%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP249-1 : TPTP v9.2.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.oIDU32zUj6 true
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:36:05 PM UTC 2025
% Result : Unsatisfiable 40.67s 6.41s
% Output : Refutation 40.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP249-1 : TPTP v9.2.0. Released v2.5.0.
% 0.11/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.oIDU32zUj6 true
% 0.13/0.34 % Computer : n024.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 1 14:14:38 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.57/0.69 % Total configuration time : 435
% 0.57/0.69 % Estimated wc time : 1092
% 0.57/0.69 % Estimated cpu time (7 cpus) : 156.0
% 0.59/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.59/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.59/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.59/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.59/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.59/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.59/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 40.67/6.41 % Solved by fo/fo3_bce.sh.
% 40.67/6.41 % BCE start: 40
% 40.67/6.41 % BCE eliminated: 0
% 40.67/6.41 % PE start: 40
% 40.67/6.41 logic: eq
% 40.67/6.41 % PE eliminated: 0
% 40.67/6.41 % done 6630 iterations in 5.601s
% 40.67/6.41 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 40.67/6.41 % SZS output start Refutation
% 40.67/6.41 thf(sk_c6_type, type, sk_c6: $i).
% 40.67/6.41 thf(sk_c8_type, type, sk_c8: $i).
% 40.67/6.41 thf(sk_c3_type, type, sk_c3: $i).
% 40.67/6.41 thf(sk_c5_type, type, sk_c5: $i).
% 40.67/6.41 thf(sk_c4_type, type, sk_c4: $i).
% 40.67/6.41 thf(identity_type, type, identity: $i).
% 40.67/6.41 thf(multiply_type, type, multiply: $i > $i > $i).
% 40.67/6.41 thf(sk_c9_type, type, sk_c9: $i).
% 40.67/6.41 thf(inverse_type, type, inverse: $i > $i).
% 40.67/6.41 thf(sk_c7_type, type, sk_c7: $i).
% 40.67/6.41 thf(sk_c2_type, type, sk_c2: $i).
% 40.67/6.41 thf(sk_c1_type, type, sk_c1: $i).
% 40.67/6.41 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 40.67/6.41 thf(zip_derived_cl1, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_inverse])).
% 40.67/6.41 thf(zip_derived_cl1, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_inverse])).
% 40.67/6.41 thf(associativity, axiom,
% 40.67/6.41 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 40.67/6.41 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 40.67/6.41 thf(zip_derived_cl2, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 40.67/6.41 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 40.67/6.41 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 40.67/6.41 inference('cnf', [status(esa)], [associativity])).
% 40.67/6.41 thf(zip_derived_cl52, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i]:
% 40.67/6.41 ((multiply @ identity @ X0)
% 40.67/6.41 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 40.67/6.41 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 40.67/6.41 thf(zip_derived_cl0, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_identity])).
% 40.67/6.41 thf(zip_derived_cl59, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i]:
% 40.67/6.41 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 40.67/6.41 thf(zip_derived_cl534, plain,
% 40.67/6.41 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl59])).
% 40.67/6.41 thf(zip_derived_cl59, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i]:
% 40.67/6.41 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 40.67/6.41 thf(zip_derived_cl59, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i]:
% 40.67/6.41 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 40.67/6.41 thf(zip_derived_cl529, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i]:
% 40.67/6.41 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl59, zip_derived_cl59])).
% 40.67/6.41 thf(zip_derived_cl14357, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl534, zip_derived_cl529])).
% 40.67/6.41 thf(zip_derived_cl1, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_inverse])).
% 40.67/6.41 thf(zip_derived_cl15206, plain, (((inverse @ identity) = (identity))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl14357, zip_derived_cl1])).
% 40.67/6.41 thf(prove_this_26, conjecture,
% 40.67/6.41 (~( ( ( inverse @ sk_c4 ) = ( sk_c9 ) ) |
% 40.67/6.41 ( ( inverse @ sk_c3 ) = ( sk_c9 ) ) ))).
% 40.67/6.41 thf(zf_stmt_0, negated_conjecture,
% 40.67/6.41 (( ( inverse @ sk_c4 ) = ( sk_c9 ) ) | ( ( inverse @ sk_c3 ) = ( sk_c9 ) )),
% 40.67/6.41 inference('cnf.neg', [status(esa)], [prove_this_26])).
% 40.67/6.41 thf(zip_derived_cl28, plain,
% 40.67/6.41 ((((inverse @ sk_c4) = (sk_c9)) | ((inverse @ sk_c3) = (sk_c9)))),
% 40.67/6.41 inference('cnf', [status(esa)], [zf_stmt_0])).
% 40.67/6.41 thf(zip_derived_cl1, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_inverse])).
% 40.67/6.41 thf(zip_derived_cl47, plain,
% 40.67/6.41 ((((multiply @ sk_c9 @ sk_c3) = (identity))
% 40.67/6.41 | ((inverse @ sk_c4) = (sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl28, zip_derived_cl1])).
% 40.67/6.41 thf(prove_this_14, conjecture,
% 40.67/6.41 (~( ( ( inverse @ sk_c4 ) = ( sk_c9 ) ) |
% 40.67/6.41 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) ) ))).
% 40.67/6.41 thf(zf_stmt_1, negated_conjecture,
% 40.67/6.41 (( ( inverse @ sk_c4 ) = ( sk_c9 ) ) |
% 40.67/6.41 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) )),
% 40.67/6.41 inference('cnf.neg', [status(esa)], [prove_this_14])).
% 40.67/6.41 thf(zip_derived_cl16, plain,
% 40.67/6.41 ((((inverse @ sk_c4) = (sk_c9)) | ((multiply @ sk_c2 @ sk_c8) = (sk_c7)))),
% 40.67/6.41 inference('cnf', [status(esa)], [zf_stmt_1])).
% 40.67/6.41 thf(prove_this_20, conjecture,
% 40.67/6.41 (~( ( ( inverse @ sk_c4 ) = ( sk_c9 ) ) |
% 40.67/6.41 ( ( inverse @ sk_c2 ) = ( sk_c8 ) ) ))).
% 40.67/6.41 thf(zf_stmt_2, negated_conjecture,
% 40.67/6.41 (( ( inverse @ sk_c4 ) = ( sk_c9 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c8 ) )),
% 40.67/6.41 inference('cnf.neg', [status(esa)], [prove_this_20])).
% 40.67/6.41 thf(zip_derived_cl22, plain,
% 40.67/6.41 ((((inverse @ sk_c4) = (sk_c9)) | ((inverse @ sk_c2) = (sk_c8)))),
% 40.67/6.41 inference('cnf', [status(esa)], [zf_stmt_2])).
% 40.67/6.41 thf(zip_derived_cl1, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_inverse])).
% 40.67/6.41 thf(zip_derived_cl44, plain,
% 40.67/6.41 ((((multiply @ sk_c8 @ sk_c2) = (identity))
% 40.67/6.41 | ((inverse @ sk_c4) = (sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl1])).
% 40.67/6.41 thf(zip_derived_cl2, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 40.67/6.41 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 40.67/6.41 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 40.67/6.41 inference('cnf', [status(esa)], [associativity])).
% 40.67/6.41 thf(zip_derived_cl90, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((multiply @ identity @ X0)
% 40.67/6.41 = (multiply @ sk_c8 @ (multiply @ sk_c2 @ X0)))
% 40.67/6.41 | ((inverse @ sk_c4) = (sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl44, zip_derived_cl2])).
% 40.67/6.41 thf(zip_derived_cl0, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_identity])).
% 40.67/6.41 thf(zip_derived_cl91, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((X0) = (multiply @ sk_c8 @ (multiply @ sk_c2 @ X0)))
% 40.67/6.41 | ((inverse @ sk_c4) = (sk_c9)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl90, zip_derived_cl0])).
% 40.67/6.41 thf(zip_derived_cl226, plain,
% 40.67/6.41 ((((sk_c8) = (multiply @ sk_c8 @ sk_c7))
% 40.67/6.41 | ((inverse @ sk_c4) = (sk_c9))
% 40.67/6.41 | ((inverse @ sk_c4) = (sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl16, zip_derived_cl91])).
% 40.67/6.41 thf(zip_derived_cl231, plain,
% 40.67/6.41 ((((inverse @ sk_c4) = (sk_c9)) | ((sk_c8) = (multiply @ sk_c8 @ sk_c7)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl226])).
% 40.67/6.41 thf(prove_this_2, conjecture,
% 40.67/6.41 (~( ( ( inverse @ sk_c4 ) = ( sk_c9 ) ) |
% 40.67/6.41 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 40.67/6.41 thf(zf_stmt_3, negated_conjecture,
% 40.67/6.41 (( ( inverse @ sk_c4 ) = ( sk_c9 ) ) |
% 40.67/6.41 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) )),
% 40.67/6.41 inference('cnf.neg', [status(esa)], [prove_this_2])).
% 40.67/6.41 thf(zip_derived_cl4, plain,
% 40.67/6.41 ((((inverse @ sk_c4) = (sk_c9)) | ((multiply @ sk_c1 @ sk_c9) = (sk_c8)))),
% 40.67/6.41 inference('cnf', [status(esa)], [zf_stmt_3])).
% 40.67/6.41 thf(zip_derived_cl2, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 40.67/6.41 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 40.67/6.41 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 40.67/6.41 inference('cnf', [status(esa)], [associativity])).
% 40.67/6.41 thf(zip_derived_cl54, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((multiply @ sk_c8 @ X0)
% 40.67/6.41 = (multiply @ sk_c1 @ (multiply @ sk_c9 @ X0)))
% 40.67/6.41 | ((inverse @ sk_c4) = (sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl2])).
% 40.67/6.41 thf(zip_derived_cl237, plain,
% 40.67/6.41 ((((sk_c8) = (multiply @ sk_c1 @ (multiply @ sk_c9 @ sk_c7)))
% 40.67/6.41 | ((inverse @ sk_c4) = (sk_c9))
% 40.67/6.41 | ((inverse @ sk_c4) = (sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl231, zip_derived_cl54])).
