%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP272-1 : 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.DwO2hD9cQe true
% Computer : n008.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 04:36:07 PM UTC 2025
% Result : Unsatisfiable 5.62s 1.38s
% Output : Refutation 5.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP272-1 : TPTP v9.2.0. Released v2.5.0.
% 0.10/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.DwO2hD9cQe true
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 1 14:11:38 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.34 % Python version: Python 3.6.8
% 0.13/0.34 % Running in FO mode
% 0.53/0.64 % Total configuration time : 435
% 0.53/0.64 % Estimated wc time : 1092
% 0.53/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.53/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.53/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.53/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.53/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.53/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.53/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.53/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 5.62/1.38 % Solved by fo/fo13.sh.
% 5.62/1.38 % done 1464 iterations in 0.603s
% 5.62/1.38 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 5.62/1.38 % SZS output start Refutation
% 5.62/1.38 thf(sk_c2_type, type, sk_c2: $i).
% 5.62/1.38 thf(sk_c6_type, type, sk_c6: $i).
% 5.62/1.38 thf(sk_c4_type, type, sk_c4: $i).
% 5.62/1.38 thf(sk_c3_type, type, sk_c3: $i).
% 5.62/1.38 thf(identity_type, type, identity: $i).
% 5.62/1.38 thf(multiply_type, type, multiply: $i > $i > $i).
% 5.62/1.38 thf(sk_c7_type, type, sk_c7: $i).
% 5.62/1.38 thf(inverse_type, type, inverse: $i > $i).
% 5.62/1.38 thf(sk_c5_type, type, sk_c5: $i).
% 5.62/1.38 thf(sk_c1_type, type, sk_c1: $i).
% 5.62/1.38 thf(prove_this_26, conjecture,
% 5.62/1.38 (~( ( ( multiply @ X2 @ sk_c5 ) != ( sk_c6 ) ) |
% 5.62/1.38 ( ( inverse @ X2 ) != ( sk_c6 ) ) |
% 5.62/1.38 ( ( multiply @ X1 @ sk_c6 ) != ( sk_c7 ) ) |
% 5.62/1.38 ( ( inverse @ X1 ) != ( sk_c7 ) ) |
% 5.62/1.38 ( ( multiply @ sk_c6 @ sk_c7 ) != ( sk_c5 ) ) |
% 5.62/1.38 ( ( inverse @ X4 ) != ( sk_c6 ) ) |
% 5.62/1.38 ( ( multiply @ X4 @ sk_c6 ) != ( sk_c5 ) ) |
% 5.62/1.38 ( ( multiply @ sk_c7 @ sk_c5 ) != ( sk_c6 ) ) |
% 5.62/1.38 ( ( inverse @ X3 ) != ( sk_c7 ) ) |
% 5.62/1.38 ( ( multiply @ X3 @ sk_c7 ) != ( sk_c6 ) ) ))).
% 5.62/1.38 thf(zf_stmt_0, negated_conjecture,
% 5.62/1.38 (( ( multiply @ X2 @ sk_c5 ) != ( sk_c6 ) ) |
% 5.62/1.38 ( ( inverse @ X2 ) != ( sk_c6 ) ) |
% 5.62/1.38 ( ( multiply @ X1 @ sk_c6 ) != ( sk_c7 ) ) |
% 5.62/1.38 ( ( inverse @ X1 ) != ( sk_c7 ) ) |
% 5.62/1.38 ( ( multiply @ sk_c6 @ sk_c7 ) != ( sk_c5 ) ) |
% 5.62/1.38 ( ( inverse @ X4 ) != ( sk_c6 ) ) |
% 5.62/1.38 ( ( multiply @ X4 @ sk_c6 ) != ( sk_c5 ) ) |
% 5.62/1.38 ( ( multiply @ sk_c7 @ sk_c5 ) != ( sk_c6 ) ) |
% 5.62/1.38 ( ( inverse @ X3 ) != ( sk_c7 ) ) |
% 5.62/1.38 ( ( multiply @ X3 @ sk_c7 ) != ( sk_c6 ) )),
% 5.62/1.38 inference('cnf.neg', [status(esa)], [prove_this_26])).
% 5.62/1.38 thf(zip_derived_cl28, plain,
% 5.62/1.38 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 5.62/1.38 (((multiply @ X0 @ sk_c5) != (sk_c6))
% 5.62/1.38 | ((inverse @ X0) != (sk_c6))
% 5.62/1.38 | ((multiply @ X1 @ sk_c6) != (sk_c7))
% 5.62/1.38 | ((inverse @ X1) != (sk_c7))
% 5.62/1.38 | ((multiply @ sk_c6 @ sk_c7) != (sk_c5))
% 5.62/1.38 | ((inverse @ X2) != (sk_c6))
% 5.62/1.38 | ((multiply @ X2 @ sk_c6) != (sk_c5))
% 5.62/1.38 | ((multiply @ sk_c7 @ sk_c5) != (sk_c6))
% 5.62/1.38 | ((inverse @ X3) != (sk_c7))
% 5.62/1.38 | ((multiply @ X3 @ sk_c7) != (sk_c6)))),
% 5.62/1.38 inference('cnf', [status(esa)], [zf_stmt_0])).
% 5.62/1.38 thf(prove_this_24, conjecture,
% 5.62/1.38 (~( ( ( inverse @ sk_c4 ) = ( sk_c6 ) ) |
% 5.62/1.38 ( ( inverse @ sk_c2 ) = ( sk_c6 ) ) ))).
% 5.62/1.38 thf(zf_stmt_1, negated_conjecture,
% 5.62/1.38 (( ( inverse @ sk_c4 ) = ( sk_c6 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c6 ) )),
% 5.62/1.38 inference('cnf.neg', [status(esa)], [prove_this_24])).
% 5.62/1.38 thf(zip_derived_cl26, plain,
% 5.62/1.38 ((((inverse @ sk_c4) = (sk_c6)) | ((inverse @ sk_c2) = (sk_c6)))),
% 5.62/1.38 inference('cnf', [status(esa)], [zf_stmt_1])).
% 5.62/1.38 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 5.62/1.38 thf(zip_derived_cl1, plain,
% 5.62/1.38 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 5.62/1.38 inference('cnf', [status(esa)], [left_inverse])).
% 5.62/1.38 thf(associativity, axiom,
% 5.62/1.38 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 5.62/1.38 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 5.62/1.38 thf(zip_derived_cl2, plain,
% 5.62/1.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.62/1.38 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 5.62/1.38 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 5.62/1.38 inference('cnf', [status(esa)], [associativity])).
% 5.62/1.38 thf(zip_derived_cl39, plain,
% 5.62/1.38 (![X0 : $i, X1 : $i]:
% 5.62/1.38 ((multiply @ identity @ X0)
% 5.62/1.38 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 5.62/1.38 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 5.62/1.38 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 5.62/1.38 thf(zip_derived_cl0, plain,
% 5.62/1.38 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 5.62/1.38 inference('cnf', [status(esa)], [left_identity])).
% 5.62/1.38 thf(zip_derived_cl41, plain,
% 5.62/1.38 (![X0 : $i, X1 : $i]:
% 5.62/1.38 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 5.62/1.38 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl0])).
% 5.62/1.38 thf(zip_derived_cl183, plain,
% 5.62/1.38 (![X0 : $i]:
% 5.62/1.38 (((inverse @ sk_c4) = (sk_c6))
% 5.62/1.38 | ((X0) = (multiply @ sk_c6 @ (multiply @ sk_c2 @ X0))))),
% 5.62/1.38 inference('s_sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl41])).
% 5.62/1.38 thf(zip_derived_cl41, plain,
% 5.62/1.38 (![X0 : $i, X1 : $i]:
% 5.62/1.38 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 5.62/1.38 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl0])).
% 5.62/1.38 thf(zip_derived_cl211, plain,
% 5.62/1.38 (![X0 : $i]:
% 5.62/1.38 (((inverse @ sk_c4) = (sk_c6))
% 5.62/1.38 | ((multiply @ sk_c2 @ X0) = (multiply @ (inverse @ sk_c6) @ X0)))),
% 5.62/1.38 inference('s_sup+', [status(thm)], [zip_derived_cl183, zip_derived_cl41])).
% 5.62/1.38 thf(zip_derived_cl1, plain,
% 5.62/1.38 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 5.62/1.38 inference('cnf', [status(esa)], [left_inverse])).
% 5.62/1.38 thf(zip_derived_cl1159, plain,
% 5.62/1.38 ((((inverse @ sk_c4) = (sk_c6))
% 5.62/1.38 | ((multiply @ sk_c2 @ sk_c6) = (identity)))),
% 5.62/1.38 inference('s_sup+', [status(thm)], [zip_derived_cl211, zip_derived_cl1])).
% 5.62/1.38 thf(zip_derived_cl1, plain,
% 5.62/1.38 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 5.62/1.38 inference('cnf', [status(esa)], [left_inverse])).
% 5.62/1.38 thf(zip_derived_cl1169, plain,
% 5.62/1.38 ((((multiply @ sk_c2 @ sk_c6) = (identity))
% 5.62/1.38 | ((multiply @ sk_c6 @ sk_c4) = (identity)))),
% 5.62/1.38 inference('s_sup+', [status(thm)], [zip_derived_cl1159, zip_derived_cl1])).
% 5.62/1.38 thf(prove_this_19, conjecture,
% 5.62/1.38 (~( ( ( inverse @ sk_c4 ) = ( sk_c6 ) ) |
% 5.62/1.38 ( ( multiply @ sk_c2 @ sk_c6 ) = ( sk_c5 ) ) ))).
% 5.62/1.38 thf(zf_stmt_2, negated_conjecture,
% 5.62/1.38 (( ( inverse @ sk_c4 ) = ( sk_c6 ) ) |
% 5.62/1.38 ( ( multiply @ sk_c2 @ sk_c6 ) = ( sk_c5 ) )),
% 5.62/1.38 inference('cnf.neg', [status(esa)], [prove_this_19])).
% 5.62/1.38 thf(zip_derived_cl21, plain,
% 5.62/1.38 ((((inverse @ sk_c4) = (sk_c6)) | ((multiply @ sk_c2 @ sk_c6) = (sk_c5)))),
% 5.62/1.38 inference('cnf', [status(esa)], [zf_stmt_2])).
% 5.62/1.38 thf(zip_derived_cl1, plain,
% 5.62/1.38 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 5.62/1.38 inference('cnf', [status(esa)], [left_inverse])).
% 5.62/1.38 thf(zip_derived_cl48, plain,
% 5.62/1.38 ((((multiply @ sk_c2 @ sk_c6) = (sk_c5))
% 5.62/1.38 | ((multiply @ sk_c6 @ sk_c4) = (identity)))),
% 5.62/1.38 inference('s_sup+', [status(thm)], [zip_derived_cl21, zip_derived_cl1])).
% 5.62/1.38 thf(zip_derived_cl1225, plain,
% 5.62/1.38 ((((multiply @ sk_c6 @ sk_c4) = (identity))
% 5.62/1.38 | ((identity) = (sk_c5))
% 5.62/1.38 | ((multiply @ sk_c6 @ sk_c4) = (identity)))),
% 5.62/1.38 inference('s_sup+', [status(thm)], [zip_derived_cl1169, zip_derived_cl48])).
% 5.62/1.38 thf(zip_derived_cl1228, plain,
% 5.62/1.38 ((((identity) = (sk_c5)) | ((multiply @ sk_c6 @ sk_c4) = (identity)))),
% 5.62/1.38 inference('simplify', [status(thm)], [zip_derived_cl1225])).
