%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP323-1 : TPTP v9.2.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.nILGXBGqO0 true
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:36:14 PM UTC 2025
% Result : Unsatisfiable 0.54s 0.91s
% Output : Refutation 0.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : GRP323-1 : TPTP v9.2.0. Released v2.5.0.
% 0.05/0.11 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.nILGXBGqO0 true
% 0.12/0.32 % Computer : n012.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Wed Oct 1 14:13:23 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.12/0.32 % Running portfolio for 300 s
% 0.12/0.32 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.32 % Number of cores: 8
% 0.12/0.33 % Python version: Python 3.6.8
% 0.12/0.33 % Running in FO mode
% 0.44/0.60 % Total configuration time : 435
% 0.44/0.60 % Estimated wc time : 1092
% 0.44/0.60 % Estimated cpu time (7 cpus) : 156.0
% 0.52/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.52/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.52/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.52/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.52/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.52/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.52/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.54/0.91 % Solved by fo/fo7.sh.
% 0.54/0.91 % done 244 iterations in 0.159s
% 0.54/0.91 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.54/0.91 % SZS output start Refutation
% 0.54/0.91 thf(sk_c3_type, type, sk_c3: $i).
% 0.54/0.91 thf(sk_c6_type, type, sk_c6: $i).
% 0.54/0.91 thf(sk_c1_type, type, sk_c1: $i).
% 0.54/0.91 thf(sk_c5_type, type, sk_c5: $i).
% 0.54/0.91 thf(identity_type, type, identity: $i).
% 0.54/0.91 thf(multiply_type, type, multiply: $i > $i > $i).
% 0.54/0.91 thf(sk_c8_type, type, sk_c8: $i).
% 0.54/0.91 thf(inverse_type, type, inverse: $i > $i).
% 0.54/0.91 thf(sk_c4_type, type, sk_c4: $i).
% 0.54/0.91 thf(sk_c2_type, type, sk_c2: $i).
% 0.54/0.91 thf(sk_c7_type, type, sk_c7: $i).
% 0.54/0.91 thf(prove_this_31, conjecture,
% 0.54/0.91 (~( ( ( inverse @ X2 ) != ( sk_c8 ) ) |
% 0.54/0.91 ( ( multiply @ X2 @ sk_c8 ) != ( sk_c6 ) ) |
% 0.54/0.91 ( ( inverse @ X1 ) != ( sk_c8 ) ) |
% 0.54/0.91 ( ( multiply @ X1 @ sk_c8 ) != ( sk_c7 ) ) |
% 0.54/0.91 ( ( multiply @ sk_c8 @ sk_c7 ) != ( sk_c6 ) ) |
% 0.54/0.91 ( ( inverse @ X5 ) != ( sk_c8 ) ) |
% 0.54/0.91 ( ( multiply @ X5 @ sk_c8 ) != ( X4 ) ) |
% 0.54/0.91 ( ( multiply @ sk_c8 @ X4 ) != ( sk_c7 ) ) |
% 0.54/0.91 ( ( inverse @ X3 ) != ( sk_c7 ) ) |
% 0.54/0.91 ( ( multiply @ X3 @ sk_c7 ) != ( sk_c8 ) ) |
% 0.54/0.91 ( ( multiply @ sk_c7 @ sk_c8 ) != ( sk_c6 ) ) ))).
% 0.54/0.91 thf(zf_stmt_0, negated_conjecture,
% 0.54/0.91 (( ( inverse @ X2 ) != ( sk_c8 ) ) |
% 0.54/0.91 ( ( multiply @ X2 @ sk_c8 ) != ( sk_c6 ) ) |
% 0.54/0.91 ( ( inverse @ X1 ) != ( sk_c8 ) ) |
% 0.54/0.91 ( ( multiply @ X1 @ sk_c8 ) != ( sk_c7 ) ) |
% 0.54/0.91 ( ( multiply @ sk_c8 @ sk_c7 ) != ( sk_c6 ) ) |
% 0.54/0.91 ( ( inverse @ X5 ) != ( sk_c8 ) ) |
% 0.54/0.91 ( ( multiply @ X5 @ sk_c8 ) != ( X4 ) ) |
% 0.54/0.91 ( ( multiply @ sk_c8 @ X4 ) != ( sk_c7 ) ) |
% 0.54/0.91 ( ( inverse @ X3 ) != ( sk_c7 ) ) |
% 0.54/0.91 ( ( multiply @ X3 @ sk_c7 ) != ( sk_c8 ) ) |
% 0.54/0.91 ( ( multiply @ sk_c7 @ sk_c8 ) != ( sk_c6 ) )),
% 0.54/0.91 inference('cnf.neg', [status(esa)], [prove_this_31])).
% 0.54/0.91 thf(zip_derived_cl33, plain,
% 0.54/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.54/0.91 (((inverse @ X0) != (sk_c8))
% 0.54/0.91 | ((multiply @ X0 @ sk_c8) != (sk_c6))
% 0.54/0.91 | ((inverse @ X1) != (sk_c8))
% 0.54/0.91 | ((multiply @ X1 @ sk_c8) != (sk_c7))
% 0.54/0.91 | ((multiply @ sk_c8 @ sk_c7) != (sk_c6))
% 0.54/0.91 | ((inverse @ X2) != (sk_c8))
% 0.54/0.91 | ((multiply @ X2 @ sk_c8) != (X3))
% 0.54/0.91 | ((multiply @ sk_c8 @ X3) != (sk_c7))
% 0.54/0.91 | ((inverse @ X4) != (sk_c7))
% 0.54/0.91 | ((multiply @ X4 @ sk_c7) != (sk_c8))
% 0.54/0.91 | ((multiply @ sk_c7 @ sk_c8) != (sk_c6)))),
% 0.54/0.91 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.54/0.91 thf(zip_derived_cl34, plain,
% 0.54/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.54/0.91 (((inverse @ X0) != (sk_c8))
% 0.54/0.91 | ((multiply @ X0 @ sk_c8) != (multiply @ sk_c7 @ sk_c8))
% 0.54/0.91 | ((inverse @ X1) != (sk_c8))
% 0.54/0.91 | ((multiply @ X1 @ sk_c8) != (sk_c7))
% 0.54/0.91 | ((multiply @ sk_c8 @ sk_c7) != (sk_c6))
% 0.54/0.91 | ((inverse @ X2) != (sk_c8))
% 0.54/0.91 | ((multiply @ X2 @ sk_c8) != (X3))
% 0.54/0.91 | ((multiply @ sk_c8 @ X3) != (sk_c7))
% 0.54/0.91 | ((inverse @ X4) != (sk_c7))
% 0.54/0.91 | ((multiply @ X4 @ sk_c7) != (sk_c8))
% 0.54/0.91 | ((multiply @ sk_c7 @ sk_c8) != (sk_c6)))),
% 0.54/0.91 inference('local_rewriting', [status(thm)], [zip_derived_cl33])).
% 0.54/0.91 thf(prove_this_28, conjecture,
% 0.54/0.91 (~( ( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 0.54/0.91 ( ( inverse @ sk_c2 ) = ( sk_c8 ) ) ))).
% 0.54/0.91 thf(zf_stmt_1, negated_conjecture,
% 0.54/0.91 (( ( inverse @ sk_c4 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c8 ) )),
% 0.54/0.91 inference('cnf.neg', [status(esa)], [prove_this_28])).
% 0.54/0.91 thf(zip_derived_cl30, plain,
% 0.54/0.91 ((((inverse @ sk_c4) = (sk_c8)) | ((inverse @ sk_c2) = (sk_c8)))),
% 0.54/0.91 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.54/0.91 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 0.54/0.91 thf(zip_derived_cl1, plain,
% 0.54/0.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.91 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.91 thf(zip_derived_cl45, plain,
% 0.54/0.91 ((((multiply @ sk_c8 @ sk_c2) = (identity))
% 0.54/0.91 | ((inverse @ sk_c4) = (sk_c8)))),
% 0.54/0.91 inference('sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl1])).
% 0.54/0.91 thf(zip_derived_cl1, plain,
% 0.54/0.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.91 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.91 thf(associativity, axiom,
% 0.54/0.91 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 0.54/0.91 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 0.54/0.91 thf(zip_derived_cl2, plain,
% 0.54/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.54/0.91 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.54/0.91 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.54/0.91 inference('cnf', [status(esa)], [associativity])).
% 0.54/0.91 thf(zip_derived_cl54, plain,
% 0.54/0.91 (![X0 : $i, X1 : $i]:
% 0.54/0.91 ((multiply @ identity @ X0)
% 0.54/0.91 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.91 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 0.54/0.91 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 0.54/0.91 thf(zip_derived_cl0, plain,
% 0.54/0.91 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.91 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.91 thf(zip_derived_cl75, plain,
% 0.54/0.91 (![X0 : $i, X1 : $i]:
% 0.54/0.91 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.91 inference('demod', [status(thm)], [zip_derived_cl54, zip_derived_cl0])).
