TSTP Solution File: GRP266-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP266-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.dzONqbsTKr true
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:50:58 EDT 2023
% Result : Unsatisfiable 1.94s 1.25s
% Output : Refutation 1.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : GRP266-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.dzONqbsTKr true
% 0.15/0.37 % Computer : n010.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon Aug 28 22:39:19 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.15/0.37 % Running portfolio for 300 s
% 0.15/0.37 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.37 % Number of cores: 8
% 0.15/0.38 % Python version: Python 3.6.8
% 0.15/0.38 % Running in FO mode
% 0.23/0.66 % Total configuration time : 435
% 0.23/0.66 % Estimated wc time : 1092
% 0.23/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.23/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.23/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.23/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.23/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.23/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.23/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.23/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 1.94/1.25 % Solved by fo/fo7.sh.
% 1.94/1.25 % done 433 iterations in 0.424s
% 1.94/1.25 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.94/1.25 % SZS output start Refutation
% 1.94/1.25 thf(sk_c8_type, type, sk_c8: $i).
% 1.94/1.25 thf(sk_c10_type, type, sk_c10: $i).
% 1.94/1.25 thf(sk_c2_type, type, sk_c2: $i).
% 1.94/1.25 thf(sk_c9_type, type, sk_c9: $i).
% 1.94/1.25 thf(identity_type, type, identity: $i).
% 1.94/1.25 thf(multiply_type, type, multiply: $i > $i > $i).
% 1.94/1.25 thf(sk_c11_type, type, sk_c11: $i).
% 1.94/1.25 thf(sk_c3_type, type, sk_c3: $i).
% 1.94/1.25 thf(inverse_type, type, inverse: $i > $i).
% 1.94/1.25 thf(sk_c5_type, type, sk_c5: $i).
% 1.94/1.25 thf(sk_c4_type, type, sk_c4: $i).
% 1.94/1.25 thf(sk_c7_type, type, sk_c7: $i).
% 1.94/1.25 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 1.94/1.25 thf(zip_derived_cl1, plain,
% 1.94/1.25 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.94/1.25 inference('cnf', [status(esa)], [left_inverse])).
% 1.94/1.25 thf(zip_derived_cl1, plain,
% 1.94/1.25 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.94/1.25 inference('cnf', [status(esa)], [left_inverse])).
% 1.94/1.25 thf(associativity, axiom,
% 1.94/1.25 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 1.94/1.25 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 1.94/1.25 thf(zip_derived_cl2, plain,
% 1.94/1.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.94/1.25 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.94/1.25 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.94/1.25 inference('cnf', [status(esa)], [associativity])).
% 1.94/1.25 thf(zip_derived_cl150, plain,
% 1.94/1.25 (![X0 : $i, X1 : $i]:
% 1.94/1.25 ((multiply @ identity @ X0)
% 1.94/1.25 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.94/1.25 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 1.94/1.25 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 1.94/1.25 thf(zip_derived_cl0, plain,
% 1.94/1.25 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.94/1.25 inference('cnf', [status(esa)], [left_identity])).
% 1.94/1.25 thf(zip_derived_cl182, plain,
% 1.94/1.25 (![X0 : $i, X1 : $i]:
% 1.94/1.25 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.94/1.25 inference('demod', [status(thm)], [zip_derived_cl150, zip_derived_cl0])).
% 1.94/1.25 thf(zip_derived_cl198, plain,
% 1.94/1.25 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 1.94/1.25 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl182])).
% 1.94/1.25 thf(zip_derived_cl182, plain,
% 1.94/1.25 (![X0 : $i, X1 : $i]:
% 1.94/1.25 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.94/1.25 inference('demod', [status(thm)], [zip_derived_cl150, zip_derived_cl0])).
% 1.94/1.25 thf(zip_derived_cl182, plain,
% 1.94/1.25 (![X0 : $i, X1 : $i]:
% 1.94/1.25 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.94/1.25 inference('demod', [status(thm)], [zip_derived_cl150, zip_derived_cl0])).
% 1.94/1.25 thf(zip_derived_cl195, plain,
% 1.94/1.25 (![X0 : $i, X1 : $i]:
% 1.94/1.25 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 1.94/1.25 inference('sup+', [status(thm)], [zip_derived_cl182, zip_derived_cl182])).
% 1.94/1.25 thf(zip_derived_cl1152, plain,
% 1.94/1.25 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.94/1.25 inference('sup+', [status(thm)], [zip_derived_cl198, zip_derived_cl195])).
% 1.94/1.25 thf(zip_derived_cl198, plain,
% 1.94/1.25 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 1.94/1.25 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl182])).
% 1.94/1.25 thf(zip_derived_cl1199, plain,
% 1.94/1.25 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.94/1.25 inference('sup+', [status(thm)], [zip_derived_cl1152, zip_derived_cl198])).
% 1.94/1.25 thf(zip_derived_cl1199, plain,
% 1.94/1.25 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.94/1.25 inference('sup+', [status(thm)], [zip_derived_cl1152, zip_derived_cl198])).
% 1.94/1.25 thf(zip_derived_cl1199, plain,
% 1.94/1.25 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.94/1.25 inference('sup+', [status(thm)], [zip_derived_cl1152, zip_derived_cl198])).
% 1.94/1.25 thf(prove_this_50, conjecture,
% 1.94/1.25 (~( ( ( inverse @ X4 ) != ( sk_c9 ) ) |
% 1.94/1.25 ( ( multiply @ X4 @ sk_c9 ) != ( X3 ) ) |
% 1.94/1.25 ( ( multiply @ sk_c9 @ X3 ) != ( sk_c10 ) ) |
% 1.94/1.25 ( ( inverse @ X2 ) != ( sk_c9 ) ) |
% 1.94/1.25 ( ( multiply @ X2 @ sk_c9 ) != ( sk_c10 ) ) |
% 1.94/1.25 ( ( inverse @ X1 ) != ( sk_c11 ) ) |
% 1.94/1.25 ( ( multiply @ X1 @ sk_c11 ) != ( sk_c10 ) ) |
% 1.94/1.25 ( ( inverse @ X8 ) != ( sk_c10 ) ) |
% 1.94/1.25 ( ( multiply @ X8 @ sk_c10 ) != ( X7 ) ) |
% 1.94/1.25 ( ( multiply @ sk_c10 @ X7 ) != ( sk_c9 ) ) |
% 1.94/1.25 ( ( inverse @ X6 ) != ( sk_c9 ) ) |
% 1.94/1.25 ( ( multiply @ X6 @ sk_c9 ) != ( sk_c10 ) ) |
% 1.94/1.25 ( ( inverse @ X5 ) != ( sk_c11 ) ) |
% 1.94/1.25 ( ( multiply @ X5 @ sk_c11 ) != ( sk_c10 ) ) ))).
% 1.94/1.25 thf(zf_stmt_0, negated_conjecture,
% 1.94/1.25 (( ( inverse @ X4 ) != ( sk_c9 ) ) |
% 1.94/1.25 ( ( multiply @ X4 @ sk_c9 ) != ( X3 ) ) |
% 1.94/1.25 ( ( multiply @ sk_c9 @ X3 ) != ( sk_c10 ) ) |
% 1.94/1.25 ( ( inverse @ X2 ) != ( sk_c9 ) ) |
% 1.94/1.25 ( ( multiply @ X2 @ sk_c9 ) != ( sk_c10 ) ) |
% 1.94/1.25 ( ( inverse @ X1 ) != ( sk_c11 ) ) |
% 1.94/1.25 ( ( multiply @ X1 @ sk_c11 ) != ( sk_c10 ) ) |
% 1.94/1.25 ( ( inverse @ X8 ) != ( sk_c10 ) ) |
% 1.94/1.25 ( ( multiply @ X8 @ sk_c10 ) != ( X7 ) ) |
% 1.94/1.25 ( ( multiply @ sk_c10 @ X7 ) != ( sk_c9 ) ) |
% 1.94/1.25 ( ( inverse @ X6 ) != ( sk_c9 ) ) |
% 1.94/1.25 ( ( multiply @ X6 @ sk_c9 ) != ( sk_c10 ) ) |
% 1.94/1.25 ( ( inverse @ X5 ) != ( sk_c11 ) ) |
% 1.94/1.25 ( ( multiply @ X5 @ sk_c11 ) != ( sk_c10 ) )),
% 1.94/1.25 inference('cnf.neg', [status(esa)], [prove_this_50])).
