TSTP Solution File: GRP383-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP383-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.g1AA8pXODR true
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:51:26 EDT 2023
% Result : Unsatisfiable 1.30s 1.14s
% Output : Refutation 1.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP383-1 : TPTP v8.1.2. Released v2.5.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.g1AA8pXODR true
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 22:53:58 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in FO mode
% 0.21/0.66 % Total configuration time : 435
% 0.21/0.66 % Estimated wc time : 1092
% 0.21/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.99/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.99/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 1.30/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 1.30/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 1.30/1.14 % Solved by fo/fo7.sh.
% 1.30/1.14 % done 820 iterations in 0.345s
% 1.30/1.14 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.30/1.14 % SZS output start Refutation
% 1.30/1.14 thf(sk_c2_type, type, sk_c2: $i).
% 1.30/1.14 thf(sk_c6_type, type, sk_c6: $i).
% 1.30/1.14 thf(sk_c1_type, type, sk_c1: $i).
% 1.30/1.14 thf(sk_c5_type, type, sk_c5: $i).
% 1.30/1.14 thf(identity_type, type, identity: $i).
% 1.30/1.14 thf(multiply_type, type, multiply: $i > $i > $i).
% 1.30/1.14 thf(sk_c7_type, type, sk_c7: $i).
% 1.30/1.14 thf(inverse_type, type, inverse: $i > $i).
% 1.30/1.14 thf(sk_c4_type, type, sk_c4: $i).
% 1.30/1.14 thf(sk_c3_type, type, sk_c3: $i).
% 1.30/1.14 thf(sk_c8_type, type, sk_c8: $i).
% 1.30/1.14 thf(prove_this_36, conjecture,
% 1.30/1.14 (~( ( ( multiply @ X2 @ sk_c6 ) != ( sk_c7 ) ) |
% 1.30/1.14 ( ( inverse @ X2 ) != ( sk_c7 ) ) |
% 1.30/1.14 ( ( multiply @ X1 @ sk_c7 ) != ( sk_c8 ) ) |
% 1.30/1.14 ( ( inverse @ X1 ) != ( sk_c8 ) ) |
% 1.30/1.14 ( ( multiply @ sk_c7 @ sk_c8 ) != ( sk_c6 ) ) |
% 1.30/1.14 ( ( multiply @ X5 @ sk_c8 ) != ( sk_c7 ) ) |
% 1.30/1.14 ( ( inverse @ X4 ) != ( X5 ) ) |
% 1.30/1.14 ( ( multiply @ X4 @ X5 ) != ( sk_c7 ) ) |
% 1.30/1.14 ( ( multiply @ X3 @ sk_c7 ) != ( sk_c8 ) ) |
% 1.30/1.14 ( ( inverse @ X3 ) != ( sk_c8 ) ) |
% 1.30/1.14 ( ( multiply @ sk_c7 @ sk_c6 ) != ( sk_c8 ) ) |
% 1.30/1.14 ( ( inverse @ sk_c8 ) != ( sk_c7 ) ) ))).
% 1.30/1.14 thf(zf_stmt_0, negated_conjecture,
% 1.30/1.14 (( ( multiply @ X2 @ sk_c6 ) != ( sk_c7 ) ) |
% 1.30/1.14 ( ( inverse @ X2 ) != ( sk_c7 ) ) |
% 1.30/1.14 ( ( multiply @ X1 @ sk_c7 ) != ( sk_c8 ) ) |
% 1.30/1.14 ( ( inverse @ X1 ) != ( sk_c8 ) ) |
% 1.30/1.14 ( ( multiply @ sk_c7 @ sk_c8 ) != ( sk_c6 ) ) |
% 1.30/1.14 ( ( multiply @ X5 @ sk_c8 ) != ( sk_c7 ) ) |
% 1.30/1.14 ( ( inverse @ X4 ) != ( X5 ) ) |
% 1.30/1.14 ( ( multiply @ X4 @ X5 ) != ( sk_c7 ) ) |
% 1.30/1.14 ( ( multiply @ X3 @ sk_c7 ) != ( sk_c8 ) ) |
% 1.30/1.14 ( ( inverse @ X3 ) != ( sk_c8 ) ) |
% 1.30/1.14 ( ( multiply @ sk_c7 @ sk_c6 ) != ( sk_c8 ) ) |
% 1.30/1.14 ( ( inverse @ sk_c8 ) != ( sk_c7 ) )),
% 1.30/1.14 inference('cnf.neg', [status(esa)], [prove_this_36])).
% 1.30/1.14 thf(zip_derived_cl38, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.30/1.14 (((multiply @ X0 @ sk_c6) != (sk_c7))
% 1.30/1.14 | ((inverse @ X0) != (sk_c7))
% 1.30/1.14 | ((multiply @ X1 @ sk_c7) != (sk_c8))
% 1.30/1.14 | ((inverse @ X1) != (sk_c8))
% 1.30/1.14 | ((multiply @ sk_c7 @ sk_c8) != (sk_c6))
% 1.30/1.14 | ((multiply @ X2 @ sk_c8) != (sk_c7))
% 1.30/1.14 | ((inverse @ X3) != (X2))
% 1.30/1.14 | ((multiply @ X3 @ X2) != (sk_c7))
% 1.30/1.14 | ((multiply @ X4 @ sk_c7) != (sk_c8))
% 1.30/1.14 | ((inverse @ X4) != (sk_c8))
% 1.30/1.14 | ((multiply @ sk_c7 @ sk_c6) != (sk_c8))
% 1.30/1.14 | ((inverse @ sk_c8) != (sk_c7)))),
% 1.30/1.14 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.30/1.14 thf(zip_derived_cl39, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.30/1.14 (((multiply @ X0 @ (multiply @ (inverse @ sk_c8) @ sk_c8))
% 1.30/1.14 != (inverse @ sk_c8))
% 1.30/1.14 | ((inverse @ X0) != (inverse @ sk_c8))
% 1.30/1.14 | ((multiply @ X1 @ (inverse @ sk_c8)) != (sk_c8))
% 1.30/1.14 | ((inverse @ X1) != (sk_c8))
% 1.30/1.14 | ((multiply @ (inverse @ sk_c8) @ sk_c8) != (sk_c6))
% 1.30/1.14 | ((multiply @ X2 @ sk_c8) != (inverse @ sk_c8))
% 1.30/1.14 | ((inverse @ X3) != (X2))
% 1.30/1.14 | ((multiply @ X3 @ X2) != (inverse @ sk_c8))
% 1.30/1.14 | ((multiply @ X4 @ (inverse @ sk_c8)) != (sk_c8))
% 1.30/1.14 | ((inverse @ X4) != (sk_c8))
% 1.30/1.14 | ((multiply @ (inverse @ sk_c8) @
% 1.30/1.14 (multiply @ (inverse @ sk_c8) @ sk_c8)) != (sk_c8))
% 1.30/1.14 | ((inverse @ sk_c8) != (sk_c7)))),
% 1.30/1.14 inference('local_rewriting', [status(thm)], [zip_derived_cl38])).
% 1.30/1.14 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 1.30/1.14 thf(zip_derived_cl1, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.30/1.14 inference('cnf', [status(esa)], [left_inverse])).
% 1.30/1.14 thf(zip_derived_cl1, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.30/1.14 inference('cnf', [status(esa)], [left_inverse])).
% 1.30/1.14 thf(zip_derived_cl1, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.30/1.14 inference('cnf', [status(esa)], [left_inverse])).
% 1.30/1.14 thf(zip_derived_cl40, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.30/1.14 (((multiply @ X0 @ identity) != (inverse @ sk_c8))
% 1.30/1.14 | ((inverse @ X0) != (inverse @ sk_c8))
% 1.30/1.14 | ((multiply @ X1 @ (inverse @ sk_c8)) != (sk_c8))
% 1.30/1.14 | ((inverse @ X1) != (sk_c8))
% 1.30/1.14 | ((identity) != (sk_c6))
% 1.30/1.14 | ((multiply @ X2 @ sk_c8) != (inverse @ sk_c8))
% 1.30/1.14 | ((inverse @ X3) != (X2))
% 1.30/1.14 | ((multiply @ X3 @ X2) != (inverse @ sk_c8))
% 1.30/1.14 | ((multiply @ X4 @ (inverse @ sk_c8)) != (sk_c8))
% 1.30/1.14 | ((inverse @ X4) != (sk_c8))
% 1.30/1.14 | ((multiply @ (inverse @ sk_c8) @ identity) != (sk_c8))
% 1.30/1.14 | ((inverse @ sk_c8) != (sk_c7)))),
% 1.30/1.14 inference('demod', [status(thm)],
% 1.30/1.14 [zip_derived_cl39, zip_derived_cl1, zip_derived_cl1,
% 1.30/1.14 zip_derived_cl1])).
% 1.30/1.14 thf(zip_derived_cl1, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.30/1.14 inference('cnf', [status(esa)], [left_inverse])).
% 1.30/1.14 thf(zip_derived_cl1, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.30/1.14 inference('cnf', [status(esa)], [left_inverse])).
% 1.30/1.14 thf(associativity, axiom,
% 1.30/1.14 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 1.30/1.14 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 1.30/1.14 thf(zip_derived_cl2, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.30/1.14 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.30/1.14 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.30/1.14 inference('cnf', [status(esa)], [associativity])).
% 1.30/1.14 thf(zip_derived_cl94, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i]:
% 1.30/1.14 ((multiply @ identity @ X0)
% 1.30/1.14 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 1.30/1.14 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 1.30/1.14 thf(zip_derived_cl0, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.30/1.14 inference('cnf', [status(esa)], [left_identity])).
% 1.30/1.14 thf(zip_derived_cl113, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i]:
% 1.30/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl94, zip_derived_cl0])).
% 1.30/1.14 thf(zip_derived_cl124, plain,
% 1.30/1.14 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl113])).
% 1.30/1.14 thf(zip_derived_cl113, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i]:
% 1.30/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl94, zip_derived_cl0])).
% 1.30/1.14 thf(zip_derived_cl113, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i]:
% 1.30/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl94, zip_derived_cl0])).
% 1.30/1.14 thf(zip_derived_cl121, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i]:
% 1.30/1.14 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl113, zip_derived_cl113])).
% 1.30/1.14 thf(zip_derived_cl427, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl124, zip_derived_cl121])).
% 1.30/1.14 thf(zip_derived_cl427, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl124, zip_derived_cl121])).
