1.22/1.15 inference('simplify', [status(thm)], [zip_derived_cl7107])).
% 1.22/1.15 thf(zip_derived_cl7109, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.22/1.15 (((multiply @ X0 @ sk_c10) != (identity))
% 1.22/1.15 | ((inverse @ X0) != (sk_c10))
% 1.22/1.15 | ((X1) != (identity))
% 1.22/1.15 | ((inverse @ X1) != (identity))
% 1.22/1.15 | ((inverse @ identity) != (identity))
% 1.22/1.15 | ((multiply @ X2 @ sk_c10) != (identity))
% 1.22/1.15 | ((inverse @ X2) != (sk_c10)))),
% 1.22/1.15 inference('eq_res', [status(thm)], [zip_derived_cl7108])).
% 1.22/1.15 thf(zip_derived_cl1161, plain, (((inverse @ identity) = (identity))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl231, zip_derived_cl1])).
% 1.22/1.15 thf(zip_derived_cl7110, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.22/1.15 (((multiply @ X0 @ sk_c10) != (identity))
% 1.22/1.15 | ((inverse @ X0) != (sk_c10))
% 1.22/1.15 | ((X1) != (identity))
% 1.22/1.15 | ((inverse @ X1) != (identity))
% 1.22/1.15 | ((identity) != (identity))
% 1.22/1.15 | ((multiply @ X2 @ sk_c10) != (identity))
% 1.22/1.15 | ((inverse @ X2) != (sk_c10)))),
% 1.22/1.15 inference('demod', [status(thm)],
% 1.22/1.15 [zip_derived_cl7109, zip_derived_cl1161])).
% 1.22/1.15 thf(zip_derived_cl7111, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.22/1.15 (((inverse @ X2) != (sk_c10))
% 1.22/1.15 | ((multiply @ X2 @ sk_c10) != (identity))
% 1.22/1.15 | ((inverse @ X1) != (identity))
% 1.22/1.15 | ((X1) != (identity))
% 1.22/1.15 | ((inverse @ X0) != (sk_c10))
% 1.22/1.15 | ((multiply @ X0 @ sk_c10) != (identity)))),
% 1.22/1.15 inference('simplify', [status(thm)], [zip_derived_cl7110])).
% 1.22/1.15 thf(zip_derived_cl7112, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i]:
% 1.22/1.15 (((multiply @ X0 @ sk_c10) != (identity))
% 1.22/1.15 | ((inverse @ X0) != (sk_c10))
% 1.22/1.15 | ((inverse @ identity) != (identity))
% 1.22/1.15 | ((multiply @ X1 @ sk_c10) != (identity))
% 1.22/1.15 | ((inverse @ X1) != (sk_c10)))),
% 1.22/1.15 inference('eq_res', [status(thm)], [zip_derived_cl7111])).
% 1.22/1.15 thf(zip_derived_cl1161, plain, (((inverse @ identity) = (identity))),
% 1.22/1.15 inference('sup+', [status(thm)], [zip_derived_cl231, zip_derived_cl1])).
% 1.22/1.15 thf(zip_derived_cl7113, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i]:
% 1.22/1.15 (((multiply @ X0 @ sk_c10) != (identity))
% 1.22/1.15 | ((inverse @ X0) != (sk_c10))
% 1.22/1.15 | ((identity) != (identity))
% 1.22/1.15 | ((multiply @ X1 @ sk_c10) != (identity))
% 1.22/1.15 | ((inverse @ X1) != (sk_c10)))),
% 1.22/1.15 inference('demod', [status(thm)],
% 1.22/1.15 [zip_derived_cl7112, zip_derived_cl1161])).
% 1.22/1.15 thf(zip_derived_cl7114, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i]:
% 1.22/1.15 (((inverse @ X1) != (sk_c10))
% 1.22/1.15 | ((multiply @ X1 @ sk_c10) != (identity))
% 1.22/1.15 | ((inverse @ X0) != (sk_c10))
% 1.22/1.15 | ((multiply @ X0 @ sk_c10) != (identity)))),
% 1.22/1.15 inference('simplify', [status(thm)], [zip_derived_cl7113])).
% 1.22/1.15 thf(zip_derived_cl7115, plain,
% 1.22/1.15 (![X0 : $i, X1 : $i]:
% 1.22/1.15 (((X0) != (sk_c10))
% 1.22/1.15 | ((multiply @ X1 @ sk_c10) != (identity))
% 1.22/1.15 | ((inverse @ X1) != (sk_c10))
% 1.22/1.15 | ((multiply @ (inverse @ X0) @ sk_c10) != (identity)))),
% 1.22/1.15 inference('sup-', [status(thm)], [zip_derived_cl1327, zip_derived_cl7114])).
% 1.22/1.15 thf(zip_derived_cl7136, plain,
% 1.22/1.15 (![X0 : $i]:
% 1.22/1.15 (((multiply @ (inverse @ sk_c10) @ sk_c10) != (identity))
% 1.22/1.15 | ((inverse @ X0) != (sk_c10))
% 1.22/1.15 | ((multiply @ X0 @ sk_c10) != (identity)))),
% 1.22/1.15 inference('eq_res', [status(thm)], [zip_derived_cl7115])).
% 1.22/1.15 thf(zip_derived_cl1, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.22/1.15 inference('cnf', [status(esa)], [left_inverse])).
% 1.22/1.15 thf(zip_derived_cl7137, plain,
% 1.22/1.15 (![X0 : $i]:
% 1.22/1.15 (((identity) != (identity))
% 1.22/1.15 | ((inverse @ X0) != (sk_c10))
% 1.22/1.15 | ((multiply @ X0 @ sk_c10) != (identity)))),
% 1.22/1.15 inference('demod', [status(thm)], [zip_derived_cl7136, zip_derived_cl1])).
% 1.22/1.15 thf(zip_derived_cl7138, plain,
% 1.22/1.15 (![X0 : $i]:
% 1.22/1.15 (((multiply @ X0 @ sk_c10) != (identity))
% 1.22/1.15 | ((inverse @ X0) != (sk_c10)))),
% 1.22/1.15 inference('simplify', [status(thm)], [zip_derived_cl7137])).
% 1.22/1.15 thf(zip_derived_cl7178, plain,
% 1.22/1.15 (![X0 : $i]:
% 1.22/1.15 (((X0) != (sk_c10))
% 1.22/1.15 | ((multiply @ (inverse @ X0) @ sk_c10) != (identity)))),
% 1.22/1.15 inference('sup-', [status(thm)], [zip_derived_cl1327, zip_derived_cl7138])).
% 1.22/1.15 thf(zip_derived_cl7199, plain,
% 1.22/1.15 (((multiply @ (inverse @ sk_c10) @ sk_c10) != (identity))),
% 1.22/1.15 inference('eq_res', [status(thm)], [zip_derived_cl7178])).
% 1.22/1.15 thf(zip_derived_cl1, plain,
% 1.22/1.15 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.22/1.15 inference('cnf', [status(esa)], [left_inverse])).
% 1.22/1.15 thf(zip_derived_cl7200, plain, (((identity) != (identity))),
% 1.22/1.15 inference('demod', [status(thm)], [zip_derived_cl7199, zip_derived_cl1])).
% 1.22/1.15 thf(zip_derived_cl7201, plain, ($false),
% 1.22/1.15 inference('simplify', [status(thm)], [zip_derived_cl7200])).
% 1.22/1.15
% 1.22/1.15 % SZS output end Refutation
% 1.22/1.15
% 1.22/1.15
% 1.22/1.15 % Terminating...
% 4.63/1.26 % Runner terminated.
% 4.63/1.28 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------