% 0.54/0.91 thf(zip_derived_cl100, plain,
% 0.54/0.91 ((((sk_c2) = (multiply @ (inverse @ sk_c8) @ identity))
% 0.54/0.91 | ((inverse @ sk_c4) = (sk_c8)))),
% 0.54/0.91 inference('sup+', [status(thm)], [zip_derived_cl45, zip_derived_cl75])).
% 0.54/0.91 thf(prove_this_23, conjecture,
% 0.54/0.91 (~( ( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 0.54/0.91 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c3 ) ) ))).
% 0.54/0.91 thf(zf_stmt_2, negated_conjecture,
% 0.54/0.91 (( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 0.54/0.91 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c3 ) )),
% 0.54/0.91 inference('cnf.neg', [status(esa)], [prove_this_23])).
% 0.54/0.91 thf(zip_derived_cl25, plain,
% 0.54/0.91 ((((inverse @ sk_c4) = (sk_c8)) | ((multiply @ sk_c2 @ sk_c8) = (sk_c3)))),
% 0.54/0.91 inference('cnf', [status(esa)], [zf_stmt_2])).
% 0.54/0.91 thf(zip_derived_cl273, plain,
% 0.54/0.91 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 0.54/0.91 = (sk_c3))
% 0.54/0.91 | ((inverse @ sk_c4) = (sk_c8))
% 0.54/0.91 | ((inverse @ sk_c4) = (sk_c8)))),
% 0.54/0.91 inference('sup+', [status(thm)], [zip_derived_cl100, zip_derived_cl25])).
% 0.54/0.91 thf(zip_derived_cl2, plain,
% 0.54/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.54/0.91 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.54/0.91 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.54/0.91 inference('cnf', [status(esa)], [associativity])).
% 0.54/0.91 thf(zip_derived_cl0, plain,
% 0.54/0.91 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.91 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.91 thf(zip_derived_cl1, plain,
% 0.54/0.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.91 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.91 thf(zip_derived_cl284, plain,
% 0.54/0.91 ((((identity) = (sk_c3))
% 0.54/0.91 | ((inverse @ sk_c4) = (sk_c8))
% 0.54/0.91 | ((inverse @ sk_c4) = (sk_c8)))),
% 0.54/0.91 inference('demod', [status(thm)],
% 0.54/0.91 [zip_derived_cl273, zip_derived_cl2, zip_derived_cl0,
% 0.54/0.91 zip_derived_cl1])).
% 0.54/0.91 thf(zip_derived_cl285, plain,
% 0.54/0.91 ((((inverse @ sk_c4) = (sk_c8)) | ((identity) = (sk_c3)))),
% 0.54/0.91 inference('simplify', [status(thm)], [zip_derived_cl284])).
% 0.54/0.91 thf(prove_this_18, conjecture,
% 0.54/0.91 (~( ( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 0.54/0.91 ( ( multiply @ sk_c8 @ sk_c3 ) = ( sk_c7 ) ) ))).
% 0.54/0.91 thf(zf_stmt_3, negated_conjecture,
% 0.54/0.91 (( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 0.54/0.91 ( ( multiply @ sk_c8 @ sk_c3 ) = ( sk_c7 ) )),
% 0.54/0.91 inference('cnf.neg', [status(esa)], [prove_this_18])).
% 0.54/0.91 thf(zip_derived_cl20, plain,
% 0.54/0.91 ((((inverse @ sk_c4) = (sk_c8)) | ((multiply @ sk_c8 @ sk_c3) = (sk_c7)))),
% 0.54/0.91 inference('cnf', [status(esa)], [zf_stmt_3])).
% 0.54/0.91 thf(zip_derived_cl291, plain,
% 0.54/0.91 ((((multiply @ sk_c8 @ identity) = (sk_c7))
% 0.54/0.91 | ((inverse @ sk_c4) = (sk_c8))
% 0.54/0.91 | ((inverse @ sk_c4) = (sk_c8)))),
% 0.54/0.91 inference('sup+', [status(thm)], [zip_derived_cl285, zip_derived_cl20])).
% 0.54/0.91 thf(zip_derived_cl297, plain,
% 0.54/0.91 ((((inverse @ sk_c4) = (sk_c8))
% 0.54/0.91 | ((multiply @ sk_c8 @ identity) = (sk_c7)))),
% 0.54/0.91 inference('simplify', [status(thm)], [zip_derived_cl291])).
% 0.54/0.91 thf(zip_derived_cl1, plain,
% 0.54/0.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.91 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.91 thf(zip_derived_cl75, plain,
% 0.54/0.91 (![X0 : $i, X1 : $i]:
% 0.54/0.91 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.91 inference('demod', [status(thm)], [zip_derived_cl54, zip_derived_cl0])).
% 0.54/0.91 thf(zip_derived_cl89, plain,
% 0.54/0.91 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 0.54/0.91 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl75])).
% 0.54/0.91 thf(zip_derived_cl75, plain,
% 0.54/0.91 (![X0 : $i, X1 : $i]:
% 0.54/0.91 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.91 inference('demod', [status(thm)], [zip_derived_cl54, zip_derived_cl0])).
% 0.54/0.91 thf(zip_derived_cl75, plain,
% 0.54/0.91 (![X0 : $i, X1 : $i]:
% 0.54/0.91 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.91 inference('demod', [status(thm)], [zip_derived_cl54, zip_derived_cl0])).
% 0.54/0.91 thf(zip_derived_cl86, plain,
% 0.54/0.91 (![X0 : $i, X1 : $i]:
% 0.54/0.91 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 0.54/0.91 inference('sup+', [status(thm)], [zip_derived_cl75, zip_derived_cl75])).
% 0.54/0.91 thf(zip_derived_cl480, plain,
% 0.54/0.91 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.54/0.91 inference('sup+', [status(thm)], [zip_derived_cl89, zip_derived_cl86])).
% 0.54/0.91 thf(zip_derived_cl509, plain,
% 0.54/0.91 ((((inverse @ sk_c4) = (sk_c8)) | ((sk_c8) = (sk_c7)))),
% 0.54/0.91 inference('demod', [status(thm)], [zip_derived_cl297, zip_derived_cl480])).
% 0.54/0.91 thf(zip_derived_cl89, plain,
% 0.54/0.91 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 0.54/0.91 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl75])).
% 0.54/0.91 thf(zip_derived_cl524, plain,
% 0.54/0.91 ((((sk_c4) = (multiply @ (inverse @ sk_c8) @ identity))
% 0.54/0.91 | ((sk_c8) = (sk_c7)))),
% 0.54/0.91 inference('sup+', [status(thm)], [zip_derived_cl509, zip_derived_cl89])).
% 0.54/0.91 thf(zip_derived_cl480, plain,
% 0.54/0.91 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.54/0.91 inference('sup+', [status(thm)], [zip_derived_cl89, zip_derived_cl86])).
% 0.54/0.91 thf(zip_derived_cl527, plain,
% 0.54/0.91 ((((sk_c4) = (inverse @ sk_c8)) | ((sk_c8) = (sk_c7)))),
% 0.54/0.91 inference('demod', [status(thm)], [zip_derived_cl524, zip_derived_cl480])).
% 0.54/0.91 thf(prove_this_27, conjecture,
% 0.54/0.91 (~( ( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c7 ) ) |
% 0.54/0.91 ( ( inverse @ sk_c2 ) = ( sk_c8 ) ) ))).
% 0.54/0.91 thf(zf_stmt_4, negated_conjecture,
% 0.54/0.91 (( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c7 ) ) |
% 0.54/0.91 ( ( inverse @ sk_c2 ) = ( sk_c8 ) )),
% 0.54/0.91 inference('cnf.neg', [status(esa)], [prove_this_27])).
% 0.54/0.91 thf(zip_derived_cl29, plain,
% 0.54/0.91 ((((multiply @ sk_c4 @ sk_c8) = (sk_c7)) | ((inverse @ sk_c2) = (sk_c8)))),
% 0.54/0.91 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.54/0.91 thf(zip_derived_cl480, plain,
% 0.54/0.91 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.54/0.91 inference('sup+', [status(thm)], [zip_derived_cl89, zip_derived_cl86])).
% 0.54/0.91 thf(zip_derived_cl89, plain,
% 0.54/0.91 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 0.54/0.91 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl75])).
% 0.54/0.91 thf(zip_derived_cl519, plain,
% 0.54/0.91 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.54/0.91 inference('sup+', [status(thm)], [zip_derived_cl480, zip_derived_cl89])).