% 1.94/1.25 thf(zip_derived_cl52, plain,
% 1.94/1.25 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 1.94/1.25 (((inverse @ X0) != (sk_c9))
% 1.94/1.25 | ((multiply @ X0 @ sk_c9) != (X1))
% 1.94/1.25 | ((multiply @ sk_c9 @ X1) != (sk_c10))
% 1.94/1.25 | ((inverse @ X2) != (sk_c9))
% 1.94/1.25 | ((multiply @ X2 @ sk_c9) != (sk_c10))
% 1.94/1.25 | ((inverse @ X3) != (sk_c11))
% 1.94/1.25 | ((multiply @ X3 @ sk_c11) != (sk_c10))
% 1.94/1.25 | ((inverse @ X4) != (sk_c10))
% 1.94/1.25 | ((multiply @ X4 @ sk_c10) != (X5))
% 1.94/1.25 | ((multiply @ sk_c10 @ X5) != (sk_c9))
% 1.94/1.25 | ((inverse @ X6) != (sk_c9))
% 1.94/1.25 | ((multiply @ X6 @ sk_c9) != (sk_c10))
% 1.94/1.25 | ((inverse @ X7) != (sk_c11))
% 1.94/1.25 | ((multiply @ X7 @ sk_c11) != (sk_c10)))),
% 1.94/1.25 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.94/1.25 thf(zip_derived_cl1206, plain,
% 1.94/1.25 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 1.94/1.25 (((X0) != (sk_c9))
% 1.94/1.25 | ((multiply @ X1 @ sk_c11) != (sk_c10))
% 1.94/1.25 | ((inverse @ X1) != (sk_c11))
% 1.94/1.25 | ((multiply @ X2 @ sk_c9) != (sk_c10))
% 1.94/1.25 | ((inverse @ X2) != (sk_c9))
% 1.94/1.25 | ((multiply @ sk_c10 @ X3) != (sk_c9))
% 1.94/1.25 | ((multiply @ X4 @ sk_c10) != (X3))
% 1.94/1.25 | ((inverse @ X4) != (sk_c10))
% 1.94/1.25 | ((multiply @ X5 @ sk_c11) != (sk_c10))
% 1.94/1.25 | ((inverse @ X5) != (sk_c11))
% 1.94/1.25 | ((multiply @ X6 @ sk_c9) != (sk_c10))
% 1.94/1.25 | ((inverse @ X6) != (sk_c9))
% 1.94/1.25 | ((multiply @ sk_c9 @ X7) != (sk_c10))
% 1.94/1.25 | ((multiply @ (inverse @ X0) @ sk_c9) != (X7)))),
% 1.94/1.25 inference('sup-', [status(thm)], [zip_derived_cl1199, zip_derived_cl52])).
% 1.94/1.25 thf(zip_derived_cl1431, plain,
% 1.94/1.25 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 1.94/1.25 (((multiply @ (inverse @ sk_c9) @ sk_c9) != (X0))
% 1.94/1.25 | ((multiply @ sk_c9 @ X0) != (sk_c10))
% 1.94/1.25 | ((inverse @ X1) != (sk_c9))
% 1.94/1.25 | ((multiply @ X1 @ sk_c9) != (sk_c10))
% 1.94/1.25 | ((inverse @ X2) != (sk_c11))
% 1.94/1.25 | ((multiply @ X2 @ sk_c11) != (sk_c10))
% 1.94/1.25 | ((inverse @ X3) != (sk_c10))
% 1.94/1.25 | ((multiply @ X3 @ sk_c10) != (X4))
% 1.94/1.25 | ((multiply @ sk_c10 @ X4) != (sk_c9))
% 1.94/1.25 | ((inverse @ X5) != (sk_c9))
% 1.94/1.25 | ((multiply @ X5 @ sk_c9) != (sk_c10))
% 1.94/1.25 | ((inverse @ X6) != (sk_c11))
% 1.94/1.25 | ((multiply @ X6 @ sk_c11) != (sk_c10)))),
% 1.94/1.25 inference('eq_res', [status(thm)], [zip_derived_cl1206])).
% 1.94/1.25 thf(zip_derived_cl1, plain,
% 1.94/1.25 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.94/1.25 inference('cnf', [status(esa)], [left_inverse])).
% 1.94/1.25 thf(zip_derived_cl1432, plain,
% 1.94/1.25 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 1.94/1.25 (((identity) != (X0))
% 1.94/1.25 | ((multiply @ sk_c9 @ X0) != (sk_c10))
% 1.94/1.25 | ((inverse @ X1) != (sk_c9))
% 1.94/1.25 | ((multiply @ X1 @ sk_c9) != (sk_c10))
% 1.94/1.25 | ((inverse @ X2) != (sk_c11))
% 1.94/1.25 | ((multiply @ X2 @ sk_c11) != (sk_c10))
% 1.94/1.25 | ((inverse @ X3) != (sk_c10))
% 1.94/1.25 | ((multiply @ X3 @ sk_c10) != (X4))
% 1.94/1.25 | ((multiply @ sk_c10 @ X4) != (sk_c9))
% 1.94/1.25 | ((inverse @ X5) != (sk_c9))
% 1.94/1.25 | ((multiply @ X5 @ sk_c9) != (sk_c10))
% 1.94/1.25 | ((inverse @ X6) != (sk_c11))
% 1.94/1.25 | ((multiply @ X6 @ sk_c11) != (sk_c10)))),
% 1.94/1.25 inference('demod', [status(thm)], [zip_derived_cl1431, zip_derived_cl1])).
% 1.94/1.25 thf(prove_this_23, conjecture,
% 1.94/1.25 (~( ( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 1.94/1.25 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 1.94/1.25 thf(zf_stmt_1, negated_conjecture,
% 1.94/1.25 (( ( inverse @ sk_c5 ) = ( sk_c11 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 1.94/1.25 inference('cnf.neg', [status(esa)], [prove_this_23])).
% 1.94/1.25 thf(zip_derived_cl25, plain,
% 1.94/1.25 ((((inverse @ sk_c5) = (sk_c11)) | ((inverse @ sk_c2) = (sk_c9)))),
% 1.94/1.25 inference('cnf', [status(esa)], [zf_stmt_1])).
% 1.94/1.25 thf(zip_derived_cl1, plain,
% 1.94/1.25 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.94/1.25 inference('cnf', [status(esa)], [left_inverse])).
% 1.94/1.25 thf(zip_derived_cl69, plain,
% 1.94/1.25 ((((multiply @ sk_c9 @ sk_c2) = (identity))
% 1.94/1.25 | ((inverse @ sk_c5) = (sk_c11)))),
% 1.94/1.25 inference('sup+', [status(thm)], [zip_derived_cl25, zip_derived_cl1])).
% 1.94/1.25 thf(zip_derived_cl182, plain,
% 1.94/1.25 (![X0 : $i, X1 : $i]:
% 1.94/1.25 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.94/1.25 inference('demod', [status(thm)], [zip_derived_cl150, zip_derived_cl0])).
% 1.94/1.25 thf(zip_derived_cl217, plain,
% 1.94/1.25 ((((sk_c2) = (multiply @ (inverse @ sk_c9) @ identity))
% 1.94/1.25 | ((inverse @ sk_c5) = (sk_c11)))),
% 1.94/1.25 inference('sup+', [status(thm)], [zip_derived_cl69, zip_derived_cl182])).
% 1.94/1.25 thf(zip_derived_cl1152, plain,
% 1.94/1.25 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.94/1.25 inference('sup+', [status(thm)], [zip_derived_cl198, zip_derived_cl195])).
% 1.94/1.25 thf(zip_derived_cl1184, plain,
% 1.94/1.25 ((((sk_c2) = (inverse @ sk_c9)) | ((inverse @ sk_c5) = (sk_c11)))),
% 1.94/1.25 inference('demod', [status(thm)], [zip_derived_cl217, zip_derived_cl1152])).
% 1.94/1.25 thf(prove_this_16, conjecture,
% 1.94/1.25 (~( ( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 1.94/1.25 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c10 ) ) ))).
% 1.94/1.25 thf(zf_stmt_2, negated_conjecture,
% 1.94/1.25 (( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 1.94/1.25 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c10 ) )),
% 1.94/1.25 inference('cnf.neg', [status(esa)], [prove_this_16])).
% 1.94/1.25 thf(zip_derived_cl18, plain,
% 1.94/1.25 ((((inverse @ sk_c5) = (sk_c11))
% 1.94/1.25 | ((multiply @ sk_c2 @ sk_c9) = (sk_c10)))),
% 1.94/1.25 inference('cnf', [status(esa)], [zf_stmt_2])).
% 1.94/1.25 thf(zip_derived_cl1654, plain,
% 1.94/1.25 ((((multiply @ (inverse @ sk_c9) @ sk_c9) = (sk_c10))
% 1.94/1.25 | ((inverse @ sk_c5) = (sk_c11))
% 1.94/1.25 | ((inverse @ sk_c5) = (sk_c11)))),
% 1.94/1.25 inference('sup+', [status(thm)], [zip_derived_cl1184, zip_derived_cl18])).
