%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP310-1 : 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.Au8Z6kdbqR true
% Computer : n012.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 04:36:12 PM UTC 2025
% Result : Unsatisfiable 1.23s 1.08s
% Output : Refutation 1.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP310-1 : TPTP v9.2.0. Released v2.5.0.
% 0.10/0.12 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Au8Z6kdbqR true
% 0.11/0.33 % Computer : n012.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Oct 1 14:24:53 EDT 2025
% 0.11/0.34 % CPUTime :
% 0.11/0.34 % Running portfolio for 300 s
% 0.11/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.34 % Number of cores: 8
% 0.11/0.34 % Python version: Python 3.6.8
% 0.11/0.34 % Running in FO mode
% 0.19/0.60 % Total configuration time : 435
% 0.19/0.60 % Estimated wc time : 1092
% 0.19/0.60 % Estimated cpu time (7 cpus) : 156.0
% 0.92/0.64 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 1.00/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 1.00/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 1.00/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 1.00/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 1.00/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 1.00/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 1.23/1.08 % Solved by fo/fo7.sh.
% 1.23/1.08 % done 698 iterations in 0.351s
% 1.23/1.08 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.23/1.08 % SZS output start Refutation
% 1.23/1.08 thf(sk_c2_type, type, sk_c2: $i).
% 1.23/1.08 thf(sk_c6_type, type, sk_c6: $i).
% 1.23/1.08 thf(sk_c4_type, type, sk_c4: $i).
% 1.23/1.08 thf(sk_c5_type, type, sk_c5: $i).
% 1.23/1.08 thf(identity_type, type, identity: $i).
% 1.23/1.08 thf(multiply_type, type, multiply: $i > $i > $i).
% 1.23/1.08 thf(sk_c7_type, type, sk_c7: $i).
% 1.23/1.08 thf(inverse_type, type, inverse: $i > $i).
% 1.23/1.08 thf(sk_c3_type, type, sk_c3: $i).
% 1.23/1.08 thf(sk_c1_type, type, sk_c1: $i).
% 1.23/1.08 thf(sk_c8_type, type, sk_c8: $i).
% 1.23/1.08 thf(prove_this_27, conjecture,
% 1.23/1.08 (~( ( ( inverse @ X5 ) != ( sk_c8 ) ) |
% 1.23/1.08 ( ( multiply @ X5 @ sk_c8 ) != ( X2 ) ) |
% 1.23/1.08 ( ( multiply @ sk_c8 @ X2 ) != ( sk_c7 ) ) |
% 1.23/1.08 ( ( inverse @ X1 ) != ( sk_c8 ) ) |
% 1.23/1.08 ( ( multiply @ X1 @ sk_c8 ) != ( sk_c7 ) ) |
% 1.23/1.08 ( ( inverse @ X4 ) != ( sk_c8 ) ) |
% 1.23/1.08 ( ( multiply @ X4 @ sk_c8 ) != ( X3 ) ) |
% 1.23/1.08 ( ( multiply @ sk_c8 @ X3 ) != ( sk_c7 ) ) |
% 1.23/1.08 ( ( multiply @ sk_c6 @ sk_c7 ) != ( sk_c8 ) ) |
% 1.23/1.08 ( ( inverse @ sk_c8 ) != ( sk_c6 ) ) |
% 1.23/1.08 ( ( multiply @ sk_c8 @ sk_c7 ) != ( sk_c6 ) ) ))).
% 1.23/1.08 thf(zf_stmt_0, negated_conjecture,
% 1.23/1.08 (( ( inverse @ X5 ) != ( sk_c8 ) ) |
% 1.23/1.08 ( ( multiply @ X5 @ sk_c8 ) != ( X2 ) ) |
% 1.23/1.08 ( ( multiply @ sk_c8 @ X2 ) != ( sk_c7 ) ) |
% 1.23/1.08 ( ( inverse @ X1 ) != ( sk_c8 ) ) |
% 1.23/1.08 ( ( multiply @ X1 @ sk_c8 ) != ( sk_c7 ) ) |
% 1.23/1.08 ( ( inverse @ X4 ) != ( sk_c8 ) ) |
% 1.23/1.08 ( ( multiply @ X4 @ sk_c8 ) != ( X3 ) ) |
% 1.23/1.08 ( ( multiply @ sk_c8 @ X3 ) != ( sk_c7 ) ) |
% 1.23/1.08 ( ( multiply @ sk_c6 @ sk_c7 ) != ( sk_c8 ) ) |
% 1.23/1.08 ( ( inverse @ sk_c8 ) != ( sk_c6 ) ) |
% 1.23/1.08 ( ( multiply @ sk_c8 @ sk_c7 ) != ( sk_c6 ) )),
% 1.23/1.08 inference('cnf.neg', [status(esa)], [prove_this_27])).
% 1.23/1.08 thf(zip_derived_cl29, plain,
% 1.23/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.23/1.08 (((inverse @ X0) != (sk_c8))
% 1.23/1.08 | ((multiply @ X0 @ sk_c8) != (X1))
% 1.23/1.08 | ((multiply @ sk_c8 @ X1) != (sk_c7))
% 1.23/1.08 | ((inverse @ X2) != (sk_c8))
% 1.23/1.08 | ((multiply @ X2 @ sk_c8) != (sk_c7))
% 1.23/1.08 | ((inverse @ X3) != (sk_c8))
% 1.23/1.08 | ((multiply @ X3 @ sk_c8) != (X4))
% 1.23/1.08 | ((multiply @ sk_c8 @ X4) != (sk_c7))
% 1.23/1.08 | ((multiply @ sk_c6 @ sk_c7) != (sk_c8))
% 1.23/1.08 | ((inverse @ sk_c8) != (sk_c6))
% 1.23/1.08 | ((multiply @ sk_c8 @ sk_c7) != (sk_c6)))),
% 1.23/1.08 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.23/1.08 thf(zip_derived_cl30, plain,
% 1.23/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.23/1.08 (((inverse @ X0) != (sk_c8))
% 1.23/1.08 | ((multiply @ X0 @ sk_c8) != (X1))
% 1.23/1.08 | ((multiply @ sk_c8 @ X1) != (sk_c7))
% 1.23/1.08 | ((inverse @ X2) != (sk_c8))
% 1.23/1.08 | ((multiply @ X2 @ sk_c8) != (sk_c7))
% 1.23/1.08 | ((inverse @ X3) != (sk_c8))
% 1.23/1.08 | ((multiply @ X3 @ sk_c8) != (X4))
% 1.23/1.08 | ((multiply @ sk_c8 @ X4) != (sk_c7))
% 1.23/1.08 | ((multiply @ (multiply @ sk_c8 @ sk_c7) @ sk_c7) != (sk_c8))
% 1.23/1.08 | ((inverse @ sk_c8) != (sk_c6))
% 1.23/1.08 | ((multiply @ sk_c8 @ sk_c7) != (sk_c6)))),
% 1.23/1.08 inference('local_rewriting', [status(thm)], [zip_derived_cl29])).
% 1.23/1.08 thf(prove_this_1, conjecture, (( multiply @ sk_c8 @ sk_c7 ) != ( sk_c6 ))).
% 1.23/1.08 thf(zf_stmt_1, negated_conjecture,
% 1.23/1.08 (( multiply @ sk_c8 @ sk_c7 ) = ( sk_c6 )),
% 1.23/1.08 inference('cnf.neg', [status(esa)], [prove_this_1])).
% 1.23/1.08 thf(zip_derived_cl3, plain, (((multiply @ sk_c8 @ sk_c7) = (sk_c6))),
% 1.23/1.08 inference('cnf', [status(esa)], [zf_stmt_1])).
% 1.23/1.08 thf(zip_derived_cl3, plain, (((multiply @ sk_c8 @ sk_c7) = (sk_c6))),
% 1.23/1.08 inference('cnf', [status(esa)], [zf_stmt_1])).