% 1.30/1.14 thf(zip_derived_cl442, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.30/1.14 (((X0) != (inverse @ sk_c8))
% 1.30/1.14 | ((inverse @ X0) != (inverse @ sk_c8))
% 1.30/1.14 | ((multiply @ X1 @ (inverse @ sk_c8)) != (sk_c8))
% 1.30/1.14 | ((inverse @ X1) != (sk_c8))
% 1.30/1.14 | ((identity) != (sk_c6))
% 1.30/1.14 | ((multiply @ X2 @ sk_c8) != (inverse @ sk_c8))
% 1.30/1.14 | ((inverse @ X3) != (X2))
% 1.30/1.14 | ((multiply @ X3 @ X2) != (inverse @ sk_c8))
% 1.30/1.14 | ((multiply @ X4 @ (inverse @ sk_c8)) != (sk_c8))
% 1.30/1.14 | ((inverse @ X4) != (sk_c8))
% 1.30/1.14 | ((inverse @ sk_c8) != (sk_c8))
% 1.30/1.14 | ((inverse @ sk_c8) != (sk_c7)))),
% 1.30/1.14 inference('demod', [status(thm)],
% 1.30/1.14 [zip_derived_cl40, zip_derived_cl427, zip_derived_cl427])).
% 1.30/1.14 thf(zip_derived_cl443, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.30/1.14 (((X0) != (sk_c8))
% 1.30/1.14 | ((inverse @ X0) != (sk_c8))
% 1.30/1.14 | ((multiply @ X1 @ sk_c8) != (sk_c8))
% 1.30/1.14 | ((inverse @ X1) != (sk_c8))
% 1.30/1.14 | ((identity) != (sk_c6))
% 1.30/1.14 | ((multiply @ X2 @ sk_c8) != (sk_c8))
% 1.30/1.14 | ((inverse @ X3) != (X2))
% 1.30/1.14 | ((multiply @ X3 @ X2) != (sk_c8))
% 1.30/1.14 | ((multiply @ X4 @ sk_c8) != (sk_c8))
% 1.30/1.14 | ((inverse @ X4) != (sk_c8))
% 1.30/1.14 | ((inverse @ sk_c8) != (sk_c8))
% 1.30/1.14 | ((sk_c8) != (sk_c7)))),
% 1.30/1.14 inference('local_rewriting', [status(thm)], [zip_derived_cl442])).
% 1.30/1.14 thf(prove_this_30, conjecture,
% 1.30/1.14 (~( ( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c7 ) ) |
% 1.30/1.14 ( ( inverse @ sk_c2 ) = ( sk_c3 ) ) ))).
% 1.30/1.14 thf(zf_stmt_1, negated_conjecture,
% 1.30/1.14 (( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c7 ) ) |
% 1.30/1.14 ( ( inverse @ sk_c2 ) = ( sk_c3 ) )),
% 1.30/1.14 inference('cnf.neg', [status(esa)], [prove_this_30])).
% 1.30/1.14 thf(zip_derived_cl32, plain,
% 1.30/1.14 ((((multiply @ sk_c5 @ sk_c6) = (sk_c7)) | ((inverse @ sk_c2) = (sk_c3)))),
% 1.30/1.14 inference('cnf', [status(esa)], [zf_stmt_1])).
% 1.30/1.14 thf(prove_this_25, conjecture,
% 1.30/1.14 (~( ( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c7 ) ) |
% 1.30/1.14 ( ( multiply @ sk_c2 @ sk_c3 ) = ( sk_c7 ) ) ))).
% 1.30/1.14 thf(zf_stmt_2, negated_conjecture,
% 1.30/1.14 (( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c7 ) ) |
% 1.30/1.14 ( ( multiply @ sk_c2 @ sk_c3 ) = ( sk_c7 ) )),
% 1.30/1.14 inference('cnf.neg', [status(esa)], [prove_this_25])).
% 1.30/1.14 thf(zip_derived_cl27, plain,
% 1.30/1.14 ((((multiply @ sk_c5 @ sk_c6) = (sk_c7))
% 1.30/1.14 | ((multiply @ sk_c2 @ sk_c3) = (sk_c7)))),
% 1.30/1.14 inference('cnf', [status(esa)], [zf_stmt_2])).
% 1.30/1.14 thf(zip_derived_cl335, plain,
% 1.30/1.14 ((((multiply @ sk_c2 @ (inverse @ sk_c2)) = (sk_c7))
% 1.30/1.14 | ((multiply @ sk_c5 @ sk_c6) = (sk_c7))
% 1.30/1.14 | ((multiply @ sk_c5 @ sk_c6) = (sk_c7)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl27])).
% 1.30/1.14 thf(zip_derived_cl339, plain,
% 1.30/1.14 ((((multiply @ sk_c5 @ sk_c6) = (sk_c7))
% 1.30/1.14 | ((multiply @ sk_c2 @ (inverse @ sk_c2)) = (sk_c7)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl335])).
% 1.30/1.14 thf(zip_derived_cl427, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl124, zip_derived_cl121])).
% 1.30/1.14 thf(zip_derived_cl124, plain,
% 1.30/1.14 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl113])).
% 1.30/1.14 thf(zip_derived_cl456, plain,
% 1.30/1.14 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl427, zip_derived_cl124])).
% 1.30/1.14 thf(zip_derived_cl1, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.30/1.14 inference('cnf', [status(esa)], [left_inverse])).
% 1.30/1.14 thf(zip_derived_cl461, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl456, zip_derived_cl1])).
% 1.30/1.14 thf(zip_derived_cl5226, plain,
% 1.30/1.14 ((((multiply @ sk_c5 @ sk_c6) = (sk_c7)) | ((identity) = (sk_c7)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl339, zip_derived_cl461])).
% 1.30/1.14 thf(prove_this_29, conjecture,
% 1.30/1.14 (~( ( ( inverse @ sk_c5 ) = ( sk_c7 ) ) |
% 1.30/1.14 ( ( inverse @ sk_c2 ) = ( sk_c3 ) ) ))).
% 1.30/1.14 thf(zf_stmt_3, negated_conjecture,
% 1.30/1.14 (( ( inverse @ sk_c5 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c3 ) )),
% 1.30/1.14 inference('cnf.neg', [status(esa)], [prove_this_29])).
% 1.30/1.14 thf(zip_derived_cl31, plain,
% 1.30/1.14 ((((inverse @ sk_c5) = (sk_c7)) | ((inverse @ sk_c2) = (sk_c3)))),
% 1.30/1.14 inference('cnf', [status(esa)], [zf_stmt_3])).
% 1.30/1.14 thf(prove_this_24, conjecture,
% 1.30/1.14 (~( ( ( inverse @ sk_c5 ) = ( sk_c7 ) ) |
% 1.30/1.14 ( ( multiply @ sk_c2 @ sk_c3 ) = ( sk_c7 ) ) ))).
% 1.30/1.14 thf(zf_stmt_4, negated_conjecture,
% 1.30/1.14 (( ( inverse @ sk_c5 ) = ( sk_c7 ) ) |
% 1.30/1.14 ( ( multiply @ sk_c2 @ sk_c3 ) = ( sk_c7 ) )),
% 1.30/1.14 inference('cnf.neg', [status(esa)], [prove_this_24])).
% 1.30/1.14 thf(zip_derived_cl26, plain,
% 1.30/1.14 ((((inverse @ sk_c5) = (sk_c7)) | ((multiply @ sk_c2 @ sk_c3) = (sk_c7)))),
% 1.30/1.14 inference('cnf', [status(esa)], [zf_stmt_4])).
% 1.30/1.14 thf(zip_derived_cl70, plain,
% 1.30/1.14 ((((multiply @ sk_c2 @ (inverse @ sk_c2)) = (sk_c7))
% 1.30/1.14 | ((inverse @ sk_c5) = (sk_c7))
% 1.30/1.14 | ((inverse @ sk_c5) = (sk_c7)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl31, zip_derived_cl26])).
% 1.30/1.14 thf(zip_derived_cl72, plain,
% 1.30/1.14 ((((inverse @ sk_c5) = (sk_c7))
% 1.30/1.14 | ((multiply @ sk_c2 @ (inverse @ sk_c2)) = (sk_c7)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl70])).
% 1.30/1.14 thf(zip_derived_cl461, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl456, zip_derived_cl1])).
% 1.30/1.14 thf(zip_derived_cl1630, plain,
% 1.30/1.14 ((((inverse @ sk_c5) = (sk_c7)) | ((identity) = (sk_c7)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl72, zip_derived_cl461])).
% 1.30/1.14 thf(zip_derived_cl113, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i]:
% 1.30/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl94, zip_derived_cl0])).
% 1.30/1.14 thf(zip_derived_cl1635, plain,
% 1.30/1.14 (![X0 : $i]:
% 1.30/1.14 (((X0) = (multiply @ sk_c7 @ (multiply @ sk_c5 @ X0)))
% 1.30/1.14 | ((identity) = (sk_c7)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl1630, zip_derived_cl113])).
% 1.30/1.14 thf(zip_derived_cl5230, plain,
% 1.30/1.14 ((((sk_c6) = (multiply @ sk_c7 @ sk_c7))
% 1.30/1.14 | ((identity) = (sk_c7))
% 1.30/1.14 | ((identity) = (sk_c7)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl5226, zip_derived_cl1635])).
% 1.30/1.14 thf(zip_derived_cl5258, plain,
% 1.30/1.14 ((((identity) = (sk_c7)) | ((sk_c6) = (multiply @ sk_c7 @ sk_c7)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl5230])).
% 1.30/1.14 thf(prove_this_26, conjecture,
% 1.30/1.14 (~( ( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c6 ) ) |
% 1.30/1.14 ( ( inverse @ sk_c2 ) = ( sk_c3 ) ) ))).
% 1.30/1.14 thf(zf_stmt_5, negated_conjecture,
% 1.30/1.14 (( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c6 ) ) |
% 1.30/1.14 ( ( inverse @ sk_c2 ) = ( sk_c3 ) )),
% 1.30/1.14 inference('cnf.neg', [status(esa)], [prove_this_26])).
% 1.30/1.14 thf(zip_derived_cl28, plain,
% 1.30/1.14 ((((multiply @ sk_c7 @ sk_c8) = (sk_c6)) | ((inverse @ sk_c2) = (sk_c3)))),
% 1.30/1.14 inference('cnf', [status(esa)], [zf_stmt_5])).
% 1.30/1.14 thf(prove_this_21, conjecture,
% 1.30/1.14 (~( ( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c6 ) ) |
% 1.30/1.14 ( ( multiply @ sk_c2 @ sk_c3 ) = ( sk_c7 ) ) ))).
% 1.30/1.14 thf(zf_stmt_6, negated_conjecture,
% 1.30/1.14 (( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c6 ) ) |
% 1.30/1.14 ( ( multiply @ sk_c2 @ sk_c3 ) = ( sk_c7 ) )),
% 1.30/1.14 inference('cnf.neg', [status(esa)], [prove_this_21])).
