%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP356-1 : 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.qkddLGb7pI 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 Oct 2 04:36:18 PM UTC 2025
% Result : Unsatisfiable 4.35s 1.28s
% Output : Refutation 4.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP356-1 : TPTP v9.2.0. Released v2.5.0.
% 0.13/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.qkddLGb7pI true
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 1 14:08:38 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.36 % Python version: Python 3.6.8
% 0.13/0.36 % Running in FO mode
% 0.54/0.68 % Total configuration time : 435
% 0.54/0.68 % Estimated wc time : 1092
% 0.54/0.68 % Estimated cpu time (7 cpus) : 156.0
% 0.57/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.57/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.57/0.81 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.57/0.81 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.57/0.81 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.57/0.82 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.57/0.82 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 4.35/1.28 % Solved by fo/fo7.sh.
% 4.35/1.28 % done 1347 iterations in 0.440s
% 4.35/1.28 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 4.35/1.28 % SZS output start Refutation
% 4.35/1.28 thf(sk_c1_type, type, sk_c1: $i).
% 4.35/1.28 thf(sk_c8_type, type, sk_c8: $i).
% 4.35/1.28 thf(sk_c4_type, type, sk_c4: $i).
% 4.35/1.28 thf(sk_c5_type, type, sk_c5: $i).
% 4.35/1.28 thf(identity_type, type, identity: $i).
% 4.35/1.28 thf(multiply_type, type, multiply: $i > $i > $i).
% 4.35/1.28 thf(sk_c6_type, type, sk_c6: $i).
% 4.35/1.28 thf(inverse_type, type, inverse: $i > $i).
% 4.35/1.28 thf(sk_c3_type, type, sk_c3: $i).
% 4.35/1.28 thf(sk_c2_type, type, sk_c2: $i).
% 4.35/1.28 thf(sk_c7_type, type, sk_c7: $i).
% 4.35/1.28 thf(prove_this_31, conjecture,
% 4.35/1.28 (~( ( ( inverse @ X5 ) != ( sk_c8 ) ) |
% 4.35/1.28 ( ( multiply @ X5 @ sk_c8 ) != ( X2 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c8 @ X2 ) != ( sk_c7 ) ) |
% 4.35/1.28 ( ( inverse @ X1 ) != ( sk_c8 ) ) |
% 4.35/1.28 ( ( multiply @ X1 @ sk_c8 ) != ( sk_c7 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c8 @ sk_c7 ) != ( sk_c6 ) ) |
% 4.35/1.28 ( ( inverse @ X4 ) != ( sk_c8 ) ) |
% 4.35/1.28 ( ( multiply @ X4 @ sk_c8 ) != ( sk_c6 ) ) |
% 4.35/1.28 ( ( inverse @ X3 ) != ( sk_c7 ) ) |
% 4.35/1.28 ( ( multiply @ X3 @ sk_c7 ) != ( sk_c8 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c7 @ sk_c6 ) != ( sk_c8 ) ) ))).
% 4.35/1.28 thf(zf_stmt_0, negated_conjecture,
% 4.35/1.28 (( ( inverse @ X5 ) != ( sk_c8 ) ) |
% 4.35/1.28 ( ( multiply @ X5 @ sk_c8 ) != ( X2 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c8 @ X2 ) != ( sk_c7 ) ) |
% 4.35/1.28 ( ( inverse @ X1 ) != ( sk_c8 ) ) |
% 4.35/1.28 ( ( multiply @ X1 @ sk_c8 ) != ( sk_c7 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c8 @ sk_c7 ) != ( sk_c6 ) ) |
% 4.35/1.28 ( ( inverse @ X4 ) != ( sk_c8 ) ) |
% 4.35/1.28 ( ( multiply @ X4 @ sk_c8 ) != ( sk_c6 ) ) |
% 4.35/1.28 ( ( inverse @ X3 ) != ( sk_c7 ) ) |
% 4.35/1.28 ( ( multiply @ X3 @ sk_c7 ) != ( sk_c8 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c7 @ sk_c6 ) != ( sk_c8 ) )),
% 4.35/1.28 inference('cnf.neg', [status(esa)], [prove_this_31])).
% 4.35/1.28 thf(zip_derived_cl33, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 4.35/1.28 (((inverse @ X0) != (sk_c8))
% 4.35/1.28 | ((multiply @ X0 @ sk_c8) != (X1))
% 4.35/1.28 | ((multiply @ sk_c8 @ X1) != (sk_c7))
% 4.35/1.28 | ((inverse @ X2) != (sk_c8))
% 4.35/1.28 | ((multiply @ X2 @ sk_c8) != (sk_c7))
% 4.35/1.28 | ((multiply @ sk_c8 @ sk_c7) != (sk_c6))
% 4.35/1.28 | ((inverse @ X3) != (sk_c8))
% 4.35/1.28 | ((multiply @ X3 @ sk_c8) != (sk_c6))
% 4.35/1.28 | ((inverse @ X4) != (sk_c7))
% 4.35/1.28 | ((multiply @ X4 @ sk_c7) != (sk_c8))
% 4.35/1.28 | ((multiply @ sk_c7 @ sk_c6) != (sk_c8)))),
% 4.35/1.28 inference('cnf', [status(esa)], [zf_stmt_0])).
% 4.35/1.28 thf(zip_derived_cl34, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 4.35/1.28 (((inverse @ X0) != (multiply @ sk_c7 @ sk_c6))
% 4.35/1.28 | ((multiply @ X0 @ (multiply @ sk_c7 @ sk_c6)) != (X1))
% 4.35/1.28 | ((multiply @ (multiply @ sk_c7 @ sk_c6) @ X1) != (sk_c7))
% 4.35/1.28 | ((inverse @ X2) != (multiply @ sk_c7 @ sk_c6))
% 4.35/1.28 | ((multiply @ X2 @ (multiply @ sk_c7 @ sk_c6)) != (sk_c7))
% 4.35/1.28 | ((multiply @ (multiply @ sk_c7 @ sk_c6) @ sk_c7) != (sk_c6))
% 4.35/1.28 | ((inverse @ X3) != (multiply @ sk_c7 @ sk_c6))
% 4.35/1.28 | ((multiply @ X3 @ (multiply @ sk_c7 @ sk_c6)) != (sk_c6))
% 4.35/1.28 | ((inverse @ X4) != (sk_c7))
% 4.35/1.28 | ((multiply @ X4 @ sk_c7) != (multiply @ sk_c7 @ sk_c6))
% 4.35/1.28 | ((multiply @ sk_c7 @ sk_c6) != (sk_c8)))),
% 4.35/1.28 inference('local_rewriting', [status(thm)], [zip_derived_cl33])).
% 4.35/1.28 thf(associativity, axiom,
% 4.35/1.28 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 4.35/1.28 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 4.35/1.28 thf(zip_derived_cl2, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.35/1.28 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 4.35/1.28 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 4.35/1.28 inference('cnf', [status(esa)], [associativity])).
% 4.35/1.28 thf(zip_derived_cl2, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.35/1.28 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 4.35/1.28 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 4.35/1.28 inference('cnf', [status(esa)], [associativity])).
% 4.35/1.28 thf(zip_derived_cl49, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 4.35/1.28 (((inverse @ X0) != (multiply @ sk_c7 @ sk_c6))
% 4.35/1.28 | ((multiply @ X0 @ (multiply @ sk_c7 @ sk_c6)) != (X1))
% 4.35/1.28 | ((multiply @ sk_c7 @ (multiply @ sk_c6 @ X1)) != (sk_c7))
% 4.35/1.28 | ((inverse @ X2) != (multiply @ sk_c7 @ sk_c6))
% 4.35/1.28 | ((multiply @ X2 @ (multiply @ sk_c7 @ sk_c6)) != (sk_c7))
% 4.35/1.28 | ((multiply @ sk_c7 @ (multiply @ sk_c6 @ sk_c7)) != (sk_c6))
% 4.35/1.28 | ((inverse @ X3) != (multiply @ sk_c7 @ sk_c6))
% 4.35/1.28 | ((multiply @ X3 @ (multiply @ sk_c7 @ sk_c6)) != (sk_c6))
% 4.35/1.28 | ((inverse @ X4) != (sk_c7))
% 4.35/1.28 | ((multiply @ X4 @ sk_c7) != (multiply @ sk_c7 @ sk_c6))
% 4.35/1.28 | ((multiply @ sk_c7 @ sk_c6) != (sk_c8)))),
% 4.35/1.28 inference('demod', [status(thm)],
% 4.35/1.28 [zip_derived_cl34, zip_derived_cl2, zip_derived_cl2])).
% 4.35/1.28 thf(prove_this_18, conjecture,
% 4.35/1.28 (~( ( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 4.35/1.28 ( ( inverse @ sk_c1 ) = ( sk_c7 ) ) ))).
% 4.35/1.28 thf(zf_stmt_1, negated_conjecture,
% 4.35/1.28 (( ( inverse @ sk_c4 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c7 ) )),
% 4.35/1.28 inference('cnf.neg', [status(esa)], [prove_this_18])).
% 4.35/1.28 thf(zip_derived_cl20, plain,
% 4.35/1.28 ((((inverse @ sk_c4) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c7)))),
% 4.35/1.28 inference('cnf', [status(esa)], [zf_stmt_1])).
% 4.35/1.28 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 4.35/1.28 thf(zip_derived_cl1, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_inverse])).
% 4.35/1.28 thf(zip_derived_cl38, plain,
% 4.35/1.28 ((((multiply @ sk_c7 @ sk_c1) = (identity))
% 4.35/1.28 | ((inverse @ sk_c4) = (sk_c8)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl20, zip_derived_cl1])).
% 4.35/1.28 thf(zip_derived_cl1, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_inverse])).
% 4.35/1.28 thf(zip_derived_cl2, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.35/1.28 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 4.35/1.28 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 4.35/1.28 inference('cnf', [status(esa)], [associativity])).
% 4.35/1.28 thf(zip_derived_cl53, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i]:
% 4.35/1.28 ((multiply @ identity @ X0)
% 4.35/1.28 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 4.35/1.28 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 4.35/1.28 thf(zip_derived_cl0, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_identity])).
% 4.35/1.28 thf(zip_derived_cl69, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i]:
% 4.35/1.28 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl53, zip_derived_cl0])).
% 4.35/1.28 thf(zip_derived_cl84, plain,
% 4.35/1.28 ((((sk_c1) = (multiply @ (inverse @ sk_c7) @ identity))
% 4.35/1.28 | ((inverse @ sk_c4) = (sk_c8)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl38, zip_derived_cl69])).