% 1.23/1.08 thf(zip_derived_cl31, plain,
% 1.23/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.23/1.08 (((inverse @ X0) != (sk_c8))
% 1.23/1.08 | ((multiply @ X0 @ sk_c8) != (X1))
% 1.23/1.08 | ((multiply @ sk_c8 @ X1) != (sk_c7))
% 1.23/1.08 | ((inverse @ X2) != (sk_c8))
% 1.23/1.08 | ((multiply @ X2 @ sk_c8) != (sk_c7))
% 1.23/1.08 | ((inverse @ X3) != (sk_c8))
% 1.23/1.08 | ((multiply @ X3 @ sk_c8) != (X4))
% 1.23/1.08 | ((multiply @ sk_c8 @ X4) != (sk_c7))
% 1.23/1.08 | ((multiply @ (multiply @ sk_c8 @ sk_c7) @ sk_c7) != (sk_c8))
% 1.23/1.08 | ((inverse @ sk_c8) != (multiply @ sk_c8 @ sk_c7))
% 1.23/1.08 | ((multiply @ sk_c8 @ sk_c7) != (multiply @ sk_c8 @ sk_c7)))),
% 1.23/1.08 inference('demod', [status(thm)],
% 1.23/1.08 [zip_derived_cl30, zip_derived_cl3, zip_derived_cl3])).
% 1.23/1.08 thf(zip_derived_cl32, plain,
% 1.23/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.23/1.08 (((inverse @ sk_c8) != (multiply @ sk_c8 @ sk_c7))
% 1.23/1.08 | ((multiply @ (multiply @ sk_c8 @ sk_c7) @ sk_c7) != (sk_c8))
% 1.23/1.08 | ((multiply @ sk_c8 @ X4) != (sk_c7))
% 1.23/1.08 | ((multiply @ X3 @ sk_c8) != (X4))
% 1.23/1.08 | ((inverse @ X3) != (sk_c8))
% 1.23/1.08 | ((multiply @ X2 @ sk_c8) != (sk_c7))
% 1.23/1.08 | ((inverse @ X2) != (sk_c8))
% 1.23/1.08 | ((multiply @ sk_c8 @ X1) != (sk_c7))
% 1.23/1.08 | ((multiply @ X0 @ sk_c8) != (X1))
% 1.23/1.08 | ((inverse @ X0) != (sk_c8)))),
% 1.23/1.08 inference('simplify', [status(thm)], [zip_derived_cl31])).
% 1.23/1.08 thf(zip_derived_cl33, plain,
% 1.23/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.23/1.08 (((inverse @ sk_c8) != (multiply @ sk_c8 @ sk_c7))
% 1.23/1.08 | ((multiply @ (inverse @ sk_c8) @ sk_c7) != (sk_c8))
% 1.23/1.08 | ((multiply @ sk_c8 @ X4) != (sk_c7))
% 1.23/1.08 | ((multiply @ X3 @ sk_c8) != (X4))
% 1.23/1.08 | ((inverse @ X3) != (sk_c8))
% 1.23/1.08 | ((multiply @ X2 @ sk_c8) != (sk_c7))
% 1.23/1.08 | ((inverse @ X2) != (sk_c8))
% 1.23/1.08 | ((multiply @ sk_c8 @ X1) != (sk_c7))
% 1.23/1.08 | ((multiply @ X0 @ sk_c8) != (X1))
% 1.23/1.08 | ((inverse @ X0) != (sk_c8)))),
% 1.23/1.08 inference('local_rewriting', [status(thm)], [zip_derived_cl32])).
% 1.23/1.08 thf(prove_this_26, conjecture,
% 1.23/1.08 (~( ( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 1.23/1.08 ( ( inverse @ sk_c1 ) = ( sk_c8 ) ) ))).
% 1.23/1.08 thf(zf_stmt_2, negated_conjecture,
% 1.23/1.08 (( ( inverse @ sk_c4 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c8 ) )),
% 1.23/1.08 inference('cnf.neg', [status(esa)], [prove_this_26])).
% 1.23/1.08 thf(zip_derived_cl28, plain,
% 1.23/1.08 ((((inverse @ sk_c4) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c8)))),
% 1.23/1.08 inference('cnf', [status(esa)], [zf_stmt_2])).
% 1.23/1.08 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 1.23/1.08 thf(zip_derived_cl1, plain,
% 1.23/1.08 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.23/1.08 inference('cnf', [status(esa)], [left_inverse])).
% 1.23/1.08 thf(zip_derived_cl39, plain,
% 1.23/1.08 ((((multiply @ sk_c8 @ sk_c1) = (identity))
% 1.23/1.08 | ((inverse @ sk_c4) = (sk_c8)))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl28, zip_derived_cl1])).
% 1.23/1.08 thf(zip_derived_cl1, plain,
% 1.23/1.08 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.23/1.08 inference('cnf', [status(esa)], [left_inverse])).
% 1.23/1.08 thf(associativity, axiom,
% 1.23/1.08 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 1.23/1.08 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 1.23/1.08 thf(zip_derived_cl2, plain,
% 1.23/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.23/1.08 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.23/1.08 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.23/1.08 inference('cnf', [status(esa)], [associativity])).
% 1.23/1.08 thf(zip_derived_cl61, plain,
% 1.23/1.08 (![X0 : $i, X1 : $i]:
% 1.23/1.08 ((multiply @ identity @ X0)
% 1.23/1.08 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 1.23/1.08 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 1.23/1.08 thf(zip_derived_cl0, plain,
% 1.23/1.08 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.23/1.08 inference('cnf', [status(esa)], [left_identity])).
% 1.23/1.08 thf(zip_derived_cl75, plain,
% 1.23/1.08 (![X0 : $i, X1 : $i]:
% 1.23/1.08 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.23/1.08 inference('demod', [status(thm)], [zip_derived_cl61, zip_derived_cl0])).
% 1.23/1.08 thf(zip_derived_cl92, plain,
% 1.23/1.08 ((((sk_c1) = (multiply @ (inverse @ sk_c8) @ identity))
% 1.23/1.08 | ((inverse @ sk_c4) = (sk_c8)))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl39, zip_derived_cl75])).
% 1.23/1.08 thf(prove_this_21, conjecture,
% 1.23/1.08 (~( ( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 1.23/1.08 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c2 ) ) ))).
% 1.23/1.08 thf(zf_stmt_3, negated_conjecture,
% 1.23/1.08 (( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 1.23/1.08 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c2 ) )),
% 1.23/1.08 inference('cnf.neg', [status(esa)], [prove_this_21])).
% 1.23/1.08 thf(zip_derived_cl23, plain,
% 1.23/1.08 ((((inverse @ sk_c4) = (sk_c8)) | ((multiply @ sk_c1 @ sk_c8) = (sk_c2)))),
% 1.23/1.08 inference('cnf', [status(esa)], [zf_stmt_3])).
% 1.23/1.08 thf(zip_derived_cl146, plain,
% 1.23/1.08 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 1.23/1.08 = (sk_c2))
% 1.23/1.08 | ((inverse @ sk_c4) = (sk_c8))
% 1.23/1.08 | ((inverse @ sk_c4) = (sk_c8)))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl92, zip_derived_cl23])).
% 1.23/1.08 thf(zip_derived_cl2, plain,
% 1.23/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.23/1.08 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.23/1.08 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.23/1.08 inference('cnf', [status(esa)], [associativity])).
% 1.23/1.08 thf(zip_derived_cl0, plain,
% 1.23/1.08 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.23/1.08 inference('cnf', [status(esa)], [left_identity])).
% 1.23/1.08 thf(zip_derived_cl1, plain,
% 1.23/1.08 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.23/1.08 inference('cnf', [status(esa)], [left_inverse])).