% 1.30/1.14 thf(zip_derived_cl23, plain,
% 1.30/1.14 ((((multiply @ sk_c7 @ sk_c8) = (sk_c6))
% 1.30/1.14 | ((multiply @ sk_c2 @ sk_c3) = (sk_c7)))),
% 1.30/1.14 inference('cnf', [status(esa)], [zf_stmt_6])).
% 1.30/1.14 thf(zip_derived_cl61, plain,
% 1.30/1.14 ((((multiply @ sk_c2 @ (inverse @ sk_c2)) = (sk_c7))
% 1.30/1.14 | ((multiply @ sk_c7 @ sk_c8) = (sk_c6))
% 1.30/1.14 | ((multiply @ sk_c7 @ sk_c8) = (sk_c6)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl28, zip_derived_cl23])).
% 1.30/1.14 thf(zip_derived_cl66, plain,
% 1.30/1.14 ((((multiply @ sk_c7 @ sk_c8) = (sk_c6))
% 1.30/1.14 | ((multiply @ sk_c2 @ (inverse @ sk_c2)) = (sk_c7)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl61])).
% 1.30/1.14 thf(zip_derived_cl461, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl456, zip_derived_cl1])).
% 1.30/1.14 thf(zip_derived_cl1776, plain,
% 1.30/1.14 ((((multiply @ sk_c7 @ sk_c8) = (sk_c6)) | ((identity) = (sk_c7)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl66, zip_derived_cl461])).
% 1.30/1.14 thf(zip_derived_cl5313, plain,
% 1.30/1.14 ((((multiply @ sk_c7 @ sk_c8) = (multiply @ sk_c7 @ sk_c7))
% 1.30/1.14 | ((identity) = (sk_c7))
% 1.30/1.14 | ((identity) = (sk_c7)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl5258, zip_derived_cl1776])).
% 1.30/1.14 thf(zip_derived_cl5328, plain,
% 1.30/1.14 ((((identity) = (sk_c7))
% 1.30/1.14 | ((multiply @ sk_c7 @ sk_c8) = (multiply @ sk_c7 @ sk_c7)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl5313])).
% 1.30/1.14 thf(zip_derived_cl113, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i]:
% 1.30/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl94, zip_derived_cl0])).
% 1.30/1.14 thf(zip_derived_cl5436, plain,
% 1.30/1.14 ((((sk_c7) = (multiply @ (inverse @ sk_c7) @ (multiply @ sk_c7 @ sk_c8)))
% 1.30/1.14 | ((identity) = (sk_c7)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl5328, zip_derived_cl113])).
% 1.30/1.14 thf(zip_derived_cl113, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i]:
% 1.30/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl94, zip_derived_cl0])).
% 1.30/1.14 thf(zip_derived_cl5482, plain,
% 1.30/1.14 ((((sk_c7) = (sk_c8)) | ((identity) = (sk_c7)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl5436, zip_derived_cl113])).
% 1.30/1.14 thf(prove_this_12, conjecture,
% 1.30/1.14 (~( ( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 1.30/1.14 ( ( inverse @ sk_c1 ) = ( sk_c8 ) ) ))).
% 1.30/1.14 thf(zf_stmt_7, negated_conjecture,
% 1.30/1.14 (( ( inverse @ sk_c4 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c8 ) )),
% 1.30/1.14 inference('cnf.neg', [status(esa)], [prove_this_12])).
% 1.30/1.14 thf(zip_derived_cl14, plain,
% 1.30/1.14 ((((inverse @ sk_c4) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c8)))),
% 1.30/1.14 inference('cnf', [status(esa)], [zf_stmt_7])).
% 1.30/1.14 thf(zip_derived_cl1, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.30/1.14 inference('cnf', [status(esa)], [left_inverse])).
% 1.30/1.14 thf(zip_derived_cl44, plain,
% 1.30/1.14 ((((multiply @ sk_c8 @ sk_c1) = (identity))
% 1.30/1.14 | ((inverse @ sk_c4) = (sk_c8)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl1])).
% 1.30/1.14 thf(zip_derived_cl113, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i]:
% 1.30/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl94, zip_derived_cl0])).
% 1.30/1.14 thf(zip_derived_cl128, plain,
% 1.30/1.14 ((((sk_c1) = (multiply @ (inverse @ sk_c8) @ identity))
% 1.30/1.14 | ((inverse @ sk_c4) = (sk_c8)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl44, zip_derived_cl113])).
% 1.30/1.14 thf(prove_this_17, conjecture,
% 1.30/1.14 (~( ( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 1.30/1.14 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) ) ))).
% 1.30/1.14 thf(zf_stmt_8, negated_conjecture,
% 1.30/1.14 (( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 1.30/1.14 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) )),
% 1.30/1.14 inference('cnf.neg', [status(esa)], [prove_this_17])).
% 1.30/1.14 thf(zip_derived_cl19, plain,
% 1.30/1.14 ((((inverse @ sk_c4) = (sk_c8)) | ((multiply @ sk_c1 @ sk_c7) = (sk_c8)))),
% 1.30/1.14 inference('cnf', [status(esa)], [zf_stmt_8])).
% 1.30/1.14 thf(zip_derived_cl244, plain,
% 1.30/1.14 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c7)
% 1.30/1.14 = (sk_c8))
% 1.30/1.14 | ((inverse @ sk_c4) = (sk_c8))
% 1.30/1.14 | ((inverse @ sk_c4) = (sk_c8)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl128, zip_derived_cl19])).
% 1.30/1.14 thf(zip_derived_cl2, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.30/1.14 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.30/1.14 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.30/1.14 inference('cnf', [status(esa)], [associativity])).
% 1.30/1.14 thf(zip_derived_cl0, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.30/1.14 inference('cnf', [status(esa)], [left_identity])).
% 1.30/1.14 thf(zip_derived_cl253, plain,
% 1.30/1.14 ((((multiply @ (inverse @ sk_c8) @ sk_c7) = (sk_c8))
% 1.30/1.14 | ((inverse @ sk_c4) = (sk_c8))
% 1.30/1.14 | ((inverse @ sk_c4) = (sk_c8)))),
% 1.30/1.14 inference('demod', [status(thm)],
% 1.30/1.14 [zip_derived_cl244, zip_derived_cl2, zip_derived_cl0])).
% 1.30/1.14 thf(zip_derived_cl254, plain,
% 1.30/1.14 ((((inverse @ sk_c4) = (sk_c8))
% 1.30/1.14 | ((multiply @ (inverse @ sk_c8) @ sk_c7) = (sk_c8)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl253])).
% 1.30/1.14 thf(zip_derived_cl456, plain,
% 1.30/1.14 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl427, zip_derived_cl124])).
% 1.30/1.14 thf(zip_derived_cl468, plain,
% 1.30/1.14 ((((sk_c4) = (inverse @ sk_c8))
% 1.30/1.14 | ((multiply @ (inverse @ sk_c8) @ sk_c7) = (sk_c8)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl254, zip_derived_cl456])).
% 1.30/1.14 thf(prove_this_13, conjecture,
% 1.30/1.14 (~( ( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 1.30/1.14 ( ( inverse @ sk_c1 ) = ( sk_c8 ) ) ))).
% 1.30/1.14 thf(zf_stmt_9, negated_conjecture,
% 1.30/1.14 (( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 1.30/1.14 ( ( inverse @ sk_c1 ) = ( sk_c8 ) )),
% 1.30/1.14 inference('cnf.neg', [status(esa)], [prove_this_13])).
% 1.30/1.14 thf(zip_derived_cl15, plain,
% 1.30/1.14 ((((multiply @ sk_c4 @ sk_c7) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c8)))),
% 1.30/1.14 inference('cnf', [status(esa)], [zf_stmt_9])).
% 1.30/1.14 thf(zip_derived_cl1, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.30/1.14 inference('cnf', [status(esa)], [left_inverse])).
% 1.30/1.14 thf(zip_derived_cl50, plain,
% 1.30/1.14 ((((multiply @ sk_c8 @ sk_c1) = (identity))
% 1.30/1.14 | ((multiply @ sk_c4 @ sk_c7) = (sk_c8)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl15, zip_derived_cl1])).
% 1.30/1.14 thf(prove_this_27, conjecture,
% 1.30/1.14 (~( ( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 1.30/1.14 ( ( inverse @ sk_c2 ) = ( sk_c3 ) ) ))).
% 1.30/1.14 thf(zf_stmt_10, negated_conjecture,
% 1.30/1.14 (( ( inverse @ sk_c4 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c3 ) )),
% 1.30/1.14 inference('cnf.neg', [status(esa)], [prove_this_27])).
% 1.30/1.14 thf(zip_derived_cl29, plain,
% 1.30/1.14 ((((inverse @ sk_c4) = (sk_c8)) | ((inverse @ sk_c2) = (sk_c3)))),
% 1.30/1.14 inference('cnf', [status(esa)], [zf_stmt_10])).
% 1.30/1.14 thf(prove_this_22, conjecture,
% 1.30/1.14 (~( ( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 1.30/1.14 ( ( multiply @ sk_c2 @ sk_c3 ) = ( sk_c7 ) ) ))).
% 1.30/1.14 thf(zf_stmt_11, negated_conjecture,
% 1.30/1.14 (( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 1.30/1.14 ( ( multiply @ sk_c2 @ sk_c3 ) = ( sk_c7 ) )),
% 1.30/1.14 inference('cnf.neg', [status(esa)], [prove_this_22])).
% 1.30/1.14 thf(zip_derived_cl24, plain,
% 1.30/1.14 ((((inverse @ sk_c4) = (sk_c8)) | ((multiply @ sk_c2 @ sk_c3) = (sk_c7)))),
% 1.30/1.14 inference('cnf', [status(esa)], [zf_stmt_11])).
% 1.30/1.14 thf(zip_derived_cl53, plain,
% 1.30/1.14 ((((multiply @ sk_c2 @ (inverse @ sk_c2)) = (sk_c7))
% 1.30/1.14 | ((inverse @ sk_c4) = (sk_c8))
% 1.30/1.14 | ((inverse @ sk_c4) = (sk_c8)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl29, zip_derived_cl24])).
% 1.30/1.14 thf(zip_derived_cl57, plain,
% 1.30/1.14 ((((inverse @ sk_c4) = (sk_c8))
% 1.30/1.14 | ((multiply @ sk_c2 @ (inverse @ sk_c2)) = (sk_c7)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl53])).
% 1.30/1.14 thf(zip_derived_cl461, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl456, zip_derived_cl1])).
% 1.30/1.14 thf(zip_derived_cl1091, plain,
% 1.30/1.14 ((((inverse @ sk_c4) = (sk_c8)) | ((identity) = (sk_c7)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl57, zip_derived_cl461])).
% 1.30/1.14 thf(zip_derived_cl456, plain,
% 1.30/1.14 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl427, zip_derived_cl124])).
