TSTP Solution File: GRP363-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP363-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.CjkY2dTtJ2 true
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:51:21 EDT 2023
% Result : Unsatisfiable 1.31s 1.14s
% Output : Refutation 1.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP363-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.CjkY2dTtJ2 true
% 0.13/0.34 % Computer : n001.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 : Tue Aug 29 01:14:06 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.34 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.20/0.63 % Total configuration time : 435
% 0.20/0.63 % Estimated wc time : 1092
% 0.20/0.63 % Estimated cpu time (7 cpus) : 156.0
% 0.20/0.69 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.20/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.20/0.73 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.20/0.74 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.20/0.74 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.20/0.75 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.78/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 1.31/1.14 % Solved by fo/fo7.sh.
% 1.31/1.14 % done 1058 iterations in 0.376s
% 1.31/1.14 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.31/1.14 % SZS output start Refutation
% 1.31/1.14 thf(sk_c1_type, type, sk_c1: $i).
% 1.31/1.14 thf(sk_c7_type, type, sk_c7: $i).
% 1.31/1.14 thf(sk_c3_type, type, sk_c3: $i).
% 1.31/1.14 thf(sk_c4_type, type, sk_c4: $i).
% 1.31/1.14 thf(identity_type, type, identity: $i).
% 1.31/1.14 thf(multiply_type, type, multiply: $i > $i > $i).
% 1.31/1.14 thf(sk_c5_type, type, sk_c5: $i).
% 1.31/1.14 thf(inverse_type, type, inverse: $i > $i).
% 1.31/1.14 thf(sk_c2_type, type, sk_c2: $i).
% 1.31/1.14 thf(sk_c6_type, type, sk_c6: $i).
% 1.31/1.14 thf(prove_this_25, conjecture,
% 1.31/1.14 (~( ( ( inverse @ X4 ) != ( sk_c7 ) ) |
% 1.31/1.14 ( ( multiply @ X4 @ sk_c7 ) != ( X3 ) ) |
% 1.31/1.14 ( ( multiply @ sk_c7 @ X3 ) != ( sk_c6 ) ) |
% 1.31/1.14 ( ( inverse @ X1 ) != ( sk_c6 ) ) |
% 1.31/1.14 ( ( multiply @ X1 @ sk_c6 ) != ( sk_c7 ) ) |
% 1.31/1.14 ( ( multiply @ sk_c6 @ sk_c7 ) != ( sk_c5 ) ) |
% 1.31/1.14 ( ( inverse @ X2 ) != ( sk_c6 ) ) |
% 1.31/1.14 ( ( multiply @ X2 @ sk_c6 ) != ( sk_c5 ) ) |
% 1.31/1.14 ( ( inverse @ sk_c6 ) != ( sk_c5 ) ) |
% 1.31/1.14 ( ( multiply @ sk_c6 @ sk_c5 ) != ( sk_c7 ) ) ))).
% 1.31/1.14 thf(zf_stmt_0, negated_conjecture,
% 1.31/1.14 (( ( inverse @ X4 ) != ( sk_c7 ) ) |
% 1.31/1.14 ( ( multiply @ X4 @ sk_c7 ) != ( X3 ) ) |
% 1.31/1.14 ( ( multiply @ sk_c7 @ X3 ) != ( sk_c6 ) ) |
% 1.31/1.14 ( ( inverse @ X1 ) != ( sk_c6 ) ) |
% 1.31/1.14 ( ( multiply @ X1 @ sk_c6 ) != ( sk_c7 ) ) |
% 1.31/1.14 ( ( multiply @ sk_c6 @ sk_c7 ) != ( sk_c5 ) ) |
% 1.31/1.14 ( ( inverse @ X2 ) != ( sk_c6 ) ) |
% 1.31/1.14 ( ( multiply @ X2 @ sk_c6 ) != ( sk_c5 ) ) |
% 1.31/1.14 ( ( inverse @ sk_c6 ) != ( sk_c5 ) ) |
% 1.31/1.14 ( ( multiply @ sk_c6 @ sk_c5 ) != ( sk_c7 ) )),
% 1.31/1.14 inference('cnf.neg', [status(esa)], [prove_this_25])).
% 1.31/1.14 thf(zip_derived_cl27, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.14 (((inverse @ X0) != (sk_c7))
% 1.31/1.14 | ((multiply @ X0 @ sk_c7) != (X1))
% 1.31/1.14 | ((multiply @ sk_c7 @ X1) != (sk_c6))
% 1.31/1.14 | ((inverse @ X2) != (sk_c6))
% 1.31/1.14 | ((multiply @ X2 @ sk_c6) != (sk_c7))
% 1.31/1.14 | ((multiply @ sk_c6 @ sk_c7) != (sk_c5))
% 1.31/1.14 | ((inverse @ X3) != (sk_c6))
% 1.31/1.14 | ((multiply @ X3 @ sk_c6) != (sk_c5))
% 1.31/1.14 | ((inverse @ sk_c6) != (sk_c5))
% 1.31/1.14 | ((multiply @ sk_c6 @ sk_c5) != (sk_c7)))),
% 1.31/1.14 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.31/1.14 thf(zip_derived_cl28, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.14 (((inverse @ X0) != (multiply @ sk_c6 @ (inverse @ sk_c6)))
% 1.31/1.14 | ((multiply @ X0 @ (multiply @ sk_c6 @ (inverse @ sk_c6))) != (X1))
% 1.31/1.14 | ((multiply @ (multiply @ sk_c6 @ (inverse @ sk_c6)) @ X1)
% 1.31/1.14 != (sk_c6))
% 1.31/1.14 | ((inverse @ X2) != (sk_c6))
% 1.31/1.14 | ((multiply @ X2 @ sk_c6) != (multiply @ sk_c6 @ (inverse @ sk_c6)))
% 1.31/1.14 | ((multiply @ sk_c6 @ (multiply @ sk_c6 @ (inverse @ sk_c6)))
% 1.31/1.14 != (inverse @ sk_c6))
% 1.31/1.14 | ((inverse @ X3) != (sk_c6))
% 1.31/1.14 | ((multiply @ X3 @ sk_c6) != (inverse @ sk_c6))
% 1.31/1.14 | ((inverse @ sk_c6) != (sk_c5))
% 1.31/1.14 | ((multiply @ sk_c6 @ (inverse @ sk_c6)) != (sk_c7)))),
% 1.31/1.14 inference('local_rewriting', [status(thm)], [zip_derived_cl27])).
% 1.31/1.14 thf(associativity, axiom,
% 1.31/1.14 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 1.31/1.14 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 1.31/1.14 thf(zip_derived_cl2, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.31/1.14 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.31/1.14 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.31/1.14 inference('cnf', [status(esa)], [associativity])).
% 1.31/1.14 thf(zip_derived_cl39, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.14 (((inverse @ X0) != (multiply @ sk_c6 @ (inverse @ sk_c6)))
% 1.31/1.14 | ((multiply @ X0 @ (multiply @ sk_c6 @ (inverse @ sk_c6))) != (X1))
% 1.31/1.14 | ((multiply @ sk_c6 @ (multiply @ (inverse @ sk_c6) @ X1))
% 1.31/1.14 != (sk_c6))
% 1.31/1.14 | ((inverse @ X2) != (sk_c6))
% 1.31/1.14 | ((multiply @ X2 @ sk_c6) != (multiply @ sk_c6 @ (inverse @ sk_c6)))
% 1.31/1.14 | ((multiply @ sk_c6 @ (multiply @ sk_c6 @ (inverse @ sk_c6)))
% 1.31/1.14 != (inverse @ sk_c6))
% 1.31/1.14 | ((inverse @ X3) != (sk_c6))
% 1.31/1.14 | ((multiply @ X3 @ sk_c6) != (inverse @ sk_c6))
% 1.31/1.14 | ((inverse @ sk_c6) != (sk_c5))
% 1.31/1.14 | ((multiply @ sk_c6 @ (inverse @ sk_c6)) != (sk_c7)))),
% 1.31/1.14 inference('demod', [status(thm)], [zip_derived_cl28, zip_derived_cl2])).
% 1.31/1.14 thf(prove_this_9, conjecture,
% 1.31/1.14 (~( ( ( inverse @ sk_c2 ) = ( sk_c6 ) ) |
% 1.31/1.14 ( ( inverse @ sk_c6 ) = ( sk_c5 ) ) ))).
% 1.31/1.14 thf(zf_stmt_1, negated_conjecture,
% 1.31/1.14 (( ( inverse @ sk_c2 ) = ( sk_c6 ) ) | ( ( inverse @ sk_c6 ) = ( sk_c5 ) )),
% 1.31/1.14 inference('cnf.neg', [status(esa)], [prove_this_9])).
% 1.31/1.14 thf(zip_derived_cl11, plain,
% 1.31/1.14 ((((inverse @ sk_c2) = (sk_c6)) | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('cnf', [status(esa)], [zf_stmt_1])).
% 1.31/1.14 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 1.31/1.14 thf(zip_derived_cl1, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_inverse])).
% 1.31/1.14 thf(zip_derived_cl30, plain,
% 1.31/1.14 ((((multiply @ sk_c6 @ sk_c2) = (identity))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl1])).
% 1.31/1.14 thf(zip_derived_cl1, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_inverse])).