% 40.67/6.41 thf(zip_derived_cl242, plain,
% 40.67/6.41 ((((inverse @ sk_c4) = (sk_c9))
% 40.67/6.41 | ((sk_c8) = (multiply @ sk_c1 @ (multiply @ sk_c9 @ sk_c7))))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl237])).
% 40.67/6.41 thf(zip_derived_cl2, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 40.67/6.41 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 40.67/6.41 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 40.67/6.41 inference('cnf', [status(esa)], [associativity])).
% 40.67/6.41 thf(zip_derived_cl515, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((multiply @ sk_c8 @ X0)
% 40.67/6.41 = (multiply @ sk_c1 @ (multiply @ (multiply @ sk_c9 @ sk_c7) @ X0)))
% 40.67/6.41 | ((inverse @ sk_c4) = (sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl242, zip_derived_cl2])).
% 40.67/6.41 thf(zip_derived_cl2, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 40.67/6.41 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 40.67/6.41 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 40.67/6.41 inference('cnf', [status(esa)], [associativity])).
% 40.67/6.41 thf(zip_derived_cl519, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((multiply @ sk_c8 @ X0)
% 40.67/6.41 = (multiply @ sk_c1 @ (multiply @ sk_c9 @ (multiply @ sk_c7 @ X0))))
% 40.67/6.41 | ((inverse @ sk_c4) = (sk_c9)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl515, zip_derived_cl2])).
% 40.67/6.41 thf(prove_this_5, conjecture,
% 40.67/6.41 (~( ( ( inverse @ sk_c5 ) = ( sk_c6 ) ) |
% 40.67/6.41 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 40.67/6.41 thf(zf_stmt_4, negated_conjecture,
% 40.67/6.41 (( ( inverse @ sk_c5 ) = ( sk_c6 ) ) |
% 40.67/6.41 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) )),
% 40.67/6.41 inference('cnf.neg', [status(esa)], [prove_this_5])).
% 40.67/6.41 thf(zip_derived_cl7, plain,
% 40.67/6.41 ((((inverse @ sk_c5) = (sk_c6)) | ((multiply @ sk_c1 @ sk_c9) = (sk_c8)))),
% 40.67/6.41 inference('cnf', [status(esa)], [zf_stmt_4])).
% 40.67/6.41 thf(prove_this_10, conjecture,
% 40.67/6.41 (~( ( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c8 ) ) |
% 40.67/6.41 ( ( inverse @ sk_c1 ) = ( sk_c9 ) ) ))).
% 40.67/6.41 thf(zf_stmt_5, negated_conjecture,
% 40.67/6.41 (( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c8 ) ) |
% 40.67/6.41 ( ( inverse @ sk_c1 ) = ( sk_c9 ) )),
% 40.67/6.41 inference('cnf.neg', [status(esa)], [prove_this_10])).
% 40.67/6.41 thf(zip_derived_cl12, plain,
% 40.67/6.41 ((((multiply @ sk_c5 @ sk_c6) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c9)))),
% 40.67/6.41 inference('cnf', [status(esa)], [zf_stmt_5])).
% 40.67/6.41 thf(prove_this_11, conjecture,
% 40.67/6.41 (~( ( ( inverse @ sk_c5 ) = ( sk_c6 ) ) |
% 40.67/6.41 ( ( inverse @ sk_c1 ) = ( sk_c9 ) ) ))).
% 40.67/6.41 thf(zf_stmt_6, negated_conjecture,
% 40.67/6.41 (( ( inverse @ sk_c5 ) = ( sk_c6 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c9 ) )),
% 40.67/6.41 inference('cnf.neg', [status(esa)], [prove_this_11])).
% 40.67/6.41 thf(zip_derived_cl13, plain,
% 40.67/6.41 ((((inverse @ sk_c5) = (sk_c6)) | ((inverse @ sk_c1) = (sk_c9)))),
% 40.67/6.41 inference('cnf', [status(esa)], [zf_stmt_6])).
% 40.67/6.41 thf(zip_derived_cl1, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_inverse])).
% 40.67/6.41 thf(zip_derived_cl42, plain,
% 40.67/6.41 ((((multiply @ sk_c6 @ sk_c5) = (identity))
% 40.67/6.41 | ((inverse @ sk_c1) = (sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl1])).
% 40.67/6.41 thf(zip_derived_cl2, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 40.67/6.41 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 40.67/6.41 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 40.67/6.41 inference('cnf', [status(esa)], [associativity])).
% 40.67/6.41 thf(zip_derived_cl86, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((multiply @ identity @ X0)
% 40.67/6.41 = (multiply @ sk_c6 @ (multiply @ sk_c5 @ X0)))
% 40.67/6.41 | ((inverse @ sk_c1) = (sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl42, zip_derived_cl2])).
% 40.67/6.41 thf(zip_derived_cl0, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_identity])).
% 40.67/6.41 thf(zip_derived_cl87, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((X0) = (multiply @ sk_c6 @ (multiply @ sk_c5 @ X0)))
% 40.67/6.41 | ((inverse @ sk_c1) = (sk_c9)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl86, zip_derived_cl0])).
% 40.67/6.41 thf(zip_derived_cl171, plain,
% 40.67/6.41 ((((sk_c6) = (multiply @ sk_c6 @ sk_c8))
% 40.67/6.41 | ((inverse @ sk_c1) = (sk_c9))
% 40.67/6.41 | ((inverse @ sk_c1) = (sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl87])).
% 40.67/6.41 thf(zip_derived_cl174, plain,
% 40.67/6.41 ((((inverse @ sk_c1) = (sk_c9)) | ((sk_c6) = (multiply @ sk_c6 @ sk_c8)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl171])).
% 40.67/6.41 thf(zip_derived_cl12, plain,
% 40.67/6.41 ((((multiply @ sk_c5 @ sk_c6) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c9)))),
% 40.67/6.41 inference('cnf', [status(esa)], [zf_stmt_5])).
% 40.67/6.41 thf(zip_derived_cl2, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 40.67/6.41 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 40.67/6.41 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 40.67/6.41 inference('cnf', [status(esa)], [associativity])).
% 40.67/6.41 thf(zip_derived_cl57, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((multiply @ sk_c8 @ X0)
% 40.67/6.41 = (multiply @ sk_c5 @ (multiply @ sk_c6 @ X0)))
% 40.67/6.41 | ((inverse @ sk_c1) = (sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl2])).
% 40.67/6.41 thf(zip_derived_cl275, plain,
% 40.67/6.41 ((((multiply @ sk_c8 @ sk_c8) = (multiply @ sk_c5 @ sk_c6))
% 40.67/6.41 | ((inverse @ sk_c1) = (sk_c9))
% 40.67/6.41 | ((inverse @ sk_c1) = (sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl174, zip_derived_cl57])).
% 40.67/6.41 thf(zip_derived_cl282, plain,
% 40.67/6.41 ((((inverse @ sk_c1) = (sk_c9))
% 40.67/6.41 | ((multiply @ sk_c8 @ sk_c8) = (multiply @ sk_c5 @ sk_c6)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl275])).
% 40.67/6.41 thf(zip_derived_cl12, plain,
% 40.67/6.41 ((((multiply @ sk_c5 @ sk_c6) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c9)))),
% 40.67/6.41 inference('cnf', [status(esa)], [zf_stmt_5])).
% 40.67/6.41 thf(zip_derived_cl290, plain,
% 40.67/6.41 ((((multiply @ sk_c8 @ sk_c8) = (sk_c8))
% 40.67/6.41 | ((inverse @ sk_c1) = (sk_c9))
% 40.67/6.41 | ((inverse @ sk_c1) = (sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl282, zip_derived_cl12])).
% 40.67/6.41 thf(zip_derived_cl295, plain,
% 40.67/6.41 ((((inverse @ sk_c1) = (sk_c9)) | ((multiply @ sk_c8 @ sk_c8) = (sk_c8)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl290])).
% 40.67/6.41 thf(prove_this_7, conjecture,
% 40.67/6.41 (~( ( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 40.67/6.41 ( ( inverse @ sk_c1 ) = ( sk_c9 ) ) ))).
% 40.67/6.41 thf(zf_stmt_7, negated_conjecture,
% 40.67/6.41 (( ( inverse @ sk_c8 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c9 ) )),
% 40.67/6.41 inference('cnf.neg', [status(esa)], [prove_this_7])).
% 40.67/6.41 thf(zip_derived_cl9, plain,
% 40.67/6.41 ((((inverse @ sk_c8) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c9)))),
% 40.67/6.41 inference('cnf', [status(esa)], [zf_stmt_7])).
% 40.67/6.41 thf(zip_derived_cl1, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_inverse])).
% 40.67/6.41 thf(zip_derived_cl40, plain,
% 40.67/6.41 ((((multiply @ sk_c7 @ sk_c8) = (identity))
% 40.67/6.41 | ((inverse @ sk_c1) = (sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl1])).
% 40.67/6.41 thf(zip_derived_cl2, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 40.67/6.41 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 40.67/6.41 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 40.67/6.41 inference('cnf', [status(esa)], [associativity])).
% 40.67/6.41 thf(zip_derived_cl75, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((multiply @ identity @ X0)
% 40.67/6.41 = (multiply @ sk_c7 @ (multiply @ sk_c8 @ X0)))
% 40.67/6.41 | ((inverse @ sk_c1) = (sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl2])).
% 40.67/6.41 thf(zip_derived_cl0, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_identity])).
% 40.67/6.41 thf(zip_derived_cl76, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((X0) = (multiply @ sk_c7 @ (multiply @ sk_c8 @ X0)))
% 40.67/6.41 | ((inverse @ sk_c1) = (sk_c9)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl75, zip_derived_cl0])).
% 40.67/6.41 thf(zip_derived_cl301, plain,
% 40.67/6.41 ((((sk_c8) = (multiply @ sk_c7 @ sk_c8))
% 40.67/6.41 | ((inverse @ sk_c1) = (sk_c9))
% 40.67/6.41 | ((inverse @ sk_c1) = (sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl295, zip_derived_cl76])).
% 40.67/6.41 thf(zip_derived_cl303, plain,
% 40.67/6.41 ((((inverse @ sk_c1) = (sk_c9)) | ((sk_c8) = (multiply @ sk_c7 @ sk_c8)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl301])).