% 1.30/1.14 thf(zip_derived_cl113, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i]:
% 1.30/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl94, zip_derived_cl0])).
% 1.30/1.14 thf(zip_derived_cl463, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i]:
% 1.30/1.14 ((X1) = (multiply @ X0 @ (multiply @ (inverse @ X0) @ X1)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl456, zip_derived_cl113])).
% 1.30/1.14 thf(zip_derived_cl1095, plain,
% 1.30/1.14 (![X0 : $i]:
% 1.30/1.14 (((X0) = (multiply @ sk_c4 @ (multiply @ sk_c8 @ X0)))
% 1.30/1.14 | ((identity) = (sk_c7)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl1091, zip_derived_cl463])).
% 1.30/1.14 thf(zip_derived_cl1193, plain,
% 1.30/1.14 ((((sk_c1) = (multiply @ sk_c4 @ identity))
% 1.30/1.14 | ((multiply @ sk_c4 @ sk_c7) = (sk_c8))
% 1.30/1.14 | ((identity) = (sk_c7)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl1095])).
% 1.30/1.14 thf(zip_derived_cl427, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl124, zip_derived_cl121])).
% 1.30/1.14 thf(zip_derived_cl1203, plain,
% 1.30/1.14 ((((sk_c1) = (sk_c4))
% 1.30/1.14 | ((multiply @ sk_c4 @ sk_c7) = (sk_c8))
% 1.30/1.14 | ((identity) = (sk_c7)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl1193, zip_derived_cl427])).
% 1.30/1.14 thf(prove_this_18, conjecture,
% 1.30/1.14 (~( ( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 1.30/1.14 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) ) ))).
% 1.30/1.14 thf(zf_stmt_12, negated_conjecture,
% 1.30/1.14 (( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 1.30/1.14 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) )),
% 1.30/1.14 inference('cnf.neg', [status(esa)], [prove_this_18])).
% 1.30/1.14 thf(zip_derived_cl20, plain,
% 1.30/1.14 ((((multiply @ sk_c4 @ sk_c7) = (sk_c8))
% 1.30/1.14 | ((multiply @ sk_c1 @ sk_c7) = (sk_c8)))),
% 1.30/1.14 inference('cnf', [status(esa)], [zf_stmt_12])).
% 1.30/1.14 thf(zip_derived_cl1285, plain,
% 1.30/1.14 ((((multiply @ sk_c4 @ sk_c7) = (sk_c8))
% 1.30/1.14 | ((identity) = (sk_c7))
% 1.30/1.14 | ((multiply @ sk_c4 @ sk_c7) = (sk_c8))
% 1.30/1.14 | ((multiply @ sk_c4 @ sk_c7) = (sk_c8)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl1203, zip_derived_cl20])).
% 1.30/1.14 thf(zip_derived_cl1308, plain,
% 1.30/1.14 ((((identity) = (sk_c7)) | ((multiply @ sk_c4 @ sk_c7) = (sk_c8)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl1285])).
% 1.30/1.14 thf(zip_derived_cl1334, plain,
% 1.30/1.14 ((((multiply @ (inverse @ sk_c8) @ sk_c7) = (sk_c8))
% 1.30/1.14 | ((multiply @ (inverse @ sk_c8) @ sk_c7) = (sk_c8))
% 1.30/1.14 | ((identity) = (sk_c7)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl468, zip_derived_cl1308])).
% 1.30/1.14 thf(zip_derived_cl1336, plain,
% 1.30/1.14 ((((identity) = (sk_c7))
% 1.30/1.14 | ((multiply @ (inverse @ sk_c8) @ sk_c7) = (sk_c8)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl1334])).
% 1.30/1.14 thf(zip_derived_cl5515, plain,
% 1.30/1.14 ((((multiply @ (inverse @ sk_c8) @ sk_c8) = (sk_c8))
% 1.30/1.14 | ((identity) = (sk_c7))
% 1.30/1.14 | ((identity) = (sk_c7)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl5482, zip_derived_cl1336])).
% 1.30/1.14 thf(zip_derived_cl1, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.30/1.14 inference('cnf', [status(esa)], [left_inverse])).
% 1.30/1.14 thf(zip_derived_cl5564, plain,
% 1.30/1.14 ((((identity) = (sk_c8))
% 1.30/1.14 | ((identity) = (sk_c7))
% 1.30/1.14 | ((identity) = (sk_c7)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl5515, zip_derived_cl1])).
% 1.30/1.14 thf(zip_derived_cl5565, plain,
% 1.30/1.14 ((((identity) = (sk_c7)) | ((identity) = (sk_c8)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl5564])).
% 1.30/1.14 thf(zip_derived_cl5482, plain,
% 1.30/1.14 ((((sk_c7) = (sk_c8)) | ((identity) = (sk_c7)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl5436, zip_derived_cl113])).
% 1.30/1.14 thf(zip_derived_cl5557, plain,
% 1.30/1.14 ((((sk_c8) != (identity)) | ((identity) = (sk_c7)))),
% 1.30/1.14 inference('eq_fact', [status(thm)], [zip_derived_cl5482])).
% 1.30/1.14 thf(zip_derived_cl5601, plain, (((identity) = (sk_c7))),
% 1.30/1.14 inference('clc', [status(thm)], [zip_derived_cl5565, zip_derived_cl5557])).
% 1.30/1.14 thf(zip_derived_cl5677, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.30/1.14 (((X0) != (sk_c8))
% 1.30/1.14 | ((inverse @ X0) != (sk_c8))
% 1.30/1.14 | ((multiply @ X1 @ sk_c8) != (sk_c8))
% 1.30/1.14 | ((inverse @ X1) != (sk_c8))
% 1.30/1.14 | ((identity) != (sk_c6))
% 1.30/1.14 | ((multiply @ X2 @ sk_c8) != (sk_c8))
% 1.30/1.14 | ((inverse @ X3) != (X2))
% 1.30/1.14 | ((multiply @ X3 @ X2) != (sk_c8))
% 1.30/1.14 | ((multiply @ X4 @ sk_c8) != (sk_c8))
% 1.30/1.14 | ((inverse @ X4) != (sk_c8))
% 1.30/1.14 | ((inverse @ sk_c8) != (sk_c8))
% 1.30/1.14 | ((sk_c8) != (identity)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl443, zip_derived_cl5601])).
% 1.30/1.14 thf(zip_derived_cl5678, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.30/1.14 (((X0) != (identity))
% 1.30/1.14 | ((inverse @ X0) != (identity))
% 1.30/1.14 | ((multiply @ X1 @ identity) != (identity))
% 1.30/1.14 | ((inverse @ X1) != (identity))
% 1.30/1.14 | ((identity) != (sk_c6))
% 1.30/1.14 | ((multiply @ X2 @ identity) != (identity))
% 1.30/1.14 | ((inverse @ X3) != (X2))
% 1.30/1.14 | ((multiply @ X3 @ X2) != (identity))
% 1.30/1.14 | ((multiply @ X4 @ identity) != (identity))
% 1.30/1.14 | ((inverse @ X4) != (identity))
% 1.30/1.14 | ((inverse @ identity) != (identity))
% 1.30/1.14 | ((sk_c8) != (identity)))),
% 1.30/1.14 inference('local_rewriting', [status(thm)], [zip_derived_cl5677])).
% 1.30/1.14 thf(zip_derived_cl427, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl124, zip_derived_cl121])).
% 1.30/1.14 thf(zip_derived_cl427, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl124, zip_derived_cl121])).
% 1.30/1.14 thf(zip_derived_cl427, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl124, zip_derived_cl121])).
% 1.30/1.14 thf(zip_derived_cl0, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.30/1.14 inference('cnf', [status(esa)], [left_identity])).
% 1.30/1.14 thf(zip_derived_cl113, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i]:
% 1.30/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl94, zip_derived_cl0])).
% 1.30/1.14 thf(zip_derived_cl123, plain,
% 1.30/1.14 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl113])).
% 1.30/1.14 thf(zip_derived_cl113, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i]:
% 1.30/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl94, zip_derived_cl0])).
% 1.30/1.14 thf(zip_derived_cl154, plain,
% 1.30/1.14 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ identity)) @ X0))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl123, zip_derived_cl113])).
% 1.30/1.14 thf(zip_derived_cl1, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.30/1.14 inference('cnf', [status(esa)], [left_inverse])).
% 1.30/1.14 thf(zip_derived_cl309, plain, (((inverse @ identity) = (identity))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl154, zip_derived_cl1])).
% 1.30/1.14 thf(zip_derived_cl5679, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.30/1.14 (((X0) != (identity))
% 1.30/1.14 | ((inverse @ X0) != (identity))
% 1.30/1.14 | ((X1) != (identity))
% 1.30/1.14 | ((inverse @ X1) != (identity))
% 1.30/1.14 | ((identity) != (sk_c6))
% 1.30/1.14 | ((X2) != (identity))
% 1.30/1.14 | ((inverse @ X3) != (X2))
% 1.30/1.14 | ((multiply @ X3 @ X2) != (identity))
% 1.30/1.14 | ((X4) != (identity))
% 1.30/1.14 | ((inverse @ X4) != (identity))
% 1.30/1.14 | ((identity) != (identity))
% 1.30/1.14 | ((sk_c8) != (identity)))),
% 1.30/1.14 inference('demod', [status(thm)],
% 1.30/1.14 [zip_derived_cl5678, zip_derived_cl427, zip_derived_cl427,
% 1.30/1.14 zip_derived_cl427, zip_derived_cl309])).
% 1.30/1.14 thf(zip_derived_cl5680, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.30/1.14 (((sk_c8) != (identity))
% 1.30/1.14 | ((inverse @ X4) != (identity))
% 1.30/1.14 | ((X4) != (identity))
% 1.30/1.14 | ((multiply @ X3 @ X2) != (identity))
% 1.30/1.14 | ((inverse @ X3) != (X2))
% 1.30/1.14 | ((X2) != (identity))
% 1.30/1.14 | ((identity) != (sk_c6))
% 1.30/1.14 | ((inverse @ X1) != (identity))
% 1.30/1.14 | ((X1) != (identity))
% 1.30/1.14 | ((inverse @ X0) != (identity))
% 1.30/1.14 | ((X0) != (identity)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl5679])).
% 1.30/1.14 thf(prove_this_6, conjecture,
% 1.30/1.14 (~( ( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c6 ) ) |
% 1.30/1.14 ( ( multiply @ sk_c7 @ sk_c6 ) = ( sk_c8 ) ) ))).
% 1.30/1.14 thf(zf_stmt_13, negated_conjecture,
% 1.30/1.14 (( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c6 ) ) |
% 1.30/1.14 ( ( multiply @ sk_c7 @ sk_c6 ) = ( sk_c8 ) )),
% 1.30/1.14 inference('cnf.neg', [status(esa)], [prove_this_6])).