% 1.23/1.08 thf(zip_derived_cl155, plain,
% 1.23/1.08 ((((identity) = (sk_c2))
% 1.23/1.08 | ((inverse @ sk_c4) = (sk_c8))
% 1.23/1.08 | ((inverse @ sk_c4) = (sk_c8)))),
% 1.23/1.08 inference('demod', [status(thm)],
% 1.23/1.08 [zip_derived_cl146, zip_derived_cl2, zip_derived_cl0,
% 1.23/1.08 zip_derived_cl1])).
% 1.23/1.08 thf(zip_derived_cl156, plain,
% 1.23/1.08 ((((inverse @ sk_c4) = (sk_c8)) | ((identity) = (sk_c2)))),
% 1.23/1.08 inference('simplify', [status(thm)], [zip_derived_cl155])).
% 1.23/1.08 thf(prove_this_16, conjecture,
% 1.23/1.08 (~( ( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 1.23/1.08 ( ( multiply @ sk_c8 @ sk_c2 ) = ( sk_c7 ) ) ))).
% 1.23/1.08 thf(zf_stmt_4, negated_conjecture,
% 1.23/1.08 (( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 1.23/1.08 ( ( multiply @ sk_c8 @ sk_c2 ) = ( sk_c7 ) )),
% 1.23/1.08 inference('cnf.neg', [status(esa)], [prove_this_16])).
% 1.23/1.08 thf(zip_derived_cl18, plain,
% 1.23/1.08 ((((inverse @ sk_c4) = (sk_c8)) | ((multiply @ sk_c8 @ sk_c2) = (sk_c7)))),
% 1.23/1.08 inference('cnf', [status(esa)], [zf_stmt_4])).
% 1.23/1.08 thf(zip_derived_cl163, plain,
% 1.23/1.08 ((((multiply @ sk_c8 @ identity) = (sk_c7))
% 1.23/1.08 | ((inverse @ sk_c4) = (sk_c8))
% 1.23/1.08 | ((inverse @ sk_c4) = (sk_c8)))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl156, zip_derived_cl18])).
% 1.23/1.08 thf(zip_derived_cl166, plain,
% 1.23/1.08 ((((inverse @ sk_c4) = (sk_c8))
% 1.23/1.08 | ((multiply @ sk_c8 @ identity) = (sk_c7)))),
% 1.23/1.08 inference('simplify', [status(thm)], [zip_derived_cl163])).
% 1.23/1.08 thf(zip_derived_cl1, plain,
% 1.23/1.08 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.23/1.08 inference('cnf', [status(esa)], [left_inverse])).
% 1.23/1.08 thf(zip_derived_cl75, plain,
% 1.23/1.08 (![X0 : $i, X1 : $i]:
% 1.23/1.08 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.23/1.08 inference('demod', [status(thm)], [zip_derived_cl61, zip_derived_cl0])).
% 1.23/1.08 thf(zip_derived_cl83, plain,
% 1.23/1.08 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl75])).
% 1.23/1.08 thf(zip_derived_cl231, plain,
% 1.23/1.08 ((((sk_c4) = (multiply @ (inverse @ sk_c8) @ identity))
% 1.23/1.08 | ((multiply @ sk_c8 @ identity) = (sk_c7)))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl166, zip_derived_cl83])).
% 1.23/1.08 thf(zip_derived_cl83, plain,
% 1.23/1.08 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl75])).
% 1.23/1.08 thf(zip_derived_cl75, plain,
% 1.23/1.08 (![X0 : $i, X1 : $i]:
% 1.23/1.08 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.23/1.08 inference('demod', [status(thm)], [zip_derived_cl61, zip_derived_cl0])).
% 1.23/1.08 thf(zip_derived_cl75, plain,
% 1.23/1.08 (![X0 : $i, X1 : $i]:
% 1.23/1.08 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.23/1.08 inference('demod', [status(thm)], [zip_derived_cl61, zip_derived_cl0])).
% 1.23/1.08 thf(zip_derived_cl80, plain,
% 1.23/1.08 (![X0 : $i, X1 : $i]:
% 1.23/1.08 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl75, zip_derived_cl75])).
% 1.23/1.08 thf(zip_derived_cl353, plain,
% 1.23/1.08 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl83, zip_derived_cl80])).
% 1.23/1.08 thf(zip_derived_cl353, plain,
% 1.23/1.08 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl83, zip_derived_cl80])).
% 1.23/1.08 thf(zip_derived_cl375, plain,
% 1.23/1.08 ((((sk_c4) = (inverse @ sk_c8)) | ((sk_c8) = (sk_c7)))),
% 1.23/1.08 inference('demod', [status(thm)],
% 1.23/1.08 [zip_derived_cl231, zip_derived_cl353, zip_derived_cl353])).
% 1.23/1.08 thf(prove_this_25, conjecture,
% 1.23/1.08 (~( ( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c5 ) ) |
% 1.23/1.08 ( ( inverse @ sk_c1 ) = ( sk_c8 ) ) ))).
% 1.23/1.08 thf(zf_stmt_5, negated_conjecture,
% 1.23/1.08 (( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c5 ) ) |
% 1.23/1.08 ( ( inverse @ sk_c1 ) = ( sk_c8 ) )),
% 1.23/1.08 inference('cnf.neg', [status(esa)], [prove_this_25])).
% 1.23/1.08 thf(zip_derived_cl27, plain,
% 1.23/1.08 ((((multiply @ sk_c4 @ sk_c8) = (sk_c5)) | ((inverse @ sk_c1) = (sk_c8)))),
% 1.23/1.08 inference('cnf', [status(esa)], [zf_stmt_5])).
% 1.23/1.08 thf(zip_derived_cl353, plain,
% 1.23/1.08 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl83, zip_derived_cl80])).
% 1.23/1.08 thf(zip_derived_cl83, plain,
% 1.23/1.08 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl75])).
% 1.23/1.08 thf(zip_derived_cl383, plain,
% 1.23/1.08 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl353, zip_derived_cl83])).
% 1.23/1.08 thf(zip_derived_cl400, plain,
% 1.23/1.08 ((((sk_c1) = (inverse @ sk_c8)) | ((multiply @ sk_c4 @ sk_c8) = (sk_c5)))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl383])).
% 1.23/1.08 thf(prove_this_20, conjecture,
% 1.23/1.08 (~( ( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c5 ) ) |
% 1.23/1.08 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c2 ) ) ))).
% 1.23/1.08 thf(zf_stmt_6, negated_conjecture,
% 1.23/1.08 (( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c5 ) ) |
% 1.23/1.08 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c2 ) )),
% 1.23/1.08 inference('cnf.neg', [status(esa)], [prove_this_20])).
% 1.23/1.08 thf(zip_derived_cl22, plain,
% 1.23/1.08 ((((multiply @ sk_c4 @ sk_c8) = (sk_c5))
% 1.23/1.08 | ((multiply @ sk_c1 @ sk_c8) = (sk_c2)))),
% 1.23/1.08 inference('cnf', [status(esa)], [zf_stmt_6])).
% 1.23/1.08 thf(zip_derived_cl561, plain,
% 1.23/1.08 ((((multiply @ (inverse @ sk_c8) @ sk_c8) = (sk_c2))
% 1.23/1.08 | ((multiply @ sk_c4 @ sk_c8) = (sk_c5))
% 1.23/1.08 | ((multiply @ sk_c4 @ sk_c8) = (sk_c5)))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl400, zip_derived_cl22])).
% 1.23/1.08 thf(zip_derived_cl1, plain,
% 1.23/1.08 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.23/1.08 inference('cnf', [status(esa)], [left_inverse])).