% 1.31/1.14 thf(zip_derived_cl2, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.31/1.14 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.31/1.14 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.31/1.14 inference('cnf', [status(esa)], [associativity])).
% 1.31/1.14 thf(zip_derived_cl43, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i]:
% 1.31/1.14 ((multiply @ identity @ X0)
% 1.31/1.14 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 1.31/1.14 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 1.31/1.14 thf(zip_derived_cl0, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_identity])).
% 1.31/1.14 thf(zip_derived_cl61, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i]:
% 1.31/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.31/1.14 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 1.31/1.14 thf(zip_derived_cl78, plain,
% 1.31/1.14 ((((sk_c2) = (multiply @ (inverse @ sk_c6) @ identity))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl61])).
% 1.31/1.14 thf(prove_this_8, conjecture,
% 1.31/1.14 (~( ( ( multiply @ sk_c2 @ sk_c6 ) = ( sk_c7 ) ) |
% 1.31/1.14 ( ( inverse @ sk_c6 ) = ( sk_c5 ) ) ))).
% 1.31/1.14 thf(zf_stmt_2, negated_conjecture,
% 1.31/1.14 (( ( multiply @ sk_c2 @ sk_c6 ) = ( sk_c7 ) ) |
% 1.31/1.14 ( ( inverse @ sk_c6 ) = ( sk_c5 ) )),
% 1.31/1.14 inference('cnf.neg', [status(esa)], [prove_this_8])).
% 1.31/1.14 thf(zip_derived_cl10, plain,
% 1.31/1.14 ((((multiply @ sk_c2 @ sk_c6) = (sk_c7)) | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('cnf', [status(esa)], [zf_stmt_2])).
% 1.31/1.14 thf(zip_derived_cl119, plain,
% 1.31/1.14 ((((multiply @ (multiply @ (inverse @ sk_c6) @ identity) @ sk_c6)
% 1.31/1.14 = (sk_c7))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl78, zip_derived_cl10])).
% 1.31/1.14 thf(zip_derived_cl2, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.31/1.14 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.31/1.14 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.31/1.14 inference('cnf', [status(esa)], [associativity])).
% 1.31/1.14 thf(zip_derived_cl0, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_identity])).
% 1.31/1.14 thf(zip_derived_cl1, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_inverse])).
% 1.31/1.14 thf(zip_derived_cl124, plain,
% 1.31/1.14 ((((identity) = (sk_c7))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('demod', [status(thm)],
% 1.31/1.14 [zip_derived_cl119, zip_derived_cl2, zip_derived_cl0,
% 1.31/1.14 zip_derived_cl1])).
% 1.31/1.14 thf(zip_derived_cl125, plain,
% 1.31/1.14 ((((inverse @ sk_c6) = (sk_c5)) | ((identity) = (sk_c7)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl124])).
% 1.31/1.14 thf(prove_this_12, conjecture,
% 1.31/1.14 (~( ( ( inverse @ sk_c3 ) = ( sk_c7 ) ) |
% 1.31/1.14 ( ( inverse @ sk_c6 ) = ( sk_c5 ) ) ))).
% 1.31/1.14 thf(zf_stmt_3, negated_conjecture,
% 1.31/1.14 (( ( inverse @ sk_c3 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c6 ) = ( sk_c5 ) )),
% 1.31/1.14 inference('cnf.neg', [status(esa)], [prove_this_12])).
% 1.31/1.14 thf(zip_derived_cl14, plain,
% 1.31/1.14 ((((inverse @ sk_c3) = (sk_c7)) | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('cnf', [status(esa)], [zf_stmt_3])).
% 1.31/1.14 thf(zip_derived_cl1, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_inverse])).
% 1.31/1.14 thf(zip_derived_cl31, plain,
% 1.31/1.14 ((((multiply @ sk_c7 @ sk_c3) = (identity))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl1])).
% 1.31/1.14 thf(zip_derived_cl134, plain,
% 1.31/1.14 ((((multiply @ identity @ sk_c3) = (identity))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl125, zip_derived_cl31])).
% 1.31/1.14 thf(zip_derived_cl140, plain,
% 1.31/1.14 ((((inverse @ sk_c6) = (sk_c5))
% 1.31/1.14 | ((multiply @ identity @ sk_c3) = (identity)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl134])).
% 1.31/1.14 thf(zip_derived_cl0, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_identity])).
% 1.31/1.14 thf(zip_derived_cl165, plain,
% 1.31/1.14 ((((identity) = (sk_c3)) | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl140, zip_derived_cl0])).
% 1.31/1.14 thf(prove_this_11, conjecture,
% 1.31/1.14 (~( ( ( multiply @ sk_c3 @ sk_c7 ) = ( sk_c4 ) ) |
% 1.31/1.14 ( ( inverse @ sk_c6 ) = ( sk_c5 ) ) ))).
% 1.31/1.14 thf(zf_stmt_4, negated_conjecture,
% 1.31/1.14 (( ( multiply @ sk_c3 @ sk_c7 ) = ( sk_c4 ) ) |
% 1.31/1.14 ( ( inverse @ sk_c6 ) = ( sk_c5 ) )),
% 1.31/1.14 inference('cnf.neg', [status(esa)], [prove_this_11])).
% 1.31/1.14 thf(zip_derived_cl13, plain,
% 1.31/1.14 ((((multiply @ sk_c3 @ sk_c7) = (sk_c4)) | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('cnf', [status(esa)], [zf_stmt_4])).
% 1.31/1.14 thf(zip_derived_cl170, plain,
% 1.31/1.14 ((((multiply @ identity @ sk_c7) = (sk_c4))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl165, zip_derived_cl13])).
% 1.31/1.14 thf(zip_derived_cl0, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_identity])).
% 1.31/1.14 thf(zip_derived_cl177, plain,
% 1.31/1.14 ((((sk_c7) = (sk_c4))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('demod', [status(thm)], [zip_derived_cl170, zip_derived_cl0])).
% 1.31/1.14 thf(zip_derived_cl178, plain,
% 1.31/1.14 ((((inverse @ sk_c6) = (sk_c5)) | ((sk_c7) = (sk_c4)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl177])).
% 1.31/1.14 thf(zip_derived_cl178, plain,
% 1.31/1.14 ((((inverse @ sk_c6) = (sk_c5)) | ((sk_c7) = (sk_c4)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl177])).
% 1.31/1.14 thf(zip_derived_cl125, plain,
% 1.31/1.14 ((((inverse @ sk_c6) = (sk_c5)) | ((identity) = (sk_c7)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl124])).
% 1.31/1.14 thf(prove_this_10, conjecture,
% 1.31/1.14 (~( ( ( multiply @ sk_c7 @ sk_c4 ) = ( sk_c6 ) ) |
% 1.31/1.14 ( ( inverse @ sk_c6 ) = ( sk_c5 ) ) ))).
% 1.31/1.14 thf(zf_stmt_5, negated_conjecture,
% 1.31/1.14 (( ( multiply @ sk_c7 @ sk_c4 ) = ( sk_c6 ) ) |
% 1.31/1.14 ( ( inverse @ sk_c6 ) = ( sk_c5 ) )),
% 1.31/1.14 inference('cnf.neg', [status(esa)], [prove_this_10])).
% 1.31/1.14 thf(zip_derived_cl12, plain,
% 1.31/1.14 ((((multiply @ sk_c7 @ sk_c4) = (sk_c6)) | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('cnf', [status(esa)], [zf_stmt_5])).
% 1.31/1.14 thf(zip_derived_cl132, plain,
% 1.31/1.14 ((((multiply @ identity @ sk_c4) = (sk_c6))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl125, zip_derived_cl12])).
% 1.31/1.14 thf(zip_derived_cl138, plain,
% 1.31/1.14 ((((inverse @ sk_c6) = (sk_c5))
% 1.31/1.14 | ((multiply @ identity @ sk_c4) = (sk_c6)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl132])).
% 1.31/1.14 thf(zip_derived_cl0, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_identity])).
% 1.31/1.14 thf(zip_derived_cl148, plain,
% 1.31/1.14 ((((sk_c6) = (sk_c4)) | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl138, zip_derived_cl0])).
% 1.31/1.14 thf(zip_derived_cl189, plain,
% 1.31/1.14 ((((sk_c6) = (sk_c7))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl178, zip_derived_cl148])).
% 1.31/1.14 thf(zip_derived_cl193, plain,
% 1.31/1.14 ((((inverse @ sk_c6) = (sk_c5)) | ((sk_c6) = (sk_c7)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl189])).
% 1.31/1.14 thf(zip_derived_cl14, plain,
% 1.31/1.14 ((((inverse @ sk_c3) = (sk_c7)) | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('cnf', [status(esa)], [zf_stmt_3])).
% 1.31/1.14 thf(zip_derived_cl13, plain,
% 1.31/1.14 ((((multiply @ sk_c3 @ sk_c7) = (sk_c4)) | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('cnf', [status(esa)], [zf_stmt_4])).
% 1.31/1.14 thf(zip_derived_cl61, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i]:
% 1.31/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.31/1.14 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 1.31/1.14 thf(zip_derived_cl88, plain,
% 1.31/1.14 ((((sk_c7) = (multiply @ (inverse @ sk_c3) @ sk_c4))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl61])).