% 4.35/1.28 thf(prove_this_12, conjecture,
% 4.35/1.28 (~( ( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) ) ))).
% 4.35/1.28 thf(zf_stmt_2, negated_conjecture,
% 4.35/1.28 (( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) )),
% 4.35/1.28 inference('cnf.neg', [status(esa)], [prove_this_12])).
% 4.35/1.28 thf(zip_derived_cl14, plain,
% 4.35/1.28 ((((inverse @ sk_c4) = (sk_c8)) | ((multiply @ sk_c1 @ sk_c7) = (sk_c8)))),
% 4.35/1.28 inference('cnf', [status(esa)], [zf_stmt_2])).
% 4.35/1.28 thf(zip_derived_cl133, plain,
% 4.35/1.28 ((((multiply @ (multiply @ (inverse @ sk_c7) @ identity) @ sk_c7)
% 4.35/1.28 = (sk_c8))
% 4.35/1.28 | ((inverse @ sk_c4) = (sk_c8))
% 4.35/1.28 | ((inverse @ sk_c4) = (sk_c8)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl84, zip_derived_cl14])).
% 4.35/1.28 thf(zip_derived_cl2, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.35/1.28 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 4.35/1.28 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 4.35/1.28 inference('cnf', [status(esa)], [associativity])).
% 4.35/1.28 thf(zip_derived_cl0, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_identity])).
% 4.35/1.28 thf(zip_derived_cl1, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_inverse])).
% 4.35/1.28 thf(zip_derived_cl143, plain,
% 4.35/1.28 ((((identity) = (sk_c8))
% 4.35/1.28 | ((inverse @ sk_c4) = (sk_c8))
% 4.35/1.28 | ((inverse @ sk_c4) = (sk_c8)))),
% 4.35/1.28 inference('demod', [status(thm)],
% 4.35/1.28 [zip_derived_cl133, zip_derived_cl2, zip_derived_cl0,
% 4.35/1.28 zip_derived_cl1])).
% 4.35/1.28 thf(zip_derived_cl144, plain,
% 4.35/1.28 ((((inverse @ sk_c4) = (sk_c8)) | ((identity) = (sk_c8)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl143])).
% 4.35/1.28 thf(zip_derived_cl1, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_inverse])).
% 4.35/1.28 thf(zip_derived_cl147, plain,
% 4.35/1.28 ((((multiply @ sk_c8 @ sk_c4) = (identity)) | ((identity) = (sk_c8)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl144, zip_derived_cl1])).
% 4.35/1.28 thf(zip_derived_cl69, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i]:
% 4.35/1.28 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl53, zip_derived_cl0])).
% 4.35/1.28 thf(zip_derived_cl153, plain,
% 4.35/1.28 ((((sk_c4) = (multiply @ (inverse @ sk_c8) @ identity))
% 4.35/1.28 | ((identity) = (sk_c8)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl147, zip_derived_cl69])).
% 4.35/1.28 thf(zip_derived_cl1, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_inverse])).
% 4.35/1.28 thf(zip_derived_cl69, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i]:
% 4.35/1.28 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl53, zip_derived_cl0])).
% 4.35/1.28 thf(zip_derived_cl81, plain,
% 4.35/1.28 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl69])).
% 4.35/1.28 thf(zip_derived_cl69, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i]:
% 4.35/1.28 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl53, zip_derived_cl0])).
% 4.35/1.28 thf(zip_derived_cl69, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i]:
% 4.35/1.28 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl53, zip_derived_cl0])).
% 4.35/1.28 thf(zip_derived_cl78, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i]:
% 4.35/1.28 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl69, zip_derived_cl69])).
% 4.35/1.28 thf(zip_derived_cl329, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl81, zip_derived_cl78])).
% 4.35/1.28 thf(zip_derived_cl358, plain,
% 4.35/1.28 ((((sk_c4) = (inverse @ sk_c8)) | ((identity) = (sk_c8)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl153, zip_derived_cl329])).
% 4.35/1.28 thf(prove_this_17, conjecture,
% 4.35/1.28 (~( ( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c5 ) ) |
% 4.35/1.28 ( ( inverse @ sk_c1 ) = ( sk_c7 ) ) ))).
% 4.35/1.28 thf(zf_stmt_3, negated_conjecture,
% 4.35/1.28 (( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c5 ) ) |
% 4.35/1.28 ( ( inverse @ sk_c1 ) = ( sk_c7 ) )),
% 4.35/1.28 inference('cnf.neg', [status(esa)], [prove_this_17])).
% 4.35/1.28 thf(zip_derived_cl19, plain,
% 4.35/1.28 ((((multiply @ sk_c4 @ sk_c8) = (sk_c5)) | ((inverse @ sk_c1) = (sk_c7)))),
% 4.35/1.28 inference('cnf', [status(esa)], [zf_stmt_3])).
% 4.35/1.28 thf(zip_derived_cl329, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl81, zip_derived_cl78])).
% 4.35/1.28 thf(zip_derived_cl81, plain,
% 4.35/1.28 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl69])).
% 4.35/1.28 thf(zip_derived_cl367, plain,
% 4.35/1.28 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl329, zip_derived_cl81])).
% 4.35/1.28 thf(zip_derived_cl1, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_inverse])).
% 4.35/1.28 thf(zip_derived_cl373, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl367, zip_derived_cl1])).
% 4.35/1.28 thf(zip_derived_cl584, plain,
% 4.35/1.28 ((((multiply @ sk_c1 @ sk_c7) = (identity))
% 4.35/1.28 | ((multiply @ sk_c4 @ sk_c8) = (sk_c5)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl373])).
% 4.35/1.28 thf(prove_this_11, conjecture,
% 4.35/1.28 (~( ( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c5 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) ) ))).
% 4.35/1.28 thf(zf_stmt_4, negated_conjecture,
% 4.35/1.28 (( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c5 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) )),
% 4.35/1.28 inference('cnf.neg', [status(esa)], [prove_this_11])).
% 4.35/1.28 thf(zip_derived_cl13, plain,
% 4.35/1.28 ((((multiply @ sk_c4 @ sk_c8) = (sk_c5))
% 4.35/1.28 | ((multiply @ sk_c1 @ sk_c7) = (sk_c8)))),
% 4.35/1.28 inference('cnf', [status(esa)], [zf_stmt_4])).
% 4.35/1.28 thf(zip_derived_cl3807, plain,
% 4.35/1.28 ((((identity) = (sk_c8))
% 4.35/1.28 | ((multiply @ sk_c4 @ sk_c8) = (sk_c5))
% 4.35/1.28 | ((multiply @ sk_c4 @ sk_c8) = (sk_c5)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl584, zip_derived_cl13])).
% 4.35/1.28 thf(zip_derived_cl3815, plain,
% 4.35/1.28 ((((multiply @ sk_c4 @ sk_c8) = (sk_c5)) | ((identity) = (sk_c8)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl3807])).
% 4.35/1.28 thf(zip_derived_cl3849, plain,
% 4.35/1.28 ((((multiply @ (inverse @ sk_c8) @ sk_c8) = (sk_c5))
% 4.35/1.28 | ((identity) = (sk_c8))
% 4.35/1.28 | ((identity) = (sk_c8)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl358, zip_derived_cl3815])).
% 4.35/1.28 thf(zip_derived_cl1, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_inverse])).
% 4.35/1.28 thf(zip_derived_cl3861, plain,
% 4.35/1.28 ((((identity) = (sk_c5))
% 4.35/1.28 | ((identity) = (sk_c8))
% 4.35/1.28 | ((identity) = (sk_c8)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl3849, zip_derived_cl1])).
% 4.35/1.28 thf(zip_derived_cl3862, plain,
% 4.35/1.28 ((((identity) = (sk_c8)) | ((identity) = (sk_c5)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl3861])).
% 4.35/1.28 thf(prove_this_16, conjecture,
% 4.35/1.28 (~( ( ( multiply @ sk_c8 @ sk_c5 ) = ( sk_c7 ) ) |
% 4.35/1.28 ( ( inverse @ sk_c1 ) = ( sk_c7 ) ) ))).
% 4.35/1.28 thf(zf_stmt_5, negated_conjecture,
% 4.35/1.28 (( ( multiply @ sk_c8 @ sk_c5 ) = ( sk_c7 ) ) |
% 4.35/1.28 ( ( inverse @ sk_c1 ) = ( sk_c7 ) )),
% 4.35/1.28 inference('cnf.neg', [status(esa)], [prove_this_16])).
% 4.35/1.28 thf(zip_derived_cl18, plain,
% 4.35/1.28 ((((multiply @ sk_c8 @ sk_c5) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c7)))),
% 4.35/1.28 inference('cnf', [status(esa)], [zf_stmt_5])).
% 4.35/1.28 thf(zip_derived_cl367, plain,
% 4.35/1.28 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl329, zip_derived_cl81])).
% 4.35/1.28 thf(zip_derived_cl387, plain,
% 4.35/1.28 ((((sk_c1) = (inverse @ sk_c7)) | ((multiply @ sk_c8 @ sk_c5) = (sk_c7)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl18, zip_derived_cl367])).
% 4.35/1.28 thf(prove_this_10, conjecture,
% 4.35/1.28 (~( ( ( multiply @ sk_c8 @ sk_c5 ) = ( sk_c7 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) ) ))).
% 4.35/1.28 thf(zf_stmt_6, negated_conjecture,
% 4.35/1.28 (( ( multiply @ sk_c8 @ sk_c5 ) = ( sk_c7 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) )),
% 4.35/1.28 inference('cnf.neg', [status(esa)], [prove_this_10])).
% 4.35/1.28 thf(zip_derived_cl12, plain,
% 4.35/1.28 ((((multiply @ sk_c8 @ sk_c5) = (sk_c7))
% 4.35/1.28 | ((multiply @ sk_c1 @ sk_c7) = (sk_c8)))),
% 4.35/1.28 inference('cnf', [status(esa)], [zf_stmt_6])).
% 4.35/1.28 thf(zip_derived_cl3664, plain,
% 4.35/1.28 ((((multiply @ (inverse @ sk_c7) @ sk_c7) = (sk_c8))
% 4.35/1.28 | ((multiply @ sk_c8 @ sk_c5) = (sk_c7))
% 4.35/1.28 | ((multiply @ sk_c8 @ sk_c5) = (sk_c7)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl387, zip_derived_cl12])).
% 4.35/1.28 thf(zip_derived_cl1, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_inverse])).