% 40.67/6.41 thf(zip_derived_cl40, plain,
% 40.67/6.41 ((((multiply @ sk_c7 @ sk_c8) = (identity))
% 40.67/6.41 | ((inverse @ sk_c1) = (sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl1])).
% 40.67/6.41 thf(zip_derived_cl305, plain,
% 40.67/6.41 ((((sk_c8) = (identity))
% 40.67/6.41 | ((inverse @ sk_c1) = (sk_c9))
% 40.67/6.41 | ((inverse @ sk_c1) = (sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl303, zip_derived_cl40])).
% 40.67/6.41 thf(zip_derived_cl306, plain,
% 40.67/6.41 ((((inverse @ sk_c1) = (sk_c9)) | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl305])).
% 40.67/6.41 thf(zip_derived_cl1, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_inverse])).
% 40.67/6.41 thf(zip_derived_cl307, plain,
% 40.67/6.41 ((((multiply @ sk_c9 @ sk_c1) = (identity)) | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl306, zip_derived_cl1])).
% 40.67/6.41 thf(zip_derived_cl2, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 40.67/6.41 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 40.67/6.41 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 40.67/6.41 inference('cnf', [status(esa)], [associativity])).
% 40.67/6.41 thf(zip_derived_cl308, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((multiply @ identity @ X0)
% 40.67/6.41 = (multiply @ sk_c9 @ (multiply @ sk_c1 @ X0)))
% 40.67/6.41 | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl307, zip_derived_cl2])).
% 40.67/6.41 thf(zip_derived_cl0, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_identity])).
% 40.67/6.41 thf(zip_derived_cl309, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((X0) = (multiply @ sk_c9 @ (multiply @ sk_c1 @ X0)))
% 40.67/6.41 | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl308, zip_derived_cl0])).
% 40.67/6.41 thf(zip_derived_cl495, plain,
% 40.67/6.41 ((((sk_c9) = (multiply @ sk_c9 @ sk_c8))
% 40.67/6.41 | ((inverse @ sk_c5) = (sk_c6))
% 40.67/6.41 | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl309])).
% 40.67/6.41 thf(zip_derived_cl59, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i]:
% 40.67/6.41 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 40.67/6.41 thf(zip_derived_cl551, plain,
% 40.67/6.41 ((((sk_c8) = (multiply @ (inverse @ sk_c9) @ sk_c9))
% 40.67/6.41 | ((sk_c8) = (identity))
% 40.67/6.41 | ((inverse @ sk_c5) = (sk_c6)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl495, zip_derived_cl59])).
% 40.67/6.41 thf(zip_derived_cl1, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_inverse])).
% 40.67/6.41 thf(zip_derived_cl620, plain,
% 40.67/6.41 ((((sk_c8) = (identity))
% 40.67/6.41 | ((sk_c8) = (identity))
% 40.67/6.41 | ((inverse @ sk_c5) = (sk_c6)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl551, zip_derived_cl1])).
% 40.67/6.41 thf(zip_derived_cl621, plain,
% 40.67/6.41 ((((inverse @ sk_c5) = (sk_c6)) | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl620])).
% 40.67/6.41 thf(prove_this_22, conjecture,
% 40.67/6.41 (~( ( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c8 ) ) |
% 40.67/6.41 ( ( inverse @ sk_c2 ) = ( sk_c8 ) ) ))).
% 40.67/6.41 thf(zf_stmt_8, negated_conjecture,
% 40.67/6.41 (( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c8 ) ) |
% 40.67/6.41 ( ( inverse @ sk_c2 ) = ( sk_c8 ) )),
% 40.67/6.41 inference('cnf.neg', [status(esa)], [prove_this_22])).
% 40.67/6.41 thf(zip_derived_cl24, plain,
% 40.67/6.41 ((((multiply @ sk_c5 @ sk_c6) = (sk_c8)) | ((inverse @ sk_c2) = (sk_c8)))),
% 40.67/6.41 inference('cnf', [status(esa)], [zf_stmt_8])).
% 40.67/6.41 thf(zip_derived_cl59, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i]:
% 40.67/6.41 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 40.67/6.41 thf(zip_derived_cl583, plain,
% 40.67/6.41 ((((sk_c6) = (multiply @ (inverse @ sk_c5) @ sk_c8))
% 40.67/6.41 | ((inverse @ sk_c2) = (sk_c8)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl24, zip_derived_cl59])).
% 40.67/6.41 thf(zip_derived_cl751, plain,
% 40.67/6.41 ((((sk_c6) = (multiply @ sk_c6 @ sk_c8))
% 40.67/6.41 | ((sk_c8) = (identity))
% 40.67/6.41 | ((inverse @ sk_c2) = (sk_c8)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl621, zip_derived_cl583])).
% 40.67/6.41 thf(zip_derived_cl59, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i]:
% 40.67/6.41 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 40.67/6.41 thf(zip_derived_cl2551, plain,
% 40.67/6.41 ((((sk_c8) = (multiply @ (inverse @ sk_c6) @ sk_c6))
% 40.67/6.41 | ((inverse @ sk_c2) = (sk_c8))
% 40.67/6.41 | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl751, zip_derived_cl59])).
% 40.67/6.41 thf(zip_derived_cl1, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_inverse])).
% 40.67/6.41 thf(zip_derived_cl2558, plain,
% 40.67/6.41 ((((sk_c8) = (identity))
% 40.67/6.41 | ((inverse @ sk_c2) = (sk_c8))
% 40.67/6.41 | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl2551, zip_derived_cl1])).
% 40.67/6.41 thf(zip_derived_cl2559, plain,
% 40.67/6.41 ((((inverse @ sk_c2) = (sk_c8)) | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl2558])).
% 40.67/6.41 thf(zip_derived_cl1, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_inverse])).
% 40.67/6.41 thf(zip_derived_cl2561, plain,
% 40.67/6.41 ((((multiply @ sk_c8 @ sk_c2) = (identity)) | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl2559, zip_derived_cl1])).
% 40.67/6.41 thf(prove_this_1, conjecture,
% 40.67/6.41 (~( ( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 40.67/6.41 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 40.67/6.41 thf(zf_stmt_9, negated_conjecture,
% 40.67/6.41 (( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 40.67/6.41 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) )),
% 40.67/6.41 inference('cnf.neg', [status(esa)], [prove_this_1])).
% 40.67/6.41 thf(zip_derived_cl3, plain,
% 40.67/6.41 ((((inverse @ sk_c8) = (sk_c7)) | ((multiply @ sk_c1 @ sk_c9) = (sk_c8)))),
% 40.67/6.41 inference('cnf', [status(esa)], [zf_stmt_9])).
% 40.67/6.41 thf(zip_derived_cl309, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((X0) = (multiply @ sk_c9 @ (multiply @ sk_c1 @ X0)))
% 40.67/6.41 | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl308, zip_derived_cl0])).
% 40.67/6.41 thf(zip_derived_cl493, plain,
% 40.67/6.41 ((((sk_c9) = (multiply @ sk_c9 @ sk_c8))
% 40.67/6.41 | ((inverse @ sk_c8) = (sk_c7))
% 40.67/6.41 | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl309])).
% 40.67/6.41 thf(zip_derived_cl59, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i]:
% 40.67/6.41 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 40.67/6.41 thf(zip_derived_cl549, plain,
% 40.67/6.41 ((((sk_c8) = (multiply @ (inverse @ sk_c9) @ sk_c9))
% 40.67/6.41 | ((sk_c8) = (identity))
% 40.67/6.41 | ((inverse @ sk_c8) = (sk_c7)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl493, zip_derived_cl59])).
% 40.67/6.41 thf(zip_derived_cl1, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_inverse])).
% 40.67/6.41 thf(zip_derived_cl616, plain,
% 40.67/6.41 ((((sk_c8) = (identity))
% 40.67/6.41 | ((sk_c8) = (identity))
% 40.67/6.41 | ((inverse @ sk_c8) = (sk_c7)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl549, zip_derived_cl1])).
% 40.67/6.41 thf(zip_derived_cl617, plain,
% 40.67/6.41 ((((inverse @ sk_c8) = (sk_c7)) | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl616])).
% 40.67/6.41 thf(zip_derived_cl59, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i]:
% 40.67/6.41 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 40.67/6.41 thf(zip_derived_cl630, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((X0) = (multiply @ sk_c7 @ (multiply @ sk_c8 @ X0)))
% 40.67/6.41 | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl617, zip_derived_cl59])).
% 40.67/6.41 thf(zip_derived_cl2587, plain,
% 40.67/6.41 ((((sk_c2) = (multiply @ sk_c7 @ identity))
% 40.67/6.41 | ((sk_c8) = (identity))
% 40.67/6.41 | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl2561, zip_derived_cl630])).
% 40.67/6.41 thf(zip_derived_cl2592, plain,
% 40.67/6.41 ((((sk_c8) = (identity)) | ((sk_c2) = (multiply @ sk_c7 @ identity)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl2587])).
% 40.67/6.41 thf(zip_derived_cl617, plain,
% 40.67/6.41 ((((inverse @ sk_c8) = (sk_c7)) | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl616])).
% 40.67/6.41 thf(zip_derived_cl1, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_inverse])).
% 40.67/6.41 thf(zip_derived_cl629, plain,
% 40.67/6.41 ((((multiply @ sk_c7 @ sk_c8) = (identity)) | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl617, zip_derived_cl1])).
% 40.67/6.41 thf(zip_derived_cl59, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i]:
% 40.67/6.41 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 40.67/6.41 thf(zip_derived_cl662, plain,
% 40.67/6.41 ((((sk_c8) = (multiply @ (inverse @ sk_c7) @ identity))
% 40.67/6.41 | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl629, zip_derived_cl59])).
% 40.67/6.41 thf(zip_derived_cl2, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 40.67/6.41 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 40.67/6.41 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 40.67/6.41 inference('cnf', [status(esa)], [associativity])).
% 40.67/6.41 thf(zip_derived_cl798, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((multiply @ sk_c8 @ X0)
% 40.67/6.41 = (multiply @ (inverse @ sk_c7) @ (multiply @ identity @ X0)))
% 40.67/6.41 | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl662, zip_derived_cl2])).
% 40.67/6.41 thf(zip_derived_cl0, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_identity])).