% 1.31/1.14 thf(zip_derived_cl625, plain,
% 1.31/1.14 ((((sk_c7) = (multiply @ sk_c7 @ sk_c4))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl88])).
% 1.31/1.14 thf(zip_derived_cl636, plain,
% 1.31/1.14 ((((inverse @ sk_c6) = (sk_c5)) | ((sk_c7) = (multiply @ sk_c7 @ sk_c4)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl625])).
% 1.31/1.14 thf(zip_derived_cl1003, plain,
% 1.31/1.14 ((((sk_c7) = (multiply @ sk_c6 @ sk_c4))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl193, zip_derived_cl636])).
% 1.31/1.14 thf(zip_derived_cl1016, plain,
% 1.31/1.14 ((((inverse @ sk_c6) = (sk_c5)) | ((sk_c7) = (multiply @ sk_c6 @ sk_c4)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl1003])).
% 1.31/1.14 thf(zip_derived_cl1624, plain,
% 1.31/1.14 ((((sk_c7) = (multiply @ sk_c6 @ sk_c7))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl178, zip_derived_cl1016])).
% 1.31/1.14 thf(zip_derived_cl1633, plain,
% 1.31/1.14 ((((inverse @ sk_c6) = (sk_c5)) | ((sk_c7) = (multiply @ sk_c6 @ sk_c7)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl1624])).
% 1.31/1.14 thf(prove_this_7, conjecture,
% 1.31/1.14 (~( ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c5 ) ) |
% 1.31/1.14 ( ( inverse @ sk_c6 ) = ( sk_c5 ) ) ))).
% 1.31/1.14 thf(zf_stmt_6, negated_conjecture,
% 1.31/1.14 (( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c5 ) ) |
% 1.31/1.14 ( ( inverse @ sk_c6 ) = ( sk_c5 ) )),
% 1.31/1.14 inference('cnf.neg', [status(esa)], [prove_this_7])).
% 1.31/1.14 thf(zip_derived_cl9, plain,
% 1.31/1.14 ((((multiply @ sk_c6 @ sk_c7) = (sk_c5)) | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('cnf', [status(esa)], [zf_stmt_6])).
% 1.31/1.14 thf(zip_derived_cl1933, plain,
% 1.31/1.14 ((((sk_c7) = (sk_c5))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl1633, zip_derived_cl9])).
% 1.31/1.14 thf(zip_derived_cl1950, plain,
% 1.31/1.14 ((((inverse @ sk_c6) = (sk_c5)) | ((sk_c7) = (sk_c5)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl1933])).
% 1.31/1.14 thf(zip_derived_cl193, plain,
% 1.31/1.14 ((((inverse @ sk_c6) = (sk_c5)) | ((sk_c6) = (sk_c7)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl189])).
% 1.31/1.14 thf(zip_derived_cl31, plain,
% 1.31/1.14 ((((multiply @ sk_c7 @ sk_c3) = (identity))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl1])).
% 1.31/1.14 thf(zip_derived_cl214, plain,
% 1.31/1.14 ((((multiply @ sk_c6 @ sk_c3) = (identity))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl193, zip_derived_cl31])).
% 1.31/1.14 thf(zip_derived_cl221, plain,
% 1.31/1.14 ((((inverse @ sk_c6) = (sk_c5))
% 1.31/1.14 | ((multiply @ sk_c6 @ sk_c3) = (identity)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl214])).
% 1.31/1.14 thf(zip_derived_cl61, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i]:
% 1.31/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.31/1.14 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 1.31/1.14 thf(zip_derived_cl774, plain,
% 1.31/1.14 ((((sk_c3) = (multiply @ (inverse @ sk_c6) @ identity))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl221, zip_derived_cl61])).
% 1.31/1.14 thf(zip_derived_cl14, plain,
% 1.31/1.14 ((((inverse @ sk_c3) = (sk_c7)) | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('cnf', [status(esa)], [zf_stmt_3])).
% 1.31/1.14 thf(zip_derived_cl875, plain,
% 1.31/1.14 ((((inverse @ (multiply @ (inverse @ sk_c6) @ identity)) = (sk_c7))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl774, zip_derived_cl14])).
% 1.31/1.14 thf(zip_derived_cl893, plain,
% 1.31/1.14 ((((inverse @ sk_c6) = (sk_c5))
% 1.31/1.14 | ((inverse @ (multiply @ (inverse @ sk_c6) @ identity)) = (sk_c7)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl875])).
% 1.31/1.14 thf(zip_derived_cl3280, plain,
% 1.31/1.14 ((((inverse @ (multiply @ (inverse @ sk_c6) @ identity)) = (sk_c5))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl1950, zip_derived_cl893])).
% 1.31/1.14 thf(zip_derived_cl3290, plain,
% 1.31/1.14 ((((inverse @ sk_c6) = (sk_c5))
% 1.31/1.14 | ((inverse @ (multiply @ (inverse @ sk_c6) @ identity)) = (sk_c5)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl3280])).
% 1.31/1.14 thf(zip_derived_cl5932, plain,
% 1.31/1.14 ((((inverse @ (multiply @ (inverse @ sk_c6) @ identity))
% 1.31/1.14 != (inverse @ sk_c6))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('eq_fact', [status(thm)], [zip_derived_cl3290])).
% 1.31/1.14 thf(zip_derived_cl774, plain,
% 1.31/1.14 ((((sk_c3) = (multiply @ (inverse @ sk_c6) @ identity))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl221, zip_derived_cl61])).
% 1.31/1.14 thf(zip_derived_cl125, plain,
% 1.31/1.14 ((((inverse @ sk_c6) = (sk_c5)) | ((identity) = (sk_c7)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl124])).
% 1.31/1.14 thf(zip_derived_cl13, plain,
% 1.31/1.14 ((((multiply @ sk_c3 @ sk_c7) = (sk_c4)) | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('cnf', [status(esa)], [zf_stmt_4])).
% 1.31/1.14 thf(zip_derived_cl133, plain,
% 1.31/1.14 ((((multiply @ sk_c3 @ identity) = (sk_c4))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl125, zip_derived_cl13])).
% 1.31/1.14 thf(zip_derived_cl139, plain,
% 1.31/1.14 ((((inverse @ sk_c6) = (sk_c5))
% 1.31/1.14 | ((multiply @ sk_c3 @ identity) = (sk_c4)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl133])).
% 1.31/1.14 thf(zip_derived_cl881, plain,
% 1.31/1.14 ((((multiply @ (multiply @ (inverse @ sk_c6) @ identity) @ identity)
% 1.31/1.14 = (sk_c4))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl774, zip_derived_cl139])).
% 1.31/1.14 thf(zip_derived_cl2, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.31/1.14 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.31/1.14 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.31/1.14 inference('cnf', [status(esa)], [associativity])).
% 1.31/1.14 thf(zip_derived_cl0, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_identity])).
% 1.31/1.14 thf(zip_derived_cl897, plain,
% 1.31/1.14 ((((multiply @ (inverse @ sk_c6) @ identity) = (sk_c4))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('demod', [status(thm)],
% 1.31/1.14 [zip_derived_cl881, zip_derived_cl2, zip_derived_cl0])).
% 1.31/1.14 thf(zip_derived_cl898, plain,
% 1.31/1.14 ((((inverse @ sk_c6) = (sk_c5))
% 1.31/1.14 | ((multiply @ (inverse @ sk_c6) @ identity) = (sk_c4)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl897])).
% 1.31/1.14 thf(zip_derived_cl138, plain,
% 1.31/1.14 ((((inverse @ sk_c6) = (sk_c5))
% 1.31/1.14 | ((multiply @ identity @ sk_c4) = (sk_c6)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl132])).
% 1.31/1.14 thf(zip_derived_cl959, plain,
% 1.31/1.14 ((((multiply @ identity @ (multiply @ (inverse @ sk_c6) @ identity))
% 1.31/1.14 = (sk_c6))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl898, zip_derived_cl138])).
% 1.31/1.14 thf(zip_derived_cl0, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_identity])).
% 1.31/1.14 thf(zip_derived_cl972, plain,
% 1.31/1.14 ((((multiply @ (inverse @ sk_c6) @ identity) = (sk_c6))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5))
% 1.31/1.14 | ((inverse @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('demod', [status(thm)], [zip_derived_cl959, zip_derived_cl0])).
% 1.31/1.14 thf(zip_derived_cl973, plain,
% 1.31/1.14 ((((inverse @ sk_c6) = (sk_c5))
% 1.31/1.14 | ((multiply @ (inverse @ sk_c6) @ identity) = (sk_c6)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl972])).
% 1.31/1.14 thf(zip_derived_cl5966, plain, (((inverse @ sk_c6) = (sk_c5))),
% 1.31/1.14 inference('clc', [status(thm)], [zip_derived_cl5932, zip_derived_cl973])).