% 0.54/0.91 thf(zip_derived_cl675, plain,
% 0.54/0.91 ((((sk_c2) = (inverse @ sk_c8)) | ((multiply @ sk_c4 @ sk_c8) = (sk_c7)))),
% 0.54/0.91 inference('sup+', [status(thm)], [zip_derived_cl29, zip_derived_cl519])).
% 0.54/0.91 thf(prove_this_22, conjecture,
% 0.54/0.91 (~( ( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c7 ) ) |
% 0.54/0.91 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c3 ) ) ))).
% 0.54/0.91 thf(zf_stmt_5, negated_conjecture,
% 0.54/0.91 (( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c7 ) ) |
% 0.54/0.91 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c3 ) )),
% 0.54/0.91 inference('cnf.neg', [status(esa)], [prove_this_22])).
% 0.54/0.91 thf(zip_derived_cl24, plain,
% 0.54/0.91 ((((multiply @ sk_c4 @ sk_c8) = (sk_c7))
% 0.54/0.91 | ((multiply @ sk_c2 @ sk_c8) = (sk_c3)))),
% 0.54/0.91 inference('cnf', [status(esa)], [zf_stmt_5])).
% 0.54/0.91 thf(zip_derived_cl899, plain,
% 0.54/0.91 ((((multiply @ (inverse @ sk_c8) @ sk_c8) = (sk_c3))
% 0.54/0.91 | ((multiply @ sk_c4 @ sk_c8) = (sk_c7))
% 0.54/0.91 | ((multiply @ sk_c4 @ sk_c8) = (sk_c7)))),
% 0.54/0.91 inference('sup+', [status(thm)], [zip_derived_cl675, zip_derived_cl24])).
% 0.54/0.91 thf(zip_derived_cl1, plain,
% 0.54/0.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.91 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.91 thf(zip_derived_cl912, plain,
% 0.54/0.91 ((((identity) = (sk_c3))
% 0.54/0.91 | ((multiply @ sk_c4 @ sk_c8) = (sk_c7))
% 0.54/0.91 | ((multiply @ sk_c4 @ sk_c8) = (sk_c7)))),
% 0.54/0.91 inference('demod', [status(thm)], [zip_derived_cl899, zip_derived_cl1])).
% 0.54/0.91 thf(zip_derived_cl913, plain,
% 0.54/0.91 ((((multiply @ sk_c4 @ sk_c8) = (sk_c7)) | ((identity) = (sk_c3)))),
% 0.54/0.91 inference('simplify', [status(thm)], [zip_derived_cl912])).
% 0.54/0.91 thf(prove_this_17, conjecture,
% 0.54/0.91 (~( ( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c7 ) ) |
% 0.54/0.91 ( ( multiply @ sk_c8 @ sk_c3 ) = ( sk_c7 ) ) ))).
% 0.54/0.91 thf(zf_stmt_6, negated_conjecture,
% 0.54/0.91 (( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c7 ) ) |
% 0.54/0.91 ( ( multiply @ sk_c8 @ sk_c3 ) = ( sk_c7 ) )),
% 0.54/0.91 inference('cnf.neg', [status(esa)], [prove_this_17])).
% 0.54/0.91 thf(zip_derived_cl19, plain,
% 0.54/0.91 ((((multiply @ sk_c4 @ sk_c8) = (sk_c7))
% 0.54/0.91 | ((multiply @ sk_c8 @ sk_c3) = (sk_c7)))),
% 0.54/0.91 inference('cnf', [status(esa)], [zf_stmt_6])).
% 0.54/0.91 thf(zip_derived_cl927, plain,
% 0.54/0.91 ((((multiply @ sk_c8 @ identity) = (sk_c7))
% 0.54/0.91 | ((multiply @ sk_c4 @ sk_c8) = (sk_c7))
% 0.54/0.91 | ((multiply @ sk_c4 @ sk_c8) = (sk_c7)))),
% 0.54/0.91 inference('sup+', [status(thm)], [zip_derived_cl913, zip_derived_cl19])).
% 0.54/0.91 thf(zip_derived_cl480, plain,
% 0.54/0.91 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.54/0.91 inference('sup+', [status(thm)], [zip_derived_cl89, zip_derived_cl86])).
% 0.54/0.91 thf(zip_derived_cl935, plain,
% 0.54/0.91 ((((sk_c8) = (sk_c7))
% 0.54/0.91 | ((multiply @ sk_c4 @ sk_c8) = (sk_c7))
% 0.54/0.91 | ((multiply @ sk_c4 @ sk_c8) = (sk_c7)))),
% 0.54/0.91 inference('demod', [status(thm)], [zip_derived_cl927, zip_derived_cl480])).
% 0.54/0.91 thf(zip_derived_cl936, plain,
% 0.54/0.91 ((((multiply @ sk_c4 @ sk_c8) = (sk_c7)) | ((sk_c8) = (sk_c7)))),
% 0.54/0.91 inference('simplify', [status(thm)], [zip_derived_cl935])).
% 0.54/0.91 thf(zip_derived_cl1180, plain,
% 0.54/0.91 ((((multiply @ (inverse @ sk_c8) @ sk_c8) = (sk_c7))
% 0.54/0.91 | ((sk_c8) = (sk_c7))
% 0.54/0.91 | ((sk_c8) = (sk_c7)))),
% 0.54/0.91 inference('sup+', [status(thm)], [zip_derived_cl527, zip_derived_cl936])).
% 0.54/0.91 thf(zip_derived_cl1, plain,
% 0.54/0.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.91 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.91 thf(zip_derived_cl1183, plain,
% 0.54/0.91 ((((identity) = (sk_c7)) | ((sk_c8) = (sk_c7)) | ((sk_c8) = (sk_c7)))),
% 0.54/0.91 inference('demod', [status(thm)], [zip_derived_cl1180, zip_derived_cl1])).
% 0.54/0.91 thf(zip_derived_cl1184, plain,
% 0.54/0.91 ((((sk_c8) = (sk_c7)) | ((identity) = (sk_c7)))),
% 0.54/0.91 inference('simplify', [status(thm)], [zip_derived_cl1183])).
% 0.54/0.91 thf(prove_this_13, conjecture,
% 0.54/0.91 (~( ( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 0.54/0.91 ( ( inverse @ sk_c1 ) = ( sk_c7 ) ) ))).
% 0.54/0.91 thf(zf_stmt_7, negated_conjecture,
% 0.54/0.91 (( ( inverse @ sk_c4 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c7 ) )),
% 0.54/0.91 inference('cnf.neg', [status(esa)], [prove_this_13])).
% 0.54/0.91 thf(zip_derived_cl15, plain,
% 0.54/0.91 ((((inverse @ sk_c4) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c7)))),
% 0.54/0.91 inference('cnf', [status(esa)], [zf_stmt_7])).
% 0.54/0.91 thf(zip_derived_cl1, plain,
% 0.54/0.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.91 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.91 thf(zip_derived_cl42, plain,
% 0.54/0.91 ((((multiply @ sk_c7 @ sk_c1) = (identity))
% 0.54/0.91 | ((inverse @ sk_c4) = (sk_c8)))),
% 0.54/0.91 inference('sup+', [status(thm)], [zip_derived_cl15, zip_derived_cl1])).
% 0.54/0.91 thf(zip_derived_cl75, plain,
% 0.54/0.91 (![X0 : $i, X1 : $i]:
% 0.54/0.91 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.91 inference('demod', [status(thm)], [zip_derived_cl54, zip_derived_cl0])).
% 0.54/0.91 thf(zip_derived_cl92, plain,
% 0.54/0.91 ((((sk_c1) = (multiply @ (inverse @ sk_c7) @ identity))
% 0.54/0.91 | ((inverse @ sk_c4) = (sk_c8)))),
% 0.54/0.91 inference('sup+', [status(thm)], [zip_derived_cl42, zip_derived_cl75])).
% 0.54/0.91 thf(prove_this_8, conjecture,
% 0.54/0.91 (~( ( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 0.54/0.91 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) ) ))).
% 0.54/0.91 thf(zf_stmt_8, negated_conjecture,
% 0.54/0.91 (( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 0.54/0.91 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) )),
% 0.54/0.91 inference('cnf.neg', [status(esa)], [prove_this_8])).
% 0.54/0.91 thf(zip_derived_cl10, plain,
% 0.54/0.91 ((((inverse @ sk_c4) = (sk_c8)) | ((multiply @ sk_c1 @ sk_c7) = (sk_c8)))),
% 0.54/0.91 inference('cnf', [status(esa)], [zf_stmt_8])).