% 4.35/1.28 thf(zip_derived_cl3670, plain,
% 4.35/1.28 ((((identity) = (sk_c8))
% 4.35/1.28 | ((multiply @ sk_c8 @ sk_c5) = (sk_c7))
% 4.35/1.28 | ((multiply @ sk_c8 @ sk_c5) = (sk_c7)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl3664, zip_derived_cl1])).
% 4.35/1.28 thf(zip_derived_cl3671, plain,
% 4.35/1.28 ((((multiply @ sk_c8 @ sk_c5) = (sk_c7)) | ((identity) = (sk_c8)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl3670])).
% 4.35/1.28 thf(zip_derived_cl3873, plain,
% 4.35/1.28 ((((multiply @ sk_c8 @ identity) = (sk_c7))
% 4.35/1.28 | ((identity) = (sk_c8))
% 4.35/1.28 | ((identity) = (sk_c8)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl3862, zip_derived_cl3671])).
% 4.35/1.28 thf(zip_derived_cl3877, plain,
% 4.35/1.28 ((((identity) = (sk_c8)) | ((multiply @ sk_c8 @ identity) = (sk_c7)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl3873])).
% 4.35/1.28 thf(zip_derived_cl329, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl81, zip_derived_cl78])).
% 4.35/1.28 thf(zip_derived_cl4181, plain,
% 4.35/1.28 ((((sk_c7) = (sk_c8)) | ((identity) = (sk_c8)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl3877, zip_derived_cl329])).
% 4.35/1.28 thf(zip_derived_cl4290, plain,
% 4.35/1.28 ((((sk_c7) != (identity)) | ((identity) = (sk_c8)))),
% 4.35/1.28 inference('eq_fact', [status(thm)], [zip_derived_cl4181])).
% 4.35/1.28 thf(prove_this_15, conjecture,
% 4.35/1.28 (~( ( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 4.35/1.28 ( ( inverse @ sk_c1 ) = ( sk_c7 ) ) ))).
% 4.35/1.28 thf(zf_stmt_7, negated_conjecture,
% 4.35/1.28 (( ( inverse @ sk_c3 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c7 ) )),
% 4.35/1.28 inference('cnf.neg', [status(esa)], [prove_this_15])).
% 4.35/1.28 thf(zip_derived_cl17, plain,
% 4.35/1.28 ((((inverse @ sk_c3) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c7)))),
% 4.35/1.28 inference('cnf', [status(esa)], [zf_stmt_7])).
% 4.35/1.28 thf(zip_derived_cl1, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_inverse])).
% 4.35/1.28 thf(zip_derived_cl37, plain,
% 4.35/1.28 ((((multiply @ sk_c7 @ sk_c1) = (identity))
% 4.35/1.28 | ((inverse @ sk_c3) = (sk_c8)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl17, zip_derived_cl1])).
% 4.35/1.28 thf(zip_derived_cl69, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i]:
% 4.35/1.28 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl53, zip_derived_cl0])).
% 4.35/1.28 thf(zip_derived_cl83, plain,
% 4.35/1.28 ((((sk_c1) = (multiply @ (inverse @ sk_c7) @ identity))
% 4.35/1.28 | ((inverse @ sk_c3) = (sk_c8)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl37, zip_derived_cl69])).
% 4.35/1.28 thf(prove_this_9, conjecture,
% 4.35/1.28 (~( ( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) ) ))).
% 4.35/1.28 thf(zf_stmt_8, negated_conjecture,
% 4.35/1.28 (( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) )),
% 4.35/1.28 inference('cnf.neg', [status(esa)], [prove_this_9])).
% 4.35/1.28 thf(zip_derived_cl11, plain,
% 4.35/1.28 ((((inverse @ sk_c3) = (sk_c8)) | ((multiply @ sk_c1 @ sk_c7) = (sk_c8)))),
% 4.35/1.28 inference('cnf', [status(esa)], [zf_stmt_8])).
% 4.35/1.28 thf(zip_derived_cl115, plain,
% 4.35/1.28 ((((multiply @ (multiply @ (inverse @ sk_c7) @ identity) @ sk_c7)
% 4.35/1.28 = (sk_c8))
% 4.35/1.28 | ((inverse @ sk_c3) = (sk_c8))
% 4.35/1.28 | ((inverse @ sk_c3) = (sk_c8)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl83, zip_derived_cl11])).
% 4.35/1.28 thf(zip_derived_cl2, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.35/1.28 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 4.35/1.28 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 4.35/1.28 inference('cnf', [status(esa)], [associativity])).
% 4.35/1.28 thf(zip_derived_cl0, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_identity])).
% 4.35/1.28 thf(zip_derived_cl1, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_inverse])).
% 4.35/1.28 thf(zip_derived_cl125, plain,
% 4.35/1.28 ((((identity) = (sk_c8))
% 4.35/1.28 | ((inverse @ sk_c3) = (sk_c8))
% 4.35/1.28 | ((inverse @ sk_c3) = (sk_c8)))),
% 4.35/1.28 inference('demod', [status(thm)],
% 4.35/1.28 [zip_derived_cl115, zip_derived_cl2, zip_derived_cl0,
% 4.35/1.28 zip_derived_cl1])).
% 4.35/1.28 thf(zip_derived_cl126, plain,
% 4.35/1.28 ((((inverse @ sk_c3) = (sk_c8)) | ((identity) = (sk_c8)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl125])).
% 4.35/1.28 thf(zip_derived_cl1, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_inverse])).
% 4.35/1.28 thf(zip_derived_cl130, plain,
% 4.35/1.28 ((((multiply @ sk_c8 @ sk_c3) = (identity)) | ((identity) = (sk_c8)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl126, zip_derived_cl1])).
% 4.35/1.28 thf(zip_derived_cl69, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i]:
% 4.35/1.28 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl53, zip_derived_cl0])).
% 4.35/1.28 thf(zip_derived_cl150, plain,
% 4.35/1.28 ((((sk_c3) = (multiply @ (inverse @ sk_c8) @ identity))
% 4.35/1.28 | ((identity) = (sk_c8)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl130, zip_derived_cl69])).
% 4.35/1.28 thf(zip_derived_cl329, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl81, zip_derived_cl78])).
% 4.35/1.28 thf(zip_derived_cl357, plain,
% 4.35/1.28 ((((sk_c3) = (inverse @ sk_c8)) | ((identity) = (sk_c8)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl150, zip_derived_cl329])).
% 4.35/1.28 thf(prove_this_14, conjecture,
% 4.35/1.28 (~( ( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 4.35/1.28 ( ( inverse @ sk_c1 ) = ( sk_c7 ) ) ))).
% 4.35/1.28 thf(zf_stmt_9, negated_conjecture,
% 4.35/1.28 (( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 4.35/1.28 ( ( inverse @ sk_c1 ) = ( sk_c7 ) )),
% 4.35/1.28 inference('cnf.neg', [status(esa)], [prove_this_14])).
% 4.35/1.28 thf(zip_derived_cl16, plain,
% 4.35/1.28 ((((multiply @ sk_c3 @ sk_c8) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c7)))),
% 4.35/1.28 inference('cnf', [status(esa)], [zf_stmt_9])).
% 4.35/1.28 thf(zip_derived_cl367, plain,
% 4.35/1.28 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl329, zip_derived_cl81])).
% 4.35/1.28 thf(zip_derived_cl385, plain,
% 4.35/1.28 ((((sk_c1) = (inverse @ sk_c7)) | ((multiply @ sk_c3 @ sk_c8) = (sk_c7)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl16, zip_derived_cl367])).
% 4.35/1.28 thf(prove_this_8, conjecture,
% 4.35/1.28 (~( ( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) ) ))).
% 4.35/1.28 thf(zf_stmt_10, negated_conjecture,
% 4.35/1.28 (( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) )),
% 4.35/1.28 inference('cnf.neg', [status(esa)], [prove_this_8])).
% 4.35/1.28 thf(zip_derived_cl10, plain,
% 4.35/1.28 ((((multiply @ sk_c3 @ sk_c8) = (sk_c7))
% 4.35/1.28 | ((multiply @ sk_c1 @ sk_c7) = (sk_c8)))),
% 4.35/1.28 inference('cnf', [status(esa)], [zf_stmt_10])).
% 4.35/1.28 thf(zip_derived_cl1060, plain,
% 4.35/1.28 ((((multiply @ (inverse @ sk_c7) @ sk_c7) = (sk_c8))
% 4.35/1.28 | ((multiply @ sk_c3 @ sk_c8) = (sk_c7))
% 4.35/1.28 | ((multiply @ sk_c3 @ sk_c8) = (sk_c7)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl385, zip_derived_cl10])).
% 4.35/1.28 thf(zip_derived_cl1, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_inverse])).
% 4.35/1.28 thf(zip_derived_cl1066, plain,
% 4.35/1.28 ((((identity) = (sk_c8))
% 4.35/1.28 | ((multiply @ sk_c3 @ sk_c8) = (sk_c7))
% 4.35/1.28 | ((multiply @ sk_c3 @ sk_c8) = (sk_c7)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl1060, zip_derived_cl1])).
% 4.35/1.28 thf(zip_derived_cl1067, plain,
% 4.35/1.28 ((((multiply @ sk_c3 @ sk_c8) = (sk_c7)) | ((identity) = (sk_c8)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl1066])).
% 4.35/1.28 thf(zip_derived_cl1078, plain,
% 4.35/1.28 ((((multiply @ (inverse @ sk_c8) @ sk_c8) = (sk_c7))
% 4.35/1.28 | ((identity) = (sk_c8))
% 4.35/1.28 | ((identity) = (sk_c8)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl357, zip_derived_cl1067])).
% 4.35/1.28 thf(zip_derived_cl1, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_inverse])).
% 4.35/1.28 thf(zip_derived_cl1081, plain,
% 4.35/1.28 ((((identity) = (sk_c7))
% 4.35/1.28 | ((identity) = (sk_c8))
% 4.35/1.28 | ((identity) = (sk_c8)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl1078, zip_derived_cl1])).
% 4.35/1.28 thf(zip_derived_cl1082, plain,
% 4.35/1.28 ((((identity) = (sk_c8)) | ((identity) = (sk_c7)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl1081])).
% 4.35/1.28 thf(zip_derived_cl4318, plain, (((identity) = (sk_c8))),
% 4.35/1.28 inference('clc', [status(thm)], [zip_derived_cl4290, zip_derived_cl1082])).