% 1.31/1.14 thf(zip_derived_cl5979, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.14 (((inverse @ X0) != (multiply @ sk_c6 @ (inverse @ sk_c6)))
% 1.31/1.14 | ((multiply @ X0 @ (multiply @ sk_c6 @ (inverse @ sk_c6))) != (X1))
% 1.31/1.14 | ((multiply @ sk_c6 @ (multiply @ (inverse @ sk_c6) @ X1))
% 1.31/1.14 != (sk_c6))
% 1.31/1.14 | ((inverse @ X2) != (sk_c6))
% 1.31/1.14 | ((multiply @ X2 @ sk_c6) != (multiply @ sk_c6 @ (inverse @ sk_c6)))
% 1.31/1.14 | ((multiply @ sk_c6 @ (multiply @ sk_c6 @ (inverse @ sk_c6)))
% 1.31/1.14 != (inverse @ sk_c6))
% 1.31/1.14 | ((inverse @ X3) != (sk_c6))
% 1.31/1.14 | ((multiply @ X3 @ sk_c6) != (inverse @ sk_c6))
% 1.31/1.14 | ((inverse @ sk_c6) != (inverse @ sk_c6))
% 1.31/1.14 | ((multiply @ sk_c6 @ (inverse @ sk_c6)) != (sk_c7)))),
% 1.31/1.14 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl5966])).
% 1.31/1.14 thf(zip_derived_cl5980, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.14 (((multiply @ sk_c6 @ (inverse @ sk_c6)) != (sk_c7))
% 1.31/1.14 | ((multiply @ X3 @ sk_c6) != (inverse @ sk_c6))
% 1.31/1.14 | ((inverse @ X3) != (sk_c6))
% 1.31/1.14 | ((multiply @ sk_c6 @ (multiply @ sk_c6 @ (inverse @ sk_c6)))
% 1.31/1.14 != (inverse @ sk_c6))
% 1.31/1.14 | ((multiply @ X2 @ sk_c6) != (multiply @ sk_c6 @ (inverse @ sk_c6)))
% 1.31/1.14 | ((inverse @ X2) != (sk_c6))
% 1.31/1.14 | ((multiply @ sk_c6 @ (multiply @ (inverse @ sk_c6) @ X1))
% 1.31/1.14 != (sk_c6))
% 1.31/1.14 | ((multiply @ X0 @ (multiply @ sk_c6 @ (inverse @ sk_c6))) != (X1))
% 1.31/1.14 | ((inverse @ X0) != (multiply @ sk_c6 @ (inverse @ sk_c6))))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl5979])).
% 1.31/1.14 thf(zip_derived_cl1, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_inverse])).
% 1.31/1.14 thf(zip_derived_cl61, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i]:
% 1.31/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.31/1.14 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 1.31/1.14 thf(zip_derived_cl73, plain,
% 1.31/1.14 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl61])).
% 1.31/1.14 thf(zip_derived_cl61, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i]:
% 1.31/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.31/1.14 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 1.31/1.14 thf(zip_derived_cl61, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i]:
% 1.31/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.31/1.14 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 1.31/1.14 thf(zip_derived_cl70, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i]:
% 1.31/1.14 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl61, zip_derived_cl61])).
% 1.31/1.14 thf(zip_derived_cl6221, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl73, zip_derived_cl70])).
% 1.31/1.14 thf(zip_derived_cl73, plain,
% 1.31/1.14 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl61])).
% 1.31/1.14 thf(zip_derived_cl6254, plain,
% 1.31/1.14 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl6221, zip_derived_cl73])).
% 1.31/1.14 thf(zip_derived_cl1, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_inverse])).
% 1.31/1.14 thf(zip_derived_cl6328, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl6254, zip_derived_cl1])).
% 1.31/1.14 thf(zip_derived_cl6328, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl6254, zip_derived_cl1])).
% 1.31/1.14 thf(zip_derived_cl6221, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl73, zip_derived_cl70])).
% 1.31/1.14 thf(zip_derived_cl6328, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl6254, zip_derived_cl1])).
% 1.31/1.14 thf(zip_derived_cl6328, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl6254, zip_derived_cl1])).
% 1.31/1.14 thf(zip_derived_cl6221, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl73, zip_derived_cl70])).
% 1.31/1.14 thf(zip_derived_cl6328, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl6254, zip_derived_cl1])).
% 1.31/1.14 thf(zip_derived_cl6345, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.14 (((identity) != (sk_c7))
% 1.31/1.14 | ((multiply @ X3 @ sk_c6) != (inverse @ sk_c6))
% 1.31/1.14 | ((inverse @ X3) != (sk_c6))
% 1.31/1.14 | ((sk_c6) != (inverse @ sk_c6))
% 1.31/1.14 | ((multiply @ X2 @ sk_c6) != (identity))
% 1.31/1.14 | ((inverse @ X2) != (sk_c6))
% 1.31/1.14 | ((multiply @ sk_c6 @ (multiply @ (inverse @ sk_c6) @ X1))
% 1.31/1.14 != (sk_c6))
% 1.31/1.14 | ((X0) != (X1))
% 1.31/1.14 | ((inverse @ X0) != (identity)))),
% 1.31/1.14 inference('demod', [status(thm)],
% 1.31/1.14 [zip_derived_cl5980, zip_derived_cl6328, zip_derived_cl6328,
% 1.31/1.14 zip_derived_cl6221, zip_derived_cl6328, zip_derived_cl6328,
% 1.31/1.14 zip_derived_cl6221, zip_derived_cl6328])).
% 1.31/1.14 thf(zip_derived_cl6346, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.14 (((identity) != (sk_c7))
% 1.31/1.14 | ((multiply @ X3 @ sk_c6) != (sk_c6))
% 1.31/1.14 | ((inverse @ X3) != (sk_c6))
% 1.31/1.14 | ((sk_c6) != (inverse @ sk_c6))
% 1.31/1.14 | ((multiply @ X2 @ sk_c6) != (identity))
% 1.31/1.14 | ((inverse @ X2) != (sk_c6))
% 1.31/1.14 | ((multiply @ sk_c6 @ (multiply @ sk_c6 @ X1)) != (sk_c6))
% 1.31/1.14 | ((X0) != (X1))
% 1.31/1.14 | ((inverse @ X0) != (identity)))),
% 1.31/1.14 inference('local_rewriting', [status(thm)], [zip_derived_cl6345])).
% 1.31/1.14 thf(prove_this_3, conjecture,
% 1.31/1.14 (~( ( ( inverse @ sk_c2 ) = ( sk_c6 ) ) |
% 1.31/1.14 ( ( multiply @ sk_c6 @ sk_c5 ) = ( sk_c7 ) ) ))).
% 1.31/1.14 thf(zf_stmt_7, negated_conjecture,
% 1.31/1.14 (( ( inverse @ sk_c2 ) = ( sk_c6 ) ) |
% 1.31/1.14 ( ( multiply @ sk_c6 @ sk_c5 ) = ( sk_c7 ) )),
% 1.31/1.14 inference('cnf.neg', [status(esa)], [prove_this_3])).
% 1.31/1.14 thf(zip_derived_cl5, plain,
% 1.31/1.14 ((((inverse @ sk_c2) = (sk_c6)) | ((multiply @ sk_c6 @ sk_c5) = (sk_c7)))),
% 1.31/1.14 inference('cnf', [status(esa)], [zf_stmt_7])).
% 1.31/1.14 thf(zip_derived_cl1, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_inverse])).
% 1.31/1.14 thf(zip_derived_cl29, plain,
% 1.31/1.14 ((((multiply @ sk_c6 @ sk_c2) = (identity))
% 1.31/1.14 | ((multiply @ sk_c6 @ sk_c5) = (sk_c7)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl1])).
% 1.31/1.14 thf(zip_derived_cl61, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i]:
% 1.31/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.31/1.14 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 1.31/1.14 thf(zip_derived_cl77, plain,
% 1.31/1.14 ((((sk_c2) = (multiply @ (inverse @ sk_c6) @ identity))
% 1.31/1.14 | ((multiply @ sk_c6 @ sk_c5) = (sk_c7)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl29, zip_derived_cl61])).
% 1.31/1.14 thf(prove_this_2, conjecture,
% 1.31/1.14 (~( ( ( multiply @ sk_c2 @ sk_c6 ) = ( sk_c7 ) ) |
% 1.31/1.14 ( ( multiply @ sk_c6 @ sk_c5 ) = ( sk_c7 ) ) ))).
% 1.31/1.14 thf(zf_stmt_8, negated_conjecture,
% 1.31/1.14 (( ( multiply @ sk_c2 @ sk_c6 ) = ( sk_c7 ) ) |
% 1.31/1.14 ( ( multiply @ sk_c6 @ sk_c5 ) = ( sk_c7 ) )),
% 1.31/1.14 inference('cnf.neg', [status(esa)], [prove_this_2])).
% 1.31/1.14 thf(zip_derived_cl4, plain,
% 1.31/1.14 ((((multiply @ sk_c2 @ sk_c6) = (sk_c7))
% 1.31/1.14 | ((multiply @ sk_c6 @ sk_c5) = (sk_c7)))),
% 1.31/1.14 inference('cnf', [status(esa)], [zf_stmt_8])).
% 1.31/1.14 thf(zip_derived_cl471, plain,
% 1.31/1.14 ((((multiply @ (multiply @ (inverse @ sk_c6) @ identity) @ sk_c6)
% 1.31/1.14 = (sk_c7))
% 1.31/1.14 | ((multiply @ sk_c6 @ sk_c5) = (sk_c7))
% 1.31/1.14 | ((multiply @ sk_c6 @ sk_c5) = (sk_c7)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl77, zip_derived_cl4])).