% 0.54/0.91 thf(zip_derived_cl136, plain,
% 0.54/0.91 ((((multiply @ (multiply @ (inverse @ sk_c7) @ identity) @ sk_c7)
% 0.54/0.91 = (sk_c8))
% 0.54/0.91 | ((inverse @ sk_c4) = (sk_c8))
% 0.54/0.91 | ((inverse @ sk_c4) = (sk_c8)))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl92, zip_derived_cl10])).
% 0.54/0.92 thf(zip_derived_cl2, plain,
% 0.54/0.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.54/0.92 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.54/0.92 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.54/0.92 inference('cnf', [status(esa)], [associativity])).
% 0.54/0.92 thf(zip_derived_cl0, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.92 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.92 thf(zip_derived_cl1, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.92 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.92 thf(zip_derived_cl149, plain,
% 0.54/0.92 ((((identity) = (sk_c8))
% 0.54/0.92 | ((inverse @ sk_c4) = (sk_c8))
% 0.54/0.92 | ((inverse @ sk_c4) = (sk_c8)))),
% 0.54/0.92 inference('demod', [status(thm)],
% 0.54/0.92 [zip_derived_cl136, zip_derived_cl2, zip_derived_cl0,
% 0.54/0.92 zip_derived_cl1])).
% 0.54/0.92 thf(zip_derived_cl150, plain,
% 0.54/0.92 ((((inverse @ sk_c4) = (sk_c8)) | ((identity) = (sk_c8)))),
% 0.54/0.92 inference('simplify', [status(thm)], [zip_derived_cl149])).
% 0.54/0.92 thf(zip_derived_cl1, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.92 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.92 thf(zip_derived_cl176, plain,
% 0.54/0.92 ((((multiply @ sk_c8 @ sk_c4) = (identity)) | ((identity) = (sk_c8)))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl150, zip_derived_cl1])).
% 0.54/0.92 thf(zip_derived_cl75, plain,
% 0.54/0.92 (![X0 : $i, X1 : $i]:
% 0.54/0.92 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.92 inference('demod', [status(thm)], [zip_derived_cl54, zip_derived_cl0])).
% 0.54/0.92 thf(zip_derived_cl327, plain,
% 0.54/0.92 ((((sk_c4) = (multiply @ (inverse @ sk_c8) @ identity))
% 0.54/0.92 | ((identity) = (sk_c8)))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl176, zip_derived_cl75])).
% 0.54/0.92 thf(zip_derived_cl480, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl89, zip_derived_cl86])).
% 0.54/0.92 thf(zip_derived_cl511, plain,
% 0.54/0.92 ((((sk_c4) = (inverse @ sk_c8)) | ((identity) = (sk_c8)))),
% 0.54/0.92 inference('demod', [status(thm)], [zip_derived_cl327, zip_derived_cl480])).
% 0.54/0.92 thf(prove_this_12, conjecture,
% 0.54/0.92 (~( ( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c7 ) ) |
% 0.54/0.92 ( ( inverse @ sk_c1 ) = ( sk_c7 ) ) ))).
% 0.54/0.92 thf(zf_stmt_9, negated_conjecture,
% 0.54/0.92 (( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c7 ) ) |
% 0.54/0.92 ( ( inverse @ sk_c1 ) = ( sk_c7 ) )),
% 0.54/0.92 inference('cnf.neg', [status(esa)], [prove_this_12])).
% 0.54/0.92 thf(zip_derived_cl14, plain,
% 0.54/0.92 ((((multiply @ sk_c4 @ sk_c8) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c7)))),
% 0.54/0.92 inference('cnf', [status(esa)], [zf_stmt_9])).
% 0.54/0.92 thf(zip_derived_cl519, plain,
% 0.54/0.92 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl480, zip_derived_cl89])).
% 0.54/0.92 thf(zip_derived_cl670, plain,
% 0.54/0.92 ((((sk_c1) = (inverse @ sk_c7)) | ((multiply @ sk_c4 @ sk_c8) = (sk_c7)))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl519])).
% 0.54/0.92 thf(prove_this_7, conjecture,
% 0.54/0.92 (~( ( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c7 ) ) |
% 0.54/0.92 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) ) ))).
% 0.54/0.92 thf(zf_stmt_10, negated_conjecture,
% 0.54/0.92 (( ( multiply @ sk_c4 @ sk_c8 ) = ( sk_c7 ) ) |
% 0.54/0.92 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) )),
% 0.54/0.92 inference('cnf.neg', [status(esa)], [prove_this_7])).
% 0.54/0.92 thf(zip_derived_cl9, plain,
% 0.54/0.92 ((((multiply @ sk_c4 @ sk_c8) = (sk_c7))
% 0.54/0.92 | ((multiply @ sk_c1 @ sk_c7) = (sk_c8)))),
% 0.54/0.92 inference('cnf', [status(esa)], [zf_stmt_10])).
% 0.54/0.92 thf(zip_derived_cl867, plain,
% 0.54/0.92 ((((multiply @ (inverse @ sk_c7) @ sk_c7) = (sk_c8))
% 0.54/0.92 | ((multiply @ sk_c4 @ sk_c8) = (sk_c7))
% 0.54/0.92 | ((multiply @ sk_c4 @ sk_c8) = (sk_c7)))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl670, zip_derived_cl9])).
% 0.54/0.92 thf(zip_derived_cl1, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.92 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.92 thf(zip_derived_cl882, plain,
% 0.54/0.92 ((((identity) = (sk_c8))
% 0.54/0.92 | ((multiply @ sk_c4 @ sk_c8) = (sk_c7))
% 0.54/0.92 | ((multiply @ sk_c4 @ sk_c8) = (sk_c7)))),
% 0.54/0.92 inference('demod', [status(thm)], [zip_derived_cl867, zip_derived_cl1])).
% 0.54/0.92 thf(zip_derived_cl883, plain,
% 0.54/0.92 ((((multiply @ sk_c4 @ sk_c8) = (sk_c7)) | ((identity) = (sk_c8)))),
% 0.54/0.92 inference('simplify', [status(thm)], [zip_derived_cl882])).
% 0.54/0.92 thf(zip_derived_cl1073, plain,
% 0.54/0.92 ((((multiply @ (inverse @ sk_c8) @ sk_c8) = (sk_c7))
% 0.54/0.92 | ((identity) = (sk_c8))
% 0.54/0.92 | ((identity) = (sk_c8)))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl511, zip_derived_cl883])).
% 0.54/0.92 thf(zip_derived_cl1, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.92 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.92 thf(zip_derived_cl1076, plain,
% 0.54/0.92 ((((identity) = (sk_c7))
% 0.54/0.92 | ((identity) = (sk_c8))
% 0.54/0.92 | ((identity) = (sk_c8)))),
% 0.54/0.92 inference('demod', [status(thm)], [zip_derived_cl1073, zip_derived_cl1])).
% 0.54/0.92 thf(zip_derived_cl1077, plain,
% 0.54/0.92 ((((identity) = (sk_c8)) | ((identity) = (sk_c7)))),
% 0.54/0.92 inference('simplify', [status(thm)], [zip_derived_cl1076])).
% 0.54/0.92 thf(zip_derived_cl1219, plain,
% 0.54/0.92 ((((identity) = (sk_c7))
% 0.54/0.92 | ((identity) = (sk_c7))
% 0.54/0.92 | ((identity) = (sk_c7)))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl1184, zip_derived_cl1077])).
% 0.54/0.92 thf(zip_derived_cl1221, plain, (((identity) = (sk_c7))),
% 0.54/0.92 inference('simplify', [status(thm)], [zip_derived_cl1219])).
% 0.54/0.92 thf(zip_derived_cl0, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.92 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.92 thf(zip_derived_cl1221, plain, (((identity) = (sk_c7))),
% 0.54/0.92 inference('simplify', [status(thm)], [zip_derived_cl1219])).
% 0.54/0.92 thf(zip_derived_cl1221, plain, (((identity) = (sk_c7))),
% 0.54/0.92 inference('simplify', [status(thm)], [zip_derived_cl1219])).
% 0.54/0.92 thf(zip_derived_cl480, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl89, zip_derived_cl86])).
% 0.54/0.92 thf(zip_derived_cl1221, plain, (((identity) = (sk_c7))),
% 0.54/0.92 inference('simplify', [status(thm)], [zip_derived_cl1219])).
% 0.54/0.92 thf(zip_derived_cl1221, plain, (((identity) = (sk_c7))),
% 0.54/0.92 inference('simplify', [status(thm)], [zip_derived_cl1219])).
% 0.54/0.92 thf(zip_derived_cl1221, plain, (((identity) = (sk_c7))),
% 0.54/0.92 inference('simplify', [status(thm)], [zip_derived_cl1219])).
% 0.54/0.92 thf(zip_derived_cl480, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl89, zip_derived_cl86])).