% 1.23/1.08 thf(zip_derived_cl574, plain,
% 1.23/1.08 ((((identity) = (sk_c2))
% 1.23/1.08 | ((multiply @ sk_c4 @ sk_c8) = (sk_c5))
% 1.23/1.08 | ((multiply @ sk_c4 @ sk_c8) = (sk_c5)))),
% 1.23/1.08 inference('demod', [status(thm)], [zip_derived_cl561, zip_derived_cl1])).
% 1.23/1.08 thf(zip_derived_cl575, plain,
% 1.23/1.08 ((((multiply @ sk_c4 @ sk_c8) = (sk_c5)) | ((identity) = (sk_c2)))),
% 1.23/1.08 inference('simplify', [status(thm)], [zip_derived_cl574])).
% 1.23/1.08 thf(prove_this_15, conjecture,
% 1.23/1.08 (~( ( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c5 ) ) |
% 1.23/1.08 ( ( multiply @ sk_c8 @ sk_c2 ) = ( sk_c7 ) ) ))).
% 1.23/1.08 thf(zf_stmt_7, negated_conjecture,
% 1.23/1.08 (( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c5 ) ) |
% 1.23/1.08 ( ( multiply @ sk_c8 @ sk_c2 ) = ( sk_c7 ) )),
% 1.23/1.08 inference('cnf.neg', [status(esa)], [prove_this_15])).
% 1.23/1.08 thf(zip_derived_cl17, plain,
% 1.23/1.08 ((((multiply @ sk_c4 @ sk_c8) = (sk_c5))
% 1.23/1.08 | ((multiply @ sk_c8 @ sk_c2) = (sk_c7)))),
% 1.23/1.08 inference('cnf', [status(esa)], [zf_stmt_7])).
% 1.23/1.08 thf(zip_derived_cl603, plain,
% 1.23/1.08 ((((multiply @ sk_c8 @ identity) = (sk_c7))
% 1.23/1.08 | ((multiply @ sk_c4 @ sk_c8) = (sk_c5))
% 1.23/1.08 | ((multiply @ sk_c4 @ sk_c8) = (sk_c5)))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl575, zip_derived_cl17])).
% 1.23/1.08 thf(zip_derived_cl353, plain,
% 1.23/1.08 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl83, zip_derived_cl80])).
% 1.23/1.08 thf(zip_derived_cl613, plain,
% 1.23/1.08 ((((sk_c8) = (sk_c7))
% 1.23/1.08 | ((multiply @ sk_c4 @ sk_c8) = (sk_c5))
% 1.23/1.08 | ((multiply @ sk_c4 @ sk_c8) = (sk_c5)))),
% 1.23/1.08 inference('demod', [status(thm)], [zip_derived_cl603, zip_derived_cl353])).
% 1.23/1.08 thf(zip_derived_cl614, plain,
% 1.23/1.08 ((((multiply @ sk_c4 @ sk_c8) = (sk_c5)) | ((sk_c8) = (sk_c7)))),
% 1.23/1.08 inference('simplify', [status(thm)], [zip_derived_cl613])).
% 1.23/1.08 thf(zip_derived_cl720, plain,
% 1.23/1.08 ((((multiply @ (inverse @ sk_c8) @ sk_c8) = (sk_c5))
% 1.23/1.08 | ((sk_c8) = (sk_c7))
% 1.23/1.08 | ((sk_c8) = (sk_c7)))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl375, zip_derived_cl614])).
% 1.23/1.08 thf(zip_derived_cl1, plain,
% 1.23/1.08 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.23/1.08 inference('cnf', [status(esa)], [left_inverse])).
% 1.23/1.08 thf(zip_derived_cl723, plain,
% 1.23/1.08 ((((identity) = (sk_c5)) | ((sk_c8) = (sk_c7)) | ((sk_c8) = (sk_c7)))),
% 1.23/1.08 inference('demod', [status(thm)], [zip_derived_cl720, zip_derived_cl1])).
% 1.23/1.08 thf(zip_derived_cl724, plain,
% 1.23/1.08 ((((sk_c8) = (sk_c7)) | ((identity) = (sk_c5)))),
% 1.23/1.08 inference('simplify', [status(thm)], [zip_derived_cl723])).
% 1.23/1.08 thf(prove_this_24, conjecture,
% 1.23/1.08 (~( ( ( multiply @ sk_c8 @ sk_c5 ) = ( sk_c7 ) ) |
% 1.23/1.08 ( ( inverse @ sk_c1 ) = ( sk_c8 ) ) ))).
% 1.23/1.08 thf(zf_stmt_8, negated_conjecture,
% 1.23/1.08 (( ( multiply @ sk_c8 @ sk_c5 ) = ( sk_c7 ) ) |
% 1.23/1.08 ( ( inverse @ sk_c1 ) = ( sk_c8 ) )),
% 1.23/1.08 inference('cnf.neg', [status(esa)], [prove_this_24])).
% 1.23/1.08 thf(zip_derived_cl26, plain,
% 1.23/1.08 ((((multiply @ sk_c8 @ sk_c5) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c8)))),
% 1.23/1.08 inference('cnf', [status(esa)], [zf_stmt_8])).
% 1.23/1.08 thf(zip_derived_cl83, plain,
% 1.23/1.08 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl75])).
% 1.23/1.08 thf(zip_derived_cl234, plain,
% 1.23/1.08 ((((sk_c1) = (multiply @ (inverse @ sk_c8) @ identity))
% 1.23/1.08 | ((multiply @ sk_c8 @ sk_c5) = (sk_c7)))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl83])).
% 1.23/1.08 thf(prove_this_19, conjecture,
% 1.23/1.08 (~( ( ( multiply @ sk_c8 @ sk_c5 ) = ( sk_c7 ) ) |
% 1.23/1.08 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c2 ) ) ))).
% 1.23/1.08 thf(zf_stmt_9, negated_conjecture,
% 1.23/1.08 (( ( multiply @ sk_c8 @ sk_c5 ) = ( sk_c7 ) ) |
% 1.23/1.08 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c2 ) )),
% 1.23/1.08 inference('cnf.neg', [status(esa)], [prove_this_19])).
% 1.23/1.08 thf(zip_derived_cl21, plain,
% 1.23/1.08 ((((multiply @ sk_c8 @ sk_c5) = (sk_c7))
% 1.23/1.08 | ((multiply @ sk_c1 @ sk_c8) = (sk_c2)))),
% 1.23/1.08 inference('cnf', [status(esa)], [zf_stmt_9])).
% 1.23/1.08 thf(zip_derived_cl309, plain,
% 1.23/1.08 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 1.23/1.08 = (sk_c2))
% 1.23/1.08 | ((multiply @ sk_c8 @ sk_c5) = (sk_c7))
% 1.23/1.08 | ((multiply @ sk_c8 @ sk_c5) = (sk_c7)))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl234, zip_derived_cl21])).
% 1.23/1.08 thf(zip_derived_cl2, plain,
% 1.23/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.23/1.08 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.23/1.08 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.23/1.08 inference('cnf', [status(esa)], [associativity])).
% 1.23/1.08 thf(zip_derived_cl0, plain,
% 1.23/1.08 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.23/1.08 inference('cnf', [status(esa)], [left_identity])).
% 1.23/1.08 thf(zip_derived_cl1, plain,
% 1.23/1.08 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.23/1.08 inference('cnf', [status(esa)], [left_inverse])).
% 1.23/1.08 thf(zip_derived_cl322, plain,
% 1.23/1.08 ((((identity) = (sk_c2))
% 1.23/1.08 | ((multiply @ sk_c8 @ sk_c5) = (sk_c7))
% 1.23/1.08 | ((multiply @ sk_c8 @ sk_c5) = (sk_c7)))),
% 1.23/1.08 inference('demod', [status(thm)],
% 1.23/1.08 [zip_derived_cl309, zip_derived_cl2, zip_derived_cl0,
% 1.23/1.08 zip_derived_cl1])).