% 1.31/1.14 thf(zip_derived_cl2, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.31/1.14 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.31/1.14 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.31/1.14 inference('cnf', [status(esa)], [associativity])).
% 1.31/1.14 thf(zip_derived_cl0, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_identity])).
% 1.31/1.14 thf(zip_derived_cl1, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_inverse])).
% 1.31/1.14 thf(zip_derived_cl477, plain,
% 1.31/1.14 ((((identity) = (sk_c7))
% 1.31/1.14 | ((multiply @ sk_c6 @ sk_c5) = (sk_c7))
% 1.31/1.14 | ((multiply @ sk_c6 @ sk_c5) = (sk_c7)))),
% 1.31/1.14 inference('demod', [status(thm)],
% 1.31/1.14 [zip_derived_cl471, zip_derived_cl2, zip_derived_cl0,
% 1.31/1.14 zip_derived_cl1])).
% 1.31/1.14 thf(zip_derived_cl478, plain,
% 1.31/1.14 ((((multiply @ sk_c6 @ sk_c5) = (sk_c7)) | ((identity) = (sk_c7)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl477])).
% 1.31/1.14 thf(zip_derived_cl5966, plain, (((inverse @ sk_c6) = (sk_c5))),
% 1.31/1.14 inference('clc', [status(thm)], [zip_derived_cl5932, zip_derived_cl973])).
% 1.31/1.14 thf(zip_derived_cl5997, plain,
% 1.31/1.14 ((((multiply @ sk_c6 @ (inverse @ sk_c6)) = (sk_c7))
% 1.31/1.14 | ((identity) = (sk_c7)))),
% 1.31/1.14 inference('demod', [status(thm)], [zip_derived_cl478, zip_derived_cl5966])).
% 1.31/1.14 thf(zip_derived_cl6328, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl6254, zip_derived_cl1])).
% 1.31/1.14 thf(zip_derived_cl6349, plain,
% 1.31/1.14 ((((identity) = (sk_c7)) | ((identity) = (sk_c7)))),
% 1.31/1.14 inference('demod', [status(thm)],
% 1.31/1.14 [zip_derived_cl5997, zip_derived_cl6328])).
% 1.31/1.14 thf(zip_derived_cl6350, plain, (((identity) = (sk_c7))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl6349])).
% 1.31/1.14 thf(zip_derived_cl6416, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.14 (((identity) != (identity))
% 1.31/1.14 | ((multiply @ X3 @ sk_c6) != (sk_c6))
% 1.31/1.14 | ((inverse @ X3) != (sk_c6))
% 1.31/1.14 | ((sk_c6) != (inverse @ sk_c6))
% 1.31/1.14 | ((multiply @ X2 @ sk_c6) != (identity))
% 1.31/1.14 | ((inverse @ X2) != (sk_c6))
% 1.31/1.14 | ((multiply @ sk_c6 @ (multiply @ sk_c6 @ X1)) != (sk_c6))
% 1.31/1.14 | ((X0) != (X1))
% 1.31/1.14 | ((inverse @ X0) != (identity)))),
% 1.31/1.14 inference('demod', [status(thm)],
% 1.31/1.14 [zip_derived_cl6346, zip_derived_cl6350])).
% 1.31/1.14 thf(zip_derived_cl6417, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.14 (((inverse @ X0) != (identity))
% 1.31/1.14 | ((X0) != (X1))
% 1.31/1.14 | ((multiply @ sk_c6 @ (multiply @ sk_c6 @ X1)) != (sk_c6))
% 1.31/1.14 | ((inverse @ X2) != (sk_c6))
% 1.31/1.14 | ((multiply @ X2 @ sk_c6) != (identity))
% 1.31/1.14 | ((sk_c6) != (inverse @ sk_c6))
% 1.31/1.14 | ((inverse @ X3) != (sk_c6))
% 1.31/1.14 | ((multiply @ X3 @ sk_c6) != (sk_c6)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl6416])).
% 1.31/1.14 thf(zip_derived_cl6418, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.31/1.14 (((multiply @ X0 @ sk_c6) != (sk_c6))
% 1.31/1.14 | ((inverse @ X0) != (sk_c6))
% 1.31/1.14 | ((sk_c6) != (inverse @ sk_c6))
% 1.31/1.14 | ((multiply @ X1 @ sk_c6) != (identity))
% 1.31/1.14 | ((inverse @ X1) != (sk_c6))
% 1.31/1.14 | ((multiply @ sk_c6 @ (multiply @ sk_c6 @ X2)) != (sk_c6))
% 1.31/1.14 | ((inverse @ X2) != (identity)))),
% 1.31/1.14 inference('eq_res', [status(thm)], [zip_derived_cl6417])).
% 1.31/1.14 thf(prove_this_22, conjecture,
% 1.31/1.14 (~( ( ( multiply @ sk_c7 @ sk_c4 ) = ( sk_c6 ) ) |
% 1.31/1.14 ( ( inverse @ sk_c1 ) = ( sk_c6 ) ) ))).
% 1.31/1.14 thf(zf_stmt_9, negated_conjecture,
% 1.31/1.14 (( ( multiply @ sk_c7 @ sk_c4 ) = ( sk_c6 ) ) |
% 1.31/1.14 ( ( inverse @ sk_c1 ) = ( sk_c6 ) )),
% 1.31/1.14 inference('cnf.neg', [status(esa)], [prove_this_22])).
% 1.31/1.14 thf(zip_derived_cl24, plain,
% 1.31/1.14 ((((multiply @ sk_c7 @ sk_c4) = (sk_c6)) | ((inverse @ sk_c1) = (sk_c6)))),
% 1.31/1.14 inference('cnf', [status(esa)], [zf_stmt_9])).
% 1.31/1.14 thf(zip_derived_cl6350, plain, (((identity) = (sk_c7))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl6349])).
% 1.31/1.14 thf(zip_derived_cl0, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_identity])).
% 1.31/1.14 thf(zip_derived_cl6375, plain,
% 1.31/1.14 ((((sk_c4) = (sk_c6)) | ((inverse @ sk_c1) = (sk_c6)))),
% 1.31/1.14 inference('demod', [status(thm)],
% 1.31/1.14 [zip_derived_cl24, zip_derived_cl6350, zip_derived_cl0])).
% 1.31/1.14 thf(zip_derived_cl6254, plain,
% 1.31/1.14 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl6221, zip_derived_cl73])).
% 1.31/1.14 thf(zip_derived_cl6422, plain,
% 1.31/1.14 ((((sk_c1) = (inverse @ sk_c6)) | ((sk_c4) = (sk_c6)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl6375, zip_derived_cl6254])).
% 1.31/1.14 thf(prove_this_16, conjecture,
% 1.31/1.14 (~( ( ( multiply @ sk_c7 @ sk_c4 ) = ( sk_c6 ) ) |
% 1.31/1.14 ( ( multiply @ sk_c1 @ sk_c6 ) = ( sk_c5 ) ) ))).
% 1.31/1.14 thf(zf_stmt_10, negated_conjecture,
% 1.31/1.14 (( ( multiply @ sk_c7 @ sk_c4 ) = ( sk_c6 ) ) |
% 1.31/1.14 ( ( multiply @ sk_c1 @ sk_c6 ) = ( sk_c5 ) )),
% 1.31/1.14 inference('cnf.neg', [status(esa)], [prove_this_16])).
% 1.31/1.14 thf(zip_derived_cl18, plain,
% 1.31/1.14 ((((multiply @ sk_c7 @ sk_c4) = (sk_c6))
% 1.31/1.14 | ((multiply @ sk_c1 @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('cnf', [status(esa)], [zf_stmt_10])).
% 1.31/1.14 thf(zip_derived_cl6350, plain, (((identity) = (sk_c7))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl6349])).
% 1.31/1.14 thf(zip_derived_cl0, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_identity])).
% 1.31/1.14 thf(zip_derived_cl5966, plain, (((inverse @ sk_c6) = (sk_c5))),
% 1.31/1.14 inference('clc', [status(thm)], [zip_derived_cl5932, zip_derived_cl973])).
% 1.31/1.14 thf(zip_derived_cl7331, plain,
% 1.31/1.14 ((((sk_c4) = (sk_c6)) | ((multiply @ sk_c1 @ sk_c6) = (inverse @ sk_c6)))),
% 1.31/1.14 inference('demod', [status(thm)],
% 1.31/1.14 [zip_derived_cl18, zip_derived_cl6350, zip_derived_cl0,
% 1.31/1.14 zip_derived_cl5966])).
% 1.31/1.14 thf(zip_derived_cl7342, plain,
% 1.31/1.14 ((((multiply @ (inverse @ sk_c6) @ sk_c6) = (inverse @ sk_c6))
% 1.31/1.14 | ((sk_c4) = (sk_c6))
% 1.31/1.14 | ((sk_c4) = (sk_c6)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl6422, zip_derived_cl7331])).
% 1.31/1.14 thf(zip_derived_cl1, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_inverse])).
% 1.31/1.14 thf(zip_derived_cl7348, plain,
% 1.31/1.14 ((((identity) = (inverse @ sk_c6))
% 1.31/1.14 | ((sk_c4) = (sk_c6))
% 1.31/1.14 | ((sk_c4) = (sk_c6)))),
% 1.31/1.14 inference('demod', [status(thm)], [zip_derived_cl7342, zip_derived_cl1])).