% 4.35/1.28 thf(zip_derived_cl4352, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 4.35/1.28 (((inverse @ X0) != (multiply @ sk_c7 @ sk_c6))
% 4.35/1.28 | ((multiply @ X0 @ (multiply @ sk_c7 @ sk_c6)) != (X1))
% 4.35/1.28 | ((multiply @ sk_c7 @ (multiply @ sk_c6 @ X1)) != (sk_c7))
% 4.35/1.28 | ((inverse @ X2) != (multiply @ sk_c7 @ sk_c6))
% 4.35/1.28 | ((multiply @ X2 @ (multiply @ sk_c7 @ sk_c6)) != (sk_c7))
% 4.35/1.28 | ((multiply @ sk_c7 @ (multiply @ sk_c6 @ sk_c7)) != (sk_c6))
% 4.35/1.28 | ((inverse @ X3) != (multiply @ sk_c7 @ sk_c6))
% 4.35/1.28 | ((multiply @ X3 @ (multiply @ sk_c7 @ sk_c6)) != (sk_c6))
% 4.35/1.28 | ((inverse @ X4) != (sk_c7))
% 4.35/1.28 | ((multiply @ X4 @ sk_c7) != (multiply @ sk_c7 @ sk_c6))
% 4.35/1.28 | ((multiply @ sk_c7 @ sk_c6) != (identity)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl49, zip_derived_cl4318])).
% 4.35/1.28 thf(zip_derived_cl4353, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 4.35/1.28 (((inverse @ X0) != (identity))
% 4.35/1.28 | ((multiply @ X0 @ identity) != (X1))
% 4.35/1.28 | ((multiply @ sk_c7 @ (multiply @ sk_c6 @ X1)) != (sk_c7))
% 4.35/1.28 | ((inverse @ X2) != (identity))
% 4.35/1.28 | ((multiply @ X2 @ identity) != (sk_c7))
% 4.35/1.28 | ((multiply @ sk_c7 @ (multiply @ sk_c6 @ sk_c7)) != (sk_c6))
% 4.35/1.28 | ((inverse @ X3) != (identity))
% 4.35/1.28 | ((multiply @ X3 @ identity) != (sk_c6))
% 4.35/1.28 | ((inverse @ X4) != (sk_c7))
% 4.35/1.28 | ((multiply @ X4 @ sk_c7) != (identity))
% 4.35/1.28 | ((multiply @ sk_c7 @ sk_c6) != (identity)))),
% 4.35/1.28 inference('local_rewriting', [status(thm)], [zip_derived_cl4352])).
% 4.35/1.28 thf(zip_derived_cl329, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl81, zip_derived_cl78])).
% 4.35/1.28 thf(zip_derived_cl329, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl81, zip_derived_cl78])).
% 4.35/1.28 thf(zip_derived_cl329, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl81, zip_derived_cl78])).
% 4.35/1.28 thf(zip_derived_cl4354, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 4.35/1.28 (((inverse @ X0) != (identity))
% 4.35/1.28 | ((X0) != (X1))
% 4.35/1.28 | ((multiply @ sk_c7 @ (multiply @ sk_c6 @ X1)) != (sk_c7))
% 4.35/1.28 | ((inverse @ X2) != (identity))
% 4.35/1.28 | ((X2) != (sk_c7))
% 4.35/1.28 | ((multiply @ sk_c7 @ (multiply @ sk_c6 @ sk_c7)) != (sk_c6))
% 4.35/1.28 | ((inverse @ X3) != (identity))
% 4.35/1.28 | ((X3) != (sk_c6))
% 4.35/1.28 | ((inverse @ X4) != (sk_c7))
% 4.35/1.28 | ((multiply @ X4 @ sk_c7) != (identity))
% 4.35/1.28 | ((multiply @ sk_c7 @ sk_c6) != (identity)))),
% 4.35/1.28 inference('demod', [status(thm)],
% 4.35/1.28 [zip_derived_cl4353, zip_derived_cl329, zip_derived_cl329,
% 4.35/1.28 zip_derived_cl329])).
% 4.35/1.28 thf(zip_derived_cl4429, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.35/1.28 (((multiply @ sk_c7 @ sk_c6) != (identity))
% 4.35/1.28 | ((multiply @ X0 @ sk_c7) != (identity))
% 4.35/1.28 | ((inverse @ X0) != (sk_c7))
% 4.35/1.28 | ((X1) != (sk_c6))
% 4.35/1.28 | ((inverse @ X1) != (identity))
% 4.35/1.28 | ((multiply @ sk_c7 @ (multiply @ sk_c6 @ sk_c7)) != (sk_c6))
% 4.35/1.28 | ((X2) != (sk_c7))
% 4.35/1.28 | ((inverse @ X2) != (identity))
% 4.35/1.28 | ((multiply @ sk_c7 @ (multiply @ sk_c6 @ X3)) != (sk_c7))
% 4.35/1.28 | ((inverse @ X3) != (identity)))),
% 4.35/1.28 inference('eq_res', [status(thm)], [zip_derived_cl4354])).
% 4.35/1.28 thf(prove_this_20, conjecture,
% 4.35/1.28 (~( ( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c6 ) ) ))).
% 4.35/1.28 thf(zf_stmt_11, negated_conjecture,
% 4.35/1.28 (( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c6 ) )),
% 4.35/1.28 inference('cnf.neg', [status(esa)], [prove_this_20])).
% 4.35/1.28 thf(zip_derived_cl22, plain,
% 4.35/1.28 ((((multiply @ sk_c3 @ sk_c8) = (sk_c7))
% 4.35/1.28 | ((multiply @ sk_c2 @ sk_c8) = (sk_c6)))),
% 4.35/1.28 inference('cnf', [status(esa)], [zf_stmt_11])).
% 4.35/1.28 thf(zip_derived_cl4318, plain, (((identity) = (sk_c8))),
% 4.35/1.28 inference('clc', [status(thm)], [zip_derived_cl4290, zip_derived_cl1082])).
% 4.35/1.28 thf(zip_derived_cl329, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl81, zip_derived_cl78])).
% 4.35/1.28 thf(zip_derived_cl4318, plain, (((identity) = (sk_c8))),
% 4.35/1.28 inference('clc', [status(thm)], [zip_derived_cl4290, zip_derived_cl1082])).
% 4.35/1.28 thf(zip_derived_cl329, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl81, zip_derived_cl78])).
% 4.35/1.28 thf(zip_derived_cl6916, plain, ((((sk_c3) = (sk_c7)) | ((sk_c2) = (sk_c6)))),
% 4.35/1.28 inference('demod', [status(thm)],
% 4.35/1.28 [zip_derived_cl22, zip_derived_cl4318, zip_derived_cl329,
% 4.35/1.28 zip_derived_cl4318, zip_derived_cl329])).
% 4.35/1.28 thf(prove_this_26, conjecture,
% 4.35/1.28 (~( ( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 4.35/1.28 ( ( inverse @ sk_c2 ) = ( sk_c8 ) ) ))).
% 4.35/1.28 thf(zf_stmt_12, negated_conjecture,
% 4.35/1.28 (( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 4.35/1.28 ( ( inverse @ sk_c2 ) = ( sk_c8 ) )),
% 4.35/1.28 inference('cnf.neg', [status(esa)], [prove_this_26])).
% 4.35/1.28 thf(zip_derived_cl28, plain,
% 4.35/1.28 ((((multiply @ sk_c3 @ sk_c8) = (sk_c7)) | ((inverse @ sk_c2) = (sk_c8)))),
% 4.35/1.28 inference('cnf', [status(esa)], [zf_stmt_12])).
% 4.35/1.28 thf(zip_derived_cl367, plain,
% 4.35/1.28 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl329, zip_derived_cl81])).
% 4.35/1.28 thf(zip_derived_cl391, plain,
% 4.35/1.28 ((((sk_c2) = (inverse @ sk_c8)) | ((multiply @ sk_c3 @ sk_c8) = (sk_c7)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl28, zip_derived_cl367])).
% 4.35/1.28 thf(zip_derived_cl4318, plain, (((identity) = (sk_c8))),
% 4.35/1.28 inference('clc', [status(thm)], [zip_derived_cl4290, zip_derived_cl1082])).
% 4.35/1.28 thf(zip_derived_cl0, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_identity])).
% 4.35/1.28 thf(zip_derived_cl69, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i]:
% 4.35/1.28 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl53, zip_derived_cl0])).
% 4.35/1.28 thf(zip_derived_cl80, plain,
% 4.35/1.28 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl69])).
% 4.35/1.28 thf(zip_derived_cl69, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i]:
% 4.35/1.28 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl53, zip_derived_cl0])).
% 4.35/1.28 thf(zip_derived_cl113, plain,
% 4.35/1.28 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ identity)) @ X0))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl80, zip_derived_cl69])).
% 4.35/1.28 thf(zip_derived_cl1, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_inverse])).
% 4.35/1.28 thf(zip_derived_cl316, plain, (((inverse @ identity) = (identity))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl113, zip_derived_cl1])).
% 4.35/1.28 thf(zip_derived_cl4318, plain, (((identity) = (sk_c8))),
% 4.35/1.28 inference('clc', [status(thm)], [zip_derived_cl4290, zip_derived_cl1082])).
% 4.35/1.28 thf(zip_derived_cl329, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl81, zip_derived_cl78])).
% 4.35/1.28 thf(zip_derived_cl4377, plain,
% 4.35/1.28 ((((sk_c2) = (identity)) | ((sk_c3) = (sk_c7)))),
% 4.35/1.28 inference('demod', [status(thm)],
% 4.35/1.28 [zip_derived_cl391, zip_derived_cl4318, zip_derived_cl316,
% 4.35/1.28 zip_derived_cl4318, zip_derived_cl329])).
% 4.35/1.28 thf(zip_derived_cl6926, plain,
% 4.35/1.28 ((((sk_c6) = (identity)) | ((sk_c3) = (sk_c7)) | ((sk_c3) = (sk_c7)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl6916, zip_derived_cl4377])).
% 4.35/1.28 thf(zip_derived_cl6956, plain,
% 4.35/1.28 ((((sk_c3) = (sk_c7)) | ((sk_c6) = (identity)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl6926])).
% 4.35/1.28 thf(prove_this_27, conjecture,
% 4.35/1.28 (~( ( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 4.35/1.28 ( ( inverse @ sk_c2 ) = ( sk_c8 ) ) ))).
% 4.35/1.28 thf(zf_stmt_13, negated_conjecture,
% 4.35/1.28 (( ( inverse @ sk_c3 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c8 ) )),
% 4.35/1.28 inference('cnf.neg', [status(esa)], [prove_this_27])).