% 40.67/6.41 thf(zip_derived_cl801, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((multiply @ sk_c8 @ X0) = (multiply @ (inverse @ sk_c7) @ X0))
% 40.67/6.41 | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl798, zip_derived_cl0])).
% 40.67/6.41 thf(zip_derived_cl1, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_inverse])).
% 40.67/6.41 thf(zip_derived_cl2134, plain,
% 40.67/6.41 ((((multiply @ sk_c8 @ sk_c7) = (identity)) | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl801, zip_derived_cl1])).
% 40.67/6.41 thf(zip_derived_cl630, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((X0) = (multiply @ sk_c7 @ (multiply @ sk_c8 @ X0)))
% 40.67/6.41 | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl617, zip_derived_cl59])).
% 40.67/6.41 thf(zip_derived_cl2162, plain,
% 40.67/6.41 ((((sk_c7) = (multiply @ sk_c7 @ identity))
% 40.67/6.41 | ((sk_c8) = (identity))
% 40.67/6.41 | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl2134, zip_derived_cl630])).
% 40.67/6.41 thf(zip_derived_cl2170, plain,
% 40.67/6.41 ((((sk_c8) = (identity)) | ((sk_c7) = (multiply @ sk_c7 @ identity)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl2162])).
% 40.67/6.41 thf(zip_derived_cl2607, plain,
% 40.67/6.41 ((((sk_c7) = (sk_c2)) | ((sk_c8) = (identity)) | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl2592, zip_derived_cl2170])).
% 40.67/6.41 thf(zip_derived_cl2611, plain,
% 40.67/6.41 ((((sk_c8) = (identity)) | ((sk_c7) = (sk_c2)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl2607])).
% 40.67/6.41 thf(prove_this_16, conjecture,
% 40.67/6.41 (~( ( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c8 ) ) |
% 40.67/6.41 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) ) ))).
% 40.67/6.41 thf(zf_stmt_10, negated_conjecture,
% 40.67/6.41 (( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c8 ) ) |
% 40.67/6.41 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) )),
% 40.67/6.41 inference('cnf.neg', [status(esa)], [prove_this_16])).
% 40.67/6.41 thf(zip_derived_cl18, plain,
% 40.67/6.41 ((((multiply @ sk_c5 @ sk_c6) = (sk_c8))
% 40.67/6.41 | ((multiply @ sk_c2 @ sk_c8) = (sk_c7)))),
% 40.67/6.41 inference('cnf', [status(esa)], [zf_stmt_10])).
% 40.67/6.41 thf(zip_derived_cl59, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i]:
% 40.67/6.41 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 40.67/6.41 thf(zip_derived_cl596, plain,
% 40.67/6.41 ((((sk_c8) = (multiply @ (inverse @ sk_c2) @ sk_c7))
% 40.67/6.41 | ((multiply @ sk_c5 @ sk_c6) = (sk_c8)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl18, zip_derived_cl59])).
% 40.67/6.41 thf(zip_derived_cl2638, plain,
% 40.67/6.41 ((((sk_c8) = (multiply @ (inverse @ sk_c7) @ sk_c7))
% 40.67/6.41 | ((sk_c8) = (identity))
% 40.67/6.41 | ((multiply @ sk_c5 @ sk_c6) = (sk_c8)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl2611, zip_derived_cl596])).
% 40.67/6.41 thf(zip_derived_cl1, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_inverse])).
% 40.67/6.41 thf(zip_derived_cl2655, plain,
% 40.67/6.41 ((((sk_c8) = (identity))
% 40.67/6.41 | ((sk_c8) = (identity))
% 40.67/6.41 | ((multiply @ sk_c5 @ sk_c6) = (sk_c8)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl2638, zip_derived_cl1])).
% 40.67/6.41 thf(zip_derived_cl2656, plain,
% 40.67/6.41 ((((multiply @ sk_c5 @ sk_c6) = (sk_c8)) | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl2655])).
% 40.67/6.41 thf(zip_derived_cl621, plain,
% 40.67/6.41 ((((inverse @ sk_c5) = (sk_c6)) | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl620])).
% 40.67/6.41 thf(zip_derived_cl59, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i]:
% 40.67/6.41 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 40.67/6.41 thf(zip_derived_cl634, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((X0) = (multiply @ sk_c6 @ (multiply @ sk_c5 @ X0)))
% 40.67/6.41 | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl621, zip_derived_cl59])).
% 40.67/6.41 thf(zip_derived_cl2692, plain,
% 40.67/6.41 ((((sk_c6) = (multiply @ sk_c6 @ sk_c8))
% 40.67/6.41 | ((sk_c8) = (identity))
% 40.67/6.41 | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl2656, zip_derived_cl634])).
% 40.67/6.41 thf(zip_derived_cl2698, plain,
% 40.67/6.41 ((((sk_c8) = (identity)) | ((sk_c6) = (multiply @ sk_c6 @ sk_c8)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl2692])).
% 40.67/6.41 thf(zip_derived_cl59, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i]:
% 40.67/6.41 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 40.67/6.41 thf(zip_derived_cl2746, plain,
% 40.67/6.41 ((((sk_c8) = (multiply @ (inverse @ sk_c6) @ sk_c6))
% 40.67/6.41 | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl2698, zip_derived_cl59])).
% 40.67/6.41 thf(zip_derived_cl1, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_inverse])).
% 40.67/6.41 thf(zip_derived_cl2753, plain,
% 40.67/6.41 ((((sk_c8) = (identity)) | ((sk_c8) = (identity)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl2746, zip_derived_cl1])).
% 40.67/6.41 thf(zip_derived_cl2754, plain, (((sk_c8) = (identity))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl2753])).
% 40.67/6.41 thf(zip_derived_cl0, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_identity])).
% 40.67/6.41 thf(prove_this_13, conjecture,
% 40.67/6.41 (~( ( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 40.67/6.41 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) ) ))).
% 40.67/6.41 thf(zf_stmt_11, negated_conjecture,
% 40.67/6.41 (( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 40.67/6.41 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) )),
% 40.67/6.41 inference('cnf.neg', [status(esa)], [prove_this_13])).
% 40.67/6.41 thf(zip_derived_cl15, plain,
% 40.67/6.41 ((((inverse @ sk_c8) = (sk_c7)) | ((multiply @ sk_c2 @ sk_c8) = (sk_c7)))),
% 40.67/6.41 inference('cnf', [status(esa)], [zf_stmt_11])).
% 40.67/6.41 thf(prove_this_19, conjecture,
% 40.67/6.41 (~( ( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 40.67/6.41 ( ( inverse @ sk_c2 ) = ( sk_c8 ) ) ))).
% 40.67/6.41 thf(zf_stmt_12, negated_conjecture,
% 40.67/6.41 (( ( inverse @ sk_c8 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c8 ) )),
% 40.67/6.41 inference('cnf.neg', [status(esa)], [prove_this_19])).
% 40.67/6.41 thf(zip_derived_cl21, plain,
% 40.67/6.41 ((((inverse @ sk_c8) = (sk_c7)) | ((inverse @ sk_c2) = (sk_c8)))),
% 40.67/6.41 inference('cnf', [status(esa)], [zf_stmt_12])).
% 40.67/6.41 thf(zip_derived_cl1, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_inverse])).
% 40.67/6.41 thf(zip_derived_cl43, plain,
% 40.67/6.41 ((((multiply @ sk_c8 @ sk_c2) = (identity))
% 40.67/6.41 | ((inverse @ sk_c8) = (sk_c7)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl21, zip_derived_cl1])).
% 40.67/6.41 thf(zip_derived_cl2, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 40.67/6.41 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 40.67/6.41 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 40.67/6.41 inference('cnf', [status(esa)], [associativity])).
% 40.67/6.41 thf(zip_derived_cl88, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((multiply @ identity @ X0)
% 40.67/6.41 = (multiply @ sk_c8 @ (multiply @ sk_c2 @ X0)))
% 40.67/6.41 | ((inverse @ sk_c8) = (sk_c7)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl43, zip_derived_cl2])).
% 40.67/6.41 thf(zip_derived_cl0, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_identity])).
% 40.67/6.41 thf(zip_derived_cl89, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((X0) = (multiply @ sk_c8 @ (multiply @ sk_c2 @ X0)))
% 40.67/6.41 | ((inverse @ sk_c8) = (sk_c7)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl88, zip_derived_cl0])).
% 40.67/6.41 thf(zip_derived_cl182, plain,
% 40.67/6.41 ((((sk_c8) = (multiply @ sk_c8 @ sk_c7))
% 40.67/6.41 | ((inverse @ sk_c8) = (sk_c7))
% 40.67/6.41 | ((inverse @ sk_c8) = (sk_c7)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl15, zip_derived_cl89])).
% 40.67/6.41 thf(zip_derived_cl188, plain,
% 40.67/6.41 ((((inverse @ sk_c8) = (sk_c7)) | ((sk_c8) = (multiply @ sk_c8 @ sk_c7)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl182])).
% 40.67/6.41 thf(zip_derived_cl59, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i]:
% 40.67/6.41 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 40.67/6.41 thf(zip_derived_cl563, plain,
% 40.67/6.41 ((((sk_c7) = (multiply @ (inverse @ sk_c8) @ sk_c8))
% 40.67/6.41 | ((inverse @ sk_c8) = (sk_c7)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl188, zip_derived_cl59])).
% 40.67/6.41 thf(zip_derived_cl1, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_inverse])).
% 40.67/6.41 thf(zip_derived_cl623, plain,
% 40.67/6.41 ((((sk_c7) = (identity)) | ((inverse @ sk_c8) = (sk_c7)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl563, zip_derived_cl1])).
% 40.67/6.41 thf(zip_derived_cl59, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i]:
% 40.67/6.41 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 40.67/6.41 thf(zip_derived_cl636, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((X0) = (multiply @ sk_c7 @ (multiply @ sk_c8 @ X0)))
% 40.67/6.41 | ((sk_c7) = (identity)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl623, zip_derived_cl59])).
% 40.67/6.41 thf(zip_derived_cl2754, plain, (((sk_c8) = (identity))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl2753])).
% 40.67/6.41 thf(zip_derived_cl0, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_identity])).