% 5.62/1.38 thf(zip_derived_cl41, plain,
% 5.62/1.38 (![X0 : $i, X1 : $i]:
% 5.62/1.38 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 5.62/1.38 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl0])).
% 5.62/1.38 thf(zip_derived_cl1230, plain,
% 5.62/1.38 ((((identity) = (sk_c5))
% 5.62/1.38 | ((sk_c4) = (multiply @ (inverse @ sk_c6) @ identity)))),
% 5.62/1.38 inference('s_sup+', [status(thm)], [zip_derived_cl1228, zip_derived_cl41])).
% 5.62/1.38 thf(zip_derived_cl2, plain,
% 5.62/1.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.62/1.38 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 5.62/1.38 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 5.62/1.38 inference('cnf', [status(esa)], [associativity])).
% 5.62/1.38 thf(zip_derived_cl1241, plain,
% 5.62/1.38 (![X0 : $i]:
% 5.62/1.38 (((identity) = (sk_c5))
% 5.62/1.38 | ((multiply @ sk_c4 @ X0)
% 5.62/1.38 = (multiply @ (inverse @ sk_c6) @ (multiply @ identity @ X0))))),
% 5.62/1.38 inference('s_sup+', [status(thm)], [zip_derived_cl1230, zip_derived_cl2])).
% 5.62/1.38 thf(zip_derived_cl0, plain,
% 5.62/1.38 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 5.62/1.38 inference('cnf', [status(esa)], [left_identity])).
% 5.62/1.38 thf(zip_derived_cl1246, plain,
% 5.62/1.38 (![X0 : $i]:
% 5.62/1.38 (((identity) = (sk_c5))
% 5.62/1.38 | ((multiply @ sk_c4 @ X0) = (multiply @ (inverse @ sk_c6) @ X0)))),
% 5.62/1.38 inference('demod', [status(thm)], [zip_derived_cl1241, zip_derived_cl0])).
% 5.62/1.38 thf(prove_this_21, conjecture,
% 5.62/1.38 (~( ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c5 ) ) |
% 5.62/1.38 ( ( inverse @ sk_c2 ) = ( sk_c6 ) ) ))).
% 5.62/1.38 thf(zf_stmt_3, negated_conjecture,
% 5.62/1.38 (( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c5 ) ) |
% 5.62/1.38 ( ( inverse @ sk_c2 ) = ( sk_c6 ) )),
% 5.62/1.38 inference('cnf.neg', [status(esa)], [prove_this_21])).
% 5.62/1.38 thf(zip_derived_cl23, plain,
% 5.62/1.38 ((((multiply @ sk_c6 @ sk_c7) = (sk_c5)) | ((inverse @ sk_c2) = (sk_c6)))),
% 5.62/1.38 inference('cnf', [status(esa)], [zf_stmt_3])).
% 5.62/1.38 thf(prove_this_16, conjecture,
% 5.62/1.38 (~( ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c5 ) ) |
% 5.62/1.38 ( ( multiply @ sk_c2 @ sk_c6 ) = ( sk_c5 ) ) ))).
% 5.62/1.38 thf(zf_stmt_4, negated_conjecture,
% 5.62/1.38 (( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c5 ) ) |
% 5.62/1.38 ( ( multiply @ sk_c2 @ sk_c6 ) = ( sk_c5 ) )),
% 5.62/1.38 inference('cnf.neg', [status(esa)], [prove_this_16])).
% 5.62/1.38 thf(zip_derived_cl18, plain,
% 5.62/1.38 ((((multiply @ sk_c6 @ sk_c7) = (sk_c5))
% 5.62/1.38 | ((multiply @ sk_c2 @ sk_c6) = (sk_c5)))),
% 5.62/1.38 inference('cnf', [status(esa)], [zf_stmt_4])).
% 5.62/1.38 thf(zip_derived_cl41, plain,
% 5.62/1.38 (![X0 : $i, X1 : $i]:
% 5.62/1.38 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 5.62/1.38 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl0])).
% 5.62/1.38 thf(zip_derived_cl160, plain,
% 5.62/1.38 ((((multiply @ sk_c6 @ sk_c7) = (sk_c5))
% 5.62/1.38 | ((sk_c6) = (multiply @ (inverse @ sk_c2) @ sk_c5)))),
% 5.62/1.38 inference('s_sup+', [status(thm)], [zip_derived_cl18, zip_derived_cl41])).
% 5.62/1.38 thf(zip_derived_cl375, plain,
% 5.62/1.38 ((((multiply @ sk_c6 @ sk_c7) = (sk_c5))
% 5.62/1.38 | ((multiply @ sk_c6 @ sk_c7) = (sk_c5))
% 5.62/1.38 | ((sk_c6) = (multiply @ sk_c6 @ sk_c5)))),
% 5.62/1.38 inference('s_sup+', [status(thm)], [zip_derived_cl23, zip_derived_cl160])).
% 5.62/1.38 thf(zip_derived_cl380, plain,
% 5.62/1.38 ((((sk_c6) = (multiply @ sk_c6 @ sk_c5))
% 5.62/1.38 | ((multiply @ sk_c6 @ sk_c7) = (sk_c5)))),
% 5.62/1.38 inference('simplify', [status(thm)], [zip_derived_cl375])).
% 5.62/1.38 thf(zip_derived_cl41, plain,
% 5.62/1.38 (![X0 : $i, X1 : $i]:
% 5.62/1.38 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 5.62/1.38 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl0])).
% 5.62/1.38 thf(zip_derived_cl388, plain,
% 5.62/1.38 ((((multiply @ sk_c6 @ sk_c7) = (sk_c5))
% 5.62/1.38 | ((sk_c5) = (multiply @ (inverse @ sk_c6) @ sk_c6)))),
% 5.62/1.38 inference('s_sup+', [status(thm)], [zip_derived_cl380, zip_derived_cl41])).
% 5.62/1.38 thf(zip_derived_cl1, plain,
% 5.62/1.38 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 5.62/1.38 inference('cnf', [status(esa)], [left_inverse])).
% 5.62/1.38 thf(zip_derived_cl390, plain,
% 5.62/1.38 ((((multiply @ sk_c6 @ sk_c7) = (sk_c5)) | ((sk_c5) = (identity)))),
% 5.62/1.38 inference('demod', [status(thm)], [zip_derived_cl388, zip_derived_cl1])).
% 5.62/1.39 thf(zip_derived_cl41, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i]:
% 5.62/1.39 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl0])).
% 5.62/1.39 thf(zip_derived_cl392, plain,
% 5.62/1.39 ((((sk_c5) = (identity))
% 5.62/1.39 | ((sk_c7) = (multiply @ (inverse @ sk_c6) @ sk_c5)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl390, zip_derived_cl41])).
% 5.62/1.39 thf(zip_derived_cl1319, plain,
% 5.62/1.39 ((((identity) = (sk_c5))
% 5.62/1.39 | ((sk_c5) = (identity))
% 5.62/1.39 | ((sk_c7) = (multiply @ sk_c4 @ sk_c5)))),
% 5.62/1.39 inference('s_sup+', [status(thm)],
% 5.62/1.39 [zip_derived_cl1246, zip_derived_cl392])).
% 5.62/1.39 thf(zip_derived_cl1322, plain,
% 5.62/1.39 ((((sk_c7) = (multiply @ sk_c4 @ sk_c5)) | ((identity) = (sk_c5)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl1319])).
% 5.62/1.39 thf(prove_this_25, conjecture,
% 5.62/1.39 (~( ( ( multiply @ sk_c4 @ sk_c5 ) = ( sk_c6 ) ) |
% 5.62/1.39 ( ( inverse @ sk_c2 ) = ( sk_c6 ) ) ))).
% 5.62/1.39 thf(zf_stmt_5, negated_conjecture,
% 5.62/1.39 (( ( multiply @ sk_c4 @ sk_c5 ) = ( sk_c6 ) ) |
% 5.62/1.39 ( ( inverse @ sk_c2 ) = ( sk_c6 ) )),
% 5.62/1.39 inference('cnf.neg', [status(esa)], [prove_this_25])).
% 5.62/1.39 thf(zip_derived_cl27, plain,
% 5.62/1.39 ((((multiply @ sk_c4 @ sk_c5) = (sk_c6)) | ((inverse @ sk_c2) = (sk_c6)))),
% 5.62/1.39 inference('cnf', [status(esa)], [zf_stmt_5])).
% 5.62/1.39 thf(prove_this_20, conjecture,
% 5.62/1.39 (~( ( ( multiply @ sk_c4 @ sk_c5 ) = ( sk_c6 ) ) |
% 5.62/1.39 ( ( multiply @ sk_c2 @ sk_c6 ) = ( sk_c5 ) ) ))).
% 5.62/1.39 thf(zf_stmt_6, negated_conjecture,
% 5.62/1.39 (( ( multiply @ sk_c4 @ sk_c5 ) = ( sk_c6 ) ) |
% 5.62/1.39 ( ( multiply @ sk_c2 @ sk_c6 ) = ( sk_c5 ) )),
% 5.62/1.39 inference('cnf.neg', [status(esa)], [prove_this_20])).
% 5.62/1.39 thf(zip_derived_cl22, plain,
% 5.62/1.39 ((((multiply @ sk_c4 @ sk_c5) = (sk_c6))
% 5.62/1.39 | ((multiply @ sk_c2 @ sk_c6) = (sk_c5)))),
% 5.62/1.39 inference('cnf', [status(esa)], [zf_stmt_6])).
% 5.62/1.39 thf(zip_derived_cl41, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i]:
% 5.62/1.39 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl0])).
% 5.62/1.39 thf(zip_derived_cl162, plain,
% 5.62/1.39 ((((multiply @ sk_c4 @ sk_c5) = (sk_c6))
% 5.62/1.39 | ((sk_c6) = (multiply @ (inverse @ sk_c2) @ sk_c5)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl41])).
% 5.62/1.39 thf(zip_derived_cl421, plain,
% 5.62/1.39 ((((multiply @ sk_c4 @ sk_c5) = (sk_c6))
% 5.62/1.39 | ((multiply @ sk_c4 @ sk_c5) = (sk_c6))
% 5.62/1.39 | ((sk_c6) = (multiply @ sk_c6 @ sk_c5)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl162])).
% 5.62/1.39 thf(zip_derived_cl422, plain,
% 5.62/1.39 ((((sk_c6) = (multiply @ sk_c6 @ sk_c5))
% 5.62/1.39 | ((multiply @ sk_c4 @ sk_c5) = (sk_c6)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl421])).
% 5.62/1.39 thf(zip_derived_cl1348, plain,
% 5.62/1.39 ((((identity) = (sk_c5))
% 5.62/1.39 | ((sk_c6) = (multiply @ sk_c6 @ sk_c5))
% 5.62/1.39 | ((sk_c7) = (sk_c6)))),
% 5.62/1.39 inference('s_sup+', [status(thm)],
% 5.62/1.39 [zip_derived_cl1322, zip_derived_cl422])).
% 5.62/1.39 thf(zip_derived_cl41, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i]:
% 5.62/1.39 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl0])).
% 5.62/1.39 thf(zip_derived_cl1559, plain,
% 5.62/1.39 ((((sk_c7) = (sk_c6))
% 5.62/1.39 | ((identity) = (sk_c5))
% 5.62/1.39 | ((sk_c5) = (multiply @ (inverse @ sk_c6) @ sk_c6)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl1348, zip_derived_cl41])).
% 5.62/1.39 thf(zip_derived_cl1, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 5.62/1.39 inference('cnf', [status(esa)], [left_inverse])).