% 4.35/1.28 thf(zip_derived_cl29, plain,
% 4.35/1.28 ((((inverse @ sk_c3) = (sk_c8)) | ((inverse @ sk_c2) = (sk_c8)))),
% 4.35/1.28 inference('cnf', [status(esa)], [zf_stmt_13])).
% 4.35/1.28 thf(zip_derived_cl1, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_inverse])).
% 4.35/1.28 thf(zip_derived_cl39, plain,
% 4.35/1.28 ((((multiply @ sk_c8 @ sk_c2) = (identity))
% 4.35/1.28 | ((inverse @ sk_c3) = (sk_c8)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl29, zip_derived_cl1])).
% 4.35/1.28 thf(zip_derived_cl69, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i]:
% 4.35/1.28 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl53, zip_derived_cl0])).
% 4.35/1.28 thf(zip_derived_cl89, plain,
% 4.35/1.28 ((((sk_c2) = (multiply @ (inverse @ sk_c8) @ identity))
% 4.35/1.28 | ((inverse @ sk_c3) = (sk_c8)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl39, zip_derived_cl69])).
% 4.35/1.28 thf(prove_this_21, conjecture,
% 4.35/1.28 (~( ( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c6 ) ) ))).
% 4.35/1.28 thf(zf_stmt_14, negated_conjecture,
% 4.35/1.28 (( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c6 ) )),
% 4.35/1.28 inference('cnf.neg', [status(esa)], [prove_this_21])).
% 4.35/1.28 thf(zip_derived_cl23, plain,
% 4.35/1.28 ((((inverse @ sk_c3) = (sk_c8)) | ((multiply @ sk_c2 @ sk_c8) = (sk_c6)))),
% 4.35/1.28 inference('cnf', [status(esa)], [zf_stmt_14])).
% 4.35/1.28 thf(zip_derived_cl183, plain,
% 4.35/1.28 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 4.35/1.28 = (sk_c6))
% 4.35/1.28 | ((inverse @ sk_c3) = (sk_c8))
% 4.35/1.28 | ((inverse @ sk_c3) = (sk_c8)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl89, zip_derived_cl23])).
% 4.35/1.28 thf(zip_derived_cl2, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.35/1.28 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 4.35/1.28 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 4.35/1.28 inference('cnf', [status(esa)], [associativity])).
% 4.35/1.28 thf(zip_derived_cl0, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_identity])).
% 4.35/1.28 thf(zip_derived_cl1, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_inverse])).
% 4.35/1.28 thf(zip_derived_cl193, plain,
% 4.35/1.28 ((((identity) = (sk_c6))
% 4.35/1.28 | ((inverse @ sk_c3) = (sk_c8))
% 4.35/1.28 | ((inverse @ sk_c3) = (sk_c8)))),
% 4.35/1.28 inference('demod', [status(thm)],
% 4.35/1.28 [zip_derived_cl183, zip_derived_cl2, zip_derived_cl0,
% 4.35/1.28 zip_derived_cl1])).
% 4.35/1.28 thf(zip_derived_cl194, plain,
% 4.35/1.28 ((((inverse @ sk_c3) = (sk_c8)) | ((identity) = (sk_c6)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl193])).
% 4.35/1.28 thf(zip_derived_cl1, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_inverse])).
% 4.35/1.28 thf(zip_derived_cl198, plain,
% 4.35/1.28 ((((multiply @ sk_c8 @ sk_c3) = (identity)) | ((identity) = (sk_c6)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl194, zip_derived_cl1])).
% 4.35/1.28 thf(zip_derived_cl4318, plain, (((identity) = (sk_c8))),
% 4.35/1.28 inference('clc', [status(thm)], [zip_derived_cl4290, zip_derived_cl1082])).
% 4.35/1.28 thf(zip_derived_cl0, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_identity])).
% 4.35/1.28 thf(zip_derived_cl4360, plain,
% 4.35/1.28 ((((sk_c3) = (identity)) | ((identity) = (sk_c6)))),
% 4.35/1.28 inference('demod', [status(thm)],
% 4.35/1.28 [zip_derived_cl198, zip_derived_cl4318, zip_derived_cl0])).
% 4.35/1.28 thf(zip_derived_cl7023, plain,
% 4.35/1.28 ((((sk_c7) = (identity))
% 4.35/1.28 | ((sk_c6) = (identity))
% 4.35/1.28 | ((identity) = (sk_c6)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl6956, zip_derived_cl4360])).
% 4.35/1.28 thf(zip_derived_cl7035, plain,
% 4.35/1.28 ((((sk_c6) = (identity)) | ((sk_c7) = (identity)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl7023])).
% 4.35/1.28 thf(prove_this_19, conjecture,
% 4.35/1.28 (~( ( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c6 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c6 ) ) ))).
% 4.35/1.28 thf(zf_stmt_15, negated_conjecture,
% 4.35/1.28 (( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c6 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c6 ) )),
% 4.35/1.28 inference('cnf.neg', [status(esa)], [prove_this_19])).
% 4.35/1.28 thf(zip_derived_cl21, plain,
% 4.35/1.28 ((((multiply @ sk_c8 @ sk_c7) = (sk_c6))
% 4.35/1.28 | ((multiply @ sk_c2 @ sk_c8) = (sk_c6)))),
% 4.35/1.28 inference('cnf', [status(esa)], [zf_stmt_15])).
% 4.35/1.28 thf(zip_derived_cl4318, plain, (((identity) = (sk_c8))),
% 4.35/1.28 inference('clc', [status(thm)], [zip_derived_cl4290, zip_derived_cl1082])).
% 4.35/1.28 thf(zip_derived_cl0, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_identity])).
% 4.35/1.28 thf(zip_derived_cl4318, plain, (((identity) = (sk_c8))),
% 4.35/1.28 inference('clc', [status(thm)], [zip_derived_cl4290, zip_derived_cl1082])).
% 4.35/1.28 thf(zip_derived_cl329, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl81, zip_derived_cl78])).
% 4.35/1.28 thf(zip_derived_cl6439, plain, ((((sk_c7) = (sk_c6)) | ((sk_c2) = (sk_c6)))),
% 4.35/1.28 inference('demod', [status(thm)],
% 4.35/1.28 [zip_derived_cl21, zip_derived_cl4318, zip_derived_cl0,
% 4.35/1.28 zip_derived_cl4318, zip_derived_cl329])).
% 4.35/1.28 thf(prove_this_25, conjecture,
% 4.35/1.28 (~( ( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c6 ) ) |
% 4.35/1.28 ( ( inverse @ sk_c2 ) = ( sk_c8 ) ) ))).
% 4.35/1.28 thf(zf_stmt_16, negated_conjecture,
% 4.35/1.28 (( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c6 ) ) |
% 4.35/1.28 ( ( inverse @ sk_c2 ) = ( sk_c8 ) )),
% 4.35/1.28 inference('cnf.neg', [status(esa)], [prove_this_25])).
% 4.35/1.28 thf(zip_derived_cl27, plain,
% 4.35/1.28 ((((multiply @ sk_c8 @ sk_c7) = (sk_c6)) | ((inverse @ sk_c2) = (sk_c8)))),
% 4.35/1.28 inference('cnf', [status(esa)], [zf_stmt_16])).
% 4.35/1.28 thf(zip_derived_cl367, plain,
% 4.35/1.28 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl329, zip_derived_cl81])).
% 4.35/1.28 thf(zip_derived_cl390, plain,
% 4.35/1.28 ((((sk_c2) = (inverse @ sk_c8)) | ((multiply @ sk_c8 @ sk_c7) = (sk_c6)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl367])).
% 4.35/1.28 thf(zip_derived_cl4318, plain, (((identity) = (sk_c8))),
% 4.35/1.28 inference('clc', [status(thm)], [zip_derived_cl4290, zip_derived_cl1082])).
% 4.35/1.28 thf(zip_derived_cl316, plain, (((inverse @ identity) = (identity))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl113, zip_derived_cl1])).
% 4.35/1.28 thf(zip_derived_cl4318, plain, (((identity) = (sk_c8))),
% 4.35/1.28 inference('clc', [status(thm)], [zip_derived_cl4290, zip_derived_cl1082])).
% 4.35/1.28 thf(zip_derived_cl0, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_identity])).
% 4.35/1.28 thf(zip_derived_cl4376, plain,
% 4.35/1.28 ((((sk_c2) = (identity)) | ((sk_c7) = (sk_c6)))),
% 4.35/1.28 inference('demod', [status(thm)],
% 4.35/1.28 [zip_derived_cl390, zip_derived_cl4318, zip_derived_cl316,
% 4.35/1.28 zip_derived_cl4318, zip_derived_cl0])).
% 4.35/1.28 thf(zip_derived_cl6448, plain,
% 4.35/1.28 ((((sk_c6) = (identity)) | ((sk_c7) = (sk_c6)) | ((sk_c7) = (sk_c6)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl6439, zip_derived_cl4376])).
% 4.35/1.28 thf(zip_derived_cl6479, plain,
% 4.35/1.28 ((((sk_c7) = (sk_c6)) | ((sk_c6) = (identity)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl6448])).
% 4.35/1.28 thf(zip_derived_cl6506, plain,
% 4.35/1.28 ((((sk_c7) != (identity)) | ((sk_c6) = (identity)))),
% 4.35/1.28 inference('eq_fact', [status(thm)], [zip_derived_cl6479])).
% 4.35/1.28 thf(zip_derived_cl7045, plain, (((sk_c6) = (identity))),
% 4.35/1.28 inference('clc', [status(thm)], [zip_derived_cl7035, zip_derived_cl6506])).
% 4.35/1.28 thf(zip_derived_cl329, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl81, zip_derived_cl78])).
% 4.35/1.28 thf(zip_derived_cl7045, plain, (((sk_c6) = (identity))),
% 4.35/1.28 inference('clc', [status(thm)], [zip_derived_cl7035, zip_derived_cl6506])).
% 4.35/1.28 thf(zip_derived_cl7045, plain, (((sk_c6) = (identity))),
% 4.35/1.28 inference('clc', [status(thm)], [zip_derived_cl7035, zip_derived_cl6506])).
% 4.35/1.28 thf(zip_derived_cl0, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_identity])).
% 4.35/1.28 thf(zip_derived_cl7045, plain, (((sk_c6) = (identity))),
% 4.35/1.28 inference('clc', [status(thm)], [zip_derived_cl7035, zip_derived_cl6506])).