% 1.30/1.14 thf(zip_derived_cl8, plain,
% 1.30/1.14 ((((multiply @ sk_c7 @ sk_c8) = (sk_c6))
% 1.30/1.14 | ((multiply @ sk_c7 @ sk_c6) = (sk_c8)))),
% 1.30/1.14 inference('cnf', [status(esa)], [zf_stmt_13])).
% 1.30/1.14 thf(zip_derived_cl5601, plain, (((identity) = (sk_c7))),
% 1.30/1.14 inference('clc', [status(thm)], [zip_derived_cl5565, zip_derived_cl5557])).
% 1.30/1.14 thf(zip_derived_cl0, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.30/1.14 inference('cnf', [status(esa)], [left_identity])).
% 1.30/1.14 thf(zip_derived_cl5601, plain, (((identity) = (sk_c7))),
% 1.30/1.14 inference('clc', [status(thm)], [zip_derived_cl5565, zip_derived_cl5557])).
% 1.30/1.14 thf(zip_derived_cl0, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.30/1.14 inference('cnf', [status(esa)], [left_identity])).
% 1.30/1.14 thf(zip_derived_cl5607, plain, ((((sk_c8) = (sk_c6)) | ((sk_c6) = (sk_c8)))),
% 1.30/1.14 inference('demod', [status(thm)],
% 1.30/1.14 [zip_derived_cl8, zip_derived_cl5601, zip_derived_cl0,
% 1.30/1.14 zip_derived_cl5601, zip_derived_cl0])).
% 1.30/1.14 thf(zip_derived_cl5608, plain, (((sk_c8) = (sk_c6))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl5607])).
% 1.30/1.14 thf(zip_derived_cl5772, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.30/1.14 (((sk_c8) != (identity))
% 1.30/1.14 | ((inverse @ X4) != (identity))
% 1.30/1.14 | ((X4) != (identity))
% 1.30/1.14 | ((multiply @ X3 @ X2) != (identity))
% 1.30/1.14 | ((inverse @ X3) != (X2))
% 1.30/1.14 | ((X2) != (identity))
% 1.30/1.14 | ((identity) != (sk_c8))
% 1.30/1.14 | ((inverse @ X1) != (identity))
% 1.30/1.14 | ((X1) != (identity))
% 1.30/1.14 | ((inverse @ X0) != (identity))
% 1.30/1.14 | ((X0) != (identity)))),
% 1.30/1.14 inference('demod', [status(thm)],
% 1.30/1.14 [zip_derived_cl5680, zip_derived_cl5608])).
% 1.30/1.14 thf(zip_derived_cl5773, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.30/1.14 (((X0) != (identity))
% 1.30/1.14 | ((inverse @ X0) != (identity))
% 1.30/1.14 | ((X1) != (identity))
% 1.30/1.14 | ((inverse @ X1) != (identity))
% 1.30/1.14 | ((X2) != (identity))
% 1.30/1.14 | ((inverse @ X3) != (X2))
% 1.30/1.14 | ((multiply @ X3 @ X2) != (identity))
% 1.30/1.14 | ((X4) != (identity))
% 1.30/1.14 | ((inverse @ X4) != (identity))
% 1.30/1.14 | ((sk_c8) != (identity)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl5772])).
% 1.30/1.14 thf(prove_this_4, conjecture,
% 1.30/1.14 (~( ( ( inverse @ sk_c5 ) = ( sk_c7 ) ) |
% 1.30/1.14 ( ( inverse @ sk_c8 ) = ( sk_c7 ) ) ))).
% 1.30/1.14 thf(zf_stmt_14, negated_conjecture,
% 1.30/1.14 (( ( inverse @ sk_c5 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c8 ) = ( sk_c7 ) )),
% 1.30/1.14 inference('cnf.neg', [status(esa)], [prove_this_4])).
% 1.30/1.14 thf(zip_derived_cl6, plain,
% 1.30/1.14 ((((inverse @ sk_c5) = (sk_c7)) | ((inverse @ sk_c8) = (sk_c7)))),
% 1.30/1.14 inference('cnf', [status(esa)], [zf_stmt_14])).
% 1.30/1.14 thf(prove_this_5, conjecture,
% 1.30/1.14 (~( ( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c7 ) ) |
% 1.30/1.14 ( ( inverse @ sk_c8 ) = ( sk_c7 ) ) ))).
% 1.30/1.14 thf(zf_stmt_15, negated_conjecture,
% 1.30/1.14 (( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c7 ) ) |
% 1.30/1.14 ( ( inverse @ sk_c8 ) = ( sk_c7 ) )),
% 1.30/1.14 inference('cnf.neg', [status(esa)], [prove_this_5])).
% 1.30/1.14 thf(zip_derived_cl7, plain,
% 1.30/1.14 ((((multiply @ sk_c5 @ sk_c6) = (sk_c7)) | ((inverse @ sk_c8) = (sk_c7)))),
% 1.30/1.14 inference('cnf', [status(esa)], [zf_stmt_15])).
% 1.30/1.14 thf(zip_derived_cl113, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i]:
% 1.30/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl94, zip_derived_cl0])).
% 1.30/1.14 thf(zip_derived_cl133, plain,
% 1.30/1.14 ((((sk_c6) = (multiply @ (inverse @ sk_c5) @ sk_c7))
% 1.30/1.14 | ((inverse @ sk_c8) = (sk_c7)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl113])).
% 1.30/1.14 thf(zip_derived_cl381, plain,
% 1.30/1.14 ((((sk_c6) = (multiply @ sk_c7 @ sk_c7))
% 1.30/1.14 | ((inverse @ sk_c8) = (sk_c7))
% 1.30/1.14 | ((inverse @ sk_c8) = (sk_c7)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl133])).
% 1.30/1.14 thf(zip_derived_cl384, plain,
% 1.30/1.14 ((((inverse @ sk_c8) = (sk_c7)) | ((sk_c6) = (multiply @ sk_c7 @ sk_c7)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl381])).
% 1.30/1.14 thf(prove_this_1, conjecture,
% 1.30/1.14 (~( ( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c6 ) ) |
% 1.30/1.14 ( ( inverse @ sk_c8 ) = ( sk_c7 ) ) ))).
% 1.30/1.14 thf(zf_stmt_16, negated_conjecture,
% 1.30/1.14 (( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c6 ) ) |
% 1.30/1.14 ( ( inverse @ sk_c8 ) = ( sk_c7 ) )),
% 1.30/1.14 inference('cnf.neg', [status(esa)], [prove_this_1])).
% 1.30/1.14 thf(zip_derived_cl3, plain,
% 1.30/1.14 ((((multiply @ sk_c7 @ sk_c8) = (sk_c6)) | ((inverse @ sk_c8) = (sk_c7)))),
% 1.30/1.14 inference('cnf', [status(esa)], [zf_stmt_16])).
% 1.30/1.14 thf(zip_derived_cl386, plain,
% 1.30/1.14 ((((multiply @ sk_c7 @ sk_c8) = (multiply @ sk_c7 @ sk_c7))
% 1.30/1.14 | ((inverse @ sk_c8) = (sk_c7))
% 1.30/1.14 | ((inverse @ sk_c8) = (sk_c7)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl384, zip_derived_cl3])).
% 1.30/1.14 thf(zip_derived_cl392, plain,
% 1.30/1.14 ((((inverse @ sk_c8) = (sk_c7))
% 1.30/1.14 | ((multiply @ sk_c7 @ sk_c8) = (multiply @ sk_c7 @ sk_c7)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl386])).
% 1.30/1.14 thf(zip_derived_cl113, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i]:
% 1.30/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl94, zip_derived_cl0])).
% 1.30/1.14 thf(zip_derived_cl693, plain,
% 1.30/1.14 ((((sk_c7) = (multiply @ (inverse @ sk_c7) @ (multiply @ sk_c7 @ sk_c8)))
% 1.30/1.14 | ((inverse @ sk_c8) = (sk_c7)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl392, zip_derived_cl113])).
% 1.30/1.14 thf(zip_derived_cl113, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i]:
% 1.30/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl94, zip_derived_cl0])).
% 1.30/1.14 thf(zip_derived_cl695, plain,
% 1.30/1.14 ((((sk_c7) = (sk_c8)) | ((inverse @ sk_c8) = (sk_c7)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl693, zip_derived_cl113])).
% 1.30/1.14 thf(zip_derived_cl695, plain,
% 1.30/1.14 ((((sk_c7) = (sk_c8)) | ((inverse @ sk_c8) = (sk_c7)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl693, zip_derived_cl113])).
% 1.30/1.14 thf(prove_this_9, conjecture,
% 1.30/1.14 (~( ( ( inverse @ sk_c5 ) = ( sk_c7 ) ) |
% 1.30/1.14 ( ( multiply @ sk_c7 @ sk_c6 ) = ( sk_c8 ) ) ))).
% 1.30/1.14 thf(zf_stmt_17, negated_conjecture,
% 1.30/1.14 (( ( inverse @ sk_c5 ) = ( sk_c7 ) ) |
% 1.30/1.14 ( ( multiply @ sk_c7 @ sk_c6 ) = ( sk_c8 ) )),
% 1.30/1.14 inference('cnf.neg', [status(esa)], [prove_this_9])).
% 1.30/1.14 thf(zip_derived_cl11, plain,
% 1.30/1.14 ((((inverse @ sk_c5) = (sk_c7)) | ((multiply @ sk_c7 @ sk_c6) = (sk_c8)))),
% 1.30/1.14 inference('cnf', [status(esa)], [zf_stmt_17])).
% 1.30/1.14 thf(prove_this_10, conjecture,
% 1.30/1.14 (~( ( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c7 ) ) |
% 1.30/1.14 ( ( multiply @ sk_c7 @ sk_c6 ) = ( sk_c8 ) ) ))).
% 1.30/1.14 thf(zf_stmt_18, negated_conjecture,
% 1.30/1.14 (( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c7 ) ) |
% 1.30/1.14 ( ( multiply @ sk_c7 @ sk_c6 ) = ( sk_c8 ) )),
% 1.30/1.14 inference('cnf.neg', [status(esa)], [prove_this_10])).
% 1.30/1.14 thf(zip_derived_cl12, plain,
% 1.30/1.14 ((((multiply @ sk_c5 @ sk_c6) = (sk_c7))
% 1.30/1.14 | ((multiply @ sk_c7 @ sk_c6) = (sk_c8)))),
% 1.30/1.14 inference('cnf', [status(esa)], [zf_stmt_18])).
% 1.30/1.14 thf(zip_derived_cl113, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i]:
% 1.30/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl94, zip_derived_cl0])).