% 1.23/1.08 thf(zip_derived_cl323, plain,
% 1.23/1.08 ((((multiply @ sk_c8 @ sk_c5) = (sk_c7)) | ((identity) = (sk_c2)))),
% 1.23/1.08 inference('simplify', [status(thm)], [zip_derived_cl322])).
% 1.23/1.08 thf(prove_this_14, conjecture,
% 1.23/1.08 (~( ( ( multiply @ sk_c8 @ sk_c5 ) = ( sk_c7 ) ) |
% 1.23/1.08 ( ( multiply @ sk_c8 @ sk_c2 ) = ( sk_c7 ) ) ))).
% 1.23/1.08 thf(zf_stmt_10, negated_conjecture,
% 1.23/1.08 (( ( multiply @ sk_c8 @ sk_c5 ) = ( sk_c7 ) ) |
% 1.23/1.08 ( ( multiply @ sk_c8 @ sk_c2 ) = ( sk_c7 ) )),
% 1.23/1.08 inference('cnf.neg', [status(esa)], [prove_this_14])).
% 1.23/1.08 thf(zip_derived_cl16, plain,
% 1.23/1.08 ((((multiply @ sk_c8 @ sk_c5) = (sk_c7))
% 1.23/1.08 | ((multiply @ sk_c8 @ sk_c2) = (sk_c7)))),
% 1.23/1.08 inference('cnf', [status(esa)], [zf_stmt_10])).
% 1.23/1.08 thf(zip_derived_cl329, plain,
% 1.23/1.08 ((((multiply @ sk_c8 @ identity) = (sk_c7))
% 1.23/1.08 | ((multiply @ sk_c8 @ sk_c5) = (sk_c7))
% 1.23/1.08 | ((multiply @ sk_c8 @ sk_c5) = (sk_c7)))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl323, zip_derived_cl16])).
% 1.23/1.08 thf(zip_derived_cl337, plain,
% 1.23/1.08 ((((multiply @ sk_c8 @ sk_c5) = (sk_c7))
% 1.23/1.08 | ((multiply @ sk_c8 @ identity) = (sk_c7)))),
% 1.23/1.08 inference('simplify', [status(thm)], [zip_derived_cl329])).
% 1.23/1.08 thf(zip_derived_cl353, plain,
% 1.23/1.08 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl83, zip_derived_cl80])).
% 1.23/1.08 thf(zip_derived_cl990, plain,
% 1.23/1.08 ((((multiply @ sk_c8 @ sk_c5) = (sk_c7)) | ((sk_c8) = (sk_c7)))),
% 1.23/1.08 inference('demod', [status(thm)], [zip_derived_cl337, zip_derived_cl353])).
% 1.23/1.08 thf(zip_derived_cl996, plain,
% 1.23/1.08 ((((multiply @ sk_c8 @ identity) = (sk_c7))
% 1.23/1.08 | ((sk_c8) = (sk_c7))
% 1.23/1.08 | ((sk_c8) = (sk_c7)))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl724, zip_derived_cl990])).
% 1.23/1.08 thf(zip_derived_cl353, plain,
% 1.23/1.08 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl83, zip_derived_cl80])).
% 1.23/1.08 thf(zip_derived_cl999, plain,
% 1.23/1.08 ((((sk_c8) = (sk_c7)) | ((sk_c8) = (sk_c7)) | ((sk_c8) = (sk_c7)))),
% 1.23/1.08 inference('demod', [status(thm)], [zip_derived_cl996, zip_derived_cl353])).
% 1.23/1.08 thf(zip_derived_cl1000, plain, (((sk_c8) = (sk_c7))),
% 1.23/1.08 inference('simplify', [status(thm)], [zip_derived_cl999])).
% 1.23/1.08 thf(zip_derived_cl1000, plain, (((sk_c8) = (sk_c7))),
% 1.23/1.08 inference('simplify', [status(thm)], [zip_derived_cl999])).
% 1.23/1.08 thf(zip_derived_cl1, plain,
% 1.23/1.08 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.23/1.08 inference('cnf', [status(esa)], [left_inverse])).
% 1.23/1.08 thf(zip_derived_cl1000, plain, (((sk_c8) = (sk_c7))),
% 1.23/1.08 inference('simplify', [status(thm)], [zip_derived_cl999])).
% 1.23/1.08 thf(zip_derived_cl1000, plain, (((sk_c8) = (sk_c7))),
% 1.23/1.08 inference('simplify', [status(thm)], [zip_derived_cl999])).
% 1.23/1.08 thf(zip_derived_cl1000, plain, (((sk_c8) = (sk_c7))),
% 1.23/1.08 inference('simplify', [status(thm)], [zip_derived_cl999])).
% 1.23/1.08 thf(zip_derived_cl1012, plain,
% 1.23/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.23/1.08 (((inverse @ sk_c8) != (multiply @ sk_c8 @ sk_c8))
% 1.23/1.08 | ((identity) != (sk_c8))
% 1.23/1.08 | ((multiply @ sk_c8 @ X4) != (sk_c8))
% 1.23/1.08 | ((multiply @ X3 @ sk_c8) != (X4))
% 1.23/1.08 | ((inverse @ X3) != (sk_c8))
% 1.23/1.08 | ((multiply @ X2 @ sk_c8) != (sk_c8))
% 1.23/1.08 | ((inverse @ X2) != (sk_c8))
% 1.23/1.08 | ((multiply @ sk_c8 @ X1) != (sk_c8))
% 1.23/1.08 | ((multiply @ X0 @ sk_c8) != (X1))
% 1.23/1.08 | ((inverse @ X0) != (sk_c8)))),
% 1.23/1.08 inference('demod', [status(thm)],
% 1.23/1.08 [zip_derived_cl33, zip_derived_cl1000, zip_derived_cl1000,
% 1.23/1.08 zip_derived_cl1, zip_derived_cl1000, zip_derived_cl1000,
% 1.23/1.08 zip_derived_cl1000])).
% 1.23/1.08 thf(zip_derived_cl1013, plain,
% 1.23/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.23/1.08 (((inverse @ identity) != (multiply @ identity @ identity))
% 1.23/1.08 | ((identity) != (sk_c8))
% 1.23/1.08 | ((multiply @ identity @ X4) != (identity))
% 1.23/1.08 | ((multiply @ X3 @ identity) != (X4))
% 1.23/1.08 | ((inverse @ X3) != (identity))
% 1.23/1.08 | ((multiply @ X2 @ identity) != (identity))
% 1.23/1.08 | ((inverse @ X2) != (identity))
% 1.23/1.08 | ((multiply @ identity @ X1) != (identity))
% 1.23/1.08 | ((multiply @ X0 @ identity) != (X1))
% 1.23/1.08 | ((inverse @ X0) != (identity)))),
% 1.23/1.08 inference('local_rewriting', [status(thm)], [zip_derived_cl1012])).
% 1.23/1.08 thf(zip_derived_cl0, plain,
% 1.23/1.08 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.23/1.08 inference('cnf', [status(esa)], [left_identity])).
% 1.23/1.08 thf(zip_derived_cl75, plain,
% 1.23/1.08 (![X0 : $i, X1 : $i]:
% 1.23/1.08 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.23/1.08 inference('demod', [status(thm)], [zip_derived_cl61, zip_derived_cl0])).
% 1.23/1.08 thf(zip_derived_cl82, plain,
% 1.23/1.08 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl75])).
% 1.23/1.08 thf(zip_derived_cl75, plain,
% 1.23/1.08 (![X0 : $i, X1 : $i]:
% 1.23/1.08 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.23/1.08 inference('demod', [status(thm)], [zip_derived_cl61, zip_derived_cl0])).
% 1.23/1.08 thf(zip_derived_cl106, plain,
% 1.23/1.08 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ identity)) @ X0))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl82, zip_derived_cl75])).