% 1.31/1.14 thf(zip_derived_cl7349, plain,
% 1.31/1.14 ((((sk_c4) = (sk_c6)) | ((identity) = (inverse @ sk_c6)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl7348])).
% 1.31/1.14 thf(prove_this_23, conjecture,
% 1.31/1.14 (~( ( ( multiply @ sk_c3 @ sk_c7 ) = ( sk_c4 ) ) |
% 1.31/1.14 ( ( inverse @ sk_c1 ) = ( sk_c6 ) ) ))).
% 1.31/1.14 thf(zf_stmt_11, negated_conjecture,
% 1.31/1.14 (( ( multiply @ sk_c3 @ sk_c7 ) = ( sk_c4 ) ) |
% 1.31/1.14 ( ( inverse @ sk_c1 ) = ( sk_c6 ) )),
% 1.31/1.14 inference('cnf.neg', [status(esa)], [prove_this_23])).
% 1.31/1.14 thf(zip_derived_cl25, plain,
% 1.31/1.14 ((((multiply @ sk_c3 @ sk_c7) = (sk_c4)) | ((inverse @ sk_c1) = (sk_c6)))),
% 1.31/1.14 inference('cnf', [status(esa)], [zf_stmt_11])).
% 1.31/1.14 thf(zip_derived_cl73, plain,
% 1.31/1.14 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl61])).
% 1.31/1.14 thf(zip_derived_cl1327, plain,
% 1.31/1.14 ((((sk_c1) = (multiply @ (inverse @ sk_c6) @ identity))
% 1.31/1.14 | ((multiply @ sk_c3 @ sk_c7) = (sk_c4)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl25, zip_derived_cl73])).
% 1.31/1.14 thf(prove_this_17, conjecture,
% 1.31/1.14 (~( ( ( multiply @ sk_c3 @ sk_c7 ) = ( sk_c4 ) ) |
% 1.31/1.14 ( ( multiply @ sk_c1 @ sk_c6 ) = ( sk_c5 ) ) ))).
% 1.31/1.14 thf(zf_stmt_12, negated_conjecture,
% 1.31/1.14 (( ( multiply @ sk_c3 @ sk_c7 ) = ( sk_c4 ) ) |
% 1.31/1.14 ( ( multiply @ sk_c1 @ sk_c6 ) = ( sk_c5 ) )),
% 1.31/1.14 inference('cnf.neg', [status(esa)], [prove_this_17])).
% 1.31/1.14 thf(zip_derived_cl19, plain,
% 1.31/1.14 ((((multiply @ sk_c3 @ sk_c7) = (sk_c4))
% 1.31/1.14 | ((multiply @ sk_c1 @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('cnf', [status(esa)], [zf_stmt_12])).
% 1.31/1.14 thf(zip_derived_cl3859, plain,
% 1.31/1.14 ((((multiply @ (multiply @ (inverse @ sk_c6) @ identity) @ sk_c6)
% 1.31/1.14 = (sk_c5))
% 1.31/1.14 | ((multiply @ sk_c3 @ sk_c7) = (sk_c4))
% 1.31/1.14 | ((multiply @ sk_c3 @ sk_c7) = (sk_c4)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl1327, zip_derived_cl19])).
% 1.31/1.14 thf(zip_derived_cl2, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.31/1.14 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.31/1.14 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.31/1.14 inference('cnf', [status(esa)], [associativity])).
% 1.31/1.14 thf(zip_derived_cl0, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_identity])).
% 1.31/1.14 thf(zip_derived_cl1, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_inverse])).
% 1.31/1.14 thf(zip_derived_cl3862, plain,
% 1.31/1.14 ((((identity) = (sk_c5))
% 1.31/1.14 | ((multiply @ sk_c3 @ sk_c7) = (sk_c4))
% 1.31/1.14 | ((multiply @ sk_c3 @ sk_c7) = (sk_c4)))),
% 1.31/1.14 inference('demod', [status(thm)],
% 1.31/1.14 [zip_derived_cl3859, zip_derived_cl2, zip_derived_cl0,
% 1.31/1.14 zip_derived_cl1])).
% 1.31/1.14 thf(zip_derived_cl3863, plain,
% 1.31/1.14 ((((multiply @ sk_c3 @ sk_c7) = (sk_c4)) | ((identity) = (sk_c5)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl3862])).
% 1.31/1.14 thf(zip_derived_cl5966, plain, (((inverse @ sk_c6) = (sk_c5))),
% 1.31/1.14 inference('clc', [status(thm)], [zip_derived_cl5932, zip_derived_cl973])).
% 1.31/1.14 thf(zip_derived_cl6024, plain,
% 1.31/1.14 ((((multiply @ sk_c3 @ sk_c7) = (sk_c4))
% 1.31/1.14 | ((identity) = (inverse @ sk_c6)))),
% 1.31/1.14 inference('demod', [status(thm)],
% 1.31/1.14 [zip_derived_cl3863, zip_derived_cl5966])).
% 1.31/1.14 thf(zip_derived_cl6350, plain, (((identity) = (sk_c7))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl6349])).
% 1.31/1.14 thf(zip_derived_cl6221, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl73, zip_derived_cl70])).
% 1.31/1.14 thf(zip_derived_cl6384, plain,
% 1.31/1.14 ((((sk_c3) = (sk_c4)) | ((identity) = (inverse @ sk_c6)))),
% 1.31/1.14 inference('demod', [status(thm)],
% 1.31/1.14 [zip_derived_cl6024, zip_derived_cl6350, zip_derived_cl6221])).
% 1.31/1.14 thf(prove_this_24, conjecture,
% 1.31/1.14 (~( ( ( inverse @ sk_c3 ) = ( sk_c7 ) ) |
% 1.31/1.14 ( ( inverse @ sk_c1 ) = ( sk_c6 ) ) ))).
% 1.31/1.14 thf(zf_stmt_13, negated_conjecture,
% 1.31/1.14 (( ( inverse @ sk_c3 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c6 ) )),
% 1.31/1.14 inference('cnf.neg', [status(esa)], [prove_this_24])).
% 1.31/1.14 thf(zip_derived_cl26, plain,
% 1.31/1.14 ((((inverse @ sk_c3) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c6)))),
% 1.31/1.14 inference('cnf', [status(esa)], [zf_stmt_13])).
% 1.31/1.14 thf(zip_derived_cl1, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_inverse])).
% 1.31/1.14 thf(zip_derived_cl34, plain,
% 1.31/1.14 ((((multiply @ sk_c6 @ sk_c1) = (identity))
% 1.31/1.14 | ((inverse @ sk_c3) = (sk_c7)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl1])).
% 1.31/1.14 thf(zip_derived_cl61, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i]:
% 1.31/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.31/1.14 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 1.31/1.14 thf(zip_derived_cl80, plain,
% 1.31/1.14 ((((sk_c1) = (multiply @ (inverse @ sk_c6) @ identity))
% 1.31/1.14 | ((inverse @ sk_c3) = (sk_c7)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl34, zip_derived_cl61])).
% 1.31/1.14 thf(zip_derived_cl6221, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl73, zip_derived_cl70])).
% 1.31/1.14 thf(zip_derived_cl6236, plain,
% 1.31/1.14 ((((sk_c1) = (inverse @ sk_c6)) | ((inverse @ sk_c3) = (sk_c7)))),
% 1.31/1.14 inference('demod', [status(thm)], [zip_derived_cl80, zip_derived_cl6221])).
% 1.31/1.14 thf(prove_this_18, conjecture,
% 1.31/1.14 (~( ( ( inverse @ sk_c3 ) = ( sk_c7 ) ) |
% 1.31/1.14 ( ( multiply @ sk_c1 @ sk_c6 ) = ( sk_c5 ) ) ))).
% 1.31/1.14 thf(zf_stmt_14, negated_conjecture,
% 1.31/1.14 (( ( inverse @ sk_c3 ) = ( sk_c7 ) ) |
% 1.31/1.14 ( ( multiply @ sk_c1 @ sk_c6 ) = ( sk_c5 ) )),
% 1.31/1.14 inference('cnf.neg', [status(esa)], [prove_this_18])).
% 1.31/1.14 thf(zip_derived_cl20, plain,
% 1.31/1.14 ((((inverse @ sk_c3) = (sk_c7)) | ((multiply @ sk_c1 @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('cnf', [status(esa)], [zf_stmt_14])).
% 1.31/1.14 thf(zip_derived_cl5966, plain, (((inverse @ sk_c6) = (sk_c5))),
% 1.31/1.14 inference('clc', [status(thm)], [zip_derived_cl5932, zip_derived_cl973])).
% 1.31/1.14 thf(zip_derived_cl5975, plain,
% 1.31/1.14 ((((inverse @ sk_c3) = (sk_c7))
% 1.31/1.14 | ((multiply @ sk_c1 @ sk_c6) = (inverse @ sk_c6)))),
% 1.31/1.14 inference('demod', [status(thm)], [zip_derived_cl20, zip_derived_cl5966])).