% 0.54/0.92 thf(zip_derived_cl1221, plain, (((identity) = (sk_c7))),
% 0.54/0.92 inference('simplify', [status(thm)], [zip_derived_cl1219])).
% 0.54/0.92 thf(zip_derived_cl0, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.92 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.92 thf(zip_derived_cl1247, plain,
% 0.54/0.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.54/0.92 (((inverse @ X0) != (sk_c8))
% 0.54/0.92 | ((multiply @ X0 @ sk_c8) != (sk_c8))
% 0.54/0.92 | ((inverse @ X1) != (sk_c8))
% 0.54/0.92 | ((multiply @ X1 @ sk_c8) != (identity))
% 0.54/0.92 | ((sk_c8) != (sk_c6))
% 0.54/0.92 | ((inverse @ X2) != (sk_c8))
% 0.54/0.92 | ((multiply @ X2 @ sk_c8) != (X3))
% 0.54/0.92 | ((multiply @ sk_c8 @ X3) != (identity))
% 0.54/0.92 | ((inverse @ X4) != (identity))
% 0.54/0.92 | ((X4) != (sk_c8))
% 0.54/0.92 | ((sk_c8) != (sk_c6)))),
% 0.54/0.92 inference('demod', [status(thm)],
% 0.54/0.92 [zip_derived_cl34, zip_derived_cl1221, zip_derived_cl0,
% 0.54/0.92 zip_derived_cl1221, zip_derived_cl1221, zip_derived_cl480,
% 0.54/0.92 zip_derived_cl1221, zip_derived_cl1221, zip_derived_cl1221,
% 0.54/0.92 zip_derived_cl480, zip_derived_cl1221, zip_derived_cl0])).
% 0.54/0.92 thf(zip_derived_cl1248, plain,
% 0.54/0.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.54/0.92 (((X4) != (sk_c8))
% 0.54/0.92 | ((inverse @ X4) != (identity))
% 0.54/0.92 | ((multiply @ sk_c8 @ X3) != (identity))
% 0.54/0.92 | ((multiply @ X2 @ sk_c8) != (X3))
% 0.54/0.92 | ((inverse @ X2) != (sk_c8))
% 0.54/0.92 | ((sk_c8) != (sk_c6))
% 0.54/0.92 | ((multiply @ X1 @ sk_c8) != (identity))
% 0.54/0.92 | ((inverse @ X1) != (sk_c8))
% 0.54/0.92 | ((multiply @ X0 @ sk_c8) != (sk_c8))
% 0.54/0.92 | ((inverse @ X0) != (sk_c8)))),
% 0.54/0.92 inference('simplify', [status(thm)], [zip_derived_cl1247])).
% 0.54/0.92 thf(prove_this_1, conjecture,
% 0.54/0.92 (~( ( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c6 ) ) |
% 0.54/0.92 ( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c6 ) ) ))).
% 0.54/0.92 thf(zf_stmt_11, negated_conjecture,
% 0.54/0.92 (( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c6 ) ) |
% 0.54/0.92 ( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c6 ) )),
% 0.54/0.92 inference('cnf.neg', [status(esa)], [prove_this_1])).
% 0.54/0.92 thf(zip_derived_cl3, plain,
% 0.54/0.92 ((((multiply @ sk_c8 @ sk_c7) = (sk_c6))
% 0.54/0.92 | ((multiply @ sk_c7 @ sk_c8) = (sk_c6)))),
% 0.54/0.92 inference('cnf', [status(esa)], [zf_stmt_11])).
% 0.54/0.92 thf(zip_derived_cl1221, plain, (((identity) = (sk_c7))),
% 0.54/0.92 inference('simplify', [status(thm)], [zip_derived_cl1219])).
% 0.54/0.92 thf(zip_derived_cl480, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl89, zip_derived_cl86])).
% 0.54/0.92 thf(zip_derived_cl1221, plain, (((identity) = (sk_c7))),
% 0.54/0.92 inference('simplify', [status(thm)], [zip_derived_cl1219])).
% 0.54/0.92 thf(zip_derived_cl0, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.92 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.92 thf(zip_derived_cl1222, plain, ((((sk_c8) = (sk_c6)) | ((sk_c8) = (sk_c6)))),
% 0.54/0.92 inference('demod', [status(thm)],
% 0.54/0.92 [zip_derived_cl3, zip_derived_cl1221, zip_derived_cl480,
% 0.54/0.92 zip_derived_cl1221, zip_derived_cl0])).
% 0.54/0.92 thf(zip_derived_cl1223, plain, (((sk_c8) = (sk_c6))),
% 0.54/0.92 inference('simplify', [status(thm)], [zip_derived_cl1222])).
% 0.54/0.92 thf(zip_derived_cl1297, plain,
% 0.54/0.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.54/0.92 (((X4) != (sk_c8))
% 0.54/0.92 | ((inverse @ X4) != (identity))
% 0.54/0.92 | ((multiply @ sk_c8 @ X3) != (identity))
% 0.54/0.92 | ((multiply @ X2 @ sk_c8) != (X3))
% 0.54/0.92 | ((inverse @ X2) != (sk_c8))
% 0.54/0.92 | ((sk_c8) != (sk_c8))
% 0.54/0.92 | ((multiply @ X1 @ sk_c8) != (identity))
% 0.54/0.92 | ((inverse @ X1) != (sk_c8))
% 0.54/0.92 | ((multiply @ X0 @ sk_c8) != (sk_c8))
% 0.54/0.92 | ((inverse @ X0) != (sk_c8)))),
% 0.54/0.92 inference('demod', [status(thm)],
% 0.54/0.92 [zip_derived_cl1248, zip_derived_cl1223])).
% 0.54/0.92 thf(zip_derived_cl1298, plain,
% 0.54/0.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.54/0.92 (((inverse @ X0) != (sk_c8))
% 0.54/0.92 | ((multiply @ X0 @ sk_c8) != (sk_c8))
% 0.54/0.92 | ((inverse @ X1) != (sk_c8))
% 0.54/0.92 | ((multiply @ X1 @ sk_c8) != (identity))
% 0.54/0.92 | ((inverse @ X2) != (sk_c8))
% 0.54/0.92 | ((multiply @ X2 @ sk_c8) != (X3))
% 0.54/0.92 | ((multiply @ sk_c8 @ X3) != (identity))
% 0.54/0.92 | ((inverse @ X4) != (identity))
% 0.54/0.92 | ((X4) != (sk_c8)))),
% 0.54/0.92 inference('simplify', [status(thm)], [zip_derived_cl1297])).
% 0.54/0.92 thf(zip_derived_cl3, plain,
% 0.54/0.92 ((((multiply @ sk_c8 @ sk_c7) = (sk_c6))
% 0.54/0.92 | ((multiply @ sk_c7 @ sk_c8) = (sk_c6)))),
% 0.54/0.92 inference('cnf', [status(esa)], [zf_stmt_11])).
% 0.54/0.92 thf(zip_derived_cl36, plain,
% 0.54/0.92 ((((multiply @ sk_c8 @ sk_c7) != (multiply @ sk_c7 @ sk_c8))
% 0.54/0.92 | ((multiply @ sk_c7 @ sk_c8) = (sk_c6)))),
% 0.54/0.92 inference('eq_fact', [status(thm)], [zip_derived_cl3])).
% 0.54/0.92 thf(zip_derived_cl1221, plain, (((identity) = (sk_c7))),
% 0.54/0.92 inference('simplify', [status(thm)], [zip_derived_cl1219])).
% 0.54/0.92 thf(zip_derived_cl480, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl89, zip_derived_cl86])).
% 0.54/0.92 thf(zip_derived_cl1221, plain, (((identity) = (sk_c7))),
% 0.54/0.92 inference('simplify', [status(thm)], [zip_derived_cl1219])).
% 0.54/0.92 thf(zip_derived_cl0, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.92 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.92 thf(zip_derived_cl1221, plain, (((identity) = (sk_c7))),
% 0.54/0.92 inference('simplify', [status(thm)], [zip_derived_cl1219])).
% 0.54/0.92 thf(zip_derived_cl0, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.92 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.92 thf(zip_derived_cl1249, plain,
% 0.54/0.92 ((((sk_c8) != (sk_c8)) | ((sk_c8) = (sk_c6)))),
% 0.54/0.92 inference('demod', [status(thm)],
% 0.54/0.92 [zip_derived_cl36, zip_derived_cl1221, zip_derived_cl480,
% 0.54/0.92 zip_derived_cl1221, zip_derived_cl0, zip_derived_cl1221,
% 0.54/0.92 zip_derived_cl0])).
% 0.54/0.92 thf(zip_derived_cl1250, plain, (((sk_c8) = (sk_c6))),
% 0.54/0.92 inference('simplify', [status(thm)], [zip_derived_cl1249])).