% 1.23/1.08 thf(zip_derived_cl1, plain,
% 1.23/1.08 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.23/1.08 inference('cnf', [status(esa)], [left_inverse])).
% 1.23/1.08 thf(zip_derived_cl245, plain, (((inverse @ identity) = (identity))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl106, zip_derived_cl1])).
% 1.23/1.08 thf(zip_derived_cl0, plain,
% 1.23/1.08 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.23/1.08 inference('cnf', [status(esa)], [left_identity])).
% 1.23/1.08 thf(zip_derived_cl0, plain,
% 1.23/1.08 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.23/1.08 inference('cnf', [status(esa)], [left_identity])).
% 1.23/1.08 thf(zip_derived_cl353, plain,
% 1.23/1.08 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl83, zip_derived_cl80])).
% 1.23/1.08 thf(zip_derived_cl353, plain,
% 1.23/1.08 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl83, zip_derived_cl80])).
% 1.23/1.08 thf(zip_derived_cl0, plain,
% 1.23/1.08 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.23/1.08 inference('cnf', [status(esa)], [left_identity])).
% 1.23/1.08 thf(zip_derived_cl353, plain,
% 1.23/1.08 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl83, zip_derived_cl80])).
% 1.23/1.08 thf(zip_derived_cl1014, plain,
% 1.23/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.23/1.08 (((identity) != (identity))
% 1.23/1.08 | ((identity) != (sk_c8))
% 1.23/1.08 | ((X4) != (identity))
% 1.23/1.08 | ((X3) != (X4))
% 1.23/1.08 | ((inverse @ X3) != (identity))
% 1.23/1.08 | ((X2) != (identity))
% 1.23/1.08 | ((inverse @ X2) != (identity))
% 1.23/1.08 | ((X1) != (identity))
% 1.23/1.08 | ((X0) != (X1))
% 1.23/1.08 | ((inverse @ X0) != (identity)))),
% 1.23/1.08 inference('demod', [status(thm)],
% 1.23/1.08 [zip_derived_cl1013, zip_derived_cl245, zip_derived_cl0,
% 1.23/1.08 zip_derived_cl0, zip_derived_cl353, zip_derived_cl353,
% 1.23/1.08 zip_derived_cl0, zip_derived_cl353])).
% 1.23/1.08 thf(zip_derived_cl1015, plain,
% 1.23/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.23/1.08 (((inverse @ X0) != (identity))
% 1.23/1.08 | ((X0) != (X1))
% 1.23/1.08 | ((X1) != (identity))
% 1.23/1.08 | ((inverse @ X2) != (identity))
% 1.23/1.08 | ((X2) != (identity))
% 1.23/1.08 | ((inverse @ X3) != (identity))
% 1.23/1.08 | ((X3) != (X4))
% 1.23/1.08 | ((X4) != (identity))
% 1.23/1.08 | ((identity) != (sk_c8)))),
% 1.23/1.08 inference('simplify', [status(thm)], [zip_derived_cl1014])).
% 1.23/1.08 thf(zip_derived_cl1051, plain,
% 1.23/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.23/1.08 (((identity) != (sk_c8))
% 1.23/1.08 | ((X0) != (identity))
% 1.23/1.08 | ((X1) != (X0))
% 1.23/1.08 | ((inverse @ X1) != (identity))
% 1.23/1.08 | ((X2) != (identity))
% 1.23/1.08 | ((inverse @ X2) != (identity))
% 1.23/1.08 | ((X3) != (identity))
% 1.23/1.08 | ((inverse @ X3) != (identity)))),
% 1.23/1.08 inference('eq_res', [status(thm)], [zip_derived_cl1015])).
% 1.23/1.08 thf(zip_derived_cl1052, plain,
% 1.23/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.23/1.08 (((inverse @ X0) != (identity))
% 1.23/1.08 | ((X0) != (identity))
% 1.23/1.08 | ((inverse @ X1) != (identity))
% 1.23/1.08 | ((X1) != (identity))
% 1.23/1.08 | ((inverse @ X2) != (identity))
% 1.23/1.08 | ((X2) != (identity))
% 1.23/1.08 | ((identity) != (sk_c8)))),
% 1.23/1.08 inference('eq_res', [status(thm)], [zip_derived_cl1051])).
% 1.23/1.08 thf(prove_this_8, conjecture,
% 1.23/1.08 (~( ( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 1.23/1.08 ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c8 ) ) ))).
% 1.23/1.08 thf(zf_stmt_11, negated_conjecture,
% 1.23/1.08 (( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 1.23/1.08 ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c8 ) )),
% 1.23/1.08 inference('cnf.neg', [status(esa)], [prove_this_8])).
% 1.23/1.08 thf(zip_derived_cl10, plain,
% 1.23/1.08 ((((inverse @ sk_c3) = (sk_c8)) | ((multiply @ sk_c6 @ sk_c7) = (sk_c8)))),
% 1.23/1.08 inference('cnf', [status(esa)], [zf_stmt_11])).
% 1.23/1.08 thf(zip_derived_cl3, plain, (((multiply @ sk_c8 @ sk_c7) = (sk_c6))),
% 1.23/1.08 inference('cnf', [status(esa)], [zf_stmt_1])).
% 1.23/1.08 thf(zip_derived_cl40, plain,
% 1.23/1.08 ((((inverse @ sk_c3) = (sk_c8))
% 1.23/1.08 | ((multiply @ (multiply @ sk_c8 @ sk_c7) @ sk_c7) = (sk_c8)))),
% 1.23/1.08 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl3])).
% 1.23/1.08 thf(zip_derived_cl2, plain,
% 1.23/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.23/1.08 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.23/1.08 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.23/1.08 inference('cnf', [status(esa)], [associativity])).
% 1.23/1.08 thf(zip_derived_cl53, plain,
% 1.23/1.08 ((((inverse @ sk_c3) = (sk_c8))
% 1.23/1.08 | ((multiply @ sk_c8 @ (multiply @ sk_c7 @ sk_c7)) = (sk_c8)))),
% 1.23/1.08 inference('demod', [status(thm)], [zip_derived_cl40, zip_derived_cl2])).
% 1.23/1.08 thf(zip_derived_cl1000, plain, (((sk_c8) = (sk_c7))),
% 1.23/1.08 inference('simplify', [status(thm)], [zip_derived_cl999])).
% 1.23/1.08 thf(zip_derived_cl1000, plain, (((sk_c8) = (sk_c7))),
% 1.23/1.08 inference('simplify', [status(thm)], [zip_derived_cl999])).
% 1.23/1.08 thf(zip_derived_cl1266, plain,
% 1.23/1.08 ((((inverse @ sk_c3) = (sk_c8))
% 1.23/1.08 | ((multiply @ sk_c8 @ (multiply @ sk_c8 @ sk_c8)) = (sk_c8)))),
% 1.23/1.08 inference('demod', [status(thm)],
% 1.23/1.08 [zip_derived_cl53, zip_derived_cl1000, zip_derived_cl1000])).
% 1.23/1.08 thf(zip_derived_cl383, plain,
% 1.23/1.08 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl353, zip_derived_cl83])).
% 1.23/1.08 thf(zip_derived_cl1268, plain,
% 1.23/1.08 ((((sk_c3) = (inverse @ sk_c8))
% 1.23/1.08 | ((multiply @ sk_c8 @ (multiply @ sk_c8 @ sk_c8)) = (sk_c8)))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl1266, zip_derived_cl383])).
% 1.23/1.08 thf(prove_this_7, conjecture,
% 1.23/1.08 (~( ( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 1.23/1.08 ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c8 ) ) ))).
% 1.23/1.08 thf(zf_stmt_12, negated_conjecture,
% 1.23/1.08 (( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 1.23/1.08 ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c8 ) )),
% 1.23/1.08 inference('cnf.neg', [status(esa)], [prove_this_7])).