% 1.31/1.14 thf(zip_derived_cl6284, plain,
% 1.31/1.14 ((((multiply @ (inverse @ sk_c6) @ sk_c6) = (inverse @ sk_c6))
% 1.31/1.14 | ((inverse @ sk_c3) = (sk_c7))
% 1.31/1.14 | ((inverse @ sk_c3) = (sk_c7)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl6236, zip_derived_cl5975])).
% 1.31/1.14 thf(zip_derived_cl1, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_inverse])).
% 1.31/1.14 thf(zip_derived_cl6289, plain,
% 1.31/1.14 ((((identity) = (inverse @ sk_c6))
% 1.31/1.14 | ((inverse @ sk_c3) = (sk_c7))
% 1.31/1.14 | ((inverse @ sk_c3) = (sk_c7)))),
% 1.31/1.14 inference('demod', [status(thm)], [zip_derived_cl6284, zip_derived_cl1])).
% 1.31/1.14 thf(zip_derived_cl6290, plain,
% 1.31/1.14 ((((inverse @ sk_c3) = (sk_c7)) | ((identity) = (inverse @ sk_c6)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl6289])).
% 1.31/1.14 thf(zip_derived_cl6350, plain, (((identity) = (sk_c7))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl6349])).
% 1.31/1.14 thf(zip_derived_cl6450, plain,
% 1.31/1.14 ((((inverse @ sk_c3) = (identity)) | ((identity) = (inverse @ sk_c6)))),
% 1.31/1.14 inference('demod', [status(thm)],
% 1.31/1.14 [zip_derived_cl6290, zip_derived_cl6350])).
% 1.31/1.14 thf(zip_derived_cl6456, plain,
% 1.31/1.14 ((((inverse @ sk_c4) = (identity))
% 1.31/1.14 | ((identity) = (inverse @ sk_c6))
% 1.31/1.14 | ((identity) = (inverse @ sk_c6)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl6384, zip_derived_cl6450])).
% 1.31/1.14 thf(zip_derived_cl6459, plain,
% 1.31/1.14 ((((identity) = (inverse @ sk_c6)) | ((inverse @ sk_c4) = (identity)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl6456])).
% 1.31/1.14 thf(zip_derived_cl7354, plain,
% 1.31/1.14 ((((inverse @ sk_c6) = (identity))
% 1.31/1.14 | ((identity) = (inverse @ sk_c6))
% 1.31/1.14 | ((identity) = (inverse @ sk_c6)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl7349, zip_derived_cl6459])).
% 1.31/1.14 thf(zip_derived_cl7360, plain, (((inverse @ sk_c6) = (identity))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl7354])).
% 1.31/1.14 thf(zip_derived_cl7386, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.31/1.14 (((multiply @ X0 @ sk_c6) != (sk_c6))
% 1.31/1.14 | ((inverse @ X0) != (sk_c6))
% 1.31/1.14 | ((sk_c6) != (identity))
% 1.31/1.14 | ((multiply @ X1 @ sk_c6) != (identity))
% 1.31/1.14 | ((inverse @ X1) != (sk_c6))
% 1.31/1.14 | ((multiply @ sk_c6 @ (multiply @ sk_c6 @ X2)) != (sk_c6))
% 1.31/1.14 | ((inverse @ X2) != (identity)))),
% 1.31/1.14 inference('demod', [status(thm)],
% 1.31/1.14 [zip_derived_cl6418, zip_derived_cl7360])).
% 1.31/1.14 thf(zip_derived_cl7387, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.31/1.14 (((multiply @ X0 @ identity) != (identity))
% 1.31/1.14 | ((inverse @ X0) != (identity))
% 1.31/1.14 | ((sk_c6) != (identity))
% 1.31/1.14 | ((multiply @ X1 @ identity) != (identity))
% 1.31/1.14 | ((inverse @ X1) != (identity))
% 1.31/1.14 | ((multiply @ identity @ (multiply @ identity @ X2)) != (identity))
% 1.31/1.14 | ((inverse @ X2) != (identity)))),
% 1.31/1.14 inference('local_rewriting', [status(thm)], [zip_derived_cl7386])).
% 1.31/1.14 thf(zip_derived_cl6221, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl73, zip_derived_cl70])).
% 1.31/1.14 thf(zip_derived_cl6221, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl73, zip_derived_cl70])).
% 1.31/1.14 thf(zip_derived_cl0, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_identity])).
% 1.31/1.14 thf(zip_derived_cl0, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_identity])).
% 1.31/1.14 thf(zip_derived_cl7388, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.31/1.14 (((X0) != (identity))
% 1.31/1.14 | ((inverse @ X0) != (identity))
% 1.31/1.14 | ((sk_c6) != (identity))
% 1.31/1.14 | ((X1) != (identity))
% 1.31/1.14 | ((inverse @ X1) != (identity))
% 1.31/1.14 | ((X2) != (identity))
% 1.31/1.14 | ((inverse @ X2) != (identity)))),
% 1.31/1.14 inference('demod', [status(thm)],
% 1.31/1.14 [zip_derived_cl7387, zip_derived_cl6221, zip_derived_cl6221,
% 1.31/1.14 zip_derived_cl0, zip_derived_cl0])).
% 1.31/1.14 thf(prove_this_19, conjecture,
% 1.31/1.14 (~( ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c5 ) ) |
% 1.31/1.14 ( ( inverse @ sk_c1 ) = ( sk_c6 ) ) ))).
% 1.31/1.14 thf(zf_stmt_15, negated_conjecture,
% 1.31/1.14 (( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c5 ) ) |
% 1.31/1.14 ( ( inverse @ sk_c1 ) = ( sk_c6 ) )),
% 1.31/1.14 inference('cnf.neg', [status(esa)], [prove_this_19])).
% 1.31/1.14 thf(zip_derived_cl21, plain,
% 1.31/1.14 ((((multiply @ sk_c6 @ sk_c7) = (sk_c5)) | ((inverse @ sk_c1) = (sk_c6)))),
% 1.31/1.14 inference('cnf', [status(esa)], [zf_stmt_15])).
% 1.31/1.14 thf(zip_derived_cl5966, plain, (((inverse @ sk_c6) = (sk_c5))),
% 1.31/1.14 inference('clc', [status(thm)], [zip_derived_cl5932, zip_derived_cl973])).
% 1.31/1.14 thf(zip_derived_cl5976, plain,
% 1.31/1.14 ((((multiply @ sk_c6 @ sk_c7) = (inverse @ sk_c6))
% 1.31/1.14 | ((inverse @ sk_c1) = (sk_c6)))),
% 1.31/1.14 inference('demod', [status(thm)], [zip_derived_cl21, zip_derived_cl5966])).
% 1.31/1.14 thf(zip_derived_cl6350, plain, (((identity) = (sk_c7))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl6349])).
% 1.31/1.14 thf(zip_derived_cl6221, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl73, zip_derived_cl70])).
% 1.31/1.14 thf(zip_derived_cl6381, plain,
% 1.31/1.14 ((((sk_c6) = (inverse @ sk_c6)) | ((inverse @ sk_c1) = (sk_c6)))),
% 1.31/1.14 inference('demod', [status(thm)],
% 1.31/1.14 [zip_derived_cl5976, zip_derived_cl6350, zip_derived_cl6221])).
% 1.31/1.14 thf(zip_derived_cl6254, plain,
% 1.31/1.14 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl6221, zip_derived_cl73])).
% 1.31/1.14 thf(zip_derived_cl6488, plain,
% 1.31/1.14 ((((sk_c1) = (inverse @ sk_c6)) | ((sk_c6) = (inverse @ sk_c6)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl6381, zip_derived_cl6254])).
% 1.31/1.14 thf(prove_this_13, conjecture,
% 1.31/1.14 (~( ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c5 ) ) |
% 1.31/1.14 ( ( multiply @ sk_c1 @ sk_c6 ) = ( sk_c5 ) ) ))).
% 1.31/1.14 thf(zf_stmt_16, negated_conjecture,
% 1.31/1.14 (( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c5 ) ) |
% 1.31/1.14 ( ( multiply @ sk_c1 @ sk_c6 ) = ( sk_c5 ) )),
% 1.31/1.14 inference('cnf.neg', [status(esa)], [prove_this_13])).
% 1.31/1.14 thf(zip_derived_cl15, plain,
% 1.31/1.14 ((((multiply @ sk_c6 @ sk_c7) = (sk_c5))
% 1.31/1.14 | ((multiply @ sk_c1 @ sk_c6) = (sk_c5)))),
% 1.31/1.14 inference('cnf', [status(esa)], [zf_stmt_16])).
% 1.31/1.14 thf(zip_derived_cl6350, plain, (((identity) = (sk_c7))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl6349])).
% 1.31/1.14 thf(zip_derived_cl6221, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl73, zip_derived_cl70])).
% 1.31/1.14 thf(zip_derived_cl5966, plain, (((inverse @ sk_c6) = (sk_c5))),
% 1.31/1.14 inference('clc', [status(thm)], [zip_derived_cl5932, zip_derived_cl973])).
% 1.31/1.14 thf(zip_derived_cl5966, plain, (((inverse @ sk_c6) = (sk_c5))),
% 1.31/1.14 inference('clc', [status(thm)], [zip_derived_cl5932, zip_derived_cl973])).