% 1.94/1.25 thf(zip_derived_cl1, plain,
% 1.94/1.25 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.94/1.25 inference('cnf', [status(esa)], [left_inverse])).
% 1.94/1.25 thf(zip_derived_cl1675, plain,
% 1.94/1.25 ((((identity) = (sk_c10))
% 1.94/1.25 | ((inverse @ sk_c5) = (sk_c11))
% 1.94/1.25 | ((inverse @ sk_c5) = (sk_c11)))),
% 1.94/1.25 inference('demod', [status(thm)], [zip_derived_cl1654, zip_derived_cl1])).
% 1.94/1.25 thf(zip_derived_cl1676, plain,
% 1.94/1.25 ((((inverse @ sk_c5) = (sk_c11)) | ((identity) = (sk_c10)))),
% 1.94/1.25 inference('simplify', [status(thm)], [zip_derived_cl1675])).
% 1.94/1.25 thf(zip_derived_cl1199, plain,
% 1.94/1.25 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.94/1.25 inference('sup+', [status(thm)], [zip_derived_cl1152, zip_derived_cl198])).
% 1.94/1.25 thf(zip_derived_cl1705, plain,
% 1.94/1.25 ((((sk_c5) = (inverse @ sk_c11)) | ((identity) = (sk_c10)))),
% 1.94/1.25 inference('sup+', [status(thm)], [zip_derived_cl1676, zip_derived_cl1199])).
% 1.94/1.25 thf(prove_this_22, conjecture,
% 1.94/1.25 (~( ( ( multiply @ sk_c5 @ sk_c11 ) = ( sk_c10 ) ) |
% 1.94/1.25 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 1.94/1.25 thf(zf_stmt_3, negated_conjecture,
% 1.94/1.25 (( ( multiply @ sk_c5 @ sk_c11 ) = ( sk_c10 ) ) |
% 1.94/1.25 ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 1.94/1.25 inference('cnf.neg', [status(esa)], [prove_this_22])).
% 1.94/1.25 thf(zip_derived_cl24, plain,
% 1.94/1.25 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))
% 1.94/1.25 | ((inverse @ sk_c2) = (sk_c9)))),
% 1.94/1.25 inference('cnf', [status(esa)], [zf_stmt_3])).
% 1.94/1.25 thf(zip_derived_cl1199, plain,
% 1.94/1.25 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.94/1.25 inference('sup+', [status(thm)], [zip_derived_cl1152, zip_derived_cl198])).
% 1.94/1.25 thf(zip_derived_cl1216, plain,
% 1.94/1.25 ((((sk_c2) = (inverse @ sk_c9))
% 1.94/1.25 | ((multiply @ sk_c5 @ sk_c11) = (sk_c10)))),
% 1.94/1.25 inference('sup+', [status(thm)], [zip_derived_cl24, zip_derived_cl1199])).
% 1.94/1.25 thf(prove_this_15, conjecture,
% 1.94/1.25 (~( ( ( multiply @ sk_c5 @ sk_c11 ) = ( sk_c10 ) ) |
% 1.94/1.25 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c10 ) ) ))).
% 1.94/1.25 thf(zf_stmt_4, negated_conjecture,
% 1.94/1.25 (( ( multiply @ sk_c5 @ sk_c11 ) = ( sk_c10 ) ) |
% 1.94/1.25 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c10 ) )),
% 1.94/1.25 inference('cnf.neg', [status(esa)], [prove_this_15])).
% 1.94/1.25 thf(zip_derived_cl17, plain,
% 1.94/1.25 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))
% 1.94/1.25 | ((multiply @ sk_c2 @ sk_c9) = (sk_c10)))),
% 1.94/1.25 inference('cnf', [status(esa)], [zf_stmt_4])).
% 1.94/1.25 thf(zip_derived_cl1809, plain,
% 1.94/1.25 ((((multiply @ (inverse @ sk_c9) @ sk_c9) = (sk_c10))
% 1.94/1.25 | ((multiply @ sk_c5 @ sk_c11) = (sk_c10))
% 1.94/1.25 | ((multiply @ sk_c5 @ sk_c11) = (sk_c10)))),
% 1.94/1.25 inference('sup+', [status(thm)], [zip_derived_cl1216, zip_derived_cl17])).
% 1.94/1.25 thf(zip_derived_cl1, plain,
% 1.94/1.25 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.94/1.25 inference('cnf', [status(esa)], [left_inverse])).
% 1.94/1.25 thf(zip_derived_cl1830, plain,
% 1.94/1.25 ((((identity) = (sk_c10))
% 1.94/1.25 | ((multiply @ sk_c5 @ sk_c11) = (sk_c10))
% 1.94/1.25 | ((multiply @ sk_c5 @ sk_c11) = (sk_c10)))),
% 1.94/1.25 inference('demod', [status(thm)], [zip_derived_cl1809, zip_derived_cl1])).
% 1.94/1.25 thf(zip_derived_cl1831, plain,
% 1.94/1.25 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10)) | ((identity) = (sk_c10)))),
% 1.94/1.25 inference('simplify', [status(thm)], [zip_derived_cl1830])).
% 1.94/1.25 thf(zip_derived_cl2467, plain,
% 1.94/1.25 ((((multiply @ (inverse @ sk_c11) @ sk_c11) = (sk_c10))
% 1.94/1.25 | ((identity) = (sk_c10))
% 1.94/1.25 | ((identity) = (sk_c10)))),
% 1.94/1.25 inference('sup+', [status(thm)], [zip_derived_cl1705, zip_derived_cl1831])).
% 1.94/1.25 thf(zip_derived_cl1, plain,
% 1.94/1.25 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.94/1.25 inference('cnf', [status(esa)], [left_inverse])).
% 1.94/1.25 thf(zip_derived_cl2472, plain,
% 1.94/1.25 ((((identity) = (sk_c10))
% 1.94/1.25 | ((identity) = (sk_c10))
% 1.94/1.25 | ((identity) = (sk_c10)))),
% 1.94/1.25 inference('demod', [status(thm)], [zip_derived_cl2467, zip_derived_cl1])).
% 1.94/1.25 thf(zip_derived_cl2473, plain, (((identity) = (sk_c10))),
% 1.94/1.25 inference('simplify', [status(thm)], [zip_derived_cl2472])).
% 1.94/1.25 thf(zip_derived_cl2473, plain, (((identity) = (sk_c10))),
% 1.94/1.25 inference('simplify', [status(thm)], [zip_derived_cl2472])).
% 1.94/1.25 thf(zip_derived_cl2473, plain, (((identity) = (sk_c10))),
% 1.94/1.25 inference('simplify', [status(thm)], [zip_derived_cl2472])).
% 1.94/1.25 thf(zip_derived_cl2473, plain, (((identity) = (sk_c10))),
% 1.94/1.25 inference('simplify', [status(thm)], [zip_derived_cl2472])).
% 1.94/1.25 thf(zip_derived_cl2473, plain, (((identity) = (sk_c10))),
% 1.94/1.25 inference('simplify', [status(thm)], [zip_derived_cl2472])).
% 1.94/1.25 thf(zip_derived_cl1152, plain,
% 1.94/1.25 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.94/1.25 inference('sup+', [status(thm)], [zip_derived_cl198, zip_derived_cl195])).
% 1.94/1.25 thf(zip_derived_cl2473, plain, (((identity) = (sk_c10))),
% 1.94/1.25 inference('simplify', [status(thm)], [zip_derived_cl2472])).
% 1.94/1.25 thf(zip_derived_cl0, plain,
% 1.94/1.25 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.94/1.25 inference('cnf', [status(esa)], [left_identity])).
% 1.94/1.25 thf(zip_derived_cl2473, plain, (((identity) = (sk_c10))),
% 1.94/1.25 inference('simplify', [status(thm)], [zip_derived_cl2472])).
% 1.94/1.25 thf(zip_derived_cl2473, plain, (((identity) = (sk_c10))),
% 1.94/1.25 inference('simplify', [status(thm)], [zip_derived_cl2472])).
% 1.94/1.25 thf(zip_derived_cl2565, plain,
% 1.94/1.25 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 1.94/1.25 (((identity) != (X0))
% 1.94/1.25 | ((multiply @ sk_c9 @ X0) != (identity))
% 1.94/1.25 | ((inverse @ X1) != (sk_c9))
% 1.94/1.25 | ((multiply @ X1 @ sk_c9) != (identity))
% 1.94/1.25 | ((inverse @ X2) != (sk_c11))
% 1.94/1.25 | ((multiply @ X2 @ sk_c11) != (identity))
% 1.94/1.25 | ((inverse @ X3) != (identity))
% 1.94/1.25 | ((X3) != (X4))
% 1.94/1.25 | ((X4) != (sk_c9))
% 1.94/1.25 | ((inverse @ X5) != (sk_c9))
% 1.94/1.25 | ((multiply @ X5 @ sk_c9) != (identity))
% 1.94/1.25 | ((inverse @ X6) != (sk_c11))
% 1.94/1.25 | ((multiply @ X6 @ sk_c11) != (identity)))),
% 1.94/1.25 inference('demod', [status(thm)],
% 1.94/1.25 [zip_derived_cl1432, zip_derived_cl2473, zip_derived_cl2473,
% 1.94/1.25 zip_derived_cl2473, zip_derived_cl2473, zip_derived_cl2473,
% 1.94/1.25 zip_derived_cl1152, zip_derived_cl2473, zip_derived_cl0,
% 1.94/1.25 zip_derived_cl2473, zip_derived_cl2473])).