% 4.35/1.28 thf(zip_derived_cl7045, plain, (((sk_c6) = (identity))),
% 4.35/1.28 inference('clc', [status(thm)], [zip_derived_cl7035, zip_derived_cl6506])).
% 4.35/1.28 thf(zip_derived_cl0, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_identity])).
% 4.35/1.28 thf(zip_derived_cl7072, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.35/1.28 (((sk_c7) != (identity))
% 4.35/1.28 | ((multiply @ X0 @ sk_c7) != (identity))
% 4.35/1.28 | ((inverse @ X0) != (sk_c7))
% 4.35/1.28 | ((X1) != (identity))
% 4.35/1.28 | ((inverse @ X1) != (identity))
% 4.35/1.28 | ((multiply @ sk_c7 @ sk_c7) != (identity))
% 4.35/1.28 | ((X2) != (sk_c7))
% 4.35/1.28 | ((inverse @ X2) != (identity))
% 4.35/1.28 | ((multiply @ sk_c7 @ X3) != (sk_c7))
% 4.35/1.28 | ((inverse @ X3) != (identity)))),
% 4.35/1.28 inference('demod', [status(thm)],
% 4.35/1.28 [zip_derived_cl4429, zip_derived_cl7045, zip_derived_cl329,
% 4.35/1.28 zip_derived_cl7045, zip_derived_cl7045, zip_derived_cl0,
% 4.35/1.28 zip_derived_cl7045, zip_derived_cl7045, zip_derived_cl0])).
% 4.35/1.28 thf(zip_derived_cl7073, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.35/1.28 (((sk_c7) != (identity))
% 4.35/1.28 | ((multiply @ X0 @ identity) != (identity))
% 4.35/1.28 | ((inverse @ X0) != (identity))
% 4.35/1.28 | ((X1) != (identity))
% 4.35/1.28 | ((inverse @ X1) != (identity))
% 4.35/1.28 | ((multiply @ identity @ identity) != (identity))
% 4.35/1.28 | ((X2) != (identity))
% 4.35/1.28 | ((inverse @ X2) != (identity))
% 4.35/1.28 | ((multiply @ identity @ X3) != (identity))
% 4.35/1.28 | ((inverse @ X3) != (identity)))),
% 4.35/1.28 inference('local_rewriting', [status(thm)], [zip_derived_cl7072])).
% 4.35/1.28 thf(zip_derived_cl329, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl81, zip_derived_cl78])).
% 4.35/1.28 thf(zip_derived_cl0, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_identity])).
% 4.35/1.28 thf(zip_derived_cl0, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_identity])).
% 4.35/1.28 thf(zip_derived_cl7074, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.35/1.28 (((sk_c7) != (identity))
% 4.35/1.28 | ((X0) != (identity))
% 4.35/1.28 | ((inverse @ X0) != (identity))
% 4.35/1.28 | ((X1) != (identity))
% 4.35/1.28 | ((inverse @ X1) != (identity))
% 4.35/1.28 | ((identity) != (identity))
% 4.35/1.28 | ((X2) != (identity))
% 4.35/1.28 | ((inverse @ X2) != (identity))
% 4.35/1.28 | ((X3) != (identity))
% 4.35/1.28 | ((inverse @ X3) != (identity)))),
% 4.35/1.28 inference('demod', [status(thm)],
% 4.35/1.28 [zip_derived_cl7073, zip_derived_cl329, zip_derived_cl0,
% 4.35/1.28 zip_derived_cl0])).
% 4.35/1.28 thf(zip_derived_cl7075, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.35/1.28 (((inverse @ X3) != (identity))
% 4.35/1.28 | ((X3) != (identity))
% 4.35/1.28 | ((inverse @ X2) != (identity))
% 4.35/1.28 | ((X2) != (identity))
% 4.35/1.28 | ((inverse @ X1) != (identity))
% 4.35/1.28 | ((X1) != (identity))
% 4.35/1.28 | ((inverse @ X0) != (identity))
% 4.35/1.28 | ((X0) != (identity))
% 4.35/1.28 | ((sk_c7) != (identity)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl7074])).
% 4.35/1.28 thf(zip_derived_cl3862, plain,
% 4.35/1.28 ((((identity) = (sk_c8)) | ((identity) = (sk_c5)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl3861])).
% 4.35/1.28 thf(zip_derived_cl126, plain,
% 4.35/1.28 ((((inverse @ sk_c3) = (sk_c8)) | ((identity) = (sk_c8)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl125])).
% 4.35/1.28 thf(zip_derived_cl1067, plain,
% 4.35/1.28 ((((multiply @ sk_c3 @ sk_c8) = (sk_c7)) | ((identity) = (sk_c8)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl1066])).
% 4.35/1.28 thf(zip_derived_cl69, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i]:
% 4.35/1.28 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl53, zip_derived_cl0])).
% 4.35/1.28 thf(zip_derived_cl1071, plain,
% 4.35/1.28 ((((sk_c8) = (multiply @ (inverse @ sk_c3) @ sk_c7))
% 4.35/1.28 | ((identity) = (sk_c8)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl1067, zip_derived_cl69])).
% 4.35/1.28 thf(zip_derived_cl1129, plain,
% 4.35/1.28 ((((sk_c8) = (multiply @ sk_c8 @ sk_c7))
% 4.35/1.28 | ((identity) = (sk_c8))
% 4.35/1.28 | ((identity) = (sk_c8)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl126, zip_derived_cl1071])).
% 4.35/1.28 thf(zip_derived_cl1134, plain,
% 4.35/1.28 ((((identity) = (sk_c8)) | ((sk_c8) = (multiply @ sk_c8 @ sk_c7)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl1129])).
% 4.35/1.28 thf(prove_this_13, conjecture,
% 4.35/1.28 (~( ( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c6 ) ) |
% 4.35/1.28 ( ( inverse @ sk_c1 ) = ( sk_c7 ) ) ))).
% 4.35/1.28 thf(zf_stmt_17, negated_conjecture,
% 4.35/1.28 (( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c6 ) ) |
% 4.35/1.28 ( ( inverse @ sk_c1 ) = ( sk_c7 ) )),
% 4.35/1.28 inference('cnf.neg', [status(esa)], [prove_this_13])).
% 4.35/1.28 thf(zip_derived_cl15, plain,
% 4.35/1.28 ((((multiply @ sk_c8 @ sk_c7) = (sk_c6)) | ((inverse @ sk_c1) = (sk_c7)))),
% 4.35/1.28 inference('cnf', [status(esa)], [zf_stmt_17])).
% 4.35/1.28 thf(zip_derived_cl81, plain,
% 4.35/1.28 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl69])).
% 4.35/1.28 thf(zip_derived_cl272, plain,
% 4.35/1.28 ((((sk_c1) = (multiply @ (inverse @ sk_c7) @ identity))
% 4.35/1.28 | ((multiply @ sk_c8 @ sk_c7) = (sk_c6)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl15, zip_derived_cl81])).
% 4.35/1.28 thf(prove_this_7, conjecture,
% 4.35/1.28 (~( ( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c6 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) ) ))).
% 4.35/1.28 thf(zf_stmt_18, negated_conjecture,
% 4.35/1.28 (( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c6 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) )),
% 4.35/1.28 inference('cnf.neg', [status(esa)], [prove_this_7])).
% 4.35/1.28 thf(zip_derived_cl9, plain,
% 4.35/1.28 ((((multiply @ sk_c8 @ sk_c7) = (sk_c6))
% 4.35/1.28 | ((multiply @ sk_c1 @ sk_c7) = (sk_c8)))),
% 4.35/1.28 inference('cnf', [status(esa)], [zf_stmt_18])).
% 4.35/1.28 thf(zip_derived_cl296, plain,
% 4.35/1.28 ((((multiply @ (multiply @ (inverse @ sk_c7) @ identity) @ sk_c7)
% 4.35/1.28 = (sk_c8))
% 4.35/1.28 | ((multiply @ sk_c8 @ sk_c7) = (sk_c6))
% 4.35/1.28 | ((multiply @ sk_c8 @ sk_c7) = (sk_c6)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl272, zip_derived_cl9])).
% 4.35/1.28 thf(zip_derived_cl2, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.35/1.28 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 4.35/1.28 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 4.35/1.28 inference('cnf', [status(esa)], [associativity])).
% 4.35/1.28 thf(zip_derived_cl0, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_identity])).
% 4.35/1.28 thf(zip_derived_cl1, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_inverse])).
% 4.35/1.28 thf(zip_derived_cl307, plain,
% 4.35/1.28 ((((identity) = (sk_c8))
% 4.35/1.28 | ((multiply @ sk_c8 @ sk_c7) = (sk_c6))
% 4.35/1.28 | ((multiply @ sk_c8 @ sk_c7) = (sk_c6)))),
% 4.35/1.28 inference('demod', [status(thm)],
% 4.35/1.28 [zip_derived_cl296, zip_derived_cl2, zip_derived_cl0,
% 4.35/1.28 zip_derived_cl1])).
% 4.35/1.28 thf(zip_derived_cl308, plain,
% 4.35/1.28 ((((multiply @ sk_c8 @ sk_c7) = (sk_c6)) | ((identity) = (sk_c8)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl307])).
% 4.35/1.28 thf(zip_derived_cl1210, plain,
% 4.35/1.28 ((((sk_c8) = (sk_c6)) | ((identity) = (sk_c8)) | ((identity) = (sk_c8)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl1134, zip_derived_cl308])).
% 4.35/1.28 thf(zip_derived_cl1218, plain,
% 4.35/1.28 ((((identity) = (sk_c8)) | ((sk_c8) = (sk_c6)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl1210])).
% 4.35/1.28 thf(zip_derived_cl3671, plain,
% 4.35/1.28 ((((multiply @ sk_c8 @ sk_c5) = (sk_c7)) | ((identity) = (sk_c8)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl3670])).
% 4.35/1.28 thf(zip_derived_cl3682, plain,
% 4.35/1.28 ((((multiply @ sk_c6 @ sk_c5) = (sk_c7))
% 4.35/1.28 | ((identity) = (sk_c8))
% 4.35/1.28 | ((identity) = (sk_c8)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl1218, zip_derived_cl3671])).
% 4.35/1.28 thf(zip_derived_cl3698, plain,
% 4.35/1.28 ((((identity) = (sk_c8)) | ((multiply @ sk_c6 @ sk_c5) = (sk_c7)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl3682])).