% 40.67/6.41 thf(zip_derived_cl3045, plain,
% 40.67/6.41 (![X0 : $i]: (((X0) = (multiply @ sk_c7 @ X0)) | ((sk_c7) = (identity)))),
% 40.67/6.41 inference('demod', [status(thm)],
% 40.67/6.41 [zip_derived_cl636, zip_derived_cl2754, zip_derived_cl0])).
% 40.67/6.41 thf(zip_derived_cl59, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i]:
% 40.67/6.41 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 40.67/6.41 thf(zip_derived_cl3243, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((X0) = (multiply @ (inverse @ sk_c7) @ X0)) | ((sk_c7) = (identity)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl3045, zip_derived_cl59])).
% 40.67/6.41 thf(zip_derived_cl1, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_inverse])).
% 40.67/6.41 thf(zip_derived_cl3935, plain,
% 40.67/6.41 ((((sk_c7) = (identity)) | ((sk_c7) = (identity)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl3243, zip_derived_cl1])).
% 40.67/6.41 thf(zip_derived_cl3953, plain, (((sk_c7) = (identity))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl3935])).
% 40.67/6.41 thf(zip_derived_cl0, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_identity])).
% 40.67/6.41 thf(zip_derived_cl12474, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((X0) = (multiply @ sk_c1 @ (multiply @ sk_c9 @ X0)))
% 40.67/6.41 | ((inverse @ sk_c4) = (sk_c9)))),
% 40.67/6.41 inference('demod', [status(thm)],
% 40.67/6.41 [zip_derived_cl519, zip_derived_cl2754, zip_derived_cl0,
% 40.67/6.41 zip_derived_cl3953, zip_derived_cl0])).
% 40.67/6.41 thf(zip_derived_cl12547, plain,
% 40.67/6.41 ((((sk_c3) = (multiply @ sk_c1 @ identity))
% 40.67/6.41 | ((inverse @ sk_c4) = (sk_c9))
% 40.67/6.41 | ((inverse @ sk_c4) = (sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl47, zip_derived_cl12474])).
% 40.67/6.41 thf(zip_derived_cl12555, plain,
% 40.67/6.41 ((((inverse @ sk_c4) = (sk_c9))
% 40.67/6.41 | ((sk_c3) = (multiply @ sk_c1 @ identity)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl12547])).
% 40.67/6.41 thf(zip_derived_cl28, plain,
% 40.67/6.41 ((((inverse @ sk_c4) = (sk_c9)) | ((inverse @ sk_c3) = (sk_c9)))),
% 40.67/6.41 inference('cnf', [status(esa)], [zf_stmt_0])).
% 40.67/6.41 thf(prove_this_32, conjecture,
% 40.67/6.41 (~( ( ( inverse @ sk_c4 ) = ( sk_c9 ) ) |
% 40.67/6.41 ( ( multiply @ sk_c3 @ sk_c7 ) = ( sk_c9 ) ) ))).
% 40.67/6.41 thf(zf_stmt_13, negated_conjecture,
% 40.67/6.41 (( ( inverse @ sk_c4 ) = ( sk_c9 ) ) |
% 40.67/6.41 ( ( multiply @ sk_c3 @ sk_c7 ) = ( sk_c9 ) )),
% 40.67/6.41 inference('cnf.neg', [status(esa)], [prove_this_32])).
% 40.67/6.41 thf(zip_derived_cl34, plain,
% 40.67/6.41 ((((inverse @ sk_c4) = (sk_c9)) | ((multiply @ sk_c3 @ sk_c7) = (sk_c9)))),
% 40.67/6.41 inference('cnf', [status(esa)], [zf_stmt_13])).
% 40.67/6.41 thf(zip_derived_cl59, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i]:
% 40.67/6.41 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 40.67/6.41 thf(zip_derived_cl600, plain,
% 40.67/6.41 ((((sk_c7) = (multiply @ (inverse @ sk_c3) @ sk_c9))
% 40.67/6.41 | ((inverse @ sk_c4) = (sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl34, zip_derived_cl59])).
% 40.67/6.41 thf(zip_derived_cl964, plain,
% 40.67/6.41 ((((sk_c7) = (multiply @ sk_c9 @ sk_c9))
% 40.67/6.41 | ((inverse @ sk_c4) = (sk_c9))
% 40.67/6.41 | ((inverse @ sk_c4) = (sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl28, zip_derived_cl600])).
% 40.67/6.41 thf(zip_derived_cl966, plain,
% 40.67/6.41 ((((inverse @ sk_c4) = (sk_c9)) | ((sk_c7) = (multiply @ sk_c9 @ sk_c9)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl964])).
% 40.67/6.41 thf(zip_derived_cl3953, plain, (((sk_c7) = (identity))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl3935])).
% 40.67/6.41 thf(zip_derived_cl3961, plain,
% 40.67/6.41 ((((inverse @ sk_c4) = (sk_c9))
% 40.67/6.41 | ((identity) = (multiply @ sk_c9 @ sk_c9)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl966, zip_derived_cl3953])).
% 40.67/6.41 thf(zip_derived_cl12474, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((X0) = (multiply @ sk_c1 @ (multiply @ sk_c9 @ X0)))
% 40.67/6.41 | ((inverse @ sk_c4) = (sk_c9)))),
% 40.67/6.41 inference('demod', [status(thm)],
% 40.67/6.41 [zip_derived_cl519, zip_derived_cl2754, zip_derived_cl0,
% 40.67/6.41 zip_derived_cl3953, zip_derived_cl0])).
% 40.67/6.41 thf(zip_derived_cl12538, plain,
% 40.67/6.41 ((((sk_c9) = (multiply @ sk_c1 @ identity))
% 40.67/6.41 | ((inverse @ sk_c4) = (sk_c9))
% 40.67/6.41 | ((inverse @ sk_c4) = (sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)],
% 40.67/6.41 [zip_derived_cl3961, zip_derived_cl12474])).
% 40.67/6.41 thf(zip_derived_cl12554, plain,
% 40.67/6.41 ((((inverse @ sk_c4) = (sk_c9))
% 40.67/6.41 | ((sk_c9) = (multiply @ sk_c1 @ identity)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl12538])).
% 40.67/6.41 thf(zip_derived_cl14445, plain,
% 40.67/6.41 ((((sk_c9) = (sk_c3))
% 40.67/6.41 | ((inverse @ sk_c4) = (sk_c9))
% 40.67/6.41 | ((inverse @ sk_c4) = (sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)],
% 40.67/6.41 [zip_derived_cl12555, zip_derived_cl12554])).
% 40.67/6.41 thf(zip_derived_cl14453, plain,
% 40.67/6.41 ((((inverse @ sk_c4) = (sk_c9)) | ((sk_c9) = (sk_c3)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl14445])).
% 40.67/6.41 thf(zip_derived_cl15206, plain, (((inverse @ identity) = (identity))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl14357, zip_derived_cl1])).
% 40.67/6.41 thf(prove_this_33, conjecture,
% 40.67/6.41 (~( ( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c9 ) ) |
% 40.67/6.41 ( ( multiply @ sk_c3 @ sk_c7 ) = ( sk_c9 ) ) ))).
% 40.67/6.41 thf(zf_stmt_14, negated_conjecture,
% 40.67/6.41 (( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c9 ) ) |
% 40.67/6.41 ( ( multiply @ sk_c3 @ sk_c7 ) = ( sk_c9 ) )),
% 40.67/6.41 inference('cnf.neg', [status(esa)], [prove_this_33])).
% 40.67/6.41 thf(zip_derived_cl35, plain,
% 40.67/6.41 ((((multiply @ sk_c4 @ sk_c8) = (sk_c9))
% 40.67/6.41 | ((multiply @ sk_c3 @ sk_c7) = (sk_c9)))),
% 40.67/6.41 inference('cnf', [status(esa)], [zf_stmt_14])).
% 40.67/6.41 thf(zip_derived_cl2754, plain, (((sk_c8) = (identity))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl2753])).
% 40.67/6.41 thf(zip_derived_cl2957, plain,
% 40.67/6.41 ((((multiply @ sk_c4 @ identity) = (sk_c9))
% 40.67/6.41 | ((multiply @ sk_c3 @ sk_c7) = (sk_c9)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl35, zip_derived_cl2754])).
% 40.67/6.41 thf(zip_derived_cl3953, plain, (((sk_c7) = (identity))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl3935])).
% 40.67/6.41 thf(zip_derived_cl7342, plain,
% 40.67/6.41 ((((multiply @ sk_c4 @ identity) = (sk_c9))
% 40.67/6.41 | ((multiply @ sk_c3 @ identity) = (sk_c9)))),
% 40.67/6.41 inference('demod', [status(thm)],
% 40.67/6.41 [zip_derived_cl2957, zip_derived_cl3953])).
% 40.67/6.41 thf(zip_derived_cl14357, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl534, zip_derived_cl529])).
% 40.67/6.41 thf(zip_derived_cl15183, plain,
% 40.67/6.41 ((((sk_c4) = (sk_c9)) | ((multiply @ sk_c3 @ identity) = (sk_c9)))),
% 40.67/6.41 inference('demod', [status(thm)],
% 40.67/6.41 [zip_derived_cl7342, zip_derived_cl14357])).
% 40.67/6.41 thf(zip_derived_cl14357, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl534, zip_derived_cl529])).
% 40.67/6.41 thf(zip_derived_cl21136, plain,
% 40.67/6.41 ((((sk_c9) = (sk_c3)) | ((sk_c4) = (sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)],
% 40.67/6.41 [zip_derived_cl15183, zip_derived_cl14357])).
% 40.67/6.41 thf(zip_derived_cl14357, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl534, zip_derived_cl529])).
% 40.67/6.41 thf(prove_this_27, conjecture,
% 40.67/6.41 (~( ( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c9 ) ) |
% 40.67/6.41 ( ( inverse @ sk_c3 ) = ( sk_c9 ) ) ))).
% 40.67/6.41 thf(zf_stmt_15, negated_conjecture,
% 40.67/6.41 (( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c9 ) ) |
% 40.67/6.41 ( ( inverse @ sk_c3 ) = ( sk_c9 ) )),
% 40.67/6.41 inference('cnf.neg', [status(esa)], [prove_this_27])).