% 5.62/1.39 thf(zip_derived_cl1574, plain,
% 5.62/1.39 ((((sk_c7) = (sk_c6)) | ((identity) = (sk_c5)) | ((sk_c5) = (identity)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl1559, zip_derived_cl1])).
% 5.62/1.39 thf(zip_derived_cl1575, plain,
% 5.62/1.39 ((((identity) = (sk_c5)) | ((sk_c7) = (sk_c6)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl1574])).
% 5.62/1.39 thf(prove_this_14, conjecture,
% 5.62/1.39 (~( ( ( inverse @ sk_c4 ) = ( sk_c6 ) ) |
% 5.62/1.39 ( ( multiply @ sk_c7 @ sk_c5 ) = ( sk_c6 ) ) ))).
% 5.62/1.39 thf(zf_stmt_7, negated_conjecture,
% 5.62/1.39 (( ( inverse @ sk_c4 ) = ( sk_c6 ) ) |
% 5.62/1.39 ( ( multiply @ sk_c7 @ sk_c5 ) = ( sk_c6 ) )),
% 5.62/1.39 inference('cnf.neg', [status(esa)], [prove_this_14])).
% 5.62/1.39 thf(zip_derived_cl16, plain,
% 5.62/1.39 ((((inverse @ sk_c4) = (sk_c6)) | ((multiply @ sk_c7 @ sk_c5) = (sk_c6)))),
% 5.62/1.39 inference('cnf', [status(esa)], [zf_stmt_7])).
% 5.62/1.39 thf(prove_this_15, conjecture,
% 5.62/1.39 (~( ( ( multiply @ sk_c4 @ sk_c5 ) = ( sk_c6 ) ) |
% 5.62/1.39 ( ( multiply @ sk_c7 @ sk_c5 ) = ( sk_c6 ) ) ))).
% 5.62/1.39 thf(zf_stmt_8, negated_conjecture,
% 5.62/1.39 (( ( multiply @ sk_c4 @ sk_c5 ) = ( sk_c6 ) ) |
% 5.62/1.39 ( ( multiply @ sk_c7 @ sk_c5 ) = ( sk_c6 ) )),
% 5.62/1.39 inference('cnf.neg', [status(esa)], [prove_this_15])).
% 5.62/1.39 thf(zip_derived_cl17, plain,
% 5.62/1.39 ((((multiply @ sk_c4 @ sk_c5) = (sk_c6))
% 5.62/1.39 | ((multiply @ sk_c7 @ sk_c5) = (sk_c6)))),
% 5.62/1.39 inference('cnf', [status(esa)], [zf_stmt_8])).
% 5.62/1.39 thf(zip_derived_cl41, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i]:
% 5.62/1.39 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl0])).
% 5.62/1.39 thf(zip_derived_cl157, plain,
% 5.62/1.39 ((((multiply @ sk_c7 @ sk_c5) = (sk_c6))
% 5.62/1.39 | ((sk_c5) = (multiply @ (inverse @ sk_c4) @ sk_c6)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl17, zip_derived_cl41])).
% 5.62/1.39 thf(zip_derived_cl366, plain,
% 5.62/1.39 ((((multiply @ sk_c7 @ sk_c5) = (sk_c6))
% 5.62/1.39 | ((multiply @ sk_c7 @ sk_c5) = (sk_c6))
% 5.62/1.39 | ((sk_c5) = (multiply @ sk_c6 @ sk_c6)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl16, zip_derived_cl157])).
% 5.62/1.39 thf(zip_derived_cl369, plain,
% 5.62/1.39 ((((sk_c5) = (multiply @ sk_c6 @ sk_c6))
% 5.62/1.39 | ((multiply @ sk_c7 @ sk_c5) = (sk_c6)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl366])).
% 5.62/1.39 thf(zip_derived_cl41, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i]:
% 5.62/1.39 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl0])).
% 5.62/1.39 thf(zip_derived_cl371, plain,
% 5.62/1.39 ((((multiply @ sk_c7 @ sk_c5) = (sk_c6))
% 5.62/1.39 | ((sk_c6) = (multiply @ (inverse @ sk_c6) @ sk_c5)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl369, zip_derived_cl41])).
% 5.62/1.39 thf(prove_this_11, conjecture,
% 5.62/1.39 (~( ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c5 ) ) |
% 5.62/1.39 ( ( multiply @ sk_c7 @ sk_c5 ) = ( sk_c6 ) ) ))).
% 5.62/1.39 thf(zf_stmt_9, negated_conjecture,
% 5.62/1.39 (( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c5 ) ) |
% 5.62/1.39 ( ( multiply @ sk_c7 @ sk_c5 ) = ( sk_c6 ) )),
% 5.62/1.39 inference('cnf.neg', [status(esa)], [prove_this_11])).
% 5.62/1.39 thf(zip_derived_cl13, plain,
% 5.62/1.39 ((((multiply @ sk_c6 @ sk_c7) = (sk_c5))
% 5.62/1.39 | ((multiply @ sk_c7 @ sk_c5) = (sk_c6)))),
% 5.62/1.39 inference('cnf', [status(esa)], [zf_stmt_9])).
% 5.62/1.39 thf(zip_derived_cl41, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i]:
% 5.62/1.39 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl0])).
% 5.62/1.39 thf(zip_derived_cl143, plain,
% 5.62/1.39 ((((multiply @ sk_c7 @ sk_c5) = (sk_c6))
% 5.62/1.39 | ((sk_c7) = (multiply @ (inverse @ sk_c6) @ sk_c5)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl41])).
% 5.62/1.39 thf(zip_derived_cl430, plain,
% 5.62/1.39 ((((multiply @ sk_c7 @ sk_c5) = (sk_c6))
% 5.62/1.39 | ((multiply @ sk_c7 @ sk_c5) = (sk_c6))
% 5.62/1.39 | ((sk_c7) = (sk_c6)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl371, zip_derived_cl143])).
% 5.62/1.39 thf(zip_derived_cl432, plain,
% 5.62/1.39 ((((sk_c7) = (sk_c6)) | ((multiply @ sk_c7 @ sk_c5) = (sk_c6)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl430])).
% 5.62/1.39 thf(zip_derived_cl1663, plain,
% 5.62/1.39 ((((sk_c7) = (sk_c6))
% 5.62/1.39 | ((sk_c7) = (sk_c6))
% 5.62/1.39 | ((multiply @ sk_c7 @ identity) = (sk_c6)))),
% 5.62/1.39 inference('s_sup+', [status(thm)],
% 5.62/1.39 [zip_derived_cl1575, zip_derived_cl432])).
% 5.62/1.39 thf(zip_derived_cl1680, plain,
% 5.62/1.39 ((((multiply @ sk_c7 @ identity) = (sk_c6)) | ((sk_c7) = (sk_c6)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl1663])).
% 5.62/1.39 thf(zip_derived_cl2, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.62/1.39 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 5.62/1.39 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 5.62/1.39 inference('cnf', [status(esa)], [associativity])).
% 5.62/1.39 thf(zip_derived_cl1686, plain,
% 5.62/1.39 (![X0 : $i]:
% 5.62/1.39 (((sk_c7) = (sk_c6))
% 5.62/1.39 | ((multiply @ sk_c6 @ X0)
% 5.62/1.39 = (multiply @ sk_c7 @ (multiply @ identity @ X0))))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl1680, zip_derived_cl2])).
% 5.62/1.39 thf(zip_derived_cl0, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 5.62/1.39 inference('cnf', [status(esa)], [left_identity])).
% 5.62/1.39 thf(zip_derived_cl1693, plain,
% 5.62/1.39 (![X0 : $i]:
% 5.62/1.39 (((sk_c7) = (sk_c6))
% 5.62/1.39 | ((multiply @ sk_c6 @ X0) = (multiply @ sk_c7 @ X0)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl1686, zip_derived_cl0])).
% 5.62/1.39 thf(zip_derived_cl1695, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ sk_c6 @ X0) = (multiply @ sk_c7 @ X0))),
% 5.62/1.39 inference('condensation', [status(thm)], [zip_derived_cl1693])).
% 5.62/1.39 thf(zip_derived_cl1699, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 5.62/1.39 (((multiply @ X0 @ sk_c5) != (sk_c6))
% 5.62/1.39 | ((inverse @ X0) != (sk_c6))
% 5.62/1.39 | ((multiply @ X1 @ sk_c6) != (sk_c7))
% 5.62/1.39 | ((inverse @ X1) != (sk_c7))
% 5.62/1.39 | ((multiply @ sk_c7 @ sk_c7) != (sk_c5))
% 5.62/1.39 | ((inverse @ X2) != (sk_c6))
% 5.62/1.39 | ((multiply @ X2 @ sk_c6) != (sk_c5))
% 5.62/1.39 | ((multiply @ sk_c7 @ sk_c5) != (sk_c6))
% 5.62/1.39 | ((inverse @ X3) != (sk_c7))
% 5.62/1.39 | ((multiply @ X3 @ sk_c7) != (sk_c6)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl28, zip_derived_cl1695])).
% 5.62/1.39 thf(zip_derived_cl1695, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ sk_c6 @ X0) = (multiply @ sk_c7 @ X0))),
% 5.62/1.39 inference('condensation', [status(thm)], [zip_derived_cl1693])).
% 5.62/1.39 thf(zip_derived_cl1246, plain,
% 5.62/1.39 (![X0 : $i]:
% 5.62/1.39 (((identity) = (sk_c5))
% 5.62/1.39 | ((multiply @ sk_c4 @ X0) = (multiply @ (inverse @ sk_c6) @ X0)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl1241, zip_derived_cl0])).
% 5.62/1.39 thf(zip_derived_cl1, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 5.62/1.39 inference('cnf', [status(esa)], [left_inverse])).
% 5.62/1.39 thf(zip_derived_cl1309, plain,
% 5.62/1.39 ((((identity) = (sk_c5)) | ((multiply @ sk_c4 @ sk_c6) = (identity)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl1246, zip_derived_cl1])).
% 5.62/1.39 thf(zip_derived_cl1228, plain,
% 5.62/1.39 ((((identity) = (sk_c5)) | ((multiply @ sk_c6 @ sk_c4) = (identity)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl1225])).
% 5.62/1.39 thf(zip_derived_cl2, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.62/1.39 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 5.62/1.39 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 5.62/1.39 inference('cnf', [status(esa)], [associativity])).
% 5.62/1.39 thf(zip_derived_cl1229, plain,
% 5.62/1.39 (![X0 : $i]:
% 5.62/1.39 (((identity) = (sk_c5))
% 5.62/1.39 | ((multiply @ identity @ X0)
% 5.62/1.39 = (multiply @ sk_c6 @ (multiply @ sk_c4 @ X0))))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl1228, zip_derived_cl2])).
% 5.62/1.39 thf(zip_derived_cl0, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 5.62/1.39 inference('cnf', [status(esa)], [left_identity])).
% 5.62/1.39 thf(zip_derived_cl1240, plain,
% 5.62/1.39 (![X0 : $i]:
% 5.62/1.39 (((identity) = (sk_c5))
% 5.62/1.39 | ((X0) = (multiply @ sk_c6 @ (multiply @ sk_c4 @ X0))))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl1229, zip_derived_cl0])).
% 5.62/1.39 thf(zip_derived_cl1327, plain,
% 5.62/1.39 ((((identity) = (sk_c5))
% 5.62/1.39 | ((identity) = (sk_c5))
% 5.62/1.39 | ((sk_c6) = (multiply @ sk_c6 @ identity)))),
% 5.62/1.39 inference('s_sup+', [status(thm)],
% 5.62/1.39 [zip_derived_cl1309, zip_derived_cl1240])).