% 4.35/1.28 thf(zip_derived_cl3875, plain,
% 4.35/1.28 ((((multiply @ sk_c6 @ identity) = (sk_c7))
% 4.35/1.28 | ((identity) = (sk_c8))
% 4.35/1.28 | ((identity) = (sk_c8)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl3862, zip_derived_cl3698])).
% 4.35/1.28 thf(zip_derived_cl329, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl81, zip_derived_cl78])).
% 4.35/1.28 thf(zip_derived_cl3879, plain,
% 4.35/1.28 ((((sk_c6) = (sk_c7)) | ((identity) = (sk_c8)) | ((identity) = (sk_c8)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl3875, zip_derived_cl329])).
% 4.35/1.28 thf(zip_derived_cl3880, plain,
% 4.35/1.28 ((((identity) = (sk_c8)) | ((sk_c6) = (sk_c7)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl3879])).
% 4.35/1.28 thf(prove_this_1, conjecture,
% 4.35/1.28 (~( ( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c6 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c7 @ sk_c6 ) = ( sk_c8 ) ) ))).
% 4.35/1.28 thf(zf_stmt_19, negated_conjecture,
% 4.35/1.28 (( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c6 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c7 @ sk_c6 ) = ( sk_c8 ) )),
% 4.35/1.28 inference('cnf.neg', [status(esa)], [prove_this_1])).
% 4.35/1.28 thf(zip_derived_cl3, plain,
% 4.35/1.28 ((((multiply @ sk_c8 @ sk_c7) = (sk_c6))
% 4.35/1.28 | ((multiply @ sk_c7 @ sk_c6) = (sk_c8)))),
% 4.35/1.28 inference('cnf', [status(esa)], [zf_stmt_19])).
% 4.35/1.28 thf(zip_derived_cl3882, plain,
% 4.35/1.28 ((((multiply @ identity @ sk_c7) = (sk_c6))
% 4.35/1.28 | ((sk_c6) = (sk_c7))
% 4.35/1.28 | ((multiply @ sk_c7 @ sk_c6) = (sk_c8)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl3880, zip_derived_cl3])).
% 4.35/1.28 thf(zip_derived_cl0, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_identity])).
% 4.35/1.28 thf(zip_derived_cl3929, plain,
% 4.35/1.28 ((((sk_c7) = (sk_c6))
% 4.35/1.28 | ((sk_c6) = (sk_c7))
% 4.35/1.28 | ((multiply @ sk_c7 @ sk_c6) = (sk_c8)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl3882, zip_derived_cl0])).
% 4.35/1.28 thf(zip_derived_cl3930, plain,
% 4.35/1.28 ((((multiply @ sk_c7 @ sk_c6) = (sk_c8)) | ((sk_c7) = (sk_c6)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl3929])).
% 4.35/1.28 thf(zip_derived_cl3880, plain,
% 4.35/1.28 ((((identity) = (sk_c8)) | ((sk_c6) = (sk_c7)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl3879])).
% 4.35/1.28 thf(zip_derived_cl4101, plain,
% 4.35/1.28 ((((identity) = (multiply @ sk_c7 @ sk_c6))
% 4.35/1.28 | ((sk_c7) = (sk_c6))
% 4.35/1.28 | ((sk_c6) = (sk_c7)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl3930, zip_derived_cl3880])).
% 4.35/1.28 thf(zip_derived_cl4110, plain,
% 4.35/1.28 ((((sk_c7) = (sk_c6)) | ((identity) = (multiply @ sk_c7 @ sk_c6)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl4101])).
% 4.35/1.28 thf(zip_derived_cl69, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i]:
% 4.35/1.28 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl53, zip_derived_cl0])).
% 4.35/1.28 thf(zip_derived_cl4847, plain,
% 4.35/1.28 ((((sk_c6) = (multiply @ (inverse @ sk_c7) @ identity))
% 4.35/1.28 | ((sk_c7) = (sk_c6)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl4110, zip_derived_cl69])).
% 4.35/1.28 thf(zip_derived_cl329, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl81, zip_derived_cl78])).
% 4.35/1.28 thf(zip_derived_cl4854, plain,
% 4.35/1.28 ((((sk_c6) = (inverse @ sk_c7)) | ((sk_c7) = (sk_c6)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl4847, zip_derived_cl329])).
% 4.35/1.28 thf(zip_derived_cl4863, plain,
% 4.35/1.28 ((((inverse @ sk_c7) != (sk_c7)) | ((sk_c7) = (sk_c6)))),
% 4.35/1.28 inference('eq_fact', [status(thm)], [zip_derived_cl4854])).
% 4.35/1.28 thf(zip_derived_cl7045, plain, (((sk_c6) = (identity))),
% 4.35/1.28 inference('clc', [status(thm)], [zip_derived_cl7035, zip_derived_cl6506])).
% 4.35/1.28 thf(zip_derived_cl7081, plain,
% 4.35/1.28 ((((inverse @ sk_c7) != (sk_c7)) | ((sk_c7) = (identity)))),
% 4.35/1.28 inference('demod', [status(thm)],
% 4.35/1.28 [zip_derived_cl4863, zip_derived_cl7045])).
% 4.35/1.28 thf(zip_derived_cl1082, plain,
% 4.35/1.28 ((((identity) = (sk_c8)) | ((identity) = (sk_c7)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl1081])).
% 4.35/1.28 thf(prove_this_3, conjecture,
% 4.35/1.28 (~( ( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c7 @ sk_c6 ) = ( sk_c8 ) ) ))).
% 4.35/1.28 thf(zf_stmt_20, negated_conjecture,
% 4.35/1.28 (( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c7 @ sk_c6 ) = ( sk_c8 ) )),
% 4.35/1.28 inference('cnf.neg', [status(esa)], [prove_this_3])).
% 4.35/1.28 thf(zip_derived_cl5, plain,
% 4.35/1.28 ((((inverse @ sk_c3) = (sk_c8)) | ((multiply @ sk_c7 @ sk_c6) = (sk_c8)))),
% 4.35/1.28 inference('cnf', [status(esa)], [zf_stmt_20])).
% 4.35/1.28 thf(zip_derived_cl1, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_inverse])).
% 4.35/1.28 thf(zip_derived_cl35, plain,
% 4.35/1.28 ((((multiply @ sk_c8 @ sk_c3) = (identity))
% 4.35/1.28 | ((multiply @ sk_c7 @ sk_c6) = (sk_c8)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl1])).
% 4.35/1.28 thf(zip_derived_cl69, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i]:
% 4.35/1.28 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl53, zip_derived_cl0])).
% 4.35/1.28 thf(zip_derived_cl86, plain,
% 4.35/1.28 ((((sk_c3) = (multiply @ (inverse @ sk_c8) @ identity))
% 4.35/1.28 | ((multiply @ sk_c7 @ sk_c6) = (sk_c8)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl69])).
% 4.35/1.28 thf(zip_derived_cl329, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl81, zip_derived_cl78])).
% 4.35/1.28 thf(zip_derived_cl353, plain,
% 4.35/1.28 ((((sk_c3) = (inverse @ sk_c8)) | ((multiply @ sk_c7 @ sk_c6) = (sk_c8)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl86, zip_derived_cl329])).
% 4.35/1.28 thf(prove_this_2, conjecture,
% 4.35/1.28 (~( ( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c7 @ sk_c6 ) = ( sk_c8 ) ) ))).
% 4.35/1.28 thf(zf_stmt_21, negated_conjecture,
% 4.35/1.28 (( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 4.35/1.28 ( ( multiply @ sk_c7 @ sk_c6 ) = ( sk_c8 ) )),
% 4.35/1.28 inference('cnf.neg', [status(esa)], [prove_this_2])).
% 4.35/1.28 thf(zip_derived_cl4, plain,
% 4.35/1.28 ((((multiply @ sk_c3 @ sk_c8) = (sk_c7))
% 4.35/1.28 | ((multiply @ sk_c7 @ sk_c6) = (sk_c8)))),
% 4.35/1.28 inference('cnf', [status(esa)], [zf_stmt_21])).
% 4.35/1.28 thf(zip_derived_cl482, plain,
% 4.35/1.28 ((((multiply @ (inverse @ sk_c8) @ sk_c8) = (sk_c7))
% 4.35/1.28 | ((multiply @ sk_c7 @ sk_c6) = (sk_c8))
% 4.35/1.28 | ((multiply @ sk_c7 @ sk_c6) = (sk_c8)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl353, zip_derived_cl4])).
% 4.35/1.28 thf(zip_derived_cl1, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_inverse])).
% 4.35/1.28 thf(zip_derived_cl489, plain,
% 4.35/1.28 ((((identity) = (sk_c7))
% 4.35/1.28 | ((multiply @ sk_c7 @ sk_c6) = (sk_c8))
% 4.35/1.28 | ((multiply @ sk_c7 @ sk_c6) = (sk_c8)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl482, zip_derived_cl1])).
% 4.35/1.28 thf(zip_derived_cl490, plain,
% 4.35/1.28 ((((multiply @ sk_c7 @ sk_c6) = (sk_c8)) | ((identity) = (sk_c7)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl489])).
% 4.35/1.28 thf(zip_derived_cl1104, plain,
% 4.35/1.28 ((((multiply @ sk_c7 @ sk_c6) = (identity))
% 4.35/1.28 | ((identity) = (sk_c7))
% 4.35/1.28 | ((identity) = (sk_c7)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl1082, zip_derived_cl490])).
% 4.35/1.28 thf(zip_derived_cl1120, plain,
% 4.35/1.28 ((((identity) = (sk_c7)) | ((multiply @ sk_c7 @ sk_c6) = (identity)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl1104])).
% 4.35/1.28 thf(zip_derived_cl69, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i]:
% 4.35/1.28 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl53, zip_derived_cl0])).
% 4.35/1.28 thf(zip_derived_cl1196, plain,
% 4.35/1.28 ((((sk_c6) = (multiply @ (inverse @ sk_c7) @ identity))
% 4.35/1.28 | ((identity) = (sk_c7)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl1120, zip_derived_cl69])).
% 4.35/1.28 thf(zip_derived_cl329, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl81, zip_derived_cl78])).
% 4.35/1.28 thf(zip_derived_cl1199, plain,
% 4.35/1.28 ((((sk_c6) = (inverse @ sk_c7)) | ((identity) = (sk_c7)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl1196, zip_derived_cl329])).