% 1.94/1.25 thf(zip_derived_cl2583, plain,
% 1.94/1.25 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 1.94/1.25 (((multiply @ X0 @ sk_c11) != (identity))
% 1.94/1.25 | ((inverse @ X0) != (sk_c11))
% 1.94/1.25 | ((multiply @ X1 @ sk_c9) != (identity))
% 1.94/1.25 | ((inverse @ X1) != (sk_c9))
% 1.94/1.25 | ((X2) != (sk_c9))
% 1.94/1.25 | ((inverse @ X2) != (identity))
% 1.94/1.25 | ((multiply @ X3 @ sk_c11) != (identity))
% 1.94/1.25 | ((inverse @ X3) != (sk_c11))
% 1.94/1.25 | ((multiply @ X4 @ sk_c9) != (identity))
% 1.94/1.25 | ((inverse @ X4) != (sk_c9))
% 1.94/1.25 | ((multiply @ sk_c9 @ X5) != (identity))
% 1.94/1.25 | ((identity) != (X5)))),
% 1.94/1.25 inference('eq_res', [status(thm)], [zip_derived_cl2565])).
% 1.94/1.25 thf(zip_derived_cl2585, plain,
% 1.94/1.25 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.94/1.25 (((identity) != (X0))
% 1.94/1.25 | ((multiply @ sk_c9 @ X0) != (identity))
% 1.94/1.25 | ((inverse @ X1) != (sk_c9))
% 1.94/1.25 | ((multiply @ X1 @ sk_c9) != (identity))
% 1.94/1.25 | ((inverse @ X2) != (sk_c11))
% 1.94/1.25 | ((multiply @ X2 @ sk_c11) != (identity))
% 1.94/1.25 | ((inverse @ sk_c9) != (identity))
% 1.94/1.25 | ((inverse @ X3) != (sk_c9))
% 1.94/1.25 | ((multiply @ X3 @ sk_c9) != (identity))
% 1.94/1.25 | ((inverse @ X4) != (sk_c11))
% 1.94/1.25 | ((multiply @ X4 @ sk_c11) != (identity)))),
% 1.94/1.25 inference('eq_res', [status(thm)], [zip_derived_cl2583])).
% 1.94/1.25 thf(prove_this_47, conjecture,
% 1.94/1.25 (~( ( ( multiply @ sk_c9 @ sk_c8 ) = ( sk_c10 ) ) |
% 1.94/1.25 ( ( inverse @ sk_c3 ) = ( sk_c10 ) ) ))).
% 1.94/1.25 thf(zf_stmt_5, negated_conjecture,
% 1.94/1.25 (( ( multiply @ sk_c9 @ sk_c8 ) = ( sk_c10 ) ) |
% 1.94/1.25 ( ( inverse @ sk_c3 ) = ( sk_c10 ) )),
% 1.94/1.25 inference('cnf.neg', [status(esa)], [prove_this_47])).
% 1.94/1.25 thf(zip_derived_cl49, plain,
% 1.94/1.25 ((((multiply @ sk_c9 @ sk_c8) = (sk_c10))
% 1.94/1.25 | ((inverse @ sk_c3) = (sk_c10)))),
% 1.94/1.25 inference('cnf', [status(esa)], [zf_stmt_5])).
% 1.94/1.25 thf(zip_derived_cl1199, plain,
% 1.94/1.25 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.94/1.25 inference('sup+', [status(thm)], [zip_derived_cl1152, zip_derived_cl198])).
% 1.94/1.25 thf(zip_derived_cl1227, plain,
% 1.94/1.25 ((((sk_c3) = (inverse @ sk_c10))
% 1.94/1.25 | ((multiply @ sk_c9 @ sk_c8) = (sk_c10)))),
% 1.94/1.25 inference('sup+', [status(thm)], [zip_derived_cl49, zip_derived_cl1199])).
% 1.94/1.25 thf(prove_this_40, conjecture,
% 1.94/1.25 (~( ( ( multiply @ sk_c9 @ sk_c8 ) = ( sk_c10 ) ) |
% 1.94/1.25 ( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c4 ) ) ))).
% 1.94/1.25 thf(zf_stmt_6, negated_conjecture,
% 1.94/1.25 (( ( multiply @ sk_c9 @ sk_c8 ) = ( sk_c10 ) ) |
% 1.94/1.25 ( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c4 ) )),
% 1.94/1.25 inference('cnf.neg', [status(esa)], [prove_this_40])).
% 1.94/1.25 thf(zip_derived_cl42, plain,
% 1.94/1.25 ((((multiply @ sk_c9 @ sk_c8) = (sk_c10))
% 1.94/1.25 | ((multiply @ sk_c3 @ sk_c10) = (sk_c4)))),
% 1.94/1.25 inference('cnf', [status(esa)], [zf_stmt_6])).
% 1.94/1.25 thf(zip_derived_cl2347, plain,
% 1.94/1.25 ((((multiply @ (inverse @ sk_c10) @ sk_c10) = (sk_c4))
% 1.94/1.25 | ((multiply @ sk_c9 @ sk_c8) = (sk_c10))
% 1.94/1.25 | ((multiply @ sk_c9 @ sk_c8) = (sk_c10)))),
% 1.94/1.25 inference('sup+', [status(thm)], [zip_derived_cl1227, zip_derived_cl42])).
% 1.94/1.25 thf(zip_derived_cl1, plain,
% 1.94/1.25 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.94/1.25 inference('cnf', [status(esa)], [left_inverse])).
% 1.94/1.25 thf(zip_derived_cl2365, plain,
% 1.94/1.25 ((((identity) = (sk_c4))
% 1.94/1.25 | ((multiply @ sk_c9 @ sk_c8) = (sk_c10))
% 1.94/1.25 | ((multiply @ sk_c9 @ sk_c8) = (sk_c10)))),
% 1.94/1.25 inference('demod', [status(thm)], [zip_derived_cl2347, zip_derived_cl1])).
% 1.94/1.25 thf(zip_derived_cl2366, plain,
% 1.94/1.25 ((((multiply @ sk_c9 @ sk_c8) = (sk_c10)) | ((identity) = (sk_c4)))),
% 1.94/1.25 inference('simplify', [status(thm)], [zip_derived_cl2365])).
% 1.94/1.25 thf(prove_this_33, conjecture,
% 1.94/1.25 (~( ( ( multiply @ sk_c9 @ sk_c8 ) = ( sk_c10 ) ) |
% 1.94/1.25 ( ( multiply @ sk_c10 @ sk_c4 ) = ( sk_c9 ) ) ))).
% 1.94/1.25 thf(zf_stmt_7, negated_conjecture,
% 1.94/1.25 (( ( multiply @ sk_c9 @ sk_c8 ) = ( sk_c10 ) ) |
% 1.94/1.25 ( ( multiply @ sk_c10 @ sk_c4 ) = ( sk_c9 ) )),
% 1.94/1.25 inference('cnf.neg', [status(esa)], [prove_this_33])).
% 1.94/1.25 thf(zip_derived_cl35, plain,
% 1.94/1.25 ((((multiply @ sk_c9 @ sk_c8) = (sk_c10))
% 1.94/1.25 | ((multiply @ sk_c10 @ sk_c4) = (sk_c9)))),
% 1.94/1.25 inference('cnf', [status(esa)], [zf_stmt_7])).
% 1.94/1.25 thf(zip_derived_cl2385, plain,
% 1.94/1.25 ((((multiply @ sk_c10 @ identity) = (sk_c9))
% 1.94/1.25 | ((multiply @ sk_c9 @ sk_c8) = (sk_c10))
% 1.94/1.25 | ((multiply @ sk_c9 @ sk_c8) = (sk_c10)))),
% 1.94/1.25 inference('sup+', [status(thm)], [zip_derived_cl2366, zip_derived_cl35])).
% 1.94/1.25 thf(zip_derived_cl1152, plain,
% 1.94/1.25 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.94/1.25 inference('sup+', [status(thm)], [zip_derived_cl198, zip_derived_cl195])).