% 5.62/1.39 thf(zip_derived_cl1329, plain,
% 5.62/1.39 ((((sk_c6) = (multiply @ sk_c6 @ identity)) | ((identity) = (sk_c5)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl1327])).
% 5.62/1.39 thf(zip_derived_cl1744, plain,
% 5.62/1.39 ((((sk_c6) = (multiply @ sk_c7 @ identity)) | ((identity) = (sk_c5)))),
% 5.62/1.39 inference('s_sup+', [status(thm)],
% 5.62/1.39 [zip_derived_cl1695, zip_derived_cl1329])).
% 5.62/1.39 thf(zip_derived_cl41, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i]:
% 5.62/1.39 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl0])).
% 5.62/1.39 thf(zip_derived_cl1817, plain,
% 5.62/1.39 ((((identity) = (sk_c5))
% 5.62/1.39 | ((identity) = (multiply @ (inverse @ sk_c7) @ sk_c6)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl1744, zip_derived_cl41])).
% 5.62/1.39 thf(prove_this_13, conjecture,
% 5.62/1.39 (~( ( ( multiply @ sk_c3 @ sk_c6 ) = ( sk_c7 ) ) |
% 5.62/1.39 ( ( multiply @ sk_c7 @ sk_c5 ) = ( sk_c6 ) ) ))).
% 5.62/1.39 thf(zf_stmt_10, negated_conjecture,
% 5.62/1.39 (( ( multiply @ sk_c3 @ sk_c6 ) = ( sk_c7 ) ) |
% 5.62/1.39 ( ( multiply @ sk_c7 @ sk_c5 ) = ( sk_c6 ) )),
% 5.62/1.39 inference('cnf.neg', [status(esa)], [prove_this_13])).
% 5.62/1.39 thf(zip_derived_cl15, plain,
% 5.62/1.39 ((((multiply @ sk_c3 @ sk_c6) = (sk_c7))
% 5.62/1.39 | ((multiply @ sk_c7 @ sk_c5) = (sk_c6)))),
% 5.62/1.39 inference('cnf', [status(esa)], [zf_stmt_10])).
% 5.62/1.39 thf(prove_this_12, conjecture,
% 5.62/1.39 (~( ( ( inverse @ sk_c3 ) = ( sk_c7 ) ) |
% 5.62/1.39 ( ( multiply @ sk_c7 @ sk_c5 ) = ( sk_c6 ) ) ))).
% 5.62/1.39 thf(zf_stmt_11, negated_conjecture,
% 5.62/1.39 (( ( inverse @ sk_c3 ) = ( sk_c7 ) ) |
% 5.62/1.39 ( ( multiply @ sk_c7 @ sk_c5 ) = ( sk_c6 ) )),
% 5.62/1.39 inference('cnf.neg', [status(esa)], [prove_this_12])).
% 5.62/1.39 thf(zip_derived_cl14, plain,
% 5.62/1.39 ((((inverse @ sk_c3) = (sk_c7)) | ((multiply @ sk_c7 @ sk_c5) = (sk_c6)))),
% 5.62/1.39 inference('cnf', [status(esa)], [zf_stmt_11])).
% 5.62/1.39 thf(zip_derived_cl1, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 5.62/1.39 inference('cnf', [status(esa)], [left_inverse])).
% 5.62/1.39 thf(zip_derived_cl45, plain,
% 5.62/1.39 ((((multiply @ sk_c7 @ sk_c5) = (sk_c6))
% 5.62/1.39 | ((multiply @ sk_c7 @ sk_c3) = (identity)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl1])).
% 5.62/1.39 thf(zip_derived_cl2, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.62/1.39 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 5.62/1.39 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 5.62/1.39 inference('cnf', [status(esa)], [associativity])).
% 5.62/1.39 thf(zip_derived_cl76, plain,
% 5.62/1.39 (![X0 : $i]:
% 5.62/1.39 (((multiply @ sk_c7 @ sk_c5) = (sk_c6))
% 5.62/1.39 | ((multiply @ identity @ X0)
% 5.62/1.39 = (multiply @ sk_c7 @ (multiply @ sk_c3 @ X0))))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl45, zip_derived_cl2])).
% 5.62/1.39 thf(zip_derived_cl0, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 5.62/1.39 inference('cnf', [status(esa)], [left_identity])).
% 5.62/1.39 thf(zip_derived_cl77, plain,
% 5.62/1.39 (![X0 : $i]:
% 5.62/1.39 (((multiply @ sk_c7 @ sk_c5) = (sk_c6))
% 5.62/1.39 | ((X0) = (multiply @ sk_c7 @ (multiply @ sk_c3 @ X0))))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl76, zip_derived_cl0])).
% 5.62/1.39 thf(zip_derived_cl117, plain,
% 5.62/1.39 ((((multiply @ sk_c7 @ sk_c5) = (sk_c6))
% 5.62/1.39 | ((multiply @ sk_c7 @ sk_c5) = (sk_c6))
% 5.62/1.39 | ((sk_c6) = (multiply @ sk_c7 @ sk_c7)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl15, zip_derived_cl77])).
% 5.62/1.39 thf(zip_derived_cl120, plain,
% 5.62/1.39 ((((sk_c6) = (multiply @ sk_c7 @ sk_c7))
% 5.62/1.39 | ((multiply @ sk_c7 @ sk_c5) = (sk_c6)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl117])).
% 5.62/1.39 thf(zip_derived_cl41, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i]:
% 5.62/1.39 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl0])).
% 5.62/1.39 thf(zip_derived_cl137, plain,
% 5.62/1.39 ((((sk_c6) = (multiply @ sk_c7 @ sk_c7))
% 5.62/1.39 | ((sk_c5) = (multiply @ (inverse @ sk_c7) @ sk_c6)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl120, zip_derived_cl41])).
% 5.62/1.39 thf(zip_derived_cl2489, plain,
% 5.62/1.39 ((((identity) = (sk_c5))
% 5.62/1.39 | ((sk_c6) = (multiply @ sk_c7 @ sk_c7))
% 5.62/1.39 | ((sk_c5) = (identity)))),
% 5.62/1.39 inference('s_sup+', [status(thm)],
% 5.62/1.39 [zip_derived_cl1817, zip_derived_cl137])).
% 5.62/1.39 thf(zip_derived_cl2498, plain,
% 5.62/1.39 ((((sk_c6) = (multiply @ sk_c7 @ sk_c7)) | ((identity) = (sk_c5)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl2489])).
% 5.62/1.39 thf(zip_derived_cl1695, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ sk_c6 @ X0) = (multiply @ sk_c7 @ X0))),
% 5.62/1.39 inference('condensation', [status(thm)], [zip_derived_cl1693])).
% 5.62/1.39 thf(zip_derived_cl390, plain,
% 5.62/1.39 ((((multiply @ sk_c6 @ sk_c7) = (sk_c5)) | ((sk_c5) = (identity)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl388, zip_derived_cl1])).
% 5.62/1.39 thf(zip_derived_cl1750, plain,
% 5.62/1.39 ((((multiply @ sk_c7 @ sk_c7) = (sk_c5)) | ((sk_c5) = (identity)))),
% 5.62/1.39 inference('s_sup+', [status(thm)],
% 5.62/1.39 [zip_derived_cl1695, zip_derived_cl390])).
% 5.62/1.39 thf(zip_derived_cl2580, plain,
% 5.62/1.39 ((((identity) = (sk_c5)) | ((sk_c6) = (sk_c5)) | ((sk_c5) = (identity)))),
% 5.62/1.39 inference('s_sup+', [status(thm)],
% 5.62/1.39 [zip_derived_cl2498, zip_derived_cl1750])).
% 5.62/1.39 thf(zip_derived_cl2586, plain,
% 5.62/1.39 ((((sk_c6) = (sk_c5)) | ((identity) = (sk_c5)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl2580])).
% 5.62/1.39 thf(zip_derived_cl1695, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ sk_c6 @ X0) = (multiply @ sk_c7 @ X0))),
% 5.62/1.39 inference('condensation', [status(thm)], [zip_derived_cl1693])).
% 5.62/1.39 thf(zip_derived_cl369, plain,
% 5.62/1.39 ((((sk_c5) = (multiply @ sk_c6 @ sk_c6))
% 5.62/1.39 | ((multiply @ sk_c7 @ sk_c5) = (sk_c6)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl366])).
% 5.62/1.39 thf(zip_derived_cl1752, plain,
% 5.62/1.39 ((((sk_c5) = (multiply @ sk_c7 @ sk_c6))
% 5.62/1.39 | ((multiply @ sk_c7 @ sk_c5) = (sk_c6)))),
% 5.62/1.39 inference('s_sup+', [status(thm)],
% 5.62/1.39 [zip_derived_cl1695, zip_derived_cl369])).
% 5.62/1.39 thf(zip_derived_cl2617, plain,
% 5.62/1.39 ((((identity) = (sk_c5))
% 5.62/1.39 | ((sk_c6) = (multiply @ sk_c7 @ sk_c6))
% 5.62/1.39 | ((multiply @ sk_c7 @ sk_c6) = (sk_c6)))),
% 5.62/1.39 inference('s_sup+', [status(thm)],
% 5.62/1.39 [zip_derived_cl2586, zip_derived_cl1752])).
% 5.62/1.39 thf(zip_derived_cl2633, plain,
% 5.62/1.39 ((((sk_c6) = (multiply @ sk_c7 @ sk_c6)) | ((identity) = (sk_c5)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl2617])).
% 5.62/1.39 thf(prove_this_22, conjecture,
% 5.62/1.39 (~( ( ( inverse @ sk_c3 ) = ( sk_c7 ) ) |
% 5.62/1.39 ( ( inverse @ sk_c2 ) = ( sk_c6 ) ) ))).
% 5.62/1.39 thf(zf_stmt_12, negated_conjecture,
% 5.62/1.39 (( ( inverse @ sk_c3 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c6 ) )),
% 5.62/1.39 inference('cnf.neg', [status(esa)], [prove_this_22])).
% 5.62/1.39 thf(zip_derived_cl24, plain,
% 5.62/1.39 ((((inverse @ sk_c3) = (sk_c7)) | ((inverse @ sk_c2) = (sk_c6)))),
% 5.62/1.39 inference('cnf', [status(esa)], [zf_stmt_12])).
% 5.62/1.39 thf(zip_derived_cl41, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i]:
% 5.62/1.39 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl0])).
% 5.62/1.39 thf(zip_derived_cl181, plain,
% 5.62/1.39 (![X0 : $i]:
% 5.62/1.39 (((inverse @ sk_c3) = (sk_c7))
% 5.62/1.39 | ((X0) = (multiply @ sk_c6 @ (multiply @ sk_c2 @ X0))))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl24, zip_derived_cl41])).
% 5.62/1.39 thf(zip_derived_cl41, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i]:
% 5.62/1.39 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl0])).
% 5.62/1.39 thf(zip_derived_cl203, plain,
% 5.62/1.39 (![X0 : $i]:
% 5.62/1.39 (((inverse @ sk_c3) = (sk_c7))
% 5.62/1.39 | ((multiply @ sk_c2 @ X0) = (multiply @ (inverse @ sk_c6) @ X0)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl41])).
% 5.62/1.39 thf(zip_derived_cl1, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 5.62/1.39 inference('cnf', [status(esa)], [left_inverse])).
% 5.62/1.39 thf(zip_derived_cl693, plain,
% 5.62/1.39 ((((inverse @ sk_c3) = (sk_c7))
% 5.62/1.39 | ((multiply @ sk_c2 @ sk_c6) = (identity)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl203, zip_derived_cl1])).