% 1.30/1.14 thf(zip_derived_cl159, plain,
% 1.30/1.14 ((((sk_c6) = (multiply @ (inverse @ sk_c5) @ sk_c7))
% 1.30/1.14 | ((multiply @ sk_c7 @ sk_c6) = (sk_c8)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl113])).
% 1.30/1.14 thf(zip_derived_cl4759, plain,
% 1.30/1.14 ((((sk_c6) = (multiply @ sk_c7 @ sk_c7))
% 1.30/1.14 | ((multiply @ sk_c7 @ sk_c6) = (sk_c8))
% 1.30/1.14 | ((multiply @ sk_c7 @ sk_c6) = (sk_c8)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl159])).
% 1.30/1.14 thf(zip_derived_cl4772, plain,
% 1.30/1.14 ((((multiply @ sk_c7 @ sk_c6) = (sk_c8))
% 1.30/1.14 | ((sk_c6) = (multiply @ sk_c7 @ sk_c7)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl4759])).
% 1.30/1.14 thf(zip_derived_cl113, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i]:
% 1.30/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl94, zip_derived_cl0])).
% 1.30/1.14 thf(zip_derived_cl4867, plain,
% 1.30/1.14 ((((sk_c6) = (multiply @ (inverse @ sk_c7) @ sk_c8))
% 1.30/1.14 | ((sk_c6) = (multiply @ sk_c7 @ sk_c7)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl4772, zip_derived_cl113])).
% 1.30/1.14 thf(zip_derived_cl4915, plain,
% 1.30/1.14 ((((multiply @ (inverse @ sk_c7) @ sk_c8) != (multiply @ sk_c7 @ sk_c7))
% 1.30/1.14 | ((sk_c6) = (multiply @ sk_c7 @ sk_c7)))),
% 1.30/1.14 inference('eq_fact', [status(thm)], [zip_derived_cl4867])).
% 1.30/1.14 thf(zip_derived_cl4924, plain,
% 1.30/1.14 ((((multiply @ (inverse @ (inverse @ sk_c8)) @ sk_c8)
% 1.30/1.14 != (multiply @ sk_c7 @ sk_c7))
% 1.30/1.14 | ((sk_c7) = (sk_c8))
% 1.30/1.14 | ((sk_c6) = (multiply @ sk_c7 @ sk_c7)))),
% 1.30/1.14 inference('sup-', [status(thm)], [zip_derived_cl695, zip_derived_cl4915])).
% 1.30/1.14 thf(zip_derived_cl456, plain,
% 1.30/1.14 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl427, zip_derived_cl124])).
% 1.30/1.14 thf(zip_derived_cl4937, plain,
% 1.30/1.14 ((((multiply @ sk_c8 @ sk_c8) != (multiply @ sk_c7 @ sk_c7))
% 1.30/1.14 | ((sk_c7) = (sk_c8))
% 1.30/1.14 | ((sk_c6) = (multiply @ sk_c7 @ sk_c7)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl4924, zip_derived_cl456])).
% 1.30/1.14 thf(zip_derived_cl4938, plain,
% 1.30/1.14 ((((multiply @ sk_c8 @ sk_c8) != (multiply @ sk_c7 @ sk_c7))
% 1.30/1.14 | ((sk_c7) = (sk_c8))
% 1.30/1.14 | ((sk_c6) = (multiply @ sk_c8 @ sk_c8)))),
% 1.30/1.14 inference('local_rewriting', [status(thm)], [zip_derived_cl4937])).
% 1.30/1.14 thf(zip_derived_cl4958, plain,
% 1.30/1.14 ((((multiply @ sk_c8 @ sk_c8) != (multiply @ sk_c7 @ (inverse @ sk_c8)))
% 1.30/1.14 | ((sk_c7) = (sk_c8))
% 1.30/1.14 | ((sk_c6) = (multiply @ sk_c8 @ sk_c8))
% 1.30/1.14 | ((sk_c7) = (sk_c8)))),
% 1.30/1.14 inference('sup-', [status(thm)], [zip_derived_cl695, zip_derived_cl4938])).
% 1.30/1.14 thf(zip_derived_cl4982, plain,
% 1.30/1.14 ((((sk_c6) = (multiply @ sk_c8 @ sk_c8))
% 1.30/1.14 | ((sk_c7) = (sk_c8))
% 1.30/1.14 | ((multiply @ sk_c8 @ sk_c8) != (multiply @ sk_c7 @ (inverse @ sk_c8))))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl4958])).
% 1.30/1.14 thf(zip_derived_cl5601, plain, (((identity) = (sk_c7))),
% 1.30/1.14 inference('clc', [status(thm)], [zip_derived_cl5565, zip_derived_cl5557])).
% 1.30/1.14 thf(zip_derived_cl5601, plain, (((identity) = (sk_c7))),
% 1.30/1.14 inference('clc', [status(thm)], [zip_derived_cl5565, zip_derived_cl5557])).
% 1.30/1.14 thf(zip_derived_cl0, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.30/1.14 inference('cnf', [status(esa)], [left_identity])).
% 1.30/1.14 thf(zip_derived_cl5763, plain,
% 1.30/1.14 ((((sk_c6) = (multiply @ sk_c8 @ sk_c8))
% 1.30/1.14 | ((identity) = (sk_c8))
% 1.30/1.14 | ((multiply @ sk_c8 @ sk_c8) != (inverse @ sk_c8)))),
% 1.30/1.14 inference('demod', [status(thm)],
% 1.30/1.14 [zip_derived_cl4982, zip_derived_cl5601, zip_derived_cl5601,
% 1.30/1.14 zip_derived_cl0])).
% 1.30/1.14 thf(zip_derived_cl5608, plain, (((sk_c8) = (sk_c6))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl5607])).
% 1.30/1.14 thf(zip_derived_cl5907, plain,
% 1.30/1.14 ((((sk_c8) = (multiply @ sk_c8 @ sk_c8))
% 1.30/1.14 | ((identity) = (sk_c8))
% 1.30/1.14 | ((multiply @ sk_c8 @ sk_c8) != (inverse @ sk_c8)))),
% 1.30/1.14 inference('demod', [status(thm)],
% 1.30/1.14 [zip_derived_cl5763, zip_derived_cl5608])).
% 1.30/1.14 thf(zip_derived_cl1091, plain,
% 1.30/1.14 ((((inverse @ sk_c4) = (sk_c8)) | ((identity) = (sk_c7)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl57, zip_derived_cl461])).
% 1.30/1.14 thf(zip_derived_cl1308, plain,
% 1.30/1.14 ((((identity) = (sk_c7)) | ((multiply @ sk_c4 @ sk_c7) = (sk_c8)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl1285])).
% 1.30/1.14 thf(zip_derived_cl113, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i]:
% 1.30/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl94, zip_derived_cl0])).
% 1.30/1.14 thf(zip_derived_cl1329, plain,
% 1.30/1.14 ((((sk_c7) = (multiply @ (inverse @ sk_c4) @ sk_c8))
% 1.30/1.14 | ((identity) = (sk_c7)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl1308, zip_derived_cl113])).
% 1.30/1.14 thf(zip_derived_cl1380, plain,
% 1.30/1.14 ((((sk_c7) = (multiply @ sk_c8 @ sk_c8))
% 1.30/1.14 | ((identity) = (sk_c7))
% 1.30/1.14 | ((identity) = (sk_c7)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl1091, zip_derived_cl1329])).
% 1.30/1.14 thf(zip_derived_cl1385, plain,
% 1.30/1.14 ((((identity) = (sk_c7)) | ((sk_c7) = (multiply @ sk_c8 @ sk_c8)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl1380])).
% 1.30/1.14 thf(zip_derived_cl695, plain,
% 1.30/1.14 ((((sk_c7) = (sk_c8)) | ((inverse @ sk_c8) = (sk_c7)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl693, zip_derived_cl113])).
% 1.30/1.14 thf(zip_derived_cl1409, plain,
% 1.30/1.14 ((((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c8))
% 1.30/1.14 | ((identity) = (sk_c7))
% 1.30/1.14 | ((sk_c7) = (sk_c8)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl1385, zip_derived_cl695])).
% 1.30/1.14 thf(zip_derived_cl1336, plain,
% 1.30/1.14 ((((identity) = (sk_c7))
% 1.30/1.14 | ((multiply @ (inverse @ sk_c8) @ sk_c7) = (sk_c8)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl1334])).
% 1.30/1.14 thf(zip_derived_cl1488, plain,
% 1.30/1.14 ((((multiply @ (inverse @ sk_c8) @ sk_c8) = (sk_c8))
% 1.30/1.14 | ((identity) = (sk_c7))
% 1.30/1.14 | ((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c8))
% 1.30/1.14 | ((identity) = (sk_c7)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl1409, zip_derived_cl1336])).
% 1.30/1.14 thf(zip_derived_cl1, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.30/1.14 inference('cnf', [status(esa)], [left_inverse])).
% 1.30/1.14 thf(zip_derived_cl1491, plain,
% 1.30/1.14 ((((identity) = (sk_c8))
% 1.30/1.14 | ((identity) = (sk_c7))
% 1.30/1.14 | ((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c8))
% 1.30/1.14 | ((identity) = (sk_c7)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl1488, zip_derived_cl1])).
% 1.30/1.14 thf(zip_derived_cl1492, plain,
% 1.30/1.14 ((((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c8))
% 1.30/1.14 | ((identity) = (sk_c7))
% 1.30/1.14 | ((identity) = (sk_c8)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl1491])).
% 1.30/1.14 thf(prove_this_2, conjecture,
% 1.30/1.14 (~( ( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 1.30/1.14 ( ( inverse @ sk_c8 ) = ( sk_c7 ) ) ))).
% 1.30/1.14 thf(zf_stmt_19, negated_conjecture,
% 1.30/1.14 (( ( inverse @ sk_c4 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c8 ) = ( sk_c7 ) )),
% 1.30/1.14 inference('cnf.neg', [status(esa)], [prove_this_2])).
% 1.30/1.14 thf(zip_derived_cl4, plain,
% 1.30/1.14 ((((inverse @ sk_c4) = (sk_c8)) | ((inverse @ sk_c8) = (sk_c7)))),
% 1.30/1.14 inference('cnf', [status(esa)], [zf_stmt_19])).
% 1.30/1.14 thf(prove_this_3, conjecture,
% 1.30/1.14 (~( ( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 1.30/1.14 ( ( inverse @ sk_c8 ) = ( sk_c7 ) ) ))).
% 1.30/1.14 thf(zf_stmt_20, negated_conjecture,
% 1.30/1.14 (( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 1.30/1.14 ( ( inverse @ sk_c8 ) = ( sk_c7 ) )),
% 1.30/1.14 inference('cnf.neg', [status(esa)], [prove_this_3])).