% 1.94/1.25 thf(zip_derived_cl2395, plain,
% 1.94/1.25 ((((sk_c10) = (sk_c9))
% 1.94/1.25 | ((multiply @ sk_c9 @ sk_c8) = (sk_c10))
% 1.94/1.25 | ((multiply @ sk_c9 @ sk_c8) = (sk_c10)))),
% 1.94/1.25 inference('demod', [status(thm)],
% 1.94/1.25 [zip_derived_cl2385, zip_derived_cl1152])).
% 1.94/1.25 thf(zip_derived_cl2396, plain,
% 1.94/1.25 ((((multiply @ sk_c9 @ sk_c8) = (sk_c10)) | ((sk_c10) = (sk_c9)))),
% 1.94/1.25 inference('simplify', [status(thm)], [zip_derived_cl2395])).
% 1.94/1.25 thf(zip_derived_cl2473, plain, (((identity) = (sk_c10))),
% 1.94/1.25 inference('simplify', [status(thm)], [zip_derived_cl2472])).
% 1.94/1.25 thf(zip_derived_cl2473, plain, (((identity) = (sk_c10))),
% 1.94/1.25 inference('simplify', [status(thm)], [zip_derived_cl2472])).
% 1.94/1.25 thf(zip_derived_cl3148, plain,
% 1.94/1.25 ((((multiply @ sk_c9 @ sk_c8) = (identity)) | ((identity) = (sk_c9)))),
% 1.94/1.25 inference('demod', [status(thm)],
% 1.94/1.25 [zip_derived_cl2396, zip_derived_cl2473, zip_derived_cl2473])).
% 1.94/1.25 thf(zip_derived_cl182, plain,
% 1.94/1.25 (![X0 : $i, X1 : $i]:
% 1.94/1.25 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.94/1.25 inference('demod', [status(thm)], [zip_derived_cl150, zip_derived_cl0])).
% 1.94/1.25 thf(zip_derived_cl3150, plain,
% 1.94/1.25 ((((sk_c8) = (multiply @ (inverse @ sk_c9) @ identity))
% 1.94/1.25 | ((identity) = (sk_c9)))),
% 1.94/1.25 inference('sup+', [status(thm)], [zip_derived_cl3148, zip_derived_cl182])).
% 1.94/1.25 thf(zip_derived_cl1152, plain,
% 1.94/1.25 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.94/1.25 inference('sup+', [status(thm)], [zip_derived_cl198, zip_derived_cl195])).
% 1.94/1.25 thf(zip_derived_cl3169, plain,
% 1.94/1.25 ((((sk_c8) = (inverse @ sk_c9)) | ((identity) = (sk_c9)))),
% 1.94/1.25 inference('demod', [status(thm)],
% 1.94/1.25 [zip_derived_cl3150, zip_derived_cl1152])).
% 1.94/1.25 thf(prove_this_49, conjecture,
% 1.94/1.25 (~( ( ( inverse @ sk_c7 ) = ( sk_c9 ) ) |
% 1.94/1.25 ( ( inverse @ sk_c3 ) = ( sk_c10 ) ) ))).
% 1.94/1.25 thf(zf_stmt_8, negated_conjecture,
% 1.94/1.25 (( ( inverse @ sk_c7 ) = ( sk_c9 ) ) | ( ( inverse @ sk_c3 ) = ( sk_c10 ) )),
% 1.94/1.25 inference('cnf.neg', [status(esa)], [prove_this_49])).
% 1.94/1.25 thf(zip_derived_cl51, plain,
% 1.94/1.25 ((((inverse @ sk_c7) = (sk_c9)) | ((inverse @ sk_c3) = (sk_c10)))),
% 1.94/1.25 inference('cnf', [status(esa)], [zf_stmt_8])).
% 1.94/1.25 thf(zip_derived_cl1, plain,
% 1.94/1.25 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.94/1.25 inference('cnf', [status(esa)], [left_inverse])).
% 1.94/1.25 thf(zip_derived_cl78, plain,
% 1.94/1.25 ((((multiply @ sk_c10 @ sk_c3) = (identity))
% 1.94/1.25 | ((inverse @ sk_c7) = (sk_c9)))),
% 1.94/1.25 inference('sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl1])).
% 1.94/1.25 thf(zip_derived_cl182, plain,
% 1.94/1.25 (![X0 : $i, X1 : $i]:
% 1.94/1.25 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.94/1.25 inference('demod', [status(thm)], [zip_derived_cl150, zip_derived_cl0])).
% 1.94/1.25 thf(zip_derived_cl207, plain,
% 1.94/1.25 ((((sk_c3) = (multiply @ (inverse @ sk_c10) @ identity))
% 1.94/1.25 | ((inverse @ sk_c7) = (sk_c9)))),
% 1.94/1.25 inference('sup+', [status(thm)], [zip_derived_cl78, zip_derived_cl182])).
% 1.94/1.25 thf(prove_this_42, conjecture,
% 1.94/1.25 (~( ( ( inverse @ sk_c7 ) = ( sk_c9 ) ) |
% 1.94/1.25 ( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c4 ) ) ))).
% 1.94/1.25 thf(zf_stmt_9, negated_conjecture,
% 1.94/1.25 (( ( inverse @ sk_c7 ) = ( sk_c9 ) ) |
% 1.94/1.25 ( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c4 ) )),
% 1.94/1.25 inference('cnf.neg', [status(esa)], [prove_this_42])).
% 1.94/1.25 thf(zip_derived_cl44, plain,
% 1.94/1.25 ((((inverse @ sk_c7) = (sk_c9)) | ((multiply @ sk_c3 @ sk_c10) = (sk_c4)))),
% 1.94/1.25 inference('cnf', [status(esa)], [zf_stmt_9])).
% 1.94/1.25 thf(zip_derived_cl493, plain,
% 1.94/1.25 ((((multiply @ (multiply @ (inverse @ sk_c10) @ identity) @ sk_c10)
% 1.94/1.25 = (sk_c4))
% 1.94/1.25 | ((inverse @ sk_c7) = (sk_c9))
% 1.94/1.25 | ((inverse @ sk_c7) = (sk_c9)))),
% 1.94/1.25 inference('sup+', [status(thm)], [zip_derived_cl207, zip_derived_cl44])).
% 1.94/1.25 thf(zip_derived_cl2, plain,
% 1.94/1.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.94/1.26 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.94/1.26 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.94/1.26 inference('cnf', [status(esa)], [associativity])).
% 1.94/1.26 thf(zip_derived_cl0, plain,
% 1.94/1.26 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.94/1.26 inference('cnf', [status(esa)], [left_identity])).
% 1.94/1.26 thf(zip_derived_cl1, plain,
% 1.94/1.26 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.94/1.26 inference('cnf', [status(esa)], [left_inverse])).
% 1.94/1.26 thf(zip_derived_cl506, plain,
% 1.94/1.26 ((((identity) = (sk_c4))
% 1.94/1.26 | ((inverse @ sk_c7) = (sk_c9))
% 1.94/1.26 | ((inverse @ sk_c7) = (sk_c9)))),
% 1.94/1.26 inference('demod', [status(thm)],
% 1.94/1.26 [zip_derived_cl493, zip_derived_cl2, zip_derived_cl0,
% 1.94/1.26 zip_derived_cl1])).
% 1.94/1.26 thf(zip_derived_cl507, plain,
% 1.94/1.26 ((((inverse @ sk_c7) = (sk_c9)) | ((identity) = (sk_c4)))),
% 1.94/1.26 inference('simplify', [status(thm)], [zip_derived_cl506])).
% 1.94/1.26 thf(prove_this_35, conjecture,
% 1.94/1.26 (~( ( ( inverse @ sk_c7 ) = ( sk_c9 ) ) |
% 1.94/1.26 ( ( multiply @ sk_c10 @ sk_c4 ) = ( sk_c9 ) ) ))).
% 1.94/1.26 thf(zf_stmt_10, negated_conjecture,
% 1.94/1.26 (( ( inverse @ sk_c7 ) = ( sk_c9 ) ) |
% 1.94/1.26 ( ( multiply @ sk_c10 @ sk_c4 ) = ( sk_c9 ) )),
% 1.94/1.26 inference('cnf.neg', [status(esa)], [prove_this_35])).
% 1.94/1.26 thf(zip_derived_cl37, plain,
% 1.94/1.26 ((((inverse @ sk_c7) = (sk_c9)) | ((multiply @ sk_c10 @ sk_c4) = (sk_c9)))),
% 1.94/1.26 inference('cnf', [status(esa)], [zf_stmt_10])).
% 1.94/1.26 thf(zip_derived_cl513, plain,
% 1.94/1.26 ((((multiply @ sk_c10 @ identity) = (sk_c9))
% 1.94/1.26 | ((inverse @ sk_c7) = (sk_c9))
% 1.94/1.26 | ((inverse @ sk_c7) = (sk_c9)))),
% 1.94/1.26 inference('sup+', [status(thm)], [zip_derived_cl507, zip_derived_cl37])).