% 5.62/1.39 thf(zip_derived_cl1, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 5.62/1.39 inference('cnf', [status(esa)], [left_inverse])).
% 5.62/1.39 thf(zip_derived_cl702, plain,
% 5.62/1.39 ((((multiply @ sk_c2 @ sk_c6) = (identity))
% 5.62/1.39 | ((multiply @ sk_c7 @ sk_c3) = (identity)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl693, zip_derived_cl1])).
% 5.62/1.39 thf(prove_this_17, conjecture,
% 5.62/1.39 (~( ( ( inverse @ sk_c3 ) = ( sk_c7 ) ) |
% 5.62/1.39 ( ( multiply @ sk_c2 @ sk_c6 ) = ( sk_c5 ) ) ))).
% 5.62/1.39 thf(zf_stmt_13, negated_conjecture,
% 5.62/1.39 (( ( inverse @ sk_c3 ) = ( sk_c7 ) ) |
% 5.62/1.39 ( ( multiply @ sk_c2 @ sk_c6 ) = ( sk_c5 ) )),
% 5.62/1.39 inference('cnf.neg', [status(esa)], [prove_this_17])).
% 5.62/1.39 thf(zip_derived_cl19, plain,
% 5.62/1.39 ((((inverse @ sk_c3) = (sk_c7)) | ((multiply @ sk_c2 @ sk_c6) = (sk_c5)))),
% 5.62/1.39 inference('cnf', [status(esa)], [zf_stmt_13])).
% 5.62/1.39 thf(zip_derived_cl1, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 5.62/1.39 inference('cnf', [status(esa)], [left_inverse])).
% 5.62/1.39 thf(zip_derived_cl47, plain,
% 5.62/1.39 ((((multiply @ sk_c2 @ sk_c6) = (sk_c5))
% 5.62/1.39 | ((multiply @ sk_c7 @ sk_c3) = (identity)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl1])).
% 5.62/1.39 thf(zip_derived_cl714, plain,
% 5.62/1.39 ((((multiply @ sk_c7 @ sk_c3) = (identity))
% 5.62/1.39 | ((identity) = (sk_c5))
% 5.62/1.39 | ((multiply @ sk_c7 @ sk_c3) = (identity)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl702, zip_derived_cl47])).
% 5.62/1.39 thf(zip_derived_cl717, plain,
% 5.62/1.39 ((((identity) = (sk_c5)) | ((multiply @ sk_c7 @ sk_c3) = (identity)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl714])).
% 5.62/1.39 thf(zip_derived_cl41, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i]:
% 5.62/1.39 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl0])).
% 5.62/1.39 thf(zip_derived_cl719, plain,
% 5.62/1.39 ((((identity) = (sk_c5))
% 5.62/1.39 | ((sk_c3) = (multiply @ (inverse @ sk_c7) @ identity)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl717, zip_derived_cl41])).
% 5.62/1.39 thf(zip_derived_cl2, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.62/1.39 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 5.62/1.39 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 5.62/1.39 inference('cnf', [status(esa)], [associativity])).
% 5.62/1.39 thf(zip_derived_cl775, plain,
% 5.62/1.39 (![X0 : $i]:
% 5.62/1.39 (((identity) = (sk_c5))
% 5.62/1.39 | ((multiply @ sk_c3 @ X0)
% 5.62/1.39 = (multiply @ (inverse @ sk_c7) @ (multiply @ identity @ X0))))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl719, zip_derived_cl2])).
% 5.62/1.39 thf(zip_derived_cl0, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 5.62/1.39 inference('cnf', [status(esa)], [left_identity])).
% 5.62/1.39 thf(zip_derived_cl778, plain,
% 5.62/1.39 (![X0 : $i]:
% 5.62/1.39 (((identity) = (sk_c5))
% 5.62/1.39 | ((multiply @ sk_c3 @ X0) = (multiply @ (inverse @ sk_c7) @ X0)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl775, zip_derived_cl0])).
% 5.62/1.39 thf(zip_derived_cl41, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i]:
% 5.62/1.39 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl0])).
% 5.62/1.39 thf(zip_derived_cl804, plain,
% 5.62/1.39 (![X0 : $i]:
% 5.62/1.39 (((identity) = (sk_c5))
% 5.62/1.39 | ((X0) = (multiply @ sk_c3 @ (multiply @ sk_c7 @ X0))))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl778, zip_derived_cl41])).
% 5.62/1.39 thf(zip_derived_cl2810, plain,
% 5.62/1.39 ((((identity) = (sk_c5))
% 5.62/1.39 | ((identity) = (sk_c5))
% 5.62/1.39 | ((sk_c6) = (multiply @ sk_c3 @ sk_c6)))),
% 5.62/1.39 inference('s_sup+', [status(thm)],
% 5.62/1.39 [zip_derived_cl2633, zip_derived_cl804])).
% 5.62/1.39 thf(zip_derived_cl2822, plain,
% 5.62/1.39 ((((sk_c6) = (multiply @ sk_c3 @ sk_c6)) | ((identity) = (sk_c5)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl2810])).
% 5.62/1.39 thf(zip_derived_cl1744, plain,
% 5.62/1.39 ((((sk_c6) = (multiply @ sk_c7 @ identity)) | ((identity) = (sk_c5)))),
% 5.62/1.39 inference('s_sup+', [status(thm)],
% 5.62/1.39 [zip_derived_cl1695, zip_derived_cl1329])).
% 5.62/1.39 thf(zip_derived_cl804, plain,
% 5.62/1.39 (![X0 : $i]:
% 5.62/1.39 (((identity) = (sk_c5))
% 5.62/1.39 | ((X0) = (multiply @ sk_c3 @ (multiply @ sk_c7 @ X0))))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl778, zip_derived_cl41])).
% 5.62/1.39 thf(zip_derived_cl1821, plain,
% 5.62/1.39 ((((identity) = (sk_c5))
% 5.62/1.39 | ((identity) = (sk_c5))
% 5.62/1.39 | ((identity) = (multiply @ sk_c3 @ sk_c6)))),
% 5.62/1.39 inference('s_sup+', [status(thm)],
% 5.62/1.39 [zip_derived_cl1744, zip_derived_cl804])).
% 5.62/1.39 thf(zip_derived_cl1827, plain,
% 5.62/1.39 ((((identity) = (multiply @ sk_c3 @ sk_c6)) | ((identity) = (sk_c5)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl1821])).
% 5.62/1.39 thf(zip_derived_cl3354, plain,
% 5.62/1.39 ((((identity) = (sk_c5))
% 5.62/1.39 | ((identity) = (sk_c6))
% 5.62/1.39 | ((identity) = (sk_c5)))),
% 5.62/1.39 inference('s_sup+', [status(thm)],
% 5.62/1.39 [zip_derived_cl2822, zip_derived_cl1827])).
% 5.62/1.39 thf(zip_derived_cl3363, plain,
% 5.62/1.39 ((((identity) = (sk_c6)) | ((identity) = (sk_c5)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl3354])).
% 5.62/1.39 thf(zip_derived_cl2586, plain,
% 5.62/1.39 ((((sk_c6) = (sk_c5)) | ((identity) = (sk_c5)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl2580])).
% 5.62/1.39 thf(zip_derived_cl2625, plain,
% 5.62/1.39 ((((sk_c6) != (identity)) | ((identity) = (sk_c5)))),
% 5.62/1.39 inference('eq_fact', [status(thm)], [zip_derived_cl2586])).
% 5.62/1.39 thf(zip_derived_cl3422, plain, (((identity) = (sk_c5))),
% 5.62/1.39 inference('clc', [status(thm)], [zip_derived_cl3363, zip_derived_cl2625])).
% 5.62/1.39 thf(zip_derived_cl1, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 5.62/1.39 inference('cnf', [status(esa)], [left_inverse])).
% 5.62/1.39 thf(zip_derived_cl41, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i]:
% 5.62/1.39 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl0])).
% 5.62/1.39 thf(zip_derived_cl132, plain,
% 5.62/1.39 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl41])).
% 5.62/1.39 thf(zip_derived_cl41, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i]:
% 5.62/1.39 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl0])).
% 5.62/1.39 thf(zip_derived_cl41, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i]:
% 5.62/1.39 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl0])).
% 5.62/1.39 thf(zip_derived_cl129, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i]:
% 5.62/1.39 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl41])).
% 5.62/1.39 thf(zip_derived_cl3388, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl132, zip_derived_cl129])).
% 5.62/1.39 thf(zip_derived_cl432, plain,
% 5.62/1.39 ((((sk_c7) = (sk_c6)) | ((multiply @ sk_c7 @ sk_c5) = (sk_c6)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl430])).
% 5.62/1.39 thf(zip_derived_cl41, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i]:
% 5.62/1.39 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl0])).
% 5.62/1.39 thf(zip_derived_cl449, plain,
% 5.62/1.39 ((((sk_c7) = (sk_c6))
% 5.62/1.39 | ((sk_c5) = (multiply @ (inverse @ sk_c7) @ sk_c6)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl432, zip_derived_cl41])).
% 5.62/1.39 thf(zip_derived_cl41, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i]:
% 5.62/1.39 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl0])).
% 5.62/1.39 thf(zip_derived_cl453, plain,
% 5.62/1.39 ((((sk_c7) = (sk_c6))
% 5.62/1.39 | ((sk_c6) = (multiply @ (inverse @ (inverse @ sk_c7)) @ sk_c5)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl449, zip_derived_cl41])).
% 5.62/1.39 thf(zip_derived_cl3422, plain, (((identity) = (sk_c5))),
% 5.62/1.39 inference('clc', [status(thm)], [zip_derived_cl3363, zip_derived_cl2625])).
% 5.62/1.39 thf(zip_derived_cl132, plain,
% 5.62/1.39 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl41])).
% 5.62/1.39 thf(zip_derived_cl3473, plain, ((((sk_c7) = (sk_c6)) | ((sk_c6) = (sk_c7)))),
% 5.62/1.39 inference('demod', [status(thm)],
% 5.62/1.39 [zip_derived_cl453, zip_derived_cl3422, zip_derived_cl132])).
% 5.62/1.39 thf(zip_derived_cl3474, plain, (((sk_c7) = (sk_c6))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl3473])).
% 5.62/1.39 thf(prove_this_8, conjecture,
% 5.62/1.39 (~( ( ( multiply @ sk_c3 @ sk_c6 ) = ( sk_c7 ) ) |
% 5.62/1.39 ( ( inverse @ sk_c1 ) = ( sk_c7 ) ) ))).
% 5.62/1.39 thf(zf_stmt_14, negated_conjecture,
% 5.62/1.39 (( ( multiply @ sk_c3 @ sk_c6 ) = ( sk_c7 ) ) |
% 5.62/1.39 ( ( inverse @ sk_c1 ) = ( sk_c7 ) )),
% 5.62/1.39 inference('cnf.neg', [status(esa)], [prove_this_8])).
% 5.62/1.39 thf(zip_derived_cl10, plain,
% 5.62/1.39 ((((multiply @ sk_c3 @ sk_c6) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c7)))),
% 5.62/1.39 inference('cnf', [status(esa)], [zf_stmt_14])).
% 5.62/1.39 thf(zip_derived_cl3474, plain, (((sk_c7) = (sk_c6))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl3473])).
% 5.62/1.39 thf(zip_derived_cl3518, plain,
% 5.62/1.39 ((((multiply @ sk_c3 @ sk_c7) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c7)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl3474])).
% 5.62/1.39 thf(prove_this_2, conjecture,
% 5.62/1.39 (~( ( ( inverse @ sk_c3 ) = ( sk_c7 ) ) |
% 5.62/1.39 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c6 ) ) ))).