% 40.67/6.41 thf(zip_derived_cl29, plain,
% 40.67/6.41 ((((multiply @ sk_c4 @ sk_c8) = (sk_c9)) | ((inverse @ sk_c3) = (sk_c9)))),
% 40.67/6.41 inference('cnf', [status(esa)], [zf_stmt_15])).
% 40.67/6.41 thf(zip_derived_cl2754, plain, (((sk_c8) = (identity))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl2753])).
% 40.67/6.41 thf(zip_derived_cl2953, plain,
% 40.67/6.41 ((((multiply @ sk_c4 @ identity) = (sk_c9))
% 40.67/6.41 | ((inverse @ sk_c3) = (sk_c9)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl29, zip_derived_cl2754])).
% 40.67/6.41 thf(zip_derived_cl15256, plain,
% 40.67/6.41 ((((sk_c4) = (sk_c9)) | ((inverse @ sk_c3) = (sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)],
% 40.67/6.41 [zip_derived_cl14357, zip_derived_cl2953])).
% 40.67/6.41 thf(zip_derived_cl21195, plain,
% 40.67/6.41 ((((inverse @ sk_c9) = (sk_c9))
% 40.67/6.41 | ((sk_c4) = (sk_c9))
% 40.67/6.41 | ((sk_c4) = (sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)],
% 40.67/6.41 [zip_derived_cl21136, zip_derived_cl15256])).
% 40.67/6.41 thf(zip_derived_cl21208, plain,
% 40.67/6.41 ((((sk_c4) = (sk_c9)) | ((inverse @ sk_c9) = (sk_c9)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl21195])).
% 40.67/6.41 thf(zip_derived_cl21208, plain,
% 40.67/6.41 ((((sk_c4) = (sk_c9)) | ((inverse @ sk_c9) = (sk_c9)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl21195])).
% 40.67/6.41 thf(zip_derived_cl15206, plain, (((inverse @ identity) = (identity))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl14357, zip_derived_cl1])).
% 40.67/6.41 thf(zip_derived_cl1, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_inverse])).
% 40.67/6.41 thf(zip_derived_cl0, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 40.67/6.41 inference('cnf', [status(esa)], [left_identity])).
% 40.67/6.41 thf(prove_this_37, conjecture,
% 40.67/6.41 (~( ( ( multiply @ X2 @ sk_c7 ) != ( sk_c8 ) ) |
% 40.67/6.41 ( ( inverse @ X3 ) != ( X2 ) ) |
% 40.67/6.41 ( ( multiply @ X3 @ X2 ) != ( sk_c8 ) ) |
% 40.67/6.41 ( ( multiply @ X1 @ sk_c8 ) != ( sk_c9 ) ) |
% 40.67/6.41 ( ( inverse @ X1 ) != ( sk_c9 ) ) |
% 40.67/6.41 ( ( inverse @ sk_c8 ) != ( sk_c7 ) ) |
% 40.67/6.41 ( ( multiply @ X6 @ sk_c7 ) != ( sk_c9 ) ) |
% 40.67/6.41 ( ( inverse @ X6 ) != ( sk_c9 ) ) |
% 40.67/6.41 ( ( inverse @ X5 ) != ( sk_c8 ) ) |
% 40.67/6.41 ( ( multiply @ X5 @ sk_c8 ) != ( sk_c7 ) ) |
% 40.67/6.41 ( ( inverse @ X4 ) != ( sk_c9 ) ) |
% 40.67/6.41 ( ( multiply @ X4 @ sk_c9 ) != ( sk_c8 ) ) ))).
% 40.67/6.41 thf(zf_stmt_16, negated_conjecture,
% 40.67/6.41 (( ( multiply @ X2 @ sk_c7 ) != ( sk_c8 ) ) |
% 40.67/6.41 ( ( inverse @ X3 ) != ( X2 ) ) |
% 40.67/6.41 ( ( multiply @ X3 @ X2 ) != ( sk_c8 ) ) |
% 40.67/6.41 ( ( multiply @ X1 @ sk_c8 ) != ( sk_c9 ) ) |
% 40.67/6.41 ( ( inverse @ X1 ) != ( sk_c9 ) ) |
% 40.67/6.41 ( ( inverse @ sk_c8 ) != ( sk_c7 ) ) |
% 40.67/6.41 ( ( multiply @ X6 @ sk_c7 ) != ( sk_c9 ) ) |
% 40.67/6.41 ( ( inverse @ X6 ) != ( sk_c9 ) ) | ( ( inverse @ X5 ) != ( sk_c8 ) ) |
% 40.67/6.41 ( ( multiply @ X5 @ sk_c8 ) != ( sk_c7 ) ) |
% 40.67/6.41 ( ( inverse @ X4 ) != ( sk_c9 ) ) |
% 40.67/6.41 ( ( multiply @ X4 @ sk_c9 ) != ( sk_c8 ) )),
% 40.67/6.41 inference('cnf.neg', [status(esa)], [prove_this_37])).
% 40.67/6.41 thf(zip_derived_cl39, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 40.67/6.41 (((multiply @ X0 @ sk_c7) != (sk_c8))
% 40.67/6.41 | ((inverse @ X1) != (X0))
% 40.67/6.41 | ((multiply @ X1 @ X0) != (sk_c8))
% 40.67/6.41 | ((multiply @ X2 @ sk_c8) != (sk_c9))
% 40.67/6.41 | ((inverse @ X2) != (sk_c9))
% 40.67/6.41 | ((inverse @ sk_c8) != (sk_c7))
% 40.67/6.41 | ((multiply @ X3 @ sk_c7) != (sk_c9))
% 40.67/6.41 | ((inverse @ X3) != (sk_c9))
% 40.67/6.41 | ((inverse @ X4) != (sk_c8))
% 40.67/6.41 | ((multiply @ X4 @ sk_c8) != (sk_c7))
% 40.67/6.41 | ((inverse @ X5) != (sk_c9))
% 40.67/6.41 | ((multiply @ X5 @ sk_c9) != (sk_c8)))),
% 40.67/6.41 inference('cnf', [status(esa)], [zf_stmt_16])).
% 40.67/6.41 thf(zip_derived_cl107, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 40.67/6.41 (((sk_c7) != (sk_c8))
% 40.67/6.41 | ((multiply @ X0 @ sk_c9) != (sk_c8))
% 40.67/6.41 | ((inverse @ X0) != (sk_c9))
% 40.67/6.41 | ((multiply @ X1 @ sk_c8) != (sk_c7))
% 40.67/6.41 | ((inverse @ X1) != (sk_c8))
% 40.67/6.41 | ((inverse @ X2) != (sk_c9))
% 40.67/6.41 | ((multiply @ X2 @ sk_c7) != (sk_c9))
% 40.67/6.41 | ((inverse @ sk_c8) != (sk_c7))
% 40.67/6.41 | ((inverse @ X3) != (sk_c9))
% 40.67/6.41 | ((multiply @ X3 @ sk_c8) != (sk_c9))
% 40.67/6.41 | ((multiply @ X4 @ identity) != (sk_c8))
% 40.67/6.41 | ((inverse @ X4) != (identity)))),
% 40.67/6.41 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl39])).
% 40.67/6.41 thf(zip_derived_cl119, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 40.67/6.41 (((sk_c7) != (sk_c8))
% 40.67/6.41 | ((multiply @ X0 @ sk_c9) != (sk_c8))
% 40.67/6.41 | ((inverse @ X0) != (sk_c9))
% 40.67/6.41 | ((multiply @ X1 @ sk_c8) != (sk_c8))
% 40.67/6.41 | ((inverse @ X1) != (sk_c8))
% 40.67/6.41 | ((inverse @ X2) != (sk_c9))
% 40.67/6.41 | ((multiply @ X2 @ sk_c8) != (sk_c9))
% 40.67/6.41 | ((inverse @ sk_c8) != (sk_c8))
% 40.67/6.41 | ((inverse @ X3) != (sk_c9))
% 40.67/6.41 | ((multiply @ X3 @ sk_c8) != (sk_c9))
% 40.67/6.41 | ((multiply @ X4 @ identity) != (sk_c8))
% 40.67/6.41 | ((inverse @ X4) != (identity)))),
% 40.67/6.41 inference('local_rewriting', [status(thm)], [zip_derived_cl107])).
% 40.67/6.41 thf(zip_derived_cl2754, plain, (((sk_c8) = (identity))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl2753])).
% 40.67/6.41 thf(zip_derived_cl2754, plain, (((sk_c8) = (identity))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl2753])).
% 40.67/6.41 thf(zip_derived_cl2754, plain, (((sk_c8) = (identity))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl2753])).
% 40.67/6.41 thf(zip_derived_cl2754, plain, (((sk_c8) = (identity))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl2753])).
% 40.67/6.41 thf(zip_derived_cl2754, plain, (((sk_c8) = (identity))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl2753])).
% 40.67/6.41 thf(zip_derived_cl2754, plain, (((sk_c8) = (identity))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl2753])).
% 40.67/6.41 thf(zip_derived_cl2754, plain, (((sk_c8) = (identity))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl2753])).
% 40.67/6.41 thf(zip_derived_cl2754, plain, (((sk_c8) = (identity))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl2753])).
% 40.67/6.41 thf(zip_derived_cl2754, plain, (((sk_c8) = (identity))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl2753])).
% 40.67/6.41 thf(zip_derived_cl2754, plain, (((sk_c8) = (identity))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl2753])).
% 40.67/6.41 thf(zip_derived_cl3108, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 40.67/6.41 (((sk_c7) != (identity))
% 40.67/6.41 | ((multiply @ X0 @ sk_c9) != (identity))
% 40.67/6.41 | ((inverse @ X0) != (sk_c9))
% 40.67/6.41 | ((multiply @ X1 @ identity) != (identity))
% 40.67/6.41 | ((inverse @ X1) != (identity))
% 40.67/6.41 | ((inverse @ X2) != (sk_c9))
% 40.67/6.41 | ((multiply @ X2 @ identity) != (sk_c9))
% 40.67/6.41 | ((inverse @ identity) != (identity))
% 40.67/6.41 | ((inverse @ X3) != (sk_c9))
% 40.67/6.41 | ((multiply @ X3 @ identity) != (sk_c9))
% 40.67/6.41 | ((multiply @ X4 @ identity) != (identity))
% 40.67/6.41 | ((inverse @ X4) != (identity)))),
% 40.67/6.41 inference('demod', [status(thm)],
% 40.67/6.41 [zip_derived_cl119, zip_derived_cl2754, zip_derived_cl2754,
% 40.67/6.41 zip_derived_cl2754, zip_derived_cl2754, zip_derived_cl2754,
% 40.67/6.41 zip_derived_cl2754, zip_derived_cl2754, zip_derived_cl2754,
% 40.67/6.41 zip_derived_cl2754, zip_derived_cl2754])).