% 1.30/1.14 thf(zip_derived_cl5, plain,
% 1.30/1.14 ((((multiply @ sk_c4 @ sk_c7) = (sk_c8)) | ((inverse @ sk_c8) = (sk_c7)))),
% 1.30/1.14 inference('cnf', [status(esa)], [zf_stmt_20])).
% 1.30/1.14 thf(zip_derived_cl113, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i]:
% 1.30/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl94, zip_derived_cl0])).
% 1.30/1.14 thf(zip_derived_cl132, plain,
% 1.30/1.14 ((((sk_c7) = (multiply @ (inverse @ sk_c4) @ sk_c8))
% 1.30/1.14 | ((inverse @ sk_c8) = (sk_c7)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl113])).
% 1.30/1.14 thf(zip_derived_cl981, plain,
% 1.30/1.14 ((((sk_c7) = (multiply @ sk_c8 @ sk_c8))
% 1.30/1.14 | ((inverse @ sk_c8) = (sk_c7))
% 1.30/1.14 | ((inverse @ sk_c8) = (sk_c7)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl132])).
% 1.30/1.14 thf(zip_derived_cl987, plain,
% 1.30/1.14 ((((inverse @ sk_c8) = (sk_c7)) | ((sk_c7) = (multiply @ sk_c8 @ sk_c8)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl981])).
% 1.30/1.14 thf(prove_this_14, conjecture,
% 1.30/1.14 (~( ( ( inverse @ sk_c5 ) = ( sk_c7 ) ) |
% 1.30/1.14 ( ( inverse @ sk_c1 ) = ( sk_c8 ) ) ))).
% 1.30/1.14 thf(zf_stmt_21, negated_conjecture,
% 1.30/1.14 (( ( inverse @ sk_c5 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c8 ) )),
% 1.30/1.14 inference('cnf.neg', [status(esa)], [prove_this_14])).
% 1.30/1.14 thf(zip_derived_cl16, plain,
% 1.30/1.14 ((((inverse @ sk_c5) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c8)))),
% 1.30/1.14 inference('cnf', [status(esa)], [zf_stmt_21])).
% 1.30/1.14 thf(prove_this_19, conjecture,
% 1.30/1.14 (~( ( ( inverse @ sk_c5 ) = ( sk_c7 ) ) |
% 1.30/1.14 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) ) ))).
% 1.30/1.14 thf(zf_stmt_22, negated_conjecture,
% 1.30/1.14 (( ( inverse @ sk_c5 ) = ( sk_c7 ) ) |
% 1.30/1.14 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) )),
% 1.30/1.14 inference('cnf.neg', [status(esa)], [prove_this_19])).
% 1.30/1.14 thf(zip_derived_cl21, plain,
% 1.30/1.14 ((((inverse @ sk_c5) = (sk_c7)) | ((multiply @ sk_c1 @ sk_c7) = (sk_c8)))),
% 1.30/1.14 inference('cnf', [status(esa)], [zf_stmt_22])).
% 1.30/1.14 thf(zip_derived_cl113, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i]:
% 1.30/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl94, zip_derived_cl0])).
% 1.30/1.14 thf(zip_derived_cl136, plain,
% 1.30/1.14 ((((sk_c7) = (multiply @ (inverse @ sk_c1) @ sk_c8))
% 1.30/1.14 | ((inverse @ sk_c5) = (sk_c7)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl21, zip_derived_cl113])).
% 1.30/1.14 thf(zip_derived_cl2277, plain,
% 1.30/1.14 ((((sk_c7) = (multiply @ sk_c8 @ sk_c8))
% 1.30/1.14 | ((inverse @ sk_c5) = (sk_c7))
% 1.30/1.14 | ((inverse @ sk_c5) = (sk_c7)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl16, zip_derived_cl136])).
% 1.30/1.14 thf(zip_derived_cl2285, plain,
% 1.30/1.14 ((((inverse @ sk_c5) = (sk_c7)) | ((sk_c7) = (multiply @ sk_c8 @ sk_c8)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl2277])).
% 1.30/1.14 thf(zip_derived_cl1, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.30/1.14 inference('cnf', [status(esa)], [left_inverse])).
% 1.30/1.14 thf(zip_derived_cl2293, plain,
% 1.30/1.14 ((((multiply @ sk_c7 @ sk_c5) = (identity))
% 1.30/1.14 | ((sk_c7) = (multiply @ sk_c8 @ sk_c8)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl2285, zip_derived_cl1])).
% 1.30/1.14 thf(zip_derived_cl2379, plain,
% 1.30/1.14 ((((multiply @ (inverse @ sk_c8) @ sk_c5) = (identity))
% 1.30/1.14 | ((sk_c7) = (multiply @ sk_c8 @ sk_c8))
% 1.30/1.14 | ((sk_c7) = (multiply @ sk_c8 @ sk_c8)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl987, zip_derived_cl2293])).
% 1.30/1.14 thf(zip_derived_cl2388, plain,
% 1.30/1.14 ((((sk_c7) = (multiply @ sk_c8 @ sk_c8))
% 1.30/1.14 | ((multiply @ (inverse @ sk_c8) @ sk_c5) = (identity)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl2379])).
% 1.30/1.14 thf(zip_derived_cl113, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i]:
% 1.30/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl94, zip_derived_cl0])).
% 1.30/1.14 thf(zip_derived_cl3899, plain,
% 1.30/1.14 ((((sk_c5) = (multiply @ (inverse @ (inverse @ sk_c8)) @ identity))
% 1.30/1.14 | ((sk_c7) = (multiply @ sk_c8 @ sk_c8)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl2388, zip_derived_cl113])).
% 1.30/1.14 thf(zip_derived_cl456, plain,
% 1.30/1.14 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl427, zip_derived_cl124])).
% 1.30/1.14 thf(zip_derived_cl427, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl124, zip_derived_cl121])).
% 1.30/1.14 thf(zip_derived_cl3911, plain,
% 1.30/1.14 ((((sk_c5) = (sk_c8)) | ((sk_c7) = (multiply @ sk_c8 @ sk_c8)))),
% 1.30/1.14 inference('demod', [status(thm)],
% 1.30/1.14 [zip_derived_cl3899, zip_derived_cl456, zip_derived_cl427])).
% 1.30/1.14 thf(zip_derived_cl2285, plain,
% 1.30/1.14 ((((inverse @ sk_c5) = (sk_c7)) | ((sk_c7) = (multiply @ sk_c8 @ sk_c8)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl2277])).
% 1.30/1.14 thf(zip_derived_cl456, plain,
% 1.30/1.14 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl427, zip_derived_cl124])).
% 1.30/1.14 thf(zip_derived_cl2294, plain,
% 1.30/1.14 ((((sk_c5) = (inverse @ sk_c7)) | ((sk_c7) = (multiply @ sk_c8 @ sk_c8)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl2285, zip_derived_cl456])).
% 1.30/1.14 thf(zip_derived_cl3943, plain,
% 1.30/1.14 ((((sk_c8) = (inverse @ sk_c7))
% 1.30/1.14 | ((sk_c7) = (multiply @ sk_c8 @ sk_c8))
% 1.30/1.14 | ((sk_c7) = (multiply @ sk_c8 @ sk_c8)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl3911, zip_derived_cl2294])).
% 1.30/1.14 thf(zip_derived_cl3961, plain,
% 1.30/1.14 ((((sk_c7) = (multiply @ sk_c8 @ sk_c8)) | ((sk_c8) = (inverse @ sk_c7)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl3943])).
% 1.30/1.14 thf(zip_derived_cl3981, plain,
% 1.30/1.14 ((((sk_c8) = (inverse @ identity))
% 1.30/1.14 | ((identity) = (sk_c8))
% 1.30/1.14 | ((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c8))
% 1.30/1.14 | ((sk_c7) = (multiply @ sk_c8 @ sk_c8)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl1492, zip_derived_cl3961])).
% 1.30/1.14 thf(zip_derived_cl309, plain, (((inverse @ identity) = (identity))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl154, zip_derived_cl1])).
% 1.30/1.14 thf(zip_derived_cl3991, plain,
% 1.30/1.14 ((((sk_c8) = (identity))
% 1.30/1.14 | ((identity) = (sk_c8))
% 1.30/1.14 | ((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c8))
% 1.30/1.14 | ((sk_c7) = (multiply @ sk_c8 @ sk_c8)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl3981, zip_derived_cl309])).
% 1.30/1.14 thf(zip_derived_cl3992, plain,
% 1.30/1.14 ((((sk_c7) = (multiply @ sk_c8 @ sk_c8))
% 1.30/1.14 | ((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c8))
% 1.30/1.14 | ((sk_c8) = (identity)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl3991])).
% 1.30/1.14 thf(zip_derived_cl987, plain,
% 1.30/1.14 ((((inverse @ sk_c8) = (sk_c7)) | ((sk_c7) = (multiply @ sk_c8 @ sk_c8)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl981])).
% 1.30/1.14 thf(zip_derived_cl1008, plain,
% 1.30/1.14 ((((inverse @ sk_c8) != (multiply @ sk_c8 @ sk_c8))
% 1.30/1.14 | ((sk_c7) = (multiply @ sk_c8 @ sk_c8)))),
% 1.30/1.14 inference('eq_fact', [status(thm)], [zip_derived_cl987])).
% 1.30/1.14 thf(zip_derived_cl4284, plain,
% 1.30/1.14 ((((sk_c8) = (identity)) | ((sk_c7) = (multiply @ sk_c8 @ sk_c8)))),
% 1.30/1.14 inference('clc', [status(thm)], [zip_derived_cl3992, zip_derived_cl1008])).
% 1.30/1.14 thf(zip_derived_cl695, plain,
% 1.30/1.14 ((((sk_c7) = (sk_c8)) | ((inverse @ sk_c8) = (sk_c7)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl693, zip_derived_cl113])).
% 1.30/1.14 thf(zip_derived_cl4307, plain,
% 1.30/1.14 ((((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c8))
% 1.30/1.14 | ((sk_c8) = (identity))
% 1.30/1.14 | ((sk_c7) = (sk_c8)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl4284, zip_derived_cl695])).
% 1.30/1.14 thf(zip_derived_cl1492, plain,
% 1.30/1.14 ((((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c8))
% 1.30/1.14 | ((identity) = (sk_c7))
% 1.30/1.14 | ((identity) = (sk_c8)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl1491])).
% 1.30/1.14 thf(zip_derived_cl4448, plain,
% 1.30/1.14 ((((identity) = (sk_c8))
% 1.30/1.14 | ((sk_c8) = (identity))
% 1.30/1.14 | ((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c8))
% 1.30/1.14 | ((identity) = (sk_c8))
% 1.30/1.14 | ((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c8)))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl4307, zip_derived_cl1492])).