% 5.62/1.39 thf(zf_stmt_15, negated_conjecture,
% 5.62/1.39 (( ( inverse @ sk_c3 ) = ( sk_c7 ) ) |
% 5.62/1.39 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c6 ) )),
% 5.62/1.39 inference('cnf.neg', [status(esa)], [prove_this_2])).
% 5.62/1.39 thf(zip_derived_cl4, plain,
% 5.62/1.39 ((((inverse @ sk_c3) = (sk_c7)) | ((multiply @ sk_c1 @ sk_c7) = (sk_c6)))),
% 5.62/1.39 inference('cnf', [status(esa)], [zf_stmt_15])).
% 5.62/1.39 thf(zip_derived_cl1, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 5.62/1.39 inference('cnf', [status(esa)], [left_inverse])).
% 5.62/1.39 thf(zip_derived_cl33, plain,
% 5.62/1.39 ((((multiply @ sk_c1 @ sk_c7) = (sk_c6))
% 5.62/1.39 | ((multiply @ sk_c7 @ sk_c3) = (identity)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl1])).
% 5.62/1.39 thf(prove_this_1, conjecture,
% 5.62/1.39 (~( ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c5 ) ) |
% 5.62/1.39 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c6 ) ) ))).
% 5.62/1.39 thf(zf_stmt_16, negated_conjecture,
% 5.62/1.39 (( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c5 ) ) |
% 5.62/1.39 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c6 ) )),
% 5.62/1.39 inference('cnf.neg', [status(esa)], [prove_this_1])).
% 5.62/1.39 thf(zip_derived_cl3, plain,
% 5.62/1.39 ((((multiply @ sk_c6 @ sk_c7) = (sk_c5))
% 5.62/1.39 | ((multiply @ sk_c1 @ sk_c7) = (sk_c6)))),
% 5.62/1.39 inference('cnf', [status(esa)], [zf_stmt_16])).
% 5.62/1.39 thf(zip_derived_cl2, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.62/1.39 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 5.62/1.39 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 5.62/1.39 inference('cnf', [status(esa)], [associativity])).
% 5.62/1.39 thf(zip_derived_cl52, plain,
% 5.62/1.39 (![X0 : $i]:
% 5.62/1.39 (((multiply @ sk_c1 @ sk_c7) = (sk_c6))
% 5.62/1.39 | ((multiply @ sk_c5 @ X0)
% 5.62/1.39 = (multiply @ sk_c6 @ (multiply @ sk_c7 @ X0))))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl2])).
% 5.62/1.39 thf(zip_derived_cl239, plain,
% 5.62/1.39 ((((multiply @ sk_c1 @ sk_c7) = (sk_c6))
% 5.62/1.39 | ((multiply @ sk_c1 @ sk_c7) = (sk_c6))
% 5.62/1.39 | ((multiply @ sk_c5 @ sk_c3) = (multiply @ sk_c6 @ identity)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl33, zip_derived_cl52])).
% 5.62/1.39 thf(zip_derived_cl244, plain,
% 5.62/1.39 ((((multiply @ sk_c5 @ sk_c3) = (multiply @ sk_c6 @ identity))
% 5.62/1.39 | ((multiply @ sk_c1 @ sk_c7) = (sk_c6)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl239])).
% 5.62/1.39 thf(zip_derived_cl3422, plain, (((identity) = (sk_c5))),
% 5.62/1.39 inference('clc', [status(thm)], [zip_derived_cl3363, zip_derived_cl2625])).
% 5.62/1.39 thf(zip_derived_cl0, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 5.62/1.39 inference('cnf', [status(esa)], [left_identity])).
% 5.62/1.39 thf(zip_derived_cl3474, plain, (((sk_c7) = (sk_c6))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl3473])).
% 5.62/1.39 thf(zip_derived_cl3474, plain, (((sk_c7) = (sk_c6))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl3473])).
% 5.62/1.39 thf(zip_derived_cl4021, plain,
% 5.62/1.39 ((((sk_c3) = (multiply @ sk_c7 @ identity))
% 5.62/1.39 | ((multiply @ sk_c1 @ sk_c7) = (sk_c7)))),
% 5.62/1.39 inference('demod', [status(thm)],
% 5.62/1.39 [zip_derived_cl244, zip_derived_cl3422, zip_derived_cl0,
% 5.62/1.39 zip_derived_cl3474, zip_derived_cl3474])).
% 5.62/1.39 thf(zip_derived_cl1695, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ sk_c6 @ X0) = (multiply @ sk_c7 @ X0))),
% 5.62/1.39 inference('condensation', [status(thm)], [zip_derived_cl1693])).
% 5.62/1.39 thf(zip_derived_cl3, plain,
% 5.62/1.39 ((((multiply @ sk_c6 @ sk_c7) = (sk_c5))
% 5.62/1.39 | ((multiply @ sk_c1 @ sk_c7) = (sk_c6)))),
% 5.62/1.39 inference('cnf', [status(esa)], [zf_stmt_16])).
% 5.62/1.39 thf(zip_derived_cl1745, plain,
% 5.62/1.39 ((((multiply @ sk_c7 @ sk_c7) = (sk_c5))
% 5.62/1.39 | ((multiply @ sk_c1 @ sk_c7) = (sk_c6)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl1695, zip_derived_cl3])).
% 5.62/1.39 thf(zip_derived_cl52, plain,
% 5.62/1.39 (![X0 : $i]:
% 5.62/1.39 (((multiply @ sk_c1 @ sk_c7) = (sk_c6))
% 5.62/1.39 | ((multiply @ sk_c5 @ X0)
% 5.62/1.39 = (multiply @ sk_c6 @ (multiply @ sk_c7 @ X0))))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl2])).
% 5.62/1.39 thf(zip_derived_cl1866, plain,
% 5.62/1.39 ((((multiply @ sk_c1 @ sk_c7) = (sk_c6))
% 5.62/1.39 | ((multiply @ sk_c1 @ sk_c7) = (sk_c6))
% 5.62/1.39 | ((multiply @ sk_c5 @ sk_c7) = (multiply @ sk_c6 @ sk_c5)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl1745, zip_derived_cl52])).
% 5.62/1.39 thf(zip_derived_cl1695, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ sk_c6 @ X0) = (multiply @ sk_c7 @ X0))),
% 5.62/1.39 inference('condensation', [status(thm)], [zip_derived_cl1693])).
% 5.62/1.39 thf(zip_derived_cl1872, plain,
% 5.62/1.39 ((((multiply @ sk_c1 @ sk_c7) = (sk_c6))
% 5.62/1.39 | ((multiply @ sk_c1 @ sk_c7) = (sk_c6))
% 5.62/1.39 | ((multiply @ sk_c5 @ sk_c7) = (multiply @ sk_c7 @ sk_c5)))),
% 5.62/1.39 inference('demod', [status(thm)],
% 5.62/1.39 [zip_derived_cl1866, zip_derived_cl1695])).
% 5.62/1.39 thf(zip_derived_cl1873, plain,
% 5.62/1.39 ((((multiply @ sk_c5 @ sk_c7) = (multiply @ sk_c7 @ sk_c5))
% 5.62/1.39 | ((multiply @ sk_c1 @ sk_c7) = (sk_c6)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl1872])).
% 5.62/1.39 thf(zip_derived_cl3422, plain, (((identity) = (sk_c5))),
% 5.62/1.39 inference('clc', [status(thm)], [zip_derived_cl3363, zip_derived_cl2625])).
% 5.62/1.39 thf(zip_derived_cl0, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 5.62/1.39 inference('cnf', [status(esa)], [left_identity])).
% 5.62/1.39 thf(zip_derived_cl3422, plain, (((identity) = (sk_c5))),
% 5.62/1.39 inference('clc', [status(thm)], [zip_derived_cl3363, zip_derived_cl2625])).
% 5.62/1.39 thf(zip_derived_cl3474, plain, (((sk_c7) = (sk_c6))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl3473])).
% 5.62/1.39 thf(zip_derived_cl3680, plain,
% 5.62/1.39 ((((sk_c7) = (multiply @ sk_c7 @ identity))
% 5.62/1.39 | ((multiply @ sk_c1 @ sk_c7) = (sk_c7)))),
% 5.62/1.39 inference('demod', [status(thm)],
% 5.62/1.39 [zip_derived_cl1873, zip_derived_cl3422, zip_derived_cl0,
% 5.62/1.39 zip_derived_cl3422, zip_derived_cl3474])).
% 5.62/1.39 thf(zip_derived_cl4030, plain,
% 5.62/1.39 ((((multiply @ sk_c1 @ sk_c7) = (sk_c7))
% 5.62/1.39 | ((sk_c7) = (sk_c3))
% 5.62/1.39 | ((multiply @ sk_c1 @ sk_c7) = (sk_c7)))),
% 5.62/1.39 inference('s_sup+', [status(thm)],
% 5.62/1.39 [zip_derived_cl4021, zip_derived_cl3680])).
% 5.62/1.39 thf(zip_derived_cl4034, plain,
% 5.62/1.39 ((((sk_c7) = (sk_c3)) | ((multiply @ sk_c1 @ sk_c7) = (sk_c7)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl4030])).
% 5.62/1.39 thf(zip_derived_cl41, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i]:
% 5.62/1.39 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl0])).
% 5.62/1.39 thf(zip_derived_cl4040, plain,
% 5.62/1.39 ((((sk_c7) = (sk_c3))
% 5.62/1.39 | ((sk_c7) = (multiply @ (inverse @ sk_c1) @ sk_c7)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl4034, zip_derived_cl41])).
% 5.62/1.39 thf(zip_derived_cl4054, plain,
% 5.62/1.39 ((((multiply @ sk_c3 @ sk_c7) = (sk_c7))
% 5.62/1.39 | ((sk_c7) = (sk_c3))
% 5.62/1.39 | ((sk_c7) = (multiply @ sk_c7 @ sk_c7)))),
% 5.62/1.39 inference('s_sup+', [status(thm)],
% 5.62/1.39 [zip_derived_cl3518, zip_derived_cl4040])).
% 5.62/1.39 thf(prove_this_7, conjecture,
% 5.62/1.39 (~( ( ( inverse @ sk_c3 ) = ( sk_c7 ) ) |
% 5.62/1.39 ( ( inverse @ sk_c1 ) = ( sk_c7 ) ) ))).
% 5.62/1.39 thf(zf_stmt_17, negated_conjecture,
% 5.62/1.39 (( ( inverse @ sk_c3 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c7 ) )),
% 5.62/1.39 inference('cnf.neg', [status(esa)], [prove_this_7])).
% 5.62/1.39 thf(zip_derived_cl9, plain,
% 5.62/1.39 ((((inverse @ sk_c3) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c7)))),
% 5.62/1.39 inference('cnf', [status(esa)], [zf_stmt_17])).
% 5.62/1.39 thf(zip_derived_cl41, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i]:
% 5.62/1.39 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl0])).
% 5.62/1.39 thf(zip_derived_cl171, plain,
% 5.62/1.39 (![X0 : $i]:
% 5.62/1.39 (((inverse @ sk_c1) = (sk_c7))
% 5.62/1.39 | ((X0) = (multiply @ sk_c7 @ (multiply @ sk_c3 @ X0))))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl41])).
% 5.62/1.39 thf(zip_derived_cl4098, plain,
% 5.62/1.39 ((((sk_c7) = (multiply @ sk_c7 @ sk_c7))
% 5.62/1.39 | ((sk_c7) = (sk_c3))
% 5.62/1.39 | ((inverse @ sk_c1) = (sk_c7))
% 5.62/1.39 | ((sk_c7) = (multiply @ sk_c7 @ sk_c7)))),
% 5.62/1.39 inference('s_sup+', [status(thm)],
% 5.62/1.39 [zip_derived_cl4054, zip_derived_cl171])).