% 1.31/1.14 thf(zip_derived_cl7018, plain,
% 1.31/1.14 ((((sk_c6) = (inverse @ sk_c6))
% 1.31/1.14 | ((multiply @ sk_c1 @ sk_c6) = (inverse @ sk_c6)))),
% 1.31/1.14 inference('demod', [status(thm)],
% 1.31/1.14 [zip_derived_cl15, zip_derived_cl6350, zip_derived_cl6221,
% 1.31/1.14 zip_derived_cl5966, zip_derived_cl5966])).
% 1.31/1.14 thf(zip_derived_cl7030, plain,
% 1.31/1.14 ((((multiply @ (inverse @ sk_c6) @ sk_c6) = (inverse @ sk_c6))
% 1.31/1.14 | ((sk_c6) = (inverse @ sk_c6))
% 1.31/1.14 | ((sk_c6) = (inverse @ sk_c6)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl6488, zip_derived_cl7018])).
% 1.31/1.14 thf(zip_derived_cl1, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_inverse])).
% 1.31/1.14 thf(zip_derived_cl7036, plain,
% 1.31/1.14 ((((identity) = (inverse @ sk_c6))
% 1.31/1.14 | ((sk_c6) = (inverse @ sk_c6))
% 1.31/1.14 | ((sk_c6) = (inverse @ sk_c6)))),
% 1.31/1.14 inference('demod', [status(thm)], [zip_derived_cl7030, zip_derived_cl1])).
% 1.31/1.14 thf(zip_derived_cl7037, plain,
% 1.31/1.14 ((((sk_c6) = (inverse @ sk_c6)) | ((identity) = (inverse @ sk_c6)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl7036])).
% 1.31/1.14 thf(zip_derived_cl1, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_inverse])).
% 1.31/1.14 thf(zip_derived_cl7048, plain,
% 1.31/1.14 ((((multiply @ sk_c6 @ sk_c6) = (identity))
% 1.31/1.14 | ((identity) = (inverse @ sk_c6)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl7037, zip_derived_cl1])).
% 1.31/1.14 thf(zip_derived_cl1, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_inverse])).
% 1.31/1.14 thf(zip_derived_cl7113, plain,
% 1.31/1.14 ((((multiply @ identity @ sk_c6) = (identity))
% 1.31/1.14 | ((multiply @ sk_c6 @ sk_c6) = (identity)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl7048, zip_derived_cl1])).
% 1.31/1.14 thf(zip_derived_cl0, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_identity])).
% 1.31/1.14 thf(zip_derived_cl7127, plain,
% 1.31/1.14 ((((sk_c6) = (identity)) | ((multiply @ sk_c6 @ sk_c6) = (identity)))),
% 1.31/1.14 inference('demod', [status(thm)], [zip_derived_cl7113, zip_derived_cl0])).
% 1.31/1.14 thf(zip_derived_cl61, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i]:
% 1.31/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.31/1.14 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 1.31/1.14 thf(zip_derived_cl7151, plain,
% 1.31/1.14 ((((sk_c6) = (multiply @ (inverse @ sk_c6) @ identity))
% 1.31/1.14 | ((sk_c6) = (identity)))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl7127, zip_derived_cl61])).
% 1.31/1.14 thf(zip_derived_cl7360, plain, (((inverse @ sk_c6) = (identity))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl7354])).
% 1.31/1.14 thf(zip_derived_cl0, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_identity])).
% 1.31/1.14 thf(zip_derived_cl7395, plain,
% 1.31/1.14 ((((sk_c6) = (identity)) | ((sk_c6) = (identity)))),
% 1.31/1.14 inference('demod', [status(thm)],
% 1.31/1.14 [zip_derived_cl7151, zip_derived_cl7360, zip_derived_cl0])).
% 1.31/1.14 thf(zip_derived_cl7396, plain, (((sk_c6) = (identity))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl7395])).
% 1.31/1.14 thf(zip_derived_cl7428, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.31/1.14 (((X0) != (identity))
% 1.31/1.14 | ((inverse @ X0) != (identity))
% 1.31/1.14 | ((identity) != (identity))
% 1.31/1.14 | ((X1) != (identity))
% 1.31/1.14 | ((inverse @ X1) != (identity))
% 1.31/1.14 | ((X2) != (identity))
% 1.31/1.14 | ((inverse @ X2) != (identity)))),
% 1.31/1.14 inference('demod', [status(thm)],
% 1.31/1.14 [zip_derived_cl7388, zip_derived_cl7396])).
% 1.31/1.14 thf(zip_derived_cl7429, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.31/1.14 (((inverse @ X2) != (identity))
% 1.31/1.14 | ((X2) != (identity))
% 1.31/1.14 | ((inverse @ X1) != (identity))
% 1.31/1.14 | ((X1) != (identity))
% 1.31/1.14 | ((inverse @ X0) != (identity))
% 1.31/1.14 | ((X0) != (identity)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl7428])).
% 1.31/1.14 thf(zip_derived_cl7430, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i]:
% 1.31/1.14 (((X0) != (identity))
% 1.31/1.14 | ((inverse @ X0) != (identity))
% 1.31/1.14 | ((X1) != (identity))
% 1.31/1.14 | ((inverse @ X1) != (identity))
% 1.31/1.14 | ((inverse @ identity) != (identity)))),
% 1.31/1.14 inference('eq_res', [status(thm)], [zip_derived_cl7429])).
% 1.31/1.14 thf(zip_derived_cl0, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_identity])).
% 1.31/1.14 thf(zip_derived_cl61, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i]:
% 1.31/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.31/1.14 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 1.31/1.14 thf(zip_derived_cl72, plain,
% 1.31/1.14 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl61])).
% 1.31/1.14 thf(zip_derived_cl61, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i]:
% 1.31/1.14 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.31/1.14 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 1.31/1.14 thf(zip_derived_cl103, plain,
% 1.31/1.14 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ identity)) @ X0))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl72, zip_derived_cl61])).
% 1.31/1.14 thf(zip_derived_cl1, plain,
% 1.31/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.31/1.14 inference('cnf', [status(esa)], [left_inverse])).
% 1.31/1.14 thf(zip_derived_cl1898, plain, (((inverse @ identity) = (identity))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl103, zip_derived_cl1])).
% 1.31/1.14 thf(zip_derived_cl7431, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i]:
% 1.31/1.14 (((X0) != (identity))
% 1.31/1.14 | ((inverse @ X0) != (identity))
% 1.31/1.14 | ((X1) != (identity))
% 1.31/1.14 | ((inverse @ X1) != (identity))
% 1.31/1.14 | ((identity) != (identity)))),
% 1.31/1.14 inference('demod', [status(thm)],
% 1.31/1.14 [zip_derived_cl7430, zip_derived_cl1898])).
% 1.31/1.14 thf(zip_derived_cl7432, plain,
% 1.31/1.14 (![X0 : $i, X1 : $i]:
% 1.31/1.14 (((inverse @ X1) != (identity))
% 1.31/1.14 | ((X1) != (identity))
% 1.31/1.14 | ((inverse @ X0) != (identity))
% 1.31/1.14 | ((X0) != (identity)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl7431])).
% 1.31/1.14 thf(zip_derived_cl7433, plain,
% 1.31/1.14 (![X0 : $i]:
% 1.31/1.14 (((X0) != (identity))
% 1.31/1.14 | ((inverse @ X0) != (identity))
% 1.31/1.14 | ((inverse @ identity) != (identity)))),
% 1.31/1.14 inference('eq_res', [status(thm)], [zip_derived_cl7432])).
% 1.31/1.14 thf(zip_derived_cl1898, plain, (((inverse @ identity) = (identity))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl103, zip_derived_cl1])).
% 1.31/1.14 thf(zip_derived_cl7434, plain,
% 1.31/1.14 (![X0 : $i]:
% 1.31/1.14 (((X0) != (identity))
% 1.31/1.14 | ((inverse @ X0) != (identity))
% 1.31/1.14 | ((identity) != (identity)))),
% 1.31/1.14 inference('demod', [status(thm)],
% 1.31/1.14 [zip_derived_cl7433, zip_derived_cl1898])).
% 1.31/1.14 thf(zip_derived_cl7435, plain,
% 1.31/1.14 (![X0 : $i]: (((inverse @ X0) != (identity)) | ((X0) != (identity)))),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl7434])).
% 1.31/1.14 thf(zip_derived_cl7436, plain, (((inverse @ identity) != (identity))),
% 1.31/1.14 inference('eq_res', [status(thm)], [zip_derived_cl7435])).
% 1.31/1.14 thf(zip_derived_cl1898, plain, (((inverse @ identity) = (identity))),
% 1.31/1.14 inference('sup+', [status(thm)], [zip_derived_cl103, zip_derived_cl1])).
% 1.31/1.14 thf(zip_derived_cl7437, plain, (((identity) != (identity))),
% 1.31/1.14 inference('demod', [status(thm)],
% 1.31/1.14 [zip_derived_cl7436, zip_derived_cl1898])).
% 1.31/1.14 thf(zip_derived_cl7438, plain, ($false),
% 1.31/1.14 inference('simplify', [status(thm)], [zip_derived_cl7437])).
% 1.31/1.14
% 1.31/1.14 % SZS output end Refutation
% 1.31/1.14
% 1.31/1.14
% 1.31/1.14 % Terminating...
% 2.16/1.24 % Runner terminated.
% 2.16/1.25 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------