% 1.94/1.26 thf(zip_derived_cl517, plain,
% 1.94/1.26 ((((inverse @ sk_c7) = (sk_c9))
% 1.94/1.26 | ((multiply @ sk_c10 @ identity) = (sk_c9)))),
% 1.94/1.26 inference('simplify', [status(thm)], [zip_derived_cl513])).
% 1.94/1.26 thf(zip_derived_cl198, plain,
% 1.94/1.26 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 1.94/1.26 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl182])).
% 1.94/1.26 thf(zip_derived_cl702, plain,
% 1.94/1.26 ((((sk_c7) = (multiply @ (inverse @ sk_c9) @ identity))
% 1.94/1.26 | ((multiply @ sk_c10 @ identity) = (sk_c9)))),
% 1.94/1.26 inference('sup+', [status(thm)], [zip_derived_cl517, zip_derived_cl198])).
% 1.94/1.26 thf(zip_derived_cl1152, plain,
% 1.94/1.26 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.94/1.26 inference('sup+', [status(thm)], [zip_derived_cl198, zip_derived_cl195])).
% 1.94/1.26 thf(zip_derived_cl1152, plain,
% 1.94/1.26 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.94/1.26 inference('sup+', [status(thm)], [zip_derived_cl198, zip_derived_cl195])).
% 1.94/1.26 thf(zip_derived_cl1192, plain,
% 1.94/1.26 ((((sk_c7) = (inverse @ sk_c9)) | ((sk_c10) = (sk_c9)))),
% 1.94/1.26 inference('demod', [status(thm)],
% 1.94/1.26 [zip_derived_cl702, zip_derived_cl1152, zip_derived_cl1152])).
% 1.94/1.26 thf(zip_derived_cl2473, plain, (((identity) = (sk_c10))),
% 1.94/1.26 inference('simplify', [status(thm)], [zip_derived_cl2472])).
% 1.94/1.26 thf(zip_derived_cl2550, plain,
% 1.94/1.26 ((((sk_c7) = (inverse @ sk_c9)) | ((identity) = (sk_c9)))),
% 1.94/1.26 inference('demod', [status(thm)],
% 1.94/1.26 [zip_derived_cl1192, zip_derived_cl2473])).
% 1.94/1.26 thf(prove_this_48, conjecture,
% 1.94/1.26 (~( ( ( multiply @ sk_c7 @ sk_c9 ) = ( sk_c8 ) ) |
% 1.94/1.26 ( ( inverse @ sk_c3 ) = ( sk_c10 ) ) ))).
% 1.94/1.26 thf(zf_stmt_11, negated_conjecture,
% 1.94/1.26 (( ( multiply @ sk_c7 @ sk_c9 ) = ( sk_c8 ) ) |
% 1.94/1.26 ( ( inverse @ sk_c3 ) = ( sk_c10 ) )),
% 1.94/1.26 inference('cnf.neg', [status(esa)], [prove_this_48])).
% 1.94/1.26 thf(zip_derived_cl50, plain,
% 1.94/1.26 ((((multiply @ sk_c7 @ sk_c9) = (sk_c8)) | ((inverse @ sk_c3) = (sk_c10)))),
% 1.94/1.26 inference('cnf', [status(esa)], [zf_stmt_11])).
% 1.94/1.26 thf(zip_derived_cl1199, plain,
% 1.94/1.26 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.94/1.26 inference('sup+', [status(thm)], [zip_derived_cl1152, zip_derived_cl198])).
% 1.94/1.26 thf(zip_derived_cl1228, plain,
% 1.94/1.26 ((((sk_c3) = (inverse @ sk_c10)) | ((multiply @ sk_c7 @ sk_c9) = (sk_c8)))),
% 1.94/1.26 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl1199])).
% 1.94/1.26 thf(prove_this_41, conjecture,
% 1.94/1.26 (~( ( ( multiply @ sk_c7 @ sk_c9 ) = ( sk_c8 ) ) |
% 1.94/1.26 ( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c4 ) ) ))).
% 1.94/1.26 thf(zf_stmt_12, negated_conjecture,
% 1.94/1.26 (( ( multiply @ sk_c7 @ sk_c9 ) = ( sk_c8 ) ) |
% 1.94/1.26 ( ( multiply @ sk_c3 @ sk_c10 ) = ( sk_c4 ) )),
% 1.94/1.26 inference('cnf.neg', [status(esa)], [prove_this_41])).
% 1.94/1.26 thf(zip_derived_cl43, plain,
% 1.94/1.26 ((((multiply @ sk_c7 @ sk_c9) = (sk_c8))
% 1.94/1.26 | ((multiply @ sk_c3 @ sk_c10) = (sk_c4)))),
% 1.94/1.26 inference('cnf', [status(esa)], [zf_stmt_12])).
% 1.94/1.26 thf(zip_derived_cl1851, plain,
% 1.94/1.26 ((((multiply @ (inverse @ sk_c10) @ sk_c10) = (sk_c4))
% 1.94/1.26 | ((multiply @ sk_c7 @ sk_c9) = (sk_c8))
% 1.94/1.26 | ((multiply @ sk_c7 @ sk_c9) = (sk_c8)))),
% 1.94/1.26 inference('sup+', [status(thm)], [zip_derived_cl1228, zip_derived_cl43])).
% 1.94/1.26 thf(zip_derived_cl1, plain,
% 1.94/1.26 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.94/1.26 inference('cnf', [status(esa)], [left_inverse])).
% 1.94/1.26 thf(zip_derived_cl1869, plain,
% 1.94/1.26 ((((identity) = (sk_c4))
% 1.94/1.26 | ((multiply @ sk_c7 @ sk_c9) = (sk_c8))
% 1.94/1.26 | ((multiply @ sk_c7 @ sk_c9) = (sk_c8)))),
% 1.94/1.26 inference('demod', [status(thm)], [zip_derived_cl1851, zip_derived_cl1])).
% 1.94/1.26 thf(zip_derived_cl1870, plain,
% 1.94/1.26 ((((multiply @ sk_c7 @ sk_c9) = (sk_c8)) | ((identity) = (sk_c4)))),
% 1.94/1.26 inference('simplify', [status(thm)], [zip_derived_cl1869])).
% 1.94/1.26 thf(prove_this_34, conjecture,
% 1.94/1.26 (~( ( ( multiply @ sk_c7 @ sk_c9 ) = ( sk_c8 ) ) |
% 1.94/1.26 ( ( multiply @ sk_c10 @ sk_c4 ) = ( sk_c9 ) ) ))).
% 1.94/1.26 thf(zf_stmt_13, negated_conjecture,
% 1.94/1.26 (( ( multiply @ sk_c7 @ sk_c9 ) = ( sk_c8 ) ) |
% 1.94/1.26 ( ( multiply @ sk_c10 @ sk_c4 ) = ( sk_c9 ) )),
% 1.94/1.26 inference('cnf.neg', [status(esa)], [prove_this_34])).
% 1.94/1.26 thf(zip_derived_cl36, plain,
% 1.94/1.26 ((((multiply @ sk_c7 @ sk_c9) = (sk_c8))
% 1.94/1.26 | ((multiply @ sk_c10 @ sk_c4) = (sk_c9)))),
% 1.94/1.26 inference('cnf', [status(esa)], [zf_stmt_13])).
% 1.94/1.26 thf(zip_derived_cl1947, plain,
% 1.94/1.26 ((((multiply @ sk_c10 @ identity) = (sk_c9))
% 1.94/1.26 | ((multiply @ sk_c7 @ sk_c9) = (sk_c8))
% 1.94/1.26 | ((multiply @ sk_c7 @ sk_c9) = (sk_c8)))),
% 1.94/1.26 inference('sup+', [status(thm)], [zip_derived_cl1870, zip_derived_cl36])).
% 1.94/1.26 thf(zip_derived_cl1152, plain,
% 1.94/1.26 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.94/1.26 inference('sup+', [status(thm)], [zip_derived_cl198, zip_derived_cl195])).
% 1.94/1.26 thf(zip_derived_cl1957, plain,
% 1.94/1.26 ((((sk_c10) = (sk_c9))
% 1.94/1.26 | ((multiply @ sk_c7 @ sk_c9) = (sk_c8))
% 1.94/1.26 | ((multiply @ sk_c7 @ sk_c9) = (sk_c8)))),
% 1.94/1.26 inference('demod', [status(thm)],
% 1.94/1.26 [zip_derived_cl1947, zip_derived_cl1152])).
% 1.94/1.26 thf(zip_derived_cl1958, plain,
% 1.94/1.26 ((((multiply @ sk_c7 @ sk_c9) = (sk_c8)) | ((sk_c10) = (sk_c9)))),
% 1.94/1.26 inference('simplify', [status(thm)], [zip_derived_cl1957])).