% 5.62/1.39 thf(zip_derived_cl4101, plain,
% 5.62/1.39 ((((inverse @ sk_c1) = (sk_c7))
% 5.62/1.39 | ((sk_c7) = (sk_c3))
% 5.62/1.39 | ((sk_c7) = (multiply @ sk_c7 @ sk_c7)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl4098])).
% 5.62/1.39 thf(zip_derived_cl4040, plain,
% 5.62/1.39 ((((sk_c7) = (sk_c3))
% 5.62/1.39 | ((sk_c7) = (multiply @ (inverse @ sk_c1) @ sk_c7)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl4034, zip_derived_cl41])).
% 5.62/1.39 thf(zip_derived_cl4108, plain,
% 5.62/1.39 ((((sk_c7) = (multiply @ sk_c7 @ sk_c7))
% 5.62/1.39 | ((sk_c7) = (sk_c3))
% 5.62/1.39 | ((sk_c7) = (sk_c3))
% 5.62/1.39 | ((sk_c7) = (multiply @ sk_c7 @ sk_c7)))),
% 5.62/1.39 inference('s_sup+', [status(thm)],
% 5.62/1.39 [zip_derived_cl4101, zip_derived_cl4040])).
% 5.62/1.39 thf(zip_derived_cl4112, plain,
% 5.62/1.39 ((((sk_c7) = (sk_c3)) | ((sk_c7) = (multiply @ sk_c7 @ sk_c7)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl4108])).
% 5.62/1.39 thf(zip_derived_cl41, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i]:
% 5.62/1.39 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl0])).
% 5.62/1.39 thf(zip_derived_cl4199, plain,
% 5.62/1.39 ((((sk_c7) = (sk_c3))
% 5.62/1.39 | ((sk_c7) = (multiply @ (inverse @ sk_c7) @ sk_c7)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl4112, zip_derived_cl41])).
% 5.62/1.39 thf(zip_derived_cl1, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 5.62/1.39 inference('cnf', [status(esa)], [left_inverse])).
% 5.62/1.39 thf(zip_derived_cl4203, plain,
% 5.62/1.39 ((((sk_c7) = (sk_c3)) | ((sk_c7) = (identity)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl4199, zip_derived_cl1])).
% 5.62/1.39 thf(zip_derived_cl10, plain,
% 5.62/1.39 ((((multiply @ sk_c3 @ sk_c6) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c7)))),
% 5.62/1.39 inference('cnf', [status(esa)], [zf_stmt_14])).
% 5.62/1.39 thf(zip_derived_cl1745, plain,
% 5.62/1.39 ((((multiply @ sk_c7 @ sk_c7) = (sk_c5))
% 5.62/1.39 | ((multiply @ sk_c1 @ sk_c7) = (sk_c6)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl1695, zip_derived_cl3])).
% 5.62/1.39 thf(prove_this_3, conjecture,
% 5.62/1.39 (~( ( ( multiply @ sk_c3 @ sk_c6 ) = ( sk_c7 ) ) |
% 5.62/1.39 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c6 ) ) ))).
% 5.62/1.39 thf(zf_stmt_18, negated_conjecture,
% 5.62/1.39 (( ( multiply @ sk_c3 @ sk_c6 ) = ( sk_c7 ) ) |
% 5.62/1.39 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c6 ) )),
% 5.62/1.39 inference('cnf.neg', [status(esa)], [prove_this_3])).
% 5.62/1.39 thf(zip_derived_cl5, plain,
% 5.62/1.39 ((((multiply @ sk_c3 @ sk_c6) = (sk_c7))
% 5.62/1.39 | ((multiply @ sk_c1 @ sk_c7) = (sk_c6)))),
% 5.62/1.39 inference('cnf', [status(esa)], [zf_stmt_18])).
% 5.62/1.39 thf(zip_derived_cl33, plain,
% 5.62/1.39 ((((multiply @ sk_c1 @ sk_c7) = (sk_c6))
% 5.62/1.39 | ((multiply @ sk_c7 @ sk_c3) = (identity)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl1])).
% 5.62/1.39 thf(zip_derived_cl2, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.62/1.39 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 5.62/1.39 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 5.62/1.39 inference('cnf', [status(esa)], [associativity])).
% 5.62/1.39 thf(zip_derived_cl66, plain,
% 5.62/1.39 (![X0 : $i]:
% 5.62/1.39 (((multiply @ sk_c1 @ sk_c7) = (sk_c6))
% 5.62/1.39 | ((multiply @ identity @ X0)
% 5.62/1.39 = (multiply @ sk_c7 @ (multiply @ sk_c3 @ X0))))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl33, zip_derived_cl2])).
% 5.62/1.39 thf(zip_derived_cl0, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 5.62/1.39 inference('cnf', [status(esa)], [left_identity])).
% 5.62/1.39 thf(zip_derived_cl67, plain,
% 5.62/1.39 (![X0 : $i]:
% 5.62/1.39 (((multiply @ sk_c1 @ sk_c7) = (sk_c6))
% 5.62/1.39 | ((X0) = (multiply @ sk_c7 @ (multiply @ sk_c3 @ X0))))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl66, zip_derived_cl0])).
% 5.62/1.39 thf(zip_derived_cl97, plain,
% 5.62/1.39 ((((multiply @ sk_c1 @ sk_c7) = (sk_c6))
% 5.62/1.39 | ((multiply @ sk_c1 @ sk_c7) = (sk_c6))
% 5.62/1.39 | ((sk_c6) = (multiply @ sk_c7 @ sk_c7)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl67])).
% 5.62/1.39 thf(zip_derived_cl101, plain,
% 5.62/1.39 ((((sk_c6) = (multiply @ sk_c7 @ sk_c7))
% 5.62/1.39 | ((multiply @ sk_c1 @ sk_c7) = (sk_c6)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl97])).
% 5.62/1.39 thf(zip_derived_cl1870, plain,
% 5.62/1.39 ((((multiply @ sk_c1 @ sk_c7) = (sk_c6))
% 5.62/1.39 | ((sk_c6) = (sk_c5))
% 5.62/1.39 | ((multiply @ sk_c1 @ sk_c7) = (sk_c6)))),
% 5.62/1.39 inference('s_sup+', [status(thm)],
% 5.62/1.39 [zip_derived_cl1745, zip_derived_cl101])).
% 5.62/1.39 thf(zip_derived_cl1876, plain,
% 5.62/1.39 ((((sk_c6) = (sk_c5)) | ((multiply @ sk_c1 @ sk_c7) = (sk_c6)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl1870])).
% 5.62/1.39 thf(zip_derived_cl41, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i]:
% 5.62/1.39 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl0])).
% 5.62/1.39 thf(zip_derived_cl1908, plain,
% 5.62/1.39 ((((sk_c6) = (sk_c5))
% 5.62/1.39 | ((sk_c7) = (multiply @ (inverse @ sk_c1) @ sk_c6)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl1876, zip_derived_cl41])).
% 5.62/1.39 thf(zip_derived_cl41, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i]:
% 5.62/1.39 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl0])).
% 5.62/1.39 thf(zip_derived_cl1983, plain,
% 5.62/1.39 ((((sk_c6) = (sk_c5))
% 5.62/1.39 | ((sk_c6) = (multiply @ (inverse @ (inverse @ sk_c1)) @ sk_c7)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl1908, zip_derived_cl41])).
% 5.62/1.39 thf(zip_derived_cl2069, plain,
% 5.62/1.39 ((((multiply @ sk_c3 @ sk_c6) = (sk_c7))
% 5.62/1.39 | ((sk_c6) = (sk_c5))
% 5.62/1.39 | ((sk_c6) = (multiply @ (inverse @ sk_c7) @ sk_c7)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl1983])).
% 5.62/1.39 thf(zip_derived_cl1, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 5.62/1.39 inference('cnf', [status(esa)], [left_inverse])).
% 5.62/1.39 thf(zip_derived_cl2079, plain,
% 5.62/1.39 ((((multiply @ sk_c3 @ sk_c6) = (sk_c7))
% 5.62/1.39 | ((sk_c6) = (sk_c5))
% 5.62/1.39 | ((sk_c6) = (identity)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl2069, zip_derived_cl1])).
% 5.62/1.39 thf(zip_derived_cl3474, plain, (((sk_c7) = (sk_c6))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl3473])).
% 5.62/1.39 thf(zip_derived_cl3474, plain, (((sk_c7) = (sk_c6))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl3473])).
% 5.62/1.39 thf(zip_derived_cl3422, plain, (((identity) = (sk_c5))),
% 5.62/1.39 inference('clc', [status(thm)], [zip_derived_cl3363, zip_derived_cl2625])).
% 5.62/1.39 thf(zip_derived_cl3474, plain, (((sk_c7) = (sk_c6))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl3473])).
% 5.62/1.39 thf(zip_derived_cl4536, plain,
% 5.62/1.39 ((((multiply @ sk_c3 @ sk_c7) = (sk_c7))
% 5.62/1.39 | ((sk_c7) = (identity))
% 5.62/1.39 | ((sk_c7) = (identity)))),
% 5.62/1.39 inference('demod', [status(thm)],
% 5.62/1.39 [zip_derived_cl2079, zip_derived_cl3474, zip_derived_cl3474,
% 5.62/1.39 zip_derived_cl3422, zip_derived_cl3474])).
% 5.62/1.39 thf(zip_derived_cl4537, plain,
% 5.62/1.39 ((((sk_c7) = (identity)) | ((multiply @ sk_c3 @ sk_c7) = (sk_c7)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl4536])).
% 5.62/1.39 thf(zip_derived_cl4549, plain,
% 5.62/1.39 ((((sk_c7) = (identity))
% 5.62/1.39 | ((sk_c7) = (identity))
% 5.62/1.39 | ((multiply @ sk_c7 @ sk_c7) = (sk_c7)))),
% 5.62/1.39 inference('s_sup+', [status(thm)],
% 5.62/1.39 [zip_derived_cl4203, zip_derived_cl4537])).
% 5.62/1.39 thf(zip_derived_cl4550, plain,
% 5.62/1.39 ((((multiply @ sk_c7 @ sk_c7) = (sk_c7)) | ((sk_c7) = (identity)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl4549])).
% 5.62/1.39 thf(zip_derived_cl41, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i]:
% 5.62/1.39 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl0])).
% 5.62/1.39 thf(zip_derived_cl4579, plain,
% 5.62/1.39 ((((sk_c7) = (identity))
% 5.62/1.39 | ((sk_c7) = (multiply @ (inverse @ sk_c7) @ sk_c7)))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl4550, zip_derived_cl41])).
% 5.62/1.39 thf(zip_derived_cl1, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 5.62/1.39 inference('cnf', [status(esa)], [left_inverse])).
% 5.62/1.39 thf(zip_derived_cl4586, plain,
% 5.62/1.39 ((((sk_c7) = (identity)) | ((sk_c7) = (identity)))),
% 5.62/1.39 inference('demod', [status(thm)], [zip_derived_cl4579, zip_derived_cl1])).
% 5.62/1.39 thf(zip_derived_cl4587, plain, (((sk_c7) = (identity))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl4586])).
% 5.62/1.39 thf(zip_derived_cl4604, plain, (((identity) = (sk_c6))),
% 5.62/1.39 inference('demod', [status(thm)],
% 5.62/1.39 [zip_derived_cl3474, zip_derived_cl4587])).