% 0.54/0.92 thf(prove_this_5, conjecture,
% 0.54/0.92 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 0.54/0.92 ( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c6 ) ) ))).
% 0.54/0.92 thf(zf_stmt_12, negated_conjecture,
% 0.54/0.92 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 0.54/0.92 ( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c6 ) )),
% 0.54/0.92 inference('cnf.neg', [status(esa)], [prove_this_5])).
% 0.54/0.92 thf(zip_derived_cl7, plain,
% 0.54/0.92 ((((inverse @ sk_c5) = (sk_c8)) | ((multiply @ sk_c7 @ sk_c8) = (sk_c6)))),
% 0.54/0.92 inference('cnf', [status(esa)], [zf_stmt_12])).
% 0.54/0.92 thf(zip_derived_cl1, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.92 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.92 thf(zip_derived_cl40, plain,
% 0.54/0.92 ((((multiply @ sk_c8 @ sk_c5) = (identity))
% 0.54/0.92 | ((multiply @ sk_c7 @ sk_c8) = (sk_c6)))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl1])).
% 0.54/0.92 thf(zip_derived_cl75, plain,
% 0.54/0.92 (![X0 : $i, X1 : $i]:
% 0.54/0.92 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.92 inference('demod', [status(thm)], [zip_derived_cl54, zip_derived_cl0])).
% 0.54/0.92 thf(zip_derived_cl95, plain,
% 0.54/0.92 ((((sk_c5) = (multiply @ (inverse @ sk_c8) @ identity))
% 0.54/0.92 | ((multiply @ sk_c7 @ sk_c8) = (sk_c6)))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl75])).
% 0.54/0.92 thf(prove_this_4, conjecture,
% 0.54/0.92 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c6 ) ) |
% 0.54/0.92 ( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c6 ) ) ))).
% 0.54/0.92 thf(zf_stmt_13, negated_conjecture,
% 0.54/0.92 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c6 ) ) |
% 0.54/0.92 ( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c6 ) )),
% 0.54/0.92 inference('cnf.neg', [status(esa)], [prove_this_4])).
% 0.54/0.92 thf(zip_derived_cl6, plain,
% 0.54/0.92 ((((multiply @ sk_c5 @ sk_c8) = (sk_c6))
% 0.54/0.92 | ((multiply @ sk_c7 @ sk_c8) = (sk_c6)))),
% 0.54/0.92 inference('cnf', [status(esa)], [zf_stmt_13])).
% 0.54/0.92 thf(zip_derived_cl214, plain,
% 0.54/0.92 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 0.54/0.92 = (sk_c6))
% 0.54/0.92 | ((multiply @ sk_c7 @ sk_c8) = (sk_c6))
% 0.54/0.92 | ((multiply @ sk_c7 @ sk_c8) = (sk_c6)))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl95, zip_derived_cl6])).
% 0.54/0.92 thf(zip_derived_cl2, plain,
% 0.54/0.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.54/0.92 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.54/0.92 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.54/0.92 inference('cnf', [status(esa)], [associativity])).
% 0.54/0.92 thf(zip_derived_cl0, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.92 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.92 thf(zip_derived_cl1, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.92 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.92 thf(zip_derived_cl218, plain,
% 0.54/0.92 ((((identity) = (sk_c6))
% 0.54/0.92 | ((multiply @ sk_c7 @ sk_c8) = (sk_c6))
% 0.54/0.92 | ((multiply @ sk_c7 @ sk_c8) = (sk_c6)))),
% 0.54/0.92 inference('demod', [status(thm)],
% 0.54/0.92 [zip_derived_cl214, zip_derived_cl2, zip_derived_cl0,
% 0.54/0.92 zip_derived_cl1])).
% 0.54/0.92 thf(zip_derived_cl219, plain,
% 0.54/0.92 ((((multiply @ sk_c7 @ sk_c8) = (sk_c6)) | ((identity) = (sk_c6)))),
% 0.54/0.92 inference('simplify', [status(thm)], [zip_derived_cl218])).
% 0.54/0.92 thf(zip_derived_cl225, plain,
% 0.54/0.92 ((((multiply @ sk_c7 @ sk_c8) != (identity)) | ((identity) = (sk_c6)))),
% 0.54/0.92 inference('eq_fact', [status(thm)], [zip_derived_cl219])).
% 0.54/0.92 thf(zip_derived_cl1221, plain, (((identity) = (sk_c7))),
% 0.54/0.92 inference('simplify', [status(thm)], [zip_derived_cl1219])).
% 0.54/0.92 thf(zip_derived_cl0, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.92 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.92 thf(zip_derived_cl1262, plain,
% 0.54/0.92 ((((sk_c8) != (identity)) | ((identity) = (sk_c6)))),
% 0.54/0.92 inference('demod', [status(thm)],
% 0.54/0.92 [zip_derived_cl225, zip_derived_cl1221, zip_derived_cl0])).
% 0.54/0.92 thf(prove_this_15, conjecture,
% 0.54/0.92 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 0.54/0.92 ( ( inverse @ sk_c1 ) = ( sk_c7 ) ) ))).
% 0.54/0.92 thf(zf_stmt_14, negated_conjecture,
% 0.54/0.92 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c7 ) )),
% 0.54/0.92 inference('cnf.neg', [status(esa)], [prove_this_15])).
% 0.54/0.92 thf(zip_derived_cl17, plain,
% 0.54/0.92 ((((inverse @ sk_c5) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c7)))),
% 0.54/0.92 inference('cnf', [status(esa)], [zf_stmt_14])).
% 0.54/0.92 thf(zip_derived_cl1, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.92 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.92 thf(zip_derived_cl43, plain,
% 0.54/0.92 ((((multiply @ sk_c7 @ sk_c1) = (identity))
% 0.54/0.92 | ((inverse @ sk_c5) = (sk_c8)))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl17, zip_derived_cl1])).
% 0.54/0.92 thf(zip_derived_cl75, plain,
% 0.54/0.92 (![X0 : $i, X1 : $i]:
% 0.54/0.92 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.92 inference('demod', [status(thm)], [zip_derived_cl54, zip_derived_cl0])).
% 0.54/0.92 thf(zip_derived_cl93, plain,
% 0.54/0.92 ((((sk_c1) = (multiply @ (inverse @ sk_c7) @ identity))
% 0.54/0.92 | ((inverse @ sk_c5) = (sk_c8)))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl43, zip_derived_cl75])).
% 0.54/0.92 thf(prove_this_10, conjecture,
% 0.54/0.92 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 0.54/0.92 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) ) ))).
% 0.54/0.92 thf(zf_stmt_15, negated_conjecture,
% 0.54/0.92 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 0.54/0.92 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) )),
% 0.54/0.92 inference('cnf.neg', [status(esa)], [prove_this_10])).
% 0.54/0.92 thf(zip_derived_cl12, plain,
% 0.54/0.92 ((((inverse @ sk_c5) = (sk_c8)) | ((multiply @ sk_c1 @ sk_c7) = (sk_c8)))),
% 0.54/0.92 inference('cnf', [status(esa)], [zf_stmt_15])).
% 0.54/0.92 thf(zip_derived_cl159, plain,
% 0.54/0.92 ((((multiply @ (multiply @ (inverse @ sk_c7) @ identity) @ sk_c7)
% 0.54/0.92 = (sk_c8))
% 0.54/0.92 | ((inverse @ sk_c5) = (sk_c8))
% 0.54/0.92 | ((inverse @ sk_c5) = (sk_c8)))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl93, zip_derived_cl12])).
% 0.54/0.92 thf(zip_derived_cl2, plain,
% 0.54/0.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.54/0.92 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.54/0.92 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.54/0.92 inference('cnf', [status(esa)], [associativity])).
% 0.54/0.92 thf(zip_derived_cl0, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.92 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.92 thf(zip_derived_cl1, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.92 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.92 thf(zip_derived_cl172, plain,
% 0.54/0.92 ((((identity) = (sk_c8))
% 0.54/0.92 | ((inverse @ sk_c5) = (sk_c8))
% 0.54/0.92 | ((inverse @ sk_c5) = (sk_c8)))),
% 0.54/0.92 inference('demod', [status(thm)],
% 0.54/0.92 [zip_derived_cl159, zip_derived_cl2, zip_derived_cl0,
% 0.54/0.92 zip_derived_cl1])).
% 0.54/0.92 thf(zip_derived_cl173, plain,
% 0.54/0.92 ((((inverse @ sk_c5) = (sk_c8)) | ((identity) = (sk_c8)))),
% 0.54/0.92 inference('simplify', [status(thm)], [zip_derived_cl172])).