% 1.30/1.14 thf(zip_derived_cl4490, plain,
% 1.30/1.14 ((((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c8))
% 1.30/1.14 | ((identity) = (sk_c8)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl4448])).
% 1.30/1.14 thf(zip_derived_cl695, plain,
% 1.30/1.14 ((((sk_c7) = (sk_c8)) | ((inverse @ sk_c8) = (sk_c7)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl693, zip_derived_cl113])).
% 1.30/1.14 thf(zip_derived_cl707, plain,
% 1.30/1.14 ((((inverse @ sk_c8) != (sk_c8)) | ((sk_c7) = (sk_c8)))),
% 1.30/1.14 inference('eq_fact', [status(thm)], [zip_derived_cl695])).
% 1.30/1.14 thf(zip_derived_cl4556, plain,
% 1.30/1.14 ((((multiply @ sk_c8 @ sk_c8) != (sk_c8))
% 1.30/1.14 | ((identity) = (sk_c8))
% 1.30/1.14 | ((sk_c7) = (sk_c8)))),
% 1.30/1.14 inference('sup-', [status(thm)], [zip_derived_cl4490, zip_derived_cl707])).
% 1.30/1.14 thf(zip_derived_cl5601, plain, (((identity) = (sk_c7))),
% 1.30/1.14 inference('clc', [status(thm)], [zip_derived_cl5565, zip_derived_cl5557])).
% 1.30/1.14 thf(zip_derived_cl5750, plain,
% 1.30/1.14 ((((multiply @ sk_c8 @ sk_c8) != (sk_c8))
% 1.30/1.14 | ((identity) = (sk_c8))
% 1.30/1.14 | ((identity) = (sk_c8)))),
% 1.30/1.14 inference('demod', [status(thm)],
% 1.30/1.14 [zip_derived_cl4556, zip_derived_cl5601])).
% 1.30/1.14 thf(zip_derived_cl5751, plain,
% 1.30/1.14 ((((identity) = (sk_c8)) | ((multiply @ sk_c8 @ sk_c8) != (sk_c8)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl5750])).
% 1.30/1.14 thf(zip_derived_cl5908, plain,
% 1.30/1.14 ((((multiply @ sk_c8 @ sk_c8) != (inverse @ sk_c8))
% 1.30/1.14 | ((identity) = (sk_c8)))),
% 1.30/1.14 inference('clc', [status(thm)], [zip_derived_cl5907, zip_derived_cl5751])).
% 1.30/1.14 thf(zip_derived_cl4490, plain,
% 1.30/1.14 ((((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c8))
% 1.30/1.14 | ((identity) = (sk_c8)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl4448])).
% 1.30/1.14 thf(zip_derived_cl5909, plain, (((identity) = (sk_c8))),
% 1.30/1.14 inference('clc', [status(thm)], [zip_derived_cl5908, zip_derived_cl4490])).
% 1.30/1.14 thf(zip_derived_cl5933, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.30/1.14 (((X0) != (identity))
% 1.30/1.14 | ((inverse @ X0) != (identity))
% 1.30/1.14 | ((X1) != (identity))
% 1.30/1.14 | ((inverse @ X1) != (identity))
% 1.30/1.14 | ((X2) != (identity))
% 1.30/1.14 | ((inverse @ X3) != (X2))
% 1.30/1.14 | ((multiply @ X3 @ X2) != (identity))
% 1.30/1.14 | ((X4) != (identity))
% 1.30/1.14 | ((inverse @ X4) != (identity))
% 1.30/1.14 | ((identity) != (identity)))),
% 1.30/1.14 inference('demod', [status(thm)],
% 1.30/1.14 [zip_derived_cl5773, zip_derived_cl5909])).
% 1.30/1.14 thf(zip_derived_cl5934, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.30/1.14 (((inverse @ X4) != (identity))
% 1.30/1.14 | ((X4) != (identity))
% 1.30/1.14 | ((multiply @ X3 @ X2) != (identity))
% 1.30/1.14 | ((inverse @ X3) != (X2))
% 1.30/1.14 | ((X2) != (identity))
% 1.30/1.14 | ((inverse @ X1) != (identity))
% 1.30/1.14 | ((X1) != (identity))
% 1.30/1.14 | ((inverse @ X0) != (identity))
% 1.30/1.14 | ((X0) != (identity)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl5933])).
% 1.30/1.14 thf(zip_derived_cl5964, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.30/1.14 (((X0) != (identity))
% 1.30/1.14 | ((inverse @ X0) != (identity))
% 1.30/1.14 | ((X1) != (identity))
% 1.30/1.14 | ((inverse @ X1) != (identity))
% 1.30/1.14 | ((X2) != (identity))
% 1.30/1.14 | ((inverse @ X3) != (X2))
% 1.30/1.14 | ((multiply @ X3 @ X2) != (identity))
% 1.30/1.14 | ((inverse @ identity) != (identity)))),
% 1.30/1.14 inference('eq_res', [status(thm)], [zip_derived_cl5934])).
% 1.30/1.14 thf(zip_derived_cl309, plain, (((inverse @ identity) = (identity))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl154, zip_derived_cl1])).
% 1.30/1.14 thf(zip_derived_cl5965, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.30/1.14 (((X0) != (identity))
% 1.30/1.14 | ((inverse @ X0) != (identity))
% 1.30/1.14 | ((X1) != (identity))
% 1.30/1.14 | ((inverse @ X1) != (identity))
% 1.30/1.14 | ((X2) != (identity))
% 1.30/1.14 | ((inverse @ X3) != (X2))
% 1.30/1.14 | ((multiply @ X3 @ X2) != (identity))
% 1.30/1.14 | ((identity) != (identity)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl5964, zip_derived_cl309])).
% 1.30/1.14 thf(zip_derived_cl5966, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.30/1.14 (((multiply @ X3 @ X2) != (identity))
% 1.30/1.14 | ((inverse @ X3) != (X2))
% 1.30/1.14 | ((X2) != (identity))
% 1.30/1.14 | ((inverse @ X1) != (identity))
% 1.30/1.14 | ((X1) != (identity))
% 1.30/1.14 | ((inverse @ X0) != (identity))
% 1.30/1.14 | ((X0) != (identity)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl5965])).
% 1.30/1.14 thf(zip_derived_cl5967, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.30/1.14 (((X0) != (identity))
% 1.30/1.14 | ((inverse @ X0) != (identity))
% 1.30/1.14 | ((X1) != (identity))
% 1.30/1.14 | ((inverse @ X1) != (identity))
% 1.30/1.14 | ((inverse @ X2) != (identity))
% 1.30/1.14 | ((multiply @ X2 @ identity) != (identity)))),
% 1.30/1.14 inference('eq_res', [status(thm)], [zip_derived_cl5966])).
% 1.30/1.14 thf(zip_derived_cl427, plain,
% 1.30/1.14 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl124, zip_derived_cl121])).
% 1.30/1.14 thf(zip_derived_cl5968, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.30/1.14 (((X0) != (identity))
% 1.30/1.14 | ((inverse @ X0) != (identity))
% 1.30/1.14 | ((X1) != (identity))
% 1.30/1.14 | ((inverse @ X1) != (identity))
% 1.30/1.14 | ((inverse @ X2) != (identity))
% 1.30/1.14 | ((X2) != (identity)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl5967, zip_derived_cl427])).
% 1.30/1.14 thf(zip_derived_cl5969, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i]:
% 1.30/1.14 (((X0) != (identity))
% 1.30/1.14 | ((inverse @ X0) != (identity))
% 1.30/1.14 | ((inverse @ X1) != (identity))
% 1.30/1.14 | ((X1) != (identity))
% 1.30/1.14 | ((inverse @ identity) != (identity)))),
% 1.30/1.14 inference('eq_res', [status(thm)], [zip_derived_cl5968])).
% 1.30/1.14 thf(zip_derived_cl309, plain, (((inverse @ identity) = (identity))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl154, zip_derived_cl1])).
% 1.30/1.14 thf(zip_derived_cl5970, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i]:
% 1.30/1.14 (((X0) != (identity))
% 1.30/1.14 | ((inverse @ X0) != (identity))
% 1.30/1.14 | ((inverse @ X1) != (identity))
% 1.30/1.14 | ((X1) != (identity))
% 1.30/1.14 | ((identity) != (identity)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl5969, zip_derived_cl309])).
% 1.30/1.14 thf(zip_derived_cl5971, plain,
% 1.30/1.14 (![X0 : $i, X1 : $i]:
% 1.30/1.14 (((X1) != (identity))
% 1.30/1.14 | ((inverse @ X1) != (identity))
% 1.30/1.14 | ((inverse @ X0) != (identity))
% 1.30/1.14 | ((X0) != (identity)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl5970])).
% 1.30/1.14 thf(zip_derived_cl5972, plain,
% 1.30/1.14 (![X0 : $i]:
% 1.30/1.14 (((X0) != (identity))
% 1.30/1.14 | ((inverse @ X0) != (identity))
% 1.30/1.14 | ((inverse @ identity) != (identity)))),
% 1.30/1.14 inference('eq_res', [status(thm)], [zip_derived_cl5971])).
% 1.30/1.14 thf(zip_derived_cl309, plain, (((inverse @ identity) = (identity))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl154, zip_derived_cl1])).
% 1.30/1.14 thf(zip_derived_cl5973, plain,
% 1.30/1.14 (![X0 : $i]:
% 1.30/1.14 (((X0) != (identity))
% 1.30/1.14 | ((inverse @ X0) != (identity))
% 1.30/1.14 | ((identity) != (identity)))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl5972, zip_derived_cl309])).
% 1.30/1.14 thf(zip_derived_cl5974, plain,
% 1.30/1.14 (![X0 : $i]: (((inverse @ X0) != (identity)) | ((X0) != (identity)))),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl5973])).
% 1.30/1.14 thf(zip_derived_cl5975, plain, (((inverse @ identity) != (identity))),
% 1.30/1.14 inference('eq_res', [status(thm)], [zip_derived_cl5974])).
% 1.30/1.14 thf(zip_derived_cl309, plain, (((inverse @ identity) = (identity))),
% 1.30/1.14 inference('sup+', [status(thm)], [zip_derived_cl154, zip_derived_cl1])).
% 1.30/1.14 thf(zip_derived_cl5976, plain, (((identity) != (identity))),
% 1.30/1.14 inference('demod', [status(thm)], [zip_derived_cl5975, zip_derived_cl309])).
% 1.30/1.14 thf(zip_derived_cl5977, plain, ($false),
% 1.30/1.14 inference('simplify', [status(thm)], [zip_derived_cl5976])).
% 1.30/1.14
% 1.30/1.14 % SZS output end Refutation
% 1.30/1.14
% 1.30/1.14
% 1.30/1.14 % Terminating...
% 1.69/1.27 % Runner terminated.
% 1.69/1.28 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------