% 1.94/1.26 thf(zip_derived_cl2473, plain, (((identity) = (sk_c10))),
% 1.94/1.26 inference('simplify', [status(thm)], [zip_derived_cl2472])).
% 1.94/1.26 thf(zip_derived_cl2843, plain,
% 1.94/1.26 ((((multiply @ sk_c7 @ sk_c9) = (sk_c8)) | ((identity) = (sk_c9)))),
% 1.94/1.26 inference('demod', [status(thm)],
% 1.94/1.26 [zip_derived_cl1958, zip_derived_cl2473])).
% 1.94/1.26 thf(zip_derived_cl2853, plain,
% 1.94/1.26 ((((multiply @ (inverse @ sk_c9) @ sk_c9) = (sk_c8))
% 1.94/1.26 | ((identity) = (sk_c9))
% 1.94/1.26 | ((identity) = (sk_c9)))),
% 1.94/1.26 inference('sup+', [status(thm)], [zip_derived_cl2550, zip_derived_cl2843])).
% 1.94/1.26 thf(zip_derived_cl1, plain,
% 1.94/1.26 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.94/1.26 inference('cnf', [status(esa)], [left_inverse])).
% 1.94/1.26 thf(zip_derived_cl2858, plain,
% 1.94/1.26 ((((identity) = (sk_c8))
% 1.94/1.26 | ((identity) = (sk_c9))
% 1.94/1.26 | ((identity) = (sk_c9)))),
% 1.94/1.26 inference('demod', [status(thm)], [zip_derived_cl2853, zip_derived_cl1])).
% 1.94/1.26 thf(zip_derived_cl2859, plain,
% 1.94/1.26 ((((identity) = (sk_c9)) | ((identity) = (sk_c8)))),
% 1.94/1.26 inference('simplify', [status(thm)], [zip_derived_cl2858])).
% 1.94/1.26 thf(zip_derived_cl3177, plain,
% 1.94/1.26 ((((identity) = (inverse @ sk_c9))
% 1.94/1.26 | ((identity) = (sk_c9))
% 1.94/1.26 | ((identity) = (sk_c9)))),
% 1.94/1.26 inference('sup+', [status(thm)], [zip_derived_cl3169, zip_derived_cl2859])).
% 1.94/1.26 thf(zip_derived_cl3179, plain,
% 1.94/1.26 ((((identity) = (sk_c9)) | ((identity) = (inverse @ sk_c9)))),
% 1.94/1.26 inference('simplify', [status(thm)], [zip_derived_cl3177])).
% 1.94/1.26 thf(zip_derived_cl1199, plain,
% 1.94/1.26 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.94/1.26 inference('sup+', [status(thm)], [zip_derived_cl1152, zip_derived_cl198])).
% 1.94/1.26 thf(zip_derived_cl3182, plain,
% 1.94/1.26 ((((sk_c9) = (inverse @ identity)) | ((identity) = (sk_c9)))),
% 1.94/1.26 inference('sup+', [status(thm)], [zip_derived_cl3179, zip_derived_cl1199])).
% 1.94/1.26 thf(zip_derived_cl0, plain,
% 1.94/1.26 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.94/1.26 inference('cnf', [status(esa)], [left_identity])).
% 1.94/1.26 thf(zip_derived_cl182, plain,
% 1.94/1.26 (![X0 : $i, X1 : $i]:
% 1.94/1.26 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.94/1.26 inference('demod', [status(thm)], [zip_derived_cl150, zip_derived_cl0])).
% 1.94/1.26 thf(zip_derived_cl197, plain,
% 1.94/1.26 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 1.94/1.26 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl182])).
% 1.94/1.26 thf(zip_derived_cl182, plain,
% 1.94/1.26 (![X0 : $i, X1 : $i]:
% 1.94/1.26 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.94/1.26 inference('demod', [status(thm)], [zip_derived_cl150, zip_derived_cl0])).
% 1.94/1.26 thf(zip_derived_cl250, plain,
% 1.94/1.26 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ identity)) @ X0))),
% 1.94/1.26 inference('sup+', [status(thm)], [zip_derived_cl197, zip_derived_cl182])).
% 1.94/1.26 thf(zip_derived_cl1, plain,
% 1.94/1.26 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.94/1.26 inference('cnf', [status(esa)], [left_inverse])).
% 1.94/1.26 thf(zip_derived_cl772, plain, (((inverse @ identity) = (identity))),
% 1.94/1.26 inference('sup+', [status(thm)], [zip_derived_cl250, zip_derived_cl1])).
% 1.94/1.26 thf(zip_derived_cl3201, plain,
% 1.94/1.26 ((((sk_c9) = (identity)) | ((identity) = (sk_c9)))),
% 1.94/1.26 inference('demod', [status(thm)], [zip_derived_cl3182, zip_derived_cl772])).
% 1.94/1.26 thf(zip_derived_cl3202, plain, (((sk_c9) = (identity))),
% 1.94/1.26 inference('simplify', [status(thm)], [zip_derived_cl3201])).
% 1.94/1.26 thf(zip_derived_cl0, plain,
% 1.94/1.26 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.94/1.26 inference('cnf', [status(esa)], [left_identity])).
% 1.94/1.26 thf(zip_derived_cl3202, plain, (((sk_c9) = (identity))),
% 1.94/1.26 inference('simplify', [status(thm)], [zip_derived_cl3201])).
% 1.94/1.26 thf(zip_derived_cl3202, plain, (((sk_c9) = (identity))),
% 1.94/1.26 inference('simplify', [status(thm)], [zip_derived_cl3201])).
% 1.94/1.26 thf(zip_derived_cl1152, plain,
% 1.94/1.26 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.94/1.26 inference('sup+', [status(thm)], [zip_derived_cl198, zip_derived_cl195])).
% 1.94/1.26 thf(zip_derived_cl3202, plain, (((sk_c9) = (identity))),
% 1.94/1.26 inference('simplify', [status(thm)], [zip_derived_cl3201])).
% 1.94/1.26 thf(zip_derived_cl772, plain, (((inverse @ identity) = (identity))),
% 1.94/1.26 inference('sup+', [status(thm)], [zip_derived_cl250, zip_derived_cl1])).
% 1.94/1.26 thf(zip_derived_cl3202, plain, (((sk_c9) = (identity))),
% 1.94/1.26 inference('simplify', [status(thm)], [zip_derived_cl3201])).
% 1.94/1.26 thf(zip_derived_cl3202, plain, (((sk_c9) = (identity))),
% 1.94/1.26 inference('simplify', [status(thm)], [zip_derived_cl3201])).
% 1.94/1.26 thf(zip_derived_cl1152, plain,
% 1.94/1.26 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.94/1.26 inference('sup+', [status(thm)], [zip_derived_cl198, zip_derived_cl195])).
% 1.94/1.26 thf(zip_derived_cl3263, plain,
% 1.94/1.26 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.94/1.26 (((identity) != (X0))
% 1.94/1.26 | ((X0) != (identity))
% 1.94/1.26 | ((inverse @ X1) != (identity))
% 1.94/1.26 | ((X1) != (identity))
% 1.94/1.26 | ((inverse @ X2) != (sk_c11))
% 1.94/1.26 | ((multiply @ X2 @ sk_c11) != (identity))
% 1.94/1.26 | ((identity) != (identity))
% 1.94/1.26 | ((inverse @ X3) != (identity))
% 1.94/1.26 | ((X3) != (identity))
% 1.94/1.26 | ((inverse @ X4) != (sk_c11))
% 1.94/1.26 | ((multiply @ X4 @ sk_c11) != (identity)))),
% 1.94/1.26 inference('demod', [status(thm)],
% 1.94/1.26 [zip_derived_cl2585, zip_derived_cl3202, zip_derived_cl0,
% 1.94/1.26 zip_derived_cl3202, zip_derived_cl3202, zip_derived_cl1152,
% 1.94/1.26 zip_derived_cl3202, zip_derived_cl772, zip_derived_cl3202,
% 1.94/1.26 zip_derived_cl3202, zip_derived_cl1152])).
% 1.94/1.26 thf(zip_derived_cl3264, plain,
% 1.94/1.26 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.94/1.26 (((multiply @ X4 @ sk_c11) != (identity))
% 1.94/1.26 | ((inverse @ X4) != (sk_c11))
% 1.94/1.26 | ((X3) != (identity))
% 1.94/1.26 | ((inverse @ X3) != (identity))
% 1.94/1.26 | ((multiply @ X2 @ sk_c11) != (identity))
% 1.94/1.26 | ((inverse @ X2) != (sk_c11))
% 1.94/1.26 | ((X1) != (identity))
% 1.94/1.26 | ((inverse @ X1) != (identity))
% 1.94/1.26 | ((identity) != (X0)))),
% 1.94/1.26 inference('simplify', [status(thm)], [zip_derived_cl3263])).