% 0.54/0.92 thf(zip_derived_cl1, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.92 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.92 thf(zip_derived_cl178, plain,
% 0.54/0.92 ((((multiply @ sk_c8 @ sk_c5) = (identity)) | ((identity) = (sk_c8)))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl173, zip_derived_cl1])).
% 0.54/0.92 thf(zip_derived_cl75, plain,
% 0.54/0.92 (![X0 : $i, X1 : $i]:
% 0.54/0.92 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.92 inference('demod', [status(thm)], [zip_derived_cl54, zip_derived_cl0])).
% 0.54/0.92 thf(zip_derived_cl331, plain,
% 0.54/0.92 ((((sk_c5) = (multiply @ (inverse @ sk_c8) @ identity))
% 0.54/0.92 | ((identity) = (sk_c8)))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl178, zip_derived_cl75])).
% 0.54/0.92 thf(prove_this_14, conjecture,
% 0.54/0.92 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c6 ) ) |
% 0.54/0.92 ( ( inverse @ sk_c1 ) = ( sk_c7 ) ) ))).
% 0.54/0.92 thf(zf_stmt_16, negated_conjecture,
% 0.54/0.92 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c6 ) ) |
% 0.54/0.92 ( ( inverse @ sk_c1 ) = ( sk_c7 ) )),
% 0.54/0.92 inference('cnf.neg', [status(esa)], [prove_this_14])).
% 0.54/0.92 thf(zip_derived_cl16, plain,
% 0.54/0.92 ((((multiply @ sk_c5 @ sk_c8) = (sk_c6)) | ((inverse @ sk_c1) = (sk_c7)))),
% 0.54/0.92 inference('cnf', [status(esa)], [zf_stmt_16])).
% 0.54/0.92 thf(zip_derived_cl89, plain,
% 0.54/0.92 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl75])).
% 0.54/0.92 thf(zip_derived_cl383, plain,
% 0.54/0.92 ((((sk_c1) = (multiply @ (inverse @ sk_c7) @ identity))
% 0.54/0.92 | ((multiply @ sk_c5 @ sk_c8) = (sk_c6)))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl16, zip_derived_cl89])).
% 0.54/0.92 thf(prove_this_9, conjecture,
% 0.54/0.92 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c6 ) ) |
% 0.54/0.92 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) ) ))).
% 0.54/0.92 thf(zf_stmt_17, negated_conjecture,
% 0.54/0.92 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c6 ) ) |
% 0.54/0.92 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) )),
% 0.54/0.92 inference('cnf.neg', [status(esa)], [prove_this_9])).
% 0.54/0.92 thf(zip_derived_cl11, plain,
% 0.54/0.92 ((((multiply @ sk_c5 @ sk_c8) = (sk_c6))
% 0.54/0.92 | ((multiply @ sk_c1 @ sk_c7) = (sk_c8)))),
% 0.54/0.92 inference('cnf', [status(esa)], [zf_stmt_17])).
% 0.54/0.92 thf(zip_derived_cl424, plain,
% 0.54/0.92 ((((multiply @ (multiply @ (inverse @ sk_c7) @ identity) @ sk_c7)
% 0.54/0.92 = (sk_c8))
% 0.54/0.92 | ((multiply @ sk_c5 @ sk_c8) = (sk_c6))
% 0.54/0.92 | ((multiply @ sk_c5 @ sk_c8) = (sk_c6)))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl383, zip_derived_cl11])).
% 0.54/0.92 thf(zip_derived_cl2, plain,
% 0.54/0.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.54/0.92 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.54/0.92 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.54/0.92 inference('cnf', [status(esa)], [associativity])).
% 0.54/0.92 thf(zip_derived_cl0, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.92 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.92 thf(zip_derived_cl1, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.92 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.92 thf(zip_derived_cl437, plain,
% 0.54/0.92 ((((identity) = (sk_c8))
% 0.54/0.92 | ((multiply @ sk_c5 @ sk_c8) = (sk_c6))
% 0.54/0.92 | ((multiply @ sk_c5 @ sk_c8) = (sk_c6)))),
% 0.54/0.92 inference('demod', [status(thm)],
% 0.54/0.92 [zip_derived_cl424, zip_derived_cl2, zip_derived_cl0,
% 0.54/0.92 zip_derived_cl1])).
% 0.54/0.92 thf(zip_derived_cl438, plain,
% 0.54/0.92 ((((multiply @ sk_c5 @ sk_c8) = (sk_c6)) | ((identity) = (sk_c8)))),
% 0.54/0.92 inference('simplify', [status(thm)], [zip_derived_cl437])).
% 0.54/0.92 thf(zip_derived_cl444, plain,
% 0.54/0.92 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 0.54/0.92 = (sk_c6))
% 0.54/0.92 | ((identity) = (sk_c8))
% 0.54/0.92 | ((identity) = (sk_c8)))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl331, zip_derived_cl438])).
% 0.54/0.92 thf(zip_derived_cl2, plain,
% 0.54/0.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.54/0.92 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.54/0.92 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.54/0.92 inference('cnf', [status(esa)], [associativity])).
% 0.54/0.92 thf(zip_derived_cl0, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.92 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.92 thf(zip_derived_cl1, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.92 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.92 thf(zip_derived_cl446, plain,
% 0.54/0.92 ((((identity) = (sk_c6))
% 0.54/0.92 | ((identity) = (sk_c8))
% 0.54/0.92 | ((identity) = (sk_c8)))),
% 0.54/0.92 inference('demod', [status(thm)],
% 0.54/0.92 [zip_derived_cl444, zip_derived_cl2, zip_derived_cl0,
% 0.54/0.92 zip_derived_cl1])).
% 0.54/0.92 thf(zip_derived_cl447, plain,
% 0.54/0.92 ((((identity) = (sk_c8)) | ((identity) = (sk_c6)))),
% 0.54/0.92 inference('simplify', [status(thm)], [zip_derived_cl446])).
% 0.54/0.92 thf(zip_derived_cl1301, plain, (((identity) = (sk_c6))),
% 0.54/0.92 inference('clc', [status(thm)], [zip_derived_cl1262, zip_derived_cl447])).
% 0.54/0.92 thf(zip_derived_cl1303, plain, (((sk_c8) = (identity))),
% 0.54/0.92 inference('demod', [status(thm)],
% 0.54/0.92 [zip_derived_cl1250, zip_derived_cl1301])).
% 0.54/0.92 thf(zip_derived_cl1303, plain, (((sk_c8) = (identity))),
% 0.54/0.92 inference('demod', [status(thm)],
% 0.54/0.92 [zip_derived_cl1250, zip_derived_cl1301])).
% 0.54/0.92 thf(zip_derived_cl480, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl89, zip_derived_cl86])).
% 0.54/0.92 thf(zip_derived_cl1303, plain, (((sk_c8) = (identity))),
% 0.54/0.92 inference('demod', [status(thm)],
% 0.54/0.92 [zip_derived_cl1250, zip_derived_cl1301])).
% 0.54/0.92 thf(zip_derived_cl1303, plain, (((sk_c8) = (identity))),
% 0.54/0.92 inference('demod', [status(thm)],
% 0.54/0.92 [zip_derived_cl1250, zip_derived_cl1301])).
% 0.54/0.92 thf(zip_derived_cl1303, plain, (((sk_c8) = (identity))),
% 0.54/0.92 inference('demod', [status(thm)],
% 0.54/0.92 [zip_derived_cl1250, zip_derived_cl1301])).
% 0.54/0.92 thf(zip_derived_cl480, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl89, zip_derived_cl86])).
% 0.54/0.92 thf(zip_derived_cl1303, plain, (((sk_c8) = (identity))),
% 0.54/0.92 inference('demod', [status(thm)],
% 0.54/0.92 [zip_derived_cl1250, zip_derived_cl1301])).
% 0.54/0.92 thf(zip_derived_cl1303, plain, (((sk_c8) = (identity))),
% 0.54/0.92 inference('demod', [status(thm)],
% 0.54/0.92 [zip_derived_cl1250, zip_derived_cl1301])).
% 0.54/0.92 thf(zip_derived_cl480, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl89, zip_derived_cl86])).
% 0.54/0.92 thf(zip_derived_cl1303, plain, (((sk_c8) = (identity))),
% 0.54/0.92 inference('demod', [status(thm)],
% 0.54/0.92 [zip_derived_cl1250, zip_derived_cl1301])).
% 0.54/0.92 thf(zip_derived_cl0, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.92 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.92 thf(zip_derived_cl1303, plain, (((sk_c8) = (identity))),
% 0.54/0.92 inference('demod', [status(thm)],
% 0.54/0.92 [zip_derived_cl1250, zip_derived_cl1301])).