% 4.35/1.28 thf(zip_derived_cl6439, plain, ((((sk_c7) = (sk_c6)) | ((sk_c2) = (sk_c6)))),
% 4.35/1.28 inference('demod', [status(thm)],
% 4.35/1.28 [zip_derived_cl21, zip_derived_cl4318, zip_derived_cl0,
% 4.35/1.28 zip_derived_cl4318, zip_derived_cl329])).
% 4.35/1.28 thf(zip_derived_cl27, plain,
% 4.35/1.28 ((((multiply @ sk_c8 @ sk_c7) = (sk_c6)) | ((inverse @ sk_c2) = (sk_c8)))),
% 4.35/1.28 inference('cnf', [status(esa)], [zf_stmt_16])).
% 4.35/1.28 thf(zip_derived_cl4318, plain, (((identity) = (sk_c8))),
% 4.35/1.28 inference('clc', [status(thm)], [zip_derived_cl4290, zip_derived_cl1082])).
% 4.35/1.28 thf(zip_derived_cl0, plain,
% 4.35/1.28 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 4.35/1.28 inference('cnf', [status(esa)], [left_identity])).
% 4.35/1.28 thf(zip_derived_cl4318, plain, (((identity) = (sk_c8))),
% 4.35/1.28 inference('clc', [status(thm)], [zip_derived_cl4290, zip_derived_cl1082])).
% 4.35/1.28 thf(zip_derived_cl4339, plain,
% 4.35/1.28 ((((sk_c7) = (sk_c6)) | ((inverse @ sk_c2) = (identity)))),
% 4.35/1.28 inference('demod', [status(thm)],
% 4.35/1.28 [zip_derived_cl27, zip_derived_cl4318, zip_derived_cl0,
% 4.35/1.28 zip_derived_cl4318])).
% 4.35/1.28 thf(zip_derived_cl6440, plain,
% 4.35/1.28 ((((inverse @ sk_c6) = (identity))
% 4.35/1.28 | ((sk_c7) = (sk_c6))
% 4.35/1.28 | ((sk_c7) = (sk_c6)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl6439, zip_derived_cl4339])).
% 4.35/1.28 thf(zip_derived_cl6478, plain,
% 4.35/1.28 ((((sk_c7) = (sk_c6)) | ((inverse @ sk_c6) = (identity)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl6440])).
% 4.35/1.28 thf(zip_derived_cl6516, plain,
% 4.35/1.28 ((((inverse @ (inverse @ sk_c7)) = (identity))
% 4.35/1.28 | ((identity) = (sk_c7))
% 4.35/1.28 | ((sk_c7) = (sk_c6)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl1199, zip_derived_cl6478])).
% 4.35/1.28 thf(zip_derived_cl367, plain,
% 4.35/1.28 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl329, zip_derived_cl81])).
% 4.35/1.28 thf(zip_derived_cl6520, plain,
% 4.35/1.28 ((((sk_c7) = (identity)) | ((identity) = (sk_c7)) | ((sk_c7) = (sk_c6)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl6516, zip_derived_cl367])).
% 4.35/1.28 thf(zip_derived_cl6521, plain,
% 4.35/1.28 ((((sk_c7) = (sk_c6)) | ((sk_c7) = (identity)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl6520])).
% 4.35/1.28 thf(zip_derived_cl1199, plain,
% 4.35/1.28 ((((sk_c6) = (inverse @ sk_c7)) | ((identity) = (sk_c7)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl1196, zip_derived_cl329])).
% 4.35/1.28 thf(zip_derived_cl6528, plain,
% 4.35/1.28 ((((sk_c7) = (inverse @ sk_c7))
% 4.35/1.28 | ((sk_c7) = (identity))
% 4.35/1.28 | ((identity) = (sk_c7)))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl6521, zip_derived_cl1199])).
% 4.35/1.28 thf(zip_derived_cl6538, plain,
% 4.35/1.28 ((((sk_c7) = (identity)) | ((sk_c7) = (inverse @ sk_c7)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl6528])).
% 4.35/1.28 thf(zip_derived_cl7113, plain, (((sk_c7) = (identity))),
% 4.35/1.28 inference('clc', [status(thm)], [zip_derived_cl7081, zip_derived_cl6538])).
% 4.35/1.28 thf(zip_derived_cl7157, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.35/1.28 (((inverse @ X3) != (identity))
% 4.35/1.28 | ((X3) != (identity))
% 4.35/1.28 | ((inverse @ X2) != (identity))
% 4.35/1.28 | ((X2) != (identity))
% 4.35/1.28 | ((inverse @ X1) != (identity))
% 4.35/1.28 | ((X1) != (identity))
% 4.35/1.28 | ((inverse @ X0) != (identity))
% 4.35/1.28 | ((X0) != (identity))
% 4.35/1.28 | ((identity) != (identity)))),
% 4.35/1.28 inference('demod', [status(thm)],
% 4.35/1.28 [zip_derived_cl7075, zip_derived_cl7113])).
% 4.35/1.28 thf(zip_derived_cl7158, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.35/1.28 (((X0) != (identity))
% 4.35/1.28 | ((inverse @ X0) != (identity))
% 4.35/1.28 | ((X1) != (identity))
% 4.35/1.28 | ((inverse @ X1) != (identity))
% 4.35/1.28 | ((X2) != (identity))
% 4.35/1.28 | ((inverse @ X2) != (identity))
% 4.35/1.28 | ((X3) != (identity))
% 4.35/1.28 | ((inverse @ X3) != (identity)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl7157])).
% 4.35/1.28 thf(zip_derived_cl7177, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.35/1.28 (((inverse @ X0) != (identity))
% 4.35/1.28 | ((X0) != (identity))
% 4.35/1.28 | ((inverse @ X1) != (identity))
% 4.35/1.28 | ((X1) != (identity))
% 4.35/1.28 | ((inverse @ X2) != (identity))
% 4.35/1.28 | ((X2) != (identity))
% 4.35/1.28 | ((inverse @ identity) != (identity)))),
% 4.35/1.28 inference('eq_res', [status(thm)], [zip_derived_cl7158])).
% 4.35/1.28 thf(zip_derived_cl316, plain, (((inverse @ identity) = (identity))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl113, zip_derived_cl1])).
% 4.35/1.28 thf(zip_derived_cl7178, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.35/1.28 (((inverse @ X0) != (identity))
% 4.35/1.28 | ((X0) != (identity))
% 4.35/1.28 | ((inverse @ X1) != (identity))
% 4.35/1.28 | ((X1) != (identity))
% 4.35/1.28 | ((inverse @ X2) != (identity))
% 4.35/1.28 | ((X2) != (identity))
% 4.35/1.28 | ((identity) != (identity)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl7177, zip_derived_cl316])).
% 4.35/1.28 thf(zip_derived_cl7179, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.35/1.28 (((X2) != (identity))
% 4.35/1.28 | ((inverse @ X2) != (identity))
% 4.35/1.28 | ((X1) != (identity))
% 4.35/1.28 | ((inverse @ X1) != (identity))
% 4.35/1.28 | ((X0) != (identity))
% 4.35/1.28 | ((inverse @ X0) != (identity)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl7178])).
% 4.35/1.28 thf(zip_derived_cl7180, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i]:
% 4.35/1.28 (((inverse @ X0) != (identity))
% 4.35/1.28 | ((X0) != (identity))
% 4.35/1.28 | ((inverse @ X1) != (identity))
% 4.35/1.28 | ((X1) != (identity))
% 4.35/1.28 | ((inverse @ identity) != (identity)))),
% 4.35/1.28 inference('eq_res', [status(thm)], [zip_derived_cl7179])).
% 4.35/1.28 thf(zip_derived_cl316, plain, (((inverse @ identity) = (identity))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl113, zip_derived_cl1])).
% 4.35/1.28 thf(zip_derived_cl7181, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i]:
% 4.35/1.28 (((inverse @ X0) != (identity))
% 4.35/1.28 | ((X0) != (identity))
% 4.35/1.28 | ((inverse @ X1) != (identity))
% 4.35/1.28 | ((X1) != (identity))
% 4.35/1.28 | ((identity) != (identity)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl7180, zip_derived_cl316])).
% 4.35/1.28 thf(zip_derived_cl7182, plain,
% 4.35/1.28 (![X0 : $i, X1 : $i]:
% 4.35/1.28 (((X1) != (identity))
% 4.35/1.28 | ((inverse @ X1) != (identity))
% 4.35/1.28 | ((X0) != (identity))
% 4.35/1.28 | ((inverse @ X0) != (identity)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl7181])).
% 4.35/1.28 thf(zip_derived_cl7183, plain,
% 4.35/1.28 (![X0 : $i]:
% 4.35/1.28 (((inverse @ X0) != (identity))
% 4.35/1.28 | ((X0) != (identity))
% 4.35/1.28 | ((inverse @ identity) != (identity)))),
% 4.35/1.28 inference('eq_res', [status(thm)], [zip_derived_cl7182])).
% 4.35/1.28 thf(zip_derived_cl316, plain, (((inverse @ identity) = (identity))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl113, zip_derived_cl1])).
% 4.35/1.28 thf(zip_derived_cl7184, plain,
% 4.35/1.28 (![X0 : $i]:
% 4.35/1.28 (((inverse @ X0) != (identity))
% 4.35/1.28 | ((X0) != (identity))
% 4.35/1.28 | ((identity) != (identity)))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl7183, zip_derived_cl316])).
% 4.35/1.28 thf(zip_derived_cl7185, plain,
% 4.35/1.28 (![X0 : $i]: (((X0) != (identity)) | ((inverse @ X0) != (identity)))),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl7184])).
% 4.35/1.28 thf(zip_derived_cl7186, plain, (((inverse @ identity) != (identity))),
% 4.35/1.28 inference('eq_res', [status(thm)], [zip_derived_cl7185])).
% 4.35/1.28 thf(zip_derived_cl316, plain, (((inverse @ identity) = (identity))),
% 4.35/1.28 inference('sup+', [status(thm)], [zip_derived_cl113, zip_derived_cl1])).
% 4.35/1.28 thf(zip_derived_cl7187, plain, (((identity) != (identity))),
% 4.35/1.28 inference('demod', [status(thm)], [zip_derived_cl7186, zip_derived_cl316])).
% 4.35/1.28 thf(zip_derived_cl7188, plain, ($false),
% 4.35/1.28 inference('simplify', [status(thm)], [zip_derived_cl7187])).
% 4.35/1.28
% 4.35/1.28 % SZS output end Refutation
% 4.35/1.28
% 4.35/1.28
% 4.35/1.28 % Terminating...
% 5.00/1.41 % Runner terminated.
% 5.00/1.43 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------