% 1.23/1.08 thf(zip_derived_cl9, plain,
% 1.23/1.08 ((((multiply @ sk_c3 @ sk_c8) = (sk_c7))
% 1.23/1.08 | ((multiply @ sk_c6 @ sk_c7) = (sk_c8)))),
% 1.23/1.08 inference('cnf', [status(esa)], [zf_stmt_12])).
% 1.23/1.08 thf(zip_derived_cl3, plain, (((multiply @ sk_c8 @ sk_c7) = (sk_c6))),
% 1.23/1.08 inference('cnf', [status(esa)], [zf_stmt_1])).
% 1.23/1.08 thf(zip_derived_cl51, plain,
% 1.23/1.08 ((((multiply @ sk_c3 @ sk_c8) = (sk_c7))
% 1.23/1.08 | ((multiply @ (multiply @ sk_c8 @ sk_c7) @ sk_c7) = (sk_c8)))),
% 1.23/1.08 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl3])).
% 1.23/1.08 thf(zip_derived_cl2, plain,
% 1.23/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.23/1.08 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.23/1.08 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.23/1.08 inference('cnf', [status(esa)], [associativity])).
% 1.23/1.08 thf(zip_derived_cl56, plain,
% 1.23/1.08 ((((multiply @ sk_c3 @ sk_c8) = (sk_c7))
% 1.23/1.08 | ((multiply @ sk_c8 @ (multiply @ sk_c7 @ sk_c7)) = (sk_c8)))),
% 1.23/1.08 inference('demod', [status(thm)], [zip_derived_cl51, zip_derived_cl2])).
% 1.23/1.08 thf(zip_derived_cl1000, plain, (((sk_c8) = (sk_c7))),
% 1.23/1.08 inference('simplify', [status(thm)], [zip_derived_cl999])).
% 1.23/1.08 thf(zip_derived_cl1000, plain, (((sk_c8) = (sk_c7))),
% 1.23/1.08 inference('simplify', [status(thm)], [zip_derived_cl999])).
% 1.23/1.08 thf(zip_derived_cl1000, plain, (((sk_c8) = (sk_c7))),
% 1.23/1.08 inference('simplify', [status(thm)], [zip_derived_cl999])).
% 1.23/1.08 thf(zip_derived_cl2439, plain,
% 1.23/1.08 ((((multiply @ sk_c3 @ sk_c8) = (sk_c8))
% 1.23/1.08 | ((multiply @ sk_c8 @ (multiply @ sk_c8 @ sk_c8)) = (sk_c8)))),
% 1.23/1.08 inference('demod', [status(thm)],
% 1.23/1.08 [zip_derived_cl56, zip_derived_cl1000, zip_derived_cl1000,
% 1.23/1.08 zip_derived_cl1000])).
% 1.23/1.08 thf(zip_derived_cl2444, plain,
% 1.23/1.08 ((((multiply @ (inverse @ sk_c8) @ sk_c8) = (sk_c8))
% 1.23/1.08 | ((multiply @ sk_c8 @ (multiply @ sk_c8 @ sk_c8)) = (sk_c8))
% 1.23/1.08 | ((multiply @ sk_c8 @ (multiply @ sk_c8 @ sk_c8)) = (sk_c8)))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl1268, zip_derived_cl2439])).
% 1.23/1.08 thf(zip_derived_cl1, plain,
% 1.23/1.08 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.23/1.08 inference('cnf', [status(esa)], [left_inverse])).
% 1.23/1.08 thf(zip_derived_cl2446, plain,
% 1.23/1.08 ((((identity) = (sk_c8))
% 1.23/1.08 | ((multiply @ sk_c8 @ (multiply @ sk_c8 @ sk_c8)) = (sk_c8))
% 1.23/1.08 | ((multiply @ sk_c8 @ (multiply @ sk_c8 @ sk_c8)) = (sk_c8)))),
% 1.23/1.08 inference('demod', [status(thm)], [zip_derived_cl2444, zip_derived_cl1])).
% 1.23/1.08 thf(zip_derived_cl2447, plain,
% 1.23/1.08 ((((multiply @ sk_c8 @ (multiply @ sk_c8 @ sk_c8)) = (sk_c8))
% 1.23/1.08 | ((identity) = (sk_c8)))),
% 1.23/1.08 inference('simplify', [status(thm)], [zip_derived_cl2446])).
% 1.23/1.08 thf(prove_this_3, conjecture,
% 1.23/1.08 (~( ( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 1.23/1.08 ( ( inverse @ sk_c8 ) = ( sk_c6 ) ) ))).
% 1.23/1.08 thf(zf_stmt_13, negated_conjecture,
% 1.23/1.08 (( ( inverse @ sk_c3 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c8 ) = ( sk_c6 ) )),
% 1.23/1.08 inference('cnf.neg', [status(esa)], [prove_this_3])).
% 1.23/1.08 thf(zip_derived_cl5, plain,
% 1.23/1.08 ((((inverse @ sk_c3) = (sk_c8)) | ((inverse @ sk_c8) = (sk_c6)))),
% 1.23/1.08 inference('cnf', [status(esa)], [zf_stmt_13])).
% 1.23/1.08 thf(zip_derived_cl3, plain, (((multiply @ sk_c8 @ sk_c7) = (sk_c6))),
% 1.23/1.08 inference('cnf', [status(esa)], [zf_stmt_1])).
% 1.23/1.08 thf(zip_derived_cl34, plain,
% 1.23/1.08 ((((inverse @ sk_c3) = (sk_c8))
% 1.23/1.08 | ((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c7)))),
% 1.23/1.08 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl3])).
% 1.23/1.08 thf(zip_derived_cl383, plain,
% 1.23/1.08 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl353, zip_derived_cl83])).
% 1.23/1.08 thf(zip_derived_cl393, plain,
% 1.23/1.08 ((((sk_c3) = (inverse @ sk_c8))
% 1.23/1.08 | ((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c7)))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl34, zip_derived_cl383])).
% 1.23/1.08 thf(prove_this_2, conjecture,
% 1.23/1.08 (~( ( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 1.23/1.08 ( ( inverse @ sk_c8 ) = ( sk_c6 ) ) ))).
% 1.23/1.08 thf(zf_stmt_14, negated_conjecture,
% 1.23/1.08 (( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 1.23/1.08 ( ( inverse @ sk_c8 ) = ( sk_c6 ) )),
% 1.23/1.08 inference('cnf.neg', [status(esa)], [prove_this_2])).
% 1.23/1.08 thf(zip_derived_cl4, plain,
% 1.23/1.08 ((((multiply @ sk_c3 @ sk_c8) = (sk_c7)) | ((inverse @ sk_c8) = (sk_c6)))),
% 1.23/1.08 inference('cnf', [status(esa)], [zf_stmt_14])).
% 1.23/1.08 thf(zip_derived_cl3, plain, (((multiply @ sk_c8 @ sk_c7) = (sk_c6))),
% 1.23/1.08 inference('cnf', [status(esa)], [zf_stmt_1])).
% 1.23/1.08 thf(zip_derived_cl47, plain,
% 1.23/1.08 ((((multiply @ sk_c3 @ sk_c8) = (sk_c7))
% 1.23/1.08 | ((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c7)))),
% 1.23/1.08 inference('demod', [status(thm)], [zip_derived_cl4, zip_derived_cl3])).
% 1.23/1.08 thf(zip_derived_cl646, plain,
% 1.23/1.08 ((((multiply @ (inverse @ sk_c8) @ sk_c8) = (sk_c7))
% 1.23/1.08 | ((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c7))
% 1.23/1.08 | ((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c7)))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl393, zip_derived_cl47])).
% 1.23/1.08 thf(zip_derived_cl1, plain,
% 1.23/1.08 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.23/1.08 inference('cnf', [status(esa)], [left_inverse])).