% 1.94/1.26 thf(zip_derived_cl3281, plain,
% 1.94/1.26 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.94/1.26 (((identity) != (X0))
% 1.94/1.26 | ((inverse @ X1) != (identity))
% 1.94/1.26 | ((X1) != (identity))
% 1.94/1.26 | ((inverse @ X2) != (sk_c11))
% 1.94/1.26 | ((multiply @ X2 @ sk_c11) != (identity))
% 1.94/1.26 | ((inverse @ identity) != (identity))
% 1.94/1.26 | ((inverse @ X3) != (sk_c11))
% 1.94/1.26 | ((multiply @ X3 @ sk_c11) != (identity)))),
% 1.94/1.26 inference('eq_res', [status(thm)], [zip_derived_cl3264])).
% 1.94/1.26 thf(zip_derived_cl772, plain, (((inverse @ identity) = (identity))),
% 1.94/1.26 inference('sup+', [status(thm)], [zip_derived_cl250, zip_derived_cl1])).
% 1.94/1.26 thf(zip_derived_cl3282, plain,
% 1.94/1.26 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.94/1.26 (((identity) != (X0))
% 1.94/1.26 | ((inverse @ X1) != (identity))
% 1.94/1.26 | ((X1) != (identity))
% 1.94/1.26 | ((inverse @ X2) != (sk_c11))
% 1.94/1.26 | ((multiply @ X2 @ sk_c11) != (identity))
% 1.94/1.26 | ((identity) != (identity))
% 1.94/1.26 | ((inverse @ X3) != (sk_c11))
% 1.94/1.26 | ((multiply @ X3 @ sk_c11) != (identity)))),
% 1.94/1.26 inference('demod', [status(thm)], [zip_derived_cl3281, zip_derived_cl772])).
% 1.94/1.26 thf(zip_derived_cl3283, plain,
% 1.94/1.26 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.94/1.26 (((multiply @ X3 @ sk_c11) != (identity))
% 1.94/1.26 | ((inverse @ X3) != (sk_c11))
% 1.94/1.26 | ((multiply @ X2 @ sk_c11) != (identity))
% 1.94/1.26 | ((inverse @ X2) != (sk_c11))
% 1.94/1.26 | ((X1) != (identity))
% 1.94/1.26 | ((inverse @ X1) != (identity))
% 1.94/1.26 | ((identity) != (X0)))),
% 1.94/1.26 inference('simplify', [status(thm)], [zip_derived_cl3282])).
% 1.94/1.26 thf(zip_derived_cl3284, plain,
% 1.94/1.26 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.94/1.26 (((identity) != (X0))
% 1.94/1.26 | ((inverse @ identity) != (identity))
% 1.94/1.26 | ((inverse @ X1) != (sk_c11))
% 1.94/1.26 | ((multiply @ X1 @ sk_c11) != (identity))
% 1.94/1.26 | ((inverse @ X2) != (sk_c11))
% 1.94/1.26 | ((multiply @ X2 @ sk_c11) != (identity)))),
% 1.94/1.26 inference('eq_res', [status(thm)], [zip_derived_cl3283])).
% 1.94/1.26 thf(zip_derived_cl772, plain, (((inverse @ identity) = (identity))),
% 1.94/1.26 inference('sup+', [status(thm)], [zip_derived_cl250, zip_derived_cl1])).
% 1.94/1.26 thf(zip_derived_cl3285, plain,
% 1.94/1.26 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.94/1.26 (((identity) != (X0))
% 1.94/1.26 | ((identity) != (identity))
% 1.94/1.26 | ((inverse @ X1) != (sk_c11))
% 1.94/1.26 | ((multiply @ X1 @ sk_c11) != (identity))
% 1.94/1.26 | ((inverse @ X2) != (sk_c11))
% 1.94/1.26 | ((multiply @ X2 @ sk_c11) != (identity)))),
% 1.94/1.26 inference('demod', [status(thm)], [zip_derived_cl3284, zip_derived_cl772])).
% 1.94/1.26 thf(zip_derived_cl3286, plain,
% 1.94/1.26 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.94/1.26 (((multiply @ X2 @ sk_c11) != (identity))
% 1.94/1.26 | ((inverse @ X2) != (sk_c11))
% 1.94/1.26 | ((multiply @ X1 @ sk_c11) != (identity))
% 1.94/1.26 | ((inverse @ X1) != (sk_c11))
% 1.94/1.26 | ((identity) != (X0)))),
% 1.94/1.26 inference('simplify', [status(thm)], [zip_derived_cl3285])).
% 1.94/1.26 thf(zip_derived_cl3287, plain,
% 1.94/1.26 (![X0 : $i, X1 : $i]:
% 1.94/1.26 (((inverse @ X0) != (sk_c11))
% 1.94/1.26 | ((multiply @ X0 @ sk_c11) != (identity))
% 1.94/1.26 | ((inverse @ X1) != (sk_c11))
% 1.94/1.26 | ((multiply @ X1 @ sk_c11) != (identity)))),
% 1.94/1.26 inference('eq_res', [status(thm)], [zip_derived_cl3286])).
% 1.94/1.26 thf(zip_derived_cl3288, plain,
% 1.94/1.26 (![X0 : $i, X1 : $i]:
% 1.94/1.26 (((X0) != (sk_c11))
% 1.94/1.26 | ((multiply @ X1 @ sk_c11) != (identity))
% 1.94/1.26 | ((inverse @ X1) != (sk_c11))
% 1.94/1.26 | ((multiply @ (inverse @ X0) @ sk_c11) != (identity)))),
% 1.94/1.26 inference('sup-', [status(thm)], [zip_derived_cl1199, zip_derived_cl3287])).
% 1.94/1.26 thf(zip_derived_cl3295, plain,
% 1.94/1.26 (![X0 : $i]:
% 1.94/1.26 (((multiply @ (inverse @ sk_c11) @ sk_c11) != (identity))
% 1.94/1.26 | ((inverse @ X0) != (sk_c11))
% 1.94/1.26 | ((multiply @ X0 @ sk_c11) != (identity)))),
% 1.94/1.26 inference('eq_res', [status(thm)], [zip_derived_cl3288])).
% 1.94/1.26 thf(zip_derived_cl1, plain,
% 1.94/1.26 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.94/1.26 inference('cnf', [status(esa)], [left_inverse])).
% 1.94/1.26 thf(zip_derived_cl3296, plain,
% 1.94/1.26 (![X0 : $i]:
% 1.94/1.26 (((identity) != (identity))
% 1.94/1.26 | ((inverse @ X0) != (sk_c11))
% 1.94/1.26 | ((multiply @ X0 @ sk_c11) != (identity)))),
% 1.94/1.26 inference('demod', [status(thm)], [zip_derived_cl3295, zip_derived_cl1])).
% 1.94/1.26 thf(zip_derived_cl3297, plain,
% 1.94/1.26 (![X0 : $i]:
% 1.94/1.26 (((multiply @ X0 @ sk_c11) != (identity))
% 1.94/1.26 | ((inverse @ X0) != (sk_c11)))),
% 1.94/1.26 inference('simplify', [status(thm)], [zip_derived_cl3296])).
% 1.94/1.26 thf(zip_derived_cl3327, plain,
% 1.94/1.26 (![X0 : $i]:
% 1.94/1.26 (((X0) != (sk_c11))
% 1.94/1.26 | ((multiply @ (inverse @ X0) @ sk_c11) != (identity)))),
% 1.94/1.26 inference('sup-', [status(thm)], [zip_derived_cl1199, zip_derived_cl3297])).
% 1.94/1.26 thf(zip_derived_cl3334, plain,
% 1.94/1.26 (((multiply @ (inverse @ sk_c11) @ sk_c11) != (identity))),
% 1.94/1.26 inference('eq_res', [status(thm)], [zip_derived_cl3327])).
% 1.94/1.26 thf(zip_derived_cl1, plain,
% 1.94/1.26 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.94/1.26 inference('cnf', [status(esa)], [left_inverse])).
% 1.94/1.26 thf(zip_derived_cl3335, plain, (((identity) != (identity))),
% 1.94/1.26 inference('demod', [status(thm)], [zip_derived_cl3334, zip_derived_cl1])).
% 1.94/1.26 thf(zip_derived_cl3336, plain, ($false),
% 1.94/1.26 inference('simplify', [status(thm)], [zip_derived_cl3335])).
% 1.94/1.26
% 1.94/1.26 % SZS output end Refutation
% 1.94/1.26
% 1.94/1.26
% 1.94/1.26 % Terminating...
% 1.97/1.38 % Runner terminated.
% 1.97/1.40 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------