% 40.67/6.41 thf(zip_derived_cl3112, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 40.67/6.41 (((identity) != (identity))
% 40.67/6.41 | ((inverse @ X0) != (identity))
% 40.67/6.41 | ((multiply @ X0 @ identity) != (identity))
% 40.67/6.41 | ((multiply @ X1 @ identity) != (sk_c9))
% 40.67/6.41 | ((inverse @ X1) != (sk_c9))
% 40.67/6.41 | ((inverse @ identity) != (identity))
% 40.67/6.41 | ((multiply @ X2 @ identity) != (sk_c9))
% 40.67/6.41 | ((inverse @ X2) != (sk_c9))
% 40.67/6.41 | ((inverse @ X3) != (identity))
% 40.67/6.41 | ((multiply @ X3 @ identity) != (identity))
% 40.67/6.41 | ((inverse @ (inverse @ sk_c9)) != (sk_c9))
% 40.67/6.41 | ((sk_c7) != (identity)))),
% 40.67/6.41 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl3108])).
% 40.67/6.41 thf(zip_derived_cl3119, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 40.67/6.41 (((sk_c7) != (identity))
% 40.67/6.41 | ((inverse @ (inverse @ sk_c9)) != (sk_c9))
% 40.67/6.41 | ((multiply @ X3 @ identity) != (identity))
% 40.67/6.41 | ((inverse @ X3) != (identity))
% 40.67/6.41 | ((inverse @ X2) != (sk_c9))
% 40.67/6.41 | ((multiply @ X2 @ identity) != (sk_c9))
% 40.67/6.41 | ((inverse @ identity) != (identity))
% 40.67/6.41 | ((inverse @ X1) != (sk_c9))
% 40.67/6.41 | ((multiply @ X1 @ identity) != (sk_c9))
% 40.67/6.41 | ((multiply @ X0 @ identity) != (identity))
% 40.67/6.41 | ((inverse @ X0) != (identity)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl3112])).
% 40.67/6.41 thf(zip_derived_cl3953, plain, (((sk_c7) = (identity))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl3935])).
% 40.67/6.41 thf(zip_derived_cl14357, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl534, zip_derived_cl529])).
% 40.67/6.41 thf(zip_derived_cl534, plain,
% 40.67/6.41 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl59])).
% 40.67/6.41 thf(zip_derived_cl15224, plain,
% 40.67/6.41 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl14357, zip_derived_cl534])).
% 40.67/6.41 thf(zip_derived_cl14357, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl534, zip_derived_cl529])).
% 40.67/6.41 thf(zip_derived_cl14357, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl534, zip_derived_cl529])).
% 40.67/6.41 thf(zip_derived_cl15206, plain, (((inverse @ identity) = (identity))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl14357, zip_derived_cl1])).
% 40.67/6.41 thf(zip_derived_cl14357, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl534, zip_derived_cl529])).
% 40.67/6.41 thf(zip_derived_cl14357, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl534, zip_derived_cl529])).
% 40.67/6.41 thf(zip_derived_cl42832, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 40.67/6.41 (((identity) != (identity))
% 40.67/6.41 | ((sk_c9) != (sk_c9))
% 40.67/6.41 | ((X3) != (identity))
% 40.67/6.41 | ((inverse @ X3) != (identity))
% 40.67/6.41 | ((inverse @ X2) != (sk_c9))
% 40.67/6.41 | ((X2) != (sk_c9))
% 40.67/6.41 | ((identity) != (identity))
% 40.67/6.41 | ((inverse @ X1) != (sk_c9))
% 40.67/6.41 | ((X1) != (sk_c9))
% 40.67/6.41 | ((X0) != (identity))
% 40.67/6.41 | ((inverse @ X0) != (identity)))),
% 40.67/6.41 inference('demod', [status(thm)],
% 40.67/6.41 [zip_derived_cl3119, zip_derived_cl3953, zip_derived_cl15224,
% 40.67/6.41 zip_derived_cl14357, zip_derived_cl14357,
% 40.67/6.41 zip_derived_cl15206, zip_derived_cl14357, zip_derived_cl14357])).
% 40.67/6.41 thf(zip_derived_cl42833, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 40.67/6.41 (((inverse @ X0) != (identity))
% 40.67/6.41 | ((X0) != (identity))
% 40.67/6.41 | ((X1) != (sk_c9))
% 40.67/6.41 | ((inverse @ X1) != (sk_c9))
% 40.67/6.41 | ((X2) != (sk_c9))
% 40.67/6.41 | ((inverse @ X2) != (sk_c9))
% 40.67/6.41 | ((inverse @ X3) != (identity))
% 40.67/6.41 | ((X3) != (identity)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl42832])).
% 40.67/6.41 thf(zip_derived_cl42840, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 40.67/6.41 (((identity) != (identity))
% 40.67/6.41 | ((X0) != (identity))
% 40.67/6.41 | ((inverse @ X0) != (identity))
% 40.67/6.41 | ((inverse @ X1) != (sk_c9))
% 40.67/6.41 | ((X1) != (sk_c9))
% 40.67/6.41 | ((inverse @ X2) != (sk_c9))
% 40.67/6.41 | ((X2) != (sk_c9))
% 40.67/6.41 | ((identity) != (identity)))),
% 40.67/6.41 inference('sup-', [status(thm)],
% 40.67/6.41 [zip_derived_cl15206, zip_derived_cl42833])).
% 40.67/6.41 thf(zip_derived_cl42922, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 40.67/6.41 (((X2) != (sk_c9))
% 40.67/6.41 | ((inverse @ X2) != (sk_c9))
% 40.67/6.41 | ((X1) != (sk_c9))
% 40.67/6.41 | ((inverse @ X1) != (sk_c9))
% 40.67/6.41 | ((inverse @ X0) != (identity))
% 40.67/6.41 | ((X0) != (identity)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl42840])).
% 40.67/6.41 thf(zip_derived_cl43021, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i]:
% 40.67/6.41 (((sk_c9) != (sk_c9))
% 40.67/6.41 | ((sk_c4) = (sk_c9))
% 40.67/6.41 | ((X0) != (identity))
% 40.67/6.41 | ((inverse @ X0) != (identity))
% 40.67/6.41 | ((inverse @ X1) != (sk_c9))
% 40.67/6.41 | ((X1) != (sk_c9))
% 40.67/6.41 | ((sk_c9) != (sk_c9)))),
% 40.67/6.41 inference('sup-', [status(thm)],
% 40.67/6.41 [zip_derived_cl21208, zip_derived_cl42922])).
% 40.67/6.41 thf(zip_derived_cl43113, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i]:
% 40.67/6.41 (((X1) != (sk_c9))
% 40.67/6.41 | ((inverse @ X1) != (sk_c9))
% 40.67/6.41 | ((inverse @ X0) != (identity))
% 40.67/6.41 | ((X0) != (identity))
% 40.67/6.41 | ((sk_c4) = (sk_c9)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl43021])).
% 40.67/6.41 thf(zip_derived_cl47891, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((sk_c9) != (sk_c9))
% 40.67/6.41 | ((sk_c4) = (sk_c9))
% 40.67/6.41 | ((sk_c4) = (sk_c9))
% 40.67/6.41 | ((X0) != (identity))
% 40.67/6.41 | ((inverse @ X0) != (identity))
% 40.67/6.41 | ((sk_c9) != (sk_c9)))),
% 40.67/6.41 inference('sup-', [status(thm)],
% 40.67/6.41 [zip_derived_cl21208, zip_derived_cl43113])).
% 40.67/6.41 thf(zip_derived_cl47960, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((inverse @ X0) != (identity))
% 40.67/6.41 | ((X0) != (identity))
% 40.67/6.41 | ((sk_c4) = (sk_c9)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl47891])).
% 40.67/6.41 thf(zip_derived_cl48007, plain,
% 40.67/6.41 ((((identity) != (identity))
% 40.67/6.41 | ((sk_c4) = (sk_c9))
% 40.67/6.41 | ((identity) != (identity)))),
% 40.67/6.41 inference('sup-', [status(thm)],
% 40.67/6.41 [zip_derived_cl15206, zip_derived_cl47960])).
% 40.67/6.41 thf(zip_derived_cl48062, plain, (((sk_c4) = (sk_c9))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl48007])).
% 40.67/6.41 thf(zip_derived_cl48171, plain,
% 40.67/6.41 ((((inverse @ sk_c9) = (sk_c9)) | ((sk_c9) = (sk_c3)))),
% 40.67/6.41 inference('demod', [status(thm)],
% 40.67/6.41 [zip_derived_cl14453, zip_derived_cl48062])).
% 40.67/6.41 thf(zip_derived_cl15206, plain, (((inverse @ identity) = (identity))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl14357, zip_derived_cl1])).
% 40.67/6.41 thf(zip_derived_cl14357, plain,
% 40.67/6.41 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl534, zip_derived_cl529])).
% 40.67/6.41 thf(zip_derived_cl47, plain,
% 40.67/6.41 ((((multiply @ sk_c9 @ sk_c3) = (identity))
% 40.67/6.41 | ((inverse @ sk_c4) = (sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl28, zip_derived_cl1])).
% 40.67/6.41 thf(zip_derived_cl59, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i]:
% 40.67/6.41 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 40.67/6.41 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 40.67/6.41 thf(zip_derived_cl554, plain,
% 40.67/6.41 ((((sk_c3) = (multiply @ (inverse @ sk_c9) @ identity))
% 40.67/6.41 | ((inverse @ sk_c4) = (sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl47, zip_derived_cl59])).