% 1.23/1.08 thf(zip_derived_cl655, plain,
% 1.23/1.08 ((((identity) = (sk_c7))
% 1.23/1.08 | ((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c7))
% 1.23/1.08 | ((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c7)))),
% 1.23/1.08 inference('demod', [status(thm)], [zip_derived_cl646, zip_derived_cl1])).
% 1.23/1.08 thf(zip_derived_cl656, plain,
% 1.23/1.08 ((((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c7))
% 1.23/1.08 | ((identity) = (sk_c7)))),
% 1.23/1.08 inference('simplify', [status(thm)], [zip_derived_cl655])).
% 1.23/1.08 thf(zip_derived_cl1000, plain, (((sk_c8) = (sk_c7))),
% 1.23/1.08 inference('simplify', [status(thm)], [zip_derived_cl999])).
% 1.23/1.08 thf(zip_derived_cl1000, plain, (((sk_c8) = (sk_c7))),
% 1.23/1.08 inference('simplify', [status(thm)], [zip_derived_cl999])).
% 1.23/1.08 thf(zip_derived_cl1040, plain,
% 1.23/1.08 ((((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c8))
% 1.23/1.08 | ((identity) = (sk_c8)))),
% 1.23/1.08 inference('demod', [status(thm)],
% 1.23/1.08 [zip_derived_cl656, zip_derived_cl1000, zip_derived_cl1000])).
% 1.23/1.08 thf(zip_derived_cl383, plain,
% 1.23/1.08 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl353, zip_derived_cl83])).
% 1.23/1.08 thf(zip_derived_cl1, plain,
% 1.23/1.08 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.23/1.08 inference('cnf', [status(esa)], [left_inverse])).
% 1.23/1.08 thf(zip_derived_cl388, plain,
% 1.23/1.08 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl383, zip_derived_cl1])).
% 1.23/1.08 thf(zip_derived_cl1141, plain,
% 1.23/1.08 ((((multiply @ sk_c8 @ (multiply @ sk_c8 @ sk_c8)) = (identity))
% 1.23/1.08 | ((identity) = (sk_c8)))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl1040, zip_derived_cl388])).
% 1.23/1.08 thf(zip_derived_cl3813, plain,
% 1.23/1.08 ((((sk_c8) = (identity))
% 1.23/1.08 | ((identity) = (sk_c8))
% 1.23/1.08 | ((identity) = (sk_c8)))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl2447, zip_derived_cl1141])).
% 1.23/1.08 thf(zip_derived_cl3819, plain, (((sk_c8) = (identity))),
% 1.23/1.08 inference('simplify', [status(thm)], [zip_derived_cl3813])).
% 1.23/1.08 thf(zip_derived_cl3883, plain,
% 1.23/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.23/1.08 (((inverse @ X0) != (identity))
% 1.23/1.08 | ((X0) != (identity))
% 1.23/1.08 | ((inverse @ X1) != (identity))
% 1.23/1.08 | ((X1) != (identity))
% 1.23/1.08 | ((inverse @ X2) != (identity))
% 1.23/1.08 | ((X2) != (identity))
% 1.23/1.08 | ((identity) != (identity)))),
% 1.23/1.08 inference('demod', [status(thm)],
% 1.23/1.08 [zip_derived_cl1052, zip_derived_cl3819])).
% 1.23/1.08 thf(zip_derived_cl3884, plain,
% 1.23/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.23/1.08 (((X2) != (identity))
% 1.23/1.08 | ((inverse @ X2) != (identity))
% 1.23/1.08 | ((X1) != (identity))
% 1.23/1.08 | ((inverse @ X1) != (identity))
% 1.23/1.08 | ((X0) != (identity))
% 1.23/1.08 | ((inverse @ X0) != (identity)))),
% 1.23/1.08 inference('simplify', [status(thm)], [zip_derived_cl3883])).
% 1.23/1.08 thf(zip_derived_cl3932, plain,
% 1.23/1.08 (![X0 : $i, X1 : $i]:
% 1.23/1.08 (((inverse @ X0) != (identity))
% 1.23/1.08 | ((X0) != (identity))
% 1.23/1.08 | ((inverse @ X1) != (identity))
% 1.23/1.08 | ((X1) != (identity))
% 1.23/1.08 | ((inverse @ identity) != (identity)))),
% 1.23/1.08 inference('eq_res', [status(thm)], [zip_derived_cl3884])).
% 1.23/1.08 thf(zip_derived_cl245, plain, (((inverse @ identity) = (identity))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl106, zip_derived_cl1])).
% 1.23/1.08 thf(zip_derived_cl3933, plain,
% 1.23/1.08 (![X0 : $i, X1 : $i]:
% 1.23/1.08 (((inverse @ X0) != (identity))
% 1.23/1.08 | ((X0) != (identity))
% 1.23/1.08 | ((inverse @ X1) != (identity))
% 1.23/1.08 | ((X1) != (identity))
% 1.23/1.08 | ((identity) != (identity)))),
% 1.23/1.08 inference('demod', [status(thm)], [zip_derived_cl3932, zip_derived_cl245])).
% 1.23/1.08 thf(zip_derived_cl3934, plain,
% 1.23/1.08 (![X0 : $i, X1 : $i]:
% 1.23/1.08 (((X1) != (identity))
% 1.23/1.08 | ((inverse @ X1) != (identity))
% 1.23/1.08 | ((X0) != (identity))
% 1.23/1.08 | ((inverse @ X0) != (identity)))),
% 1.23/1.08 inference('simplify', [status(thm)], [zip_derived_cl3933])).
% 1.23/1.08 thf(zip_derived_cl3935, plain,
% 1.23/1.08 (![X0 : $i]:
% 1.23/1.08 (((inverse @ X0) != (identity))
% 1.23/1.08 | ((X0) != (identity))
% 1.23/1.08 | ((inverse @ identity) != (identity)))),
% 1.23/1.08 inference('eq_res', [status(thm)], [zip_derived_cl3934])).
% 1.23/1.08 thf(zip_derived_cl245, plain, (((inverse @ identity) = (identity))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl106, zip_derived_cl1])).
% 1.23/1.08 thf(zip_derived_cl3936, plain,
% 1.23/1.08 (![X0 : $i]:
% 1.23/1.08 (((inverse @ X0) != (identity))
% 1.23/1.08 | ((X0) != (identity))
% 1.23/1.08 | ((identity) != (identity)))),
% 1.23/1.08 inference('demod', [status(thm)], [zip_derived_cl3935, zip_derived_cl245])).
% 1.23/1.08 thf(zip_derived_cl3937, plain,
% 1.23/1.08 (![X0 : $i]: (((X0) != (identity)) | ((inverse @ X0) != (identity)))),
% 1.23/1.08 inference('simplify', [status(thm)], [zip_derived_cl3936])).
% 1.23/1.08 thf(zip_derived_cl3938, plain, (((inverse @ identity) != (identity))),
% 1.23/1.08 inference('eq_res', [status(thm)], [zip_derived_cl3937])).
% 1.23/1.08 thf(zip_derived_cl245, plain, (((inverse @ identity) = (identity))),
% 1.23/1.08 inference('sup+', [status(thm)], [zip_derived_cl106, zip_derived_cl1])).
% 1.23/1.08 thf(zip_derived_cl3939, plain, (((identity) != (identity))),
% 1.23/1.08 inference('demod', [status(thm)], [zip_derived_cl3938, zip_derived_cl245])).
% 1.23/1.08 thf(zip_derived_cl3940, plain, ($false),
% 1.23/1.08 inference('simplify', [status(thm)], [zip_derived_cl3939])).
% 1.23/1.08
% 1.23/1.08 % SZS output end Refutation
% 1.23/1.08
% 1.23/1.08
% 1.23/1.08 % Terminating...
% 4.42/1.22 % Runner terminated.
% 4.42/1.24 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------