% 5.62/1.39 thf(zip_derived_cl4604, plain, (((identity) = (sk_c6))),
% 5.62/1.39 inference('demod', [status(thm)],
% 5.62/1.39 [zip_derived_cl3474, zip_derived_cl4587])).
% 5.62/1.39 thf(zip_derived_cl4604, plain, (((identity) = (sk_c6))),
% 5.62/1.39 inference('demod', [status(thm)],
% 5.62/1.39 [zip_derived_cl3474, zip_derived_cl4587])).
% 5.62/1.39 thf(zip_derived_cl3388, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl132, zip_derived_cl129])).
% 5.62/1.39 thf(zip_derived_cl4587, plain, (((sk_c7) = (identity))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl4586])).
% 5.62/1.39 thf(zip_derived_cl4587, plain, (((sk_c7) = (identity))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl4586])).
% 5.62/1.39 thf(zip_derived_cl4587, plain, (((sk_c7) = (identity))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl4586])).
% 5.62/1.39 thf(zip_derived_cl4587, plain, (((sk_c7) = (identity))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl4586])).
% 5.62/1.39 thf(zip_derived_cl0, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 5.62/1.39 inference('cnf', [status(esa)], [left_identity])).
% 5.62/1.39 thf(zip_derived_cl3422, plain, (((identity) = (sk_c5))),
% 5.62/1.39 inference('clc', [status(thm)], [zip_derived_cl3363, zip_derived_cl2625])).
% 5.62/1.39 thf(zip_derived_cl4604, plain, (((identity) = (sk_c6))),
% 5.62/1.39 inference('demod', [status(thm)],
% 5.62/1.39 [zip_derived_cl3474, zip_derived_cl4587])).
% 5.62/1.39 thf(zip_derived_cl4604, plain, (((identity) = (sk_c6))),
% 5.62/1.39 inference('demod', [status(thm)],
% 5.62/1.39 [zip_derived_cl3474, zip_derived_cl4587])).
% 5.62/1.39 thf(zip_derived_cl3388, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl132, zip_derived_cl129])).
% 5.62/1.39 thf(zip_derived_cl3422, plain, (((identity) = (sk_c5))),
% 5.62/1.39 inference('clc', [status(thm)], [zip_derived_cl3363, zip_derived_cl2625])).
% 5.62/1.39 thf(zip_derived_cl4587, plain, (((sk_c7) = (identity))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl4586])).
% 5.62/1.39 thf(zip_derived_cl3422, plain, (((identity) = (sk_c5))),
% 5.62/1.39 inference('clc', [status(thm)], [zip_derived_cl3363, zip_derived_cl2625])).
% 5.62/1.39 thf(zip_derived_cl0, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 5.62/1.39 inference('cnf', [status(esa)], [left_identity])).
% 5.62/1.39 thf(zip_derived_cl4604, plain, (((identity) = (sk_c6))),
% 5.62/1.39 inference('demod', [status(thm)],
% 5.62/1.39 [zip_derived_cl3474, zip_derived_cl4587])).
% 5.62/1.39 thf(zip_derived_cl4587, plain, (((sk_c7) = (identity))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl4586])).
% 5.62/1.39 thf(zip_derived_cl4587, plain, (((sk_c7) = (identity))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl4586])).
% 5.62/1.39 thf(zip_derived_cl3388, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl132, zip_derived_cl129])).
% 5.62/1.39 thf(zip_derived_cl4604, plain, (((identity) = (sk_c6))),
% 5.62/1.39 inference('demod', [status(thm)],
% 5.62/1.39 [zip_derived_cl3474, zip_derived_cl4587])).
% 5.62/1.39 thf(zip_derived_cl6926, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 5.62/1.39 (((X0) != (identity))
% 5.62/1.39 | ((inverse @ X0) != (identity))
% 5.62/1.39 | ((X1) != (identity))
% 5.62/1.39 | ((inverse @ X1) != (identity))
% 5.62/1.39 | ((identity) != (identity))
% 5.62/1.39 | ((inverse @ X2) != (identity))
% 5.62/1.39 | ((X2) != (identity))
% 5.62/1.39 | ((identity) != (identity))
% 5.62/1.39 | ((inverse @ X3) != (identity))
% 5.62/1.39 | ((X3) != (identity)))),
% 5.62/1.39 inference('demod', [status(thm)],
% 5.62/1.39 [zip_derived_cl1699, zip_derived_cl3422, zip_derived_cl3388,
% 5.62/1.39 zip_derived_cl4604, zip_derived_cl4604, zip_derived_cl4604,
% 5.62/1.39 zip_derived_cl3388, zip_derived_cl4587, zip_derived_cl4587,
% 5.62/1.39 zip_derived_cl4587, zip_derived_cl4587, zip_derived_cl0,
% 5.62/1.39 zip_derived_cl3422, zip_derived_cl4604, zip_derived_cl4604,
% 5.62/1.39 zip_derived_cl3388, zip_derived_cl3422, zip_derived_cl4587,
% 5.62/1.39 zip_derived_cl3422, zip_derived_cl0, zip_derived_cl4604,
% 5.62/1.39 zip_derived_cl4587, zip_derived_cl4587, zip_derived_cl3388,
% 5.62/1.39 zip_derived_cl4604])).
% 5.62/1.39 thf(zip_derived_cl6927, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 5.62/1.39 (((X3) != (identity))
% 5.62/1.39 | ((inverse @ X3) != (identity))
% 5.62/1.39 | ((X2) != (identity))
% 5.62/1.39 | ((inverse @ X2) != (identity))
% 5.62/1.39 | ((inverse @ X1) != (identity))
% 5.62/1.39 | ((X1) != (identity))
% 5.62/1.39 | ((inverse @ X0) != (identity))
% 5.62/1.39 | ((X0) != (identity)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl6926])).
% 5.62/1.39 thf(zip_derived_cl6928, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.62/1.39 (((X0) != (identity))
% 5.62/1.39 | ((inverse @ X0) != (identity))
% 5.62/1.39 | ((X1) != (identity))
% 5.62/1.39 | ((inverse @ X1) != (identity))
% 5.62/1.39 | ((inverse @ X2) != (identity))
% 5.62/1.39 | ((X2) != (identity))
% 5.62/1.39 | ((inverse @ identity) != (identity)))),
% 5.62/1.39 inference('eq_res', [status(thm)], [zip_derived_cl6927])).
% 5.62/1.39 thf(zip_derived_cl3388, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl132, zip_derived_cl129])).
% 5.62/1.39 thf(zip_derived_cl1, plain,
% 5.62/1.39 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 5.62/1.39 inference('cnf', [status(esa)], [left_inverse])).
% 5.62/1.39 thf(zip_derived_cl5004, plain, (((inverse @ identity) = (identity))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl3388, zip_derived_cl1])).
% 5.62/1.39 thf(zip_derived_cl6929, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.62/1.39 (((X0) != (identity))
% 5.62/1.39 | ((inverse @ X0) != (identity))
% 5.62/1.39 | ((X1) != (identity))
% 5.62/1.39 | ((inverse @ X1) != (identity))
% 5.62/1.39 | ((inverse @ X2) != (identity))
% 5.62/1.39 | ((X2) != (identity))
% 5.62/1.39 | ((identity) != (identity)))),
% 5.62/1.39 inference('demod', [status(thm)],
% 5.62/1.39 [zip_derived_cl6928, zip_derived_cl5004])).
% 5.62/1.39 thf(zip_derived_cl6930, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.62/1.39 (((X2) != (identity))
% 5.62/1.39 | ((inverse @ X2) != (identity))
% 5.62/1.39 | ((inverse @ X1) != (identity))
% 5.62/1.39 | ((X1) != (identity))
% 5.62/1.39 | ((inverse @ X0) != (identity))
% 5.62/1.39 | ((X0) != (identity)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl6929])).
% 5.62/1.39 thf(zip_derived_cl6952, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i]:
% 5.62/1.39 (((X0) != (identity))
% 5.62/1.39 | ((inverse @ X0) != (identity))
% 5.62/1.39 | ((X1) != (identity))
% 5.62/1.39 | ((inverse @ X1) != (identity))
% 5.62/1.39 | ((inverse @ identity) != (identity)))),
% 5.62/1.39 inference('eq_res', [status(thm)], [zip_derived_cl6930])).
% 5.62/1.39 thf(zip_derived_cl5004, plain, (((inverse @ identity) = (identity))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl3388, zip_derived_cl1])).
% 5.62/1.39 thf(zip_derived_cl6953, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i]:
% 5.62/1.39 (((X0) != (identity))
% 5.62/1.39 | ((inverse @ X0) != (identity))
% 5.62/1.39 | ((X1) != (identity))
% 5.62/1.39 | ((inverse @ X1) != (identity))
% 5.62/1.39 | ((identity) != (identity)))),
% 5.62/1.39 inference('demod', [status(thm)],
% 5.62/1.39 [zip_derived_cl6952, zip_derived_cl5004])).
% 5.62/1.39 thf(zip_derived_cl6954, plain,
% 5.62/1.39 (![X0 : $i, X1 : $i]:
% 5.62/1.39 (((inverse @ X1) != (identity))
% 5.62/1.39 | ((X1) != (identity))
% 5.62/1.39 | ((inverse @ X0) != (identity))
% 5.62/1.39 | ((X0) != (identity)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl6953])).
% 5.62/1.39 thf(zip_derived_cl6985, plain,
% 5.62/1.39 (![X0 : $i]:
% 5.62/1.39 (((X0) != (identity))
% 5.62/1.39 | ((inverse @ X0) != (identity))
% 5.62/1.39 | ((inverse @ identity) != (identity)))),
% 5.62/1.39 inference('eq_res', [status(thm)], [zip_derived_cl6954])).
% 5.62/1.39 thf(zip_derived_cl5004, plain, (((inverse @ identity) = (identity))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl3388, zip_derived_cl1])).
% 5.62/1.39 thf(zip_derived_cl6986, plain,
% 5.62/1.39 (![X0 : $i]:
% 5.62/1.39 (((X0) != (identity))
% 5.62/1.39 | ((inverse @ X0) != (identity))
% 5.62/1.39 | ((identity) != (identity)))),
% 5.62/1.39 inference('demod', [status(thm)],
% 5.62/1.39 [zip_derived_cl6985, zip_derived_cl5004])).
% 5.62/1.39 thf(zip_derived_cl6987, plain,
% 5.62/1.39 (![X0 : $i]: (((inverse @ X0) != (identity)) | ((X0) != (identity)))),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl6986])).
% 5.62/1.39 thf(zip_derived_cl6988, plain, (((inverse @ identity) != (identity))),
% 5.62/1.39 inference('eq_res', [status(thm)], [zip_derived_cl6987])).
% 5.62/1.39 thf(zip_derived_cl5004, plain, (((inverse @ identity) = (identity))),
% 5.62/1.39 inference('s_sup+', [status(thm)], [zip_derived_cl3388, zip_derived_cl1])).
% 5.62/1.39 thf(zip_derived_cl6989, plain, (((identity) != (identity))),
% 5.62/1.39 inference('demod', [status(thm)],
% 5.62/1.39 [zip_derived_cl6988, zip_derived_cl5004])).
% 5.62/1.39 thf(zip_derived_cl6990, plain, ($false),
% 5.62/1.39 inference('simplify', [status(thm)], [zip_derived_cl6989])).
% 5.62/1.39
% 5.62/1.39 % SZS output end Refutation
% 5.62/1.39
% 5.62/1.39
% 5.62/1.39 % Terminating...
% 5.62/1.45 % Runner terminated.
% 5.62/1.46 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------