% 40.67/6.41 thf(zip_derived_cl15227, plain,
% 40.67/6.41 ((((sk_c3) = (inverse @ sk_c9)) | ((inverse @ sk_c4) = (sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl14357, zip_derived_cl554])).
% 40.67/6.41 thf(zip_derived_cl15224, plain,
% 40.67/6.41 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 40.67/6.41 inference('sup+', [status(thm)], [zip_derived_cl14357, zip_derived_cl534])).
% 40.67/6.41 thf(zip_derived_cl17226, plain,
% 40.67/6.41 ((((sk_c4) = (inverse @ sk_c9)) | ((sk_c3) = (inverse @ sk_c9)))),
% 40.67/6.41 inference('sup+', [status(thm)],
% 40.67/6.41 [zip_derived_cl15227, zip_derived_cl15224])).
% 40.67/6.41 thf(zip_derived_cl18168, plain,
% 40.67/6.41 ((((sk_c3) != (sk_c4)) | ((sk_c4) = (inverse @ sk_c9)))),
% 40.67/6.41 inference('eq_fact', [status(thm)], [zip_derived_cl17226])).
% 40.67/6.41 thf(zip_derived_cl18168, plain,
% 40.67/6.41 ((((sk_c3) != (sk_c4)) | ((sk_c4) = (inverse @ sk_c9)))),
% 40.67/6.41 inference('eq_fact', [status(thm)], [zip_derived_cl17226])).
% 40.67/6.41 thf(zip_derived_cl42922, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 40.67/6.41 (((X2) != (sk_c9))
% 40.67/6.41 | ((inverse @ X2) != (sk_c9))
% 40.67/6.41 | ((X1) != (sk_c9))
% 40.67/6.41 | ((inverse @ X1) != (sk_c9))
% 40.67/6.41 | ((inverse @ X0) != (identity))
% 40.67/6.41 | ((X0) != (identity)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl42840])).
% 40.67/6.41 thf(zip_derived_cl43019, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i]:
% 40.67/6.41 (((sk_c4) != (sk_c9))
% 40.67/6.41 | ((sk_c3) != (sk_c4))
% 40.67/6.41 | ((X0) != (identity))
% 40.67/6.41 | ((inverse @ X0) != (identity))
% 40.67/6.41 | ((inverse @ X1) != (sk_c9))
% 40.67/6.41 | ((X1) != (sk_c9))
% 40.67/6.41 | ((sk_c9) != (sk_c9)))),
% 40.67/6.41 inference('sup-', [status(thm)],
% 40.67/6.41 [zip_derived_cl18168, zip_derived_cl42922])).
% 40.67/6.41 thf(zip_derived_cl43110, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i]:
% 40.67/6.41 (((X1) != (sk_c9))
% 40.67/6.41 | ((inverse @ X1) != (sk_c9))
% 40.67/6.41 | ((inverse @ X0) != (identity))
% 40.67/6.41 | ((X0) != (identity))
% 40.67/6.41 | ((sk_c3) != (sk_c4))
% 40.67/6.41 | ((sk_c4) != (sk_c9)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl43019])).
% 40.67/6.41 thf(zip_derived_cl43111, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i]:
% 40.67/6.41 (((X1) != (sk_c9))
% 40.67/6.41 | ((inverse @ X1) != (sk_c9))
% 40.67/6.41 | ((inverse @ X0) != (identity))
% 40.67/6.41 | ((X0) != (identity))
% 40.67/6.41 | ((sk_c3) != (sk_c9))
% 40.67/6.41 | ((sk_c4) != (sk_c9)))),
% 40.67/6.41 inference('local_rewriting', [status(thm)], [zip_derived_cl43110])).
% 40.67/6.41 thf(zip_derived_cl44656, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((sk_c4) != (sk_c9))
% 40.67/6.41 | ((sk_c3) != (sk_c4))
% 40.67/6.41 | ((sk_c4) != (sk_c9))
% 40.67/6.41 | ((sk_c3) != (sk_c9))
% 40.67/6.41 | ((X0) != (identity))
% 40.67/6.41 | ((inverse @ X0) != (identity))
% 40.67/6.41 | ((sk_c9) != (sk_c9)))),
% 40.67/6.41 inference('sup-', [status(thm)],
% 40.67/6.41 [zip_derived_cl18168, zip_derived_cl43111])).
% 40.67/6.41 thf(zip_derived_cl44764, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((inverse @ X0) != (identity))
% 40.67/6.41 | ((X0) != (identity))
% 40.67/6.41 | ((sk_c3) != (sk_c9))
% 40.67/6.41 | ((sk_c3) != (sk_c4))
% 40.67/6.41 | ((sk_c4) != (sk_c9)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl44656])).
% 40.67/6.41 thf(zip_derived_cl44765, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((inverse @ X0) != (identity))
% 40.67/6.41 | ((X0) != (identity))
% 40.67/6.41 | ((sk_c3) != (sk_c9))
% 40.67/6.41 | ((sk_c3) != (sk_c9))
% 40.67/6.41 | ((sk_c4) != (sk_c9)))),
% 40.67/6.41 inference('local_rewriting', [status(thm)], [zip_derived_cl44764])).
% 40.67/6.41 thf(zip_derived_cl44766, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((sk_c4) != (sk_c9))
% 40.67/6.41 | ((sk_c3) != (sk_c9))
% 40.67/6.41 | ((X0) != (identity))
% 40.67/6.41 | ((inverse @ X0) != (identity)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl44765])).
% 40.67/6.41 thf(zip_derived_cl44840, plain,
% 40.67/6.41 ((((identity) != (identity))
% 40.67/6.41 | ((identity) != (identity))
% 40.67/6.41 | ((sk_c3) != (sk_c9))
% 40.67/6.41 | ((sk_c4) != (sk_c9)))),
% 40.67/6.41 inference('sup-', [status(thm)],
% 40.67/6.41 [zip_derived_cl15206, zip_derived_cl44766])).
% 40.67/6.41 thf(zip_derived_cl44928, plain,
% 40.67/6.41 ((((sk_c4) != (sk_c9)) | ((sk_c3) != (sk_c9)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl44840])).
% 40.67/6.41 thf(zip_derived_cl48062, plain, (((sk_c4) = (sk_c9))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl48007])).
% 40.67/6.41 thf(zip_derived_cl48251, plain,
% 40.67/6.41 ((((sk_c9) != (sk_c9)) | ((sk_c3) != (sk_c9)))),
% 40.67/6.41 inference('demod', [status(thm)],
% 40.67/6.41 [zip_derived_cl44928, zip_derived_cl48062])).
% 40.67/6.41 thf(zip_derived_cl48252, plain, (((sk_c3) != (sk_c9))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl48251])).
% 40.67/6.41 thf(zip_derived_cl48350, plain, (((inverse @ sk_c9) = (sk_c9))),
% 40.67/6.41 inference('simplify_reflect-', [status(thm)],
% 40.67/6.41 [zip_derived_cl48171, zip_derived_cl48252])).
% 40.67/6.41 thf(zip_derived_cl48350, plain, (((inverse @ sk_c9) = (sk_c9))),
% 40.67/6.41 inference('simplify_reflect-', [status(thm)],
% 40.67/6.41 [zip_derived_cl48171, zip_derived_cl48252])).
% 40.67/6.41 thf(zip_derived_cl42922, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 40.67/6.41 (((X2) != (sk_c9))
% 40.67/6.41 | ((inverse @ X2) != (sk_c9))
% 40.67/6.41 | ((X1) != (sk_c9))
% 40.67/6.41 | ((inverse @ X1) != (sk_c9))
% 40.67/6.41 | ((inverse @ X0) != (identity))
% 40.67/6.41 | ((X0) != (identity)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl42840])).
% 40.67/6.41 thf(zip_derived_cl48356, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i]:
% 40.67/6.41 (((sk_c9) != (sk_c9))
% 40.67/6.41 | ((X0) != (identity))
% 40.67/6.41 | ((inverse @ X0) != (identity))
% 40.67/6.41 | ((inverse @ X1) != (sk_c9))
% 40.67/6.41 | ((X1) != (sk_c9))
% 40.67/6.41 | ((sk_c9) != (sk_c9)))),
% 40.67/6.41 inference('sup-', [status(thm)],
% 40.67/6.41 [zip_derived_cl48350, zip_derived_cl42922])).
% 40.67/6.41 thf(zip_derived_cl48357, plain,
% 40.67/6.41 (![X0 : $i, X1 : $i]:
% 40.67/6.41 (((X1) != (sk_c9))
% 40.67/6.41 | ((inverse @ X1) != (sk_c9))
% 40.67/6.41 | ((inverse @ X0) != (identity))
% 40.67/6.41 | ((X0) != (identity)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl48356])).
% 40.67/6.41 thf(zip_derived_cl48410, plain,
% 40.67/6.41 (![X0 : $i]:
% 40.67/6.41 (((sk_c9) != (sk_c9))
% 40.67/6.41 | ((X0) != (identity))
% 40.67/6.41 | ((inverse @ X0) != (identity))
% 40.67/6.41 | ((sk_c9) != (sk_c9)))),
% 40.67/6.41 inference('sup-', [status(thm)],
% 40.67/6.41 [zip_derived_cl48350, zip_derived_cl48357])).
% 40.67/6.41 thf(zip_derived_cl48413, plain,
% 40.67/6.41 (![X0 : $i]: (((inverse @ X0) != (identity)) | ((X0) != (identity)))),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl48410])).
% 40.67/6.41 thf(zip_derived_cl48414, plain,
% 40.67/6.41 ((((identity) != (identity)) | ((identity) != (identity)))),
% 40.67/6.41 inference('sup-', [status(thm)],
% 40.67/6.41 [zip_derived_cl15206, zip_derived_cl48413])).
% 40.67/6.41 thf(zip_derived_cl48418, plain, ($false),
% 40.67/6.41 inference('simplify', [status(thm)], [zip_derived_cl48414])).
% 40.67/6.41
% 40.67/6.41 % SZS output end Refutation
% 40.67/6.41
% 40.67/6.41
% 40.67/6.41 % Terminating...
% 41.12/6.52 % Runner terminated.
% 41.12/6.53 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------