% 0.54/0.92 thf(zip_derived_cl1341, plain,
% 0.54/0.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.54/0.92 (((inverse @ X0) != (identity))
% 0.54/0.92 | ((X0) != (identity))
% 0.54/0.92 | ((inverse @ X1) != (identity))
% 0.54/0.92 | ((X1) != (identity))
% 0.54/0.92 | ((inverse @ X2) != (identity))
% 0.54/0.92 | ((X2) != (X3))
% 0.54/0.92 | ((X3) != (identity))
% 0.54/0.92 | ((inverse @ X4) != (identity))
% 0.54/0.92 | ((X4) != (identity)))),
% 0.54/0.92 inference('demod', [status(thm)],
% 0.54/0.92 [zip_derived_cl1298, zip_derived_cl1303, zip_derived_cl1303,
% 0.54/0.92 zip_derived_cl480, zip_derived_cl1303, zip_derived_cl1303,
% 0.54/0.92 zip_derived_cl1303, zip_derived_cl480, zip_derived_cl1303,
% 0.54/0.92 zip_derived_cl1303, zip_derived_cl480, zip_derived_cl1303,
% 0.54/0.92 zip_derived_cl0, zip_derived_cl1303])).
% 0.54/0.92 thf(zip_derived_cl1342, plain,
% 0.54/0.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.54/0.92 (((X0) != (identity))
% 0.54/0.92 | ((inverse @ X0) != (identity))
% 0.54/0.92 | ((X1) != (identity))
% 0.54/0.92 | ((inverse @ X1) != (identity))
% 0.54/0.92 | ((X2) != (identity))
% 0.54/0.92 | ((inverse @ X2) != (identity))
% 0.54/0.92 | ((X3) != (identity))
% 0.54/0.92 | ((inverse @ X3) != (identity)))),
% 0.54/0.92 inference('eq_res', [status(thm)], [zip_derived_cl1341])).
% 0.54/0.92 thf(zip_derived_cl1343, plain,
% 0.54/0.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.54/0.92 (((inverse @ X0) != (identity))
% 0.54/0.92 | ((X0) != (identity))
% 0.54/0.92 | ((inverse @ X1) != (identity))
% 0.54/0.92 | ((X1) != (identity))
% 0.54/0.92 | ((inverse @ X2) != (identity))
% 0.54/0.92 | ((X2) != (identity))
% 0.54/0.92 | ((inverse @ identity) != (identity)))),
% 0.54/0.92 inference('eq_res', [status(thm)], [zip_derived_cl1342])).
% 0.54/0.92 thf(zip_derived_cl0, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.92 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.92 thf(zip_derived_cl75, plain,
% 0.54/0.92 (![X0 : $i, X1 : $i]:
% 0.54/0.92 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.92 inference('demod', [status(thm)], [zip_derived_cl54, zip_derived_cl0])).
% 0.54/0.92 thf(zip_derived_cl88, plain,
% 0.54/0.92 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl75])).
% 0.54/0.92 thf(zip_derived_cl75, plain,
% 0.54/0.92 (![X0 : $i, X1 : $i]:
% 0.54/0.92 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.92 inference('demod', [status(thm)], [zip_derived_cl54, zip_derived_cl0])).
% 0.54/0.92 thf(zip_derived_cl124, plain,
% 0.54/0.92 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ identity)) @ X0))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl88, zip_derived_cl75])).
% 0.54/0.92 thf(zip_derived_cl1, plain,
% 0.54/0.92 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.92 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.92 thf(zip_derived_cl467, plain, (((inverse @ identity) = (identity))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl124, zip_derived_cl1])).
% 0.54/0.92 thf(zip_derived_cl1344, plain,
% 0.54/0.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.54/0.92 (((inverse @ X0) != (identity))
% 0.54/0.92 | ((X0) != (identity))
% 0.54/0.92 | ((inverse @ X1) != (identity))
% 0.54/0.92 | ((X1) != (identity))
% 0.54/0.92 | ((inverse @ X2) != (identity))
% 0.54/0.92 | ((X2) != (identity))
% 0.54/0.92 | ((identity) != (identity)))),
% 0.54/0.92 inference('demod', [status(thm)], [zip_derived_cl1343, zip_derived_cl467])).
% 0.54/0.92 thf(zip_derived_cl1345, plain,
% 0.54/0.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.54/0.92 (((X2) != (identity))
% 0.54/0.92 | ((inverse @ X2) != (identity))
% 0.54/0.92 | ((X1) != (identity))
% 0.54/0.92 | ((inverse @ X1) != (identity))
% 0.54/0.92 | ((X0) != (identity))
% 0.54/0.92 | ((inverse @ X0) != (identity)))),
% 0.54/0.92 inference('simplify', [status(thm)], [zip_derived_cl1344])).
% 0.54/0.92 thf(zip_derived_cl1346, plain,
% 0.54/0.92 (![X0 : $i, X1 : $i]:
% 0.54/0.92 (((inverse @ X0) != (identity))
% 0.54/0.92 | ((X0) != (identity))
% 0.54/0.92 | ((inverse @ X1) != (identity))
% 0.54/0.92 | ((X1) != (identity))
% 0.54/0.92 | ((inverse @ identity) != (identity)))),
% 0.54/0.92 inference('eq_res', [status(thm)], [zip_derived_cl1345])).
% 0.54/0.92 thf(zip_derived_cl467, plain, (((inverse @ identity) = (identity))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl124, zip_derived_cl1])).
% 0.54/0.92 thf(zip_derived_cl1347, plain,
% 0.54/0.92 (![X0 : $i, X1 : $i]:
% 0.54/0.92 (((inverse @ X0) != (identity))
% 0.54/0.92 | ((X0) != (identity))
% 0.54/0.92 | ((inverse @ X1) != (identity))
% 0.54/0.92 | ((X1) != (identity))
% 0.54/0.92 | ((identity) != (identity)))),
% 0.54/0.92 inference('demod', [status(thm)], [zip_derived_cl1346, zip_derived_cl467])).
% 0.54/0.92 thf(zip_derived_cl1348, plain,
% 0.54/0.92 (![X0 : $i, X1 : $i]:
% 0.54/0.92 (((X1) != (identity))
% 0.54/0.92 | ((inverse @ X1) != (identity))
% 0.54/0.92 | ((X0) != (identity))
% 0.54/0.92 | ((inverse @ X0) != (identity)))),
% 0.54/0.92 inference('simplify', [status(thm)], [zip_derived_cl1347])).
% 0.54/0.92 thf(zip_derived_cl1349, plain,
% 0.54/0.92 (![X0 : $i]:
% 0.54/0.92 (((inverse @ X0) != (identity))
% 0.54/0.92 | ((X0) != (identity))
% 0.54/0.92 | ((inverse @ identity) != (identity)))),
% 0.54/0.92 inference('eq_res', [status(thm)], [zip_derived_cl1348])).
% 0.54/0.92 thf(zip_derived_cl467, plain, (((inverse @ identity) = (identity))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl124, zip_derived_cl1])).
% 0.54/0.92 thf(zip_derived_cl1350, plain,
% 0.54/0.92 (![X0 : $i]:
% 0.54/0.92 (((inverse @ X0) != (identity))
% 0.54/0.92 | ((X0) != (identity))
% 0.54/0.92 | ((identity) != (identity)))),
% 0.54/0.92 inference('demod', [status(thm)], [zip_derived_cl1349, zip_derived_cl467])).
% 0.54/0.92 thf(zip_derived_cl1351, plain,
% 0.54/0.92 (![X0 : $i]: (((X0) != (identity)) | ((inverse @ X0) != (identity)))),
% 0.54/0.92 inference('simplify', [status(thm)], [zip_derived_cl1350])).
% 0.54/0.92 thf(zip_derived_cl1352, plain, (((inverse @ identity) != (identity))),
% 0.54/0.92 inference('eq_res', [status(thm)], [zip_derived_cl1351])).
% 0.54/0.92 thf(zip_derived_cl467, plain, (((inverse @ identity) = (identity))),
% 0.54/0.92 inference('sup+', [status(thm)], [zip_derived_cl124, zip_derived_cl1])).
% 0.54/0.92 thf(zip_derived_cl1353, plain, (((identity) != (identity))),
% 0.54/0.92 inference('demod', [status(thm)], [zip_derived_cl1352, zip_derived_cl467])).
% 0.54/0.92 thf(zip_derived_cl1354, plain, ($false),
% 0.54/0.92 inference('simplify', [status(thm)], [zip_derived_cl1353])).
% 0.54/0.92
% 0.54/0.92 % SZS output end Refutation
% 0.54/0.92
% 0.54/0.92
% 0.54/0.92 % Terminating...
% 1.68/1.16 % Runner terminated.
% 1.